tag:blogger.com,1999:blog-17676726744492408542024-02-19T07:44:37.552-07:00Approachably ReclusiveThe central blog for all things John Barnes (science fiction writer, theatre historian, marketing intel math guru, and other stuff) where you can find his musings, maunderings, and misapprehensions. Links and posts here lead to many other areas of Barnesian activity.John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comBlogger155125truetag:blogger.com,1999:blog-1767672674449240854.post-30120744375226234892016-04-22T23:13:00.002-06:002016-04-22T23:22:19.820-06:00Another one of those accidental blog posts resulting from a duplication ... Why do kids give up on math?Every so often over on Quora, which I highly recommend, someone asks something I find interesting, and I start to write a post, and before I know it I've written way more than I intended. That just happened, so here's the post. You can find the Quora version, which is almost the same after the little squiggle I use to mark a major break, <a href="https://www.quora.com/What-makes-kids-give-up-on-math" target="_blank">on this Quora pag</a>e, along with the pretty-good answers of several other people. <br />
You can find a whole bunch of my Quora answers at <a href="https://www.quora.com/profile/John-Barnes-39" target="_blank">my Quora profile</a>, down below all the list of subjects that I find it interesting to read or write (or both) about. All that<br />
may not teach you anything except what it amuses me to write about when I'm bored and procrastinating.<br />
<br />
Anyway, Lauren Godfrey asked a cool question, and here's how I answered it, and I hope it's as good an answer as her question was:<br />
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<a class="question_link" href="https://www.quora.com/What-makes-kids-give-up-on-math" id="__w2_sv0wWRC_link" target="_top"><span class="question_text"><span class="rendered_qtext">What makes kids give up on math?</span></span></a></div>
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<span class="photo_tooltip" id="__w2_DobviLM_link"><a href="https://www.quora.com/profile/John-Barnes-39" id="__w2_syDeno0_link"><img alt="John Barnes" class="profile_photo_img" height="50" src="https://qsf.is.quoracdn.net/-images.new_grid.profile_pic_default_small.png064a9ab076e186d3.png" style="opacity: 1;" width="50" /></a><span id="ld_ehjoes_7383"></span></span></div>
<span class="feed_item_answer_user"><span id="ld_jwhcfe_6612"><a class="user" href="https://www.quora.com/profile/John-Barnes-39" id="__w2_sQQTrPe_link">John Barnes</a><span class="IdentitySig ActorNameSig IdentityNameSig" id="__w2_rL1IIPR_bio">, <span id="__w2_rL1IIPR_link"><span class="IdentitySig ActorNameSig IdentityNameSig" id="__w2_rL1IIPR_sig"><span class="expanded_q_text" id="__w2_mBAAL9B_text_snip"><span id="__w2_mBAAL9B_text_snip_content"><span class="rendered_qtext">Math tutor, particularly Singapore Math</span></span></span></span></span></span></span></span><br />
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<a href="https://www.blogger.com/null" name="answer_21920428"></a><span class="inline_editor_value"><span class="rendered_qtext"></span></span><br />
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<span class="inline_editor_value"><span class="rendered_qtext">Many things, so it depends on the kid. But you have to start with </span></span></div>
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<span class="inline_editor_value"><span class="rendered_qtext">0. some of them don't; you might as well ask why they stick it out (and it will be many more than one reason).</span></span></div>
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<span class="inline_editor_value"><span class="rendered_qtext">Now, off the top of my head, reasons I have seen kids give up on math:</span></span></div>
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<ol>
<li>Most
adults are not good at math (they are after all products of a system
that notoriously doesn't teach it successfully). Some of them transmit
de-motivating feelings to kids around them, such as:</li>
<ol>
<li>fear of math</li>
<li>fear the kid will quickly excel them</li>
<li>anger at having to study math</li>
<li>defensive attacks on math as unneeded or useless</li>
</ol>
<li>Well-taught
math has a solid conceptual base. A kid who never develops an
understanding of that conceptual base is going to be lost and helpless
sooner or later (the usual years for that problem are about 9-12, and
the usual sticking places are long division, fractions, decimals, and
elementary algebra).</li>
<ol>
<li>Kids who understand better conceptually
and don't get any conceptual instruction are primed for a particularly
infuriating flavor of failure because they won't be able to do what the
problems are asking later on, but they will understand that they should
be able to.</li>
<li>Kids who learn better by other means (patterning is
the most common) will try to learn more advanced math by those other
means, and at some point it can't be done. Then, since the only tool
they have is a hammer, and they are out of nails, they quit.</li>
</ol>
<li>Well-taught
math is constantly related to other subjects (science, history,
geography, many more) and kids who aren't shown those relationships
usually don't figure them out for themselves, so they give up because
"this has nothing to do with anything."</li>
<ol>
<li>Many people don't
use math where it would be to their advantage to use it, because they
don't know how; their children learn that buying too much paint or too
little tile, adapting a recipe to the scarcest ingredient and having it
come out tasting funny, never really knowing how much is in your bank
account, etc. are just how life works; in extreme cases there are adults
who simply do not believe in math at all (i.e. they don't think that
things that are routinely calculated can be known by any means other
than trial and error).</li>
<li>Many teachers were attracted to subjects <i>because</i> <i>they thought they were unmathematical.</i>
It isn't necessarily obvious to an English teacher that much of the
plot of Shakespeare's double-tetralogy of histories (from Richard II
through Henrys IV-VI to Richard III) depends on logistics, travel times,
and various other things you can calculate; there are math problems
under nearly every human activity, but a teacher who doesn't know them
can't show them.</li>
<li>Many math teachers really like abstract
problems because they like doing nifty puzzles; more concrete real world
problems aren't as much fun, and they tend to stint them (and not know
enough about the related subject to teach them).</li>
</ol>
<li>Well-taught
math demands quick effective recall (like knowing the operations
tables, the simple algorithms, some ordinary relations between
fractional and decimal representation, and so on, with almost instant
recall of accurate information). Memorization has been very out of
fashion in education for a long time (somebody ask me sometime why that
was bad. Don't ask this weekend, I'm going to be too busy. Just remember
to ask it, later). This has unfortunate consequences:</li>
<ol>
<li>Kids don't learn how to memorize for effective recall, so they don't know how to put the basic information into their heads.</li>
<li>Kids
are rarely asked to use any power of effective recall so they don't
know how to pull the information they need out of their heads and use
it.</li>
<li>Teachers don't know how to teach either of those skills so they can't help.</li>
<li>Kids and teachers therefore avoid memorization because they're not good at it and it mostly just makes them unhappy.</li>
</ol>
<li>Inane
curricula re-written by textbook consultants who didn't understand what
the textbook author was trying to say or why it mattered. Honestly,
truly, there are some textbook publishers who appear to prefer a clear
and easy to read style in the words, and nice looking graphics, to
accuracy in the math.</li>
<li>The luck of the draw in teacher quality
and/or connection; every so often a kid just gets a teacher who kills
math for him/her. That will always happen to some extent, just as it
happens for every other subject. (I enjoy working in visual arts now,
but hated it as a kid; I had 3 awful art teachers back to back, and it
took one great one in 7th grade most of a year to win me back to art. On
the other hand, as it happened, I had so many good math teachers that
by the time I had my first bad math teacher, I was incurably a math
kid).</li>
<li>Some otherwise successful-enough people seem to stick at
the concrete-operational Piaget stage, which pretty much limits you to
below-algebra math.</li>
<li>Other people have a hard time sequencing
multiple steps (lack of executive function) for any of several possible
reasons, so again they're limited to math problems that can be done in a
number of steps they can sequence.</li>
<li>And yet more kids have
problems with branching algorithms: in long division, for example, you
have to remember that if the remainder is bigger than the divisor, you
need to back up and add one or more to the last digit on the dividend.
Comparing two numbers to decide which of several possible things to do
to a third number is genuinely beyond many seemingly normal 3rd-5th
graders (almost everyone can do it by 6th grade). If the kid has to do
some kinds of math before his/her brain grows into it, that can be the
end of math for that kid.</li>
<li>Some students develop a habit early on
of simply grabbing all the numbers in a problem and more or less
randomly applying algorithms to them. "Bobby is riding in a car and
reading a book. He is 9 years old, 52 inches tall, and weighs 63 pounds.
He reads 72 pages, and there are an average of 208 words on each
page. The car takes 2 hours to travel 100 miles. What is the average
speed of the car?" There are people who can't solve that problem because
they have no sense that to compute a speed, all they need is distance
traveled and time taken. So when the teacher demonstrates the answer,
their reaction tends to be that "seven" was a perfectly good answer
because they divided the weight by the age correctly, or that the
teacher is unfairly shutting down their answer of 10,816 (number of
words on a page multiplied by height) even though they had to multiply
much bigger numbers to get it. Obviously teachers just make up the rules
as they go to cheat the kids, and to hell with this. (Sound extreme? I
have worked with four children just like this).</li>
</ol>
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Anyway, that's ten, with some subdivisions. I've seen all of those in my practice as a tutor. Hop over to <span class="qlink_container"><a class="external_link" data-tooltip="attached" href="http://thatjohnbarnes.blogspot.com/2015_09_01_archive.html" rel="noopener nofollow" target="_blank">Approachably Reclusive</a></span> (the link is to one of my better pieces) and you'll find quite a few other things I've written about problems in math teaching.</div>
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And of course, remember also the Nth and final reason why kids give up on math:</div>
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N.
Almost everyone eventually gives up on almost everything. You're not a
professional singer, firefighter, astronaut, Olympic athlete, prima
ballerina, Nobel prizewinner, or the president, are you? At some point,
we stop developing most of our capabilities, because we just can't
develop them all.<br />
<br />
Many kids give up on math earlier than is optimal for
them or for society, but we probably want to achieve a more optimal
distribution of give-up points, not fill the retirement homes with would
be Galoises and Gausses.</div>
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</span><div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-39620170211596855552016-02-11T11:24:00.001-07:002016-02-11T11:24:34.896-07:00Whatever Hope We HaveI posted this as a comment over at Daily Kos, where folks were talking about the confirmed identification of gravity waves from the merger of two infalling black holes. Then I decided I liked it enough that I wanted it to be here as well. Sorry for anyone who happens to be seeing it twice -- think of it as a sort of gravitational lensing, I guess.<br />
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<b>Whatever Hope We Have</b></div>
<br />
That was the title of a Maxwell Anderson essay back in the 1930s,
just as the world was getting ready to slide into the Second Active
Round of the 75 Years’ War. His point was this: no civilization of
human beings has lasted forever. Ours can’t be expected to either; we
can hope it ends in something better blossoming from it, rather than in
destruction and chaos, but we should face the fact that there will only
be people like us on the Earth for a limited time.<br />
<br />
In light of that, what will we be remembered for?<br />
<br />
Whether we approve of it or not, and no matter how appalling we may
think a civilization was, taken as a whole, whatever hope they (and we)
have is to be remembered for our best. We remember High Medieval Europe
more for the cathedrals and the poetry than for the Children’s Crusade;
Athens more for Euclid, Pericles, Plato, and Euripides than for the
slaves in the silver mines; the Abbasid Caliphate for its artists,
poets, scholars, and scientists and its ideal of religious tolerance
more than for its slave trade and conquests; China more for its early
explorations than for its later suppression of them, and more for its
seeking of wisdom than for its fossilization of tradition. What will be
our Notre Dame, our Taj Mahal, our Popul Vuh, when we are dust and the
debunking historians of the successor civilization begin to describe us
(as every successor civilization does of its predecessors) as “Yeah, but
….” ? **<br />
<br />
I think the answer is, probably our science. We’re the ones who found
out what sort of universe we actually have and where we are in it.<br />
<br />
And just as most Medieval Europeans never built a cathedral, and the
slaves in the silver mines under Athens didn’t write tragedies, and most
peasants historically have had only the most limited idea of what the
tax gatherer was taking the taxes away to do … most of us can’t really
understand how the physicists got things down to four fundamental
forces, and then to showing that the four are really one. Nonetheless,
in 5000 years, when they’re digging up the remnants of the Roadbuilder
Civilization (<a href="http://www.goodreads.com/book/show/128533.Eternity_Road">as Jack McDevitt dubbed us in one excellent novel</a>), we can
hope to be remembered for Einstein and his intellectual descendants.<br />
<br />
Or would you rather go into the great heap of history as the creators of Justin Bieber?<br />
<br />
§<br />
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* This is very much the same perspective Carl Sandburg in <i><a href="https://www.poets.org/poetsorg/poem/four-preludes-playthings-wind">Four Preludes On Playthings of the Wind</a>, </i>except Sandburg doesn't appear to see any hope at all.<br />
<br />
** Iron Law: Civilizations begin in heroic myths from their own glorious bards, and end up in museum drawers as "Yeah, but."<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-3522223354733189632015-12-05T02:46:00.003-07:002015-12-05T02:46:38.083-07:00Impending newsletterIt's that time of year again, and for the second year in a row there's only going to be one newsletter. Those who are already regular subscribers, look for it soon.<br />
<br />
Those who are not (or whose email changed in the last year) drop me a note and ask to be added to the mailing list.<br />
<br />
This particular newsletter will include brief personal news (where I've been for another year), brief publishing and business news (where to find my few publications in the past year and how to buy signed and personalized backlist copies), and, for the first time (and possibly the only time) instead of the usual personal essay, a new short story that will only ever be published in the newsletter. It's a light, silly Christmas fantasy, for any of you who like Christmas or things that are light and silly.<br />
<br />
Going out somewhere over this weekend, so drop me a note if you want to be on the regular mailing list and aren't already.<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-14334239809094309372015-10-28T11:33:00.003-06:002015-11-05T12:42:54.808-07:00What's wrong with "all you do is just ... "<style>
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<span style="font-family: "georgia"; font-size: 14.0pt;">If you've read this blog at all in
the past few months you know that I'm working on a book called <a href="http://thatjohnbarnes.blogspot.com/2015/02/sort-of-progress-report-on-singapore.html"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Singapore Math Figured Out for Parents</i></b></a>, and I do almost all of the math tutoring
for <a href="http://www.tutoringcolorado.com/">Tutoring Colorado</a>, my wife's tutoring business. Lately, too, I've noticed my
emotional investment in my life as a math tutor deepens with time.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">So here's some more about
Singapore Math, math tutoring, and math instruction. This one noodles through
some ideas that I'm pretty sure I need to put into the book, possibly more
diplomatically (so if this angers or offends you, this would be a helpful time
to send hate mail).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">And as I often do, I'm starting
off with seven little stories. </span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">§</span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">1</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">On break from an English comp
class at the College of Last Hopes, I was talking with one of my Adult Disadvantaged Learners about math in
general, because she'd been struggling in Pre-algebra. It's the class that the
College of Last Hopes offers to students whose math skills are somewhere south
of sixth grade. <span style="mso-spacerun: yes;"> </span>She told me about having
had to help her now-adult son with division when he was in fourth grade or so; he
was in one of the several curricula where they teach factoring before they
teach long division. Since she didn't understand factoring but knew the answer
could be gotten by dividing, she taught him the familiar algorithm for long
division. He then taught it to several of his classmates, somehow leading to a
general parental demand for long division right now. The principal eventually
intervened to tell the teacher to skip over that factoring stuff and teach long
division since that was what parents wanted.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">When the kids hit fractions, where
factoring is often the quick and easy way, things imploded. Not only was it now
necessary to go back and learn factoring (without reference to the fundamental
relationship between division and fractions), but in their battle against
factoring earlier that year, a large number of kids (and parents, beginning
with the one who was now my student) had become convinced that factoring was
innately evil and that the cruel teacher was going to force it on them. Fractions
ended up deferred till the next year when a more old-fashioned teacher taught
it as a set of arbitrary, memorizable rules.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">My student was very satisfied that
she had helped to "make sure they taught my son basic math and that's all
you need and that's all they should teach. You don't need fractions for nothing
anyway. It's just like that factoring thing, it don't make no sense and you
don't need it. I should know. My whole family's always been good at math."*</span></div>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">2</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Next story is about a much better
student. We'll call him Adam, since he's a composite, like every case from
tutoring I talk about here; the real kid behind the composite is actually at
least three kids. (That adult student in the first story, who was "good at
math" without being able to do much of it, was quite real and individual,
however. Kids get a pass into anonymity but a grandmother gets to own her
folly. Them's, as they quaintly say, the rules).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Adam, a pleasant nine-year-old who
was recovering quickly from major conceptual math problems, grumbled that now
that he could do math, he just wished he was "good at it." This
surprised me because once we got him through the block he turned out to be
conspicuously talented, with better concentration and work ethic than most kids
his age. If I had to pick a tutee who was "good at math" he'd be at
the top of the list; nor do I stint on praise with young kids, so it wasn't
like he'd never heard that he was doing well before. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">A little inquiry revealed that
"good at math" was what his friends Brian and Claudia were. Both of
them were apparently very quick at the algorithms and usually accurate. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Now, I <i style="mso-bidi-font-style: normal;">know</i> the school those kids attend, and the curriculum they teach
there. After months of tutoring, Adam knew a great deal more math, and
understood it better, than most of his peers. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Well," I said,
sympathizing, and trying to understand why he thought his fellow students were
ahead of him, "some people are just lucky enough to remember patterns
really well the first time and always get them right afterwards, and they do
get right answers very quickly."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"They don't get right
answers," Adam corrected me. "I get right answers more often than
they do."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"I thought you said they were
good at math and you don't feel like you are."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">This led to a more detailed
account of the peers he envied, establishing that, "They always remember
to write the little numbers to the left and above the original numbers, and
they cross them out left to right, and they get all the 'neat and complete'
points."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"But they don't get the right
answer?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Sometimes they forget things
or get them backwards like I used to do. I can get the right answer, but Brian
always knows how to write everything down so it looks just like in the
book.<span style="mso-spacerun: yes;"> </span>And Claudia knows a bunch of
rhymes for how to remember what order to do things in. I wish I was good at
math like that." He looked back at the page he had been working on. "I
forget. Do I add or times next?"</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">3</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">I had been struggling to steer another
tutee -- I guess we'll call this one Darcy, she lives down in Composite City near
Adam -- into a better understanding of fractions. I've been using "rectangle
models" because that's the clearest presentation of fractions I know once
a kid is old enough to get the concept. For example, here's <a href="https://www.youtube.com/watch?v=WrvDWD9HvOs">a video of a pretty good use of a rectangle model to explain why you have to get to a common denominator to add fractions</a>.** </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Chances are you were shown the
simple versions of rectangle models while you were learning; if your teacher
was somewhere in the better half of math teachers, some time was spent
explaining what it was about and why you were being shown it. (The less-good
half tends to do it because it's in the lesson plan, but doesn't talk as much about
why it works or what we can learn from it). </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">It's just the familiar business of
"so if the whole box means one, we draw a line through it and each of the
smaller boxes is one half. And we write that to show we have one of the pieces
we got by cutting it into two parts ... now here's a box cut into three pieces,
and we're going to talk about two of the pieces, how do we write that? Yes, 2/3
..." and so on. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Rectangle models are very often
used to introduce the most basic ideas about fractions, and then abandoned just
as the kid gets to the hard parts. But the good Reverend Thomas Vowler Short,
almost 200 years ago, actually developed them for teaching pretty much the
whole of fractions, all the way up through fractions made up of expressions,
and fractions and ratios in elementary algebra.<span style="mso-spacerun: yes;">
</span>They still can be a wonderfully clear view into how complicated problems
in fractions actually work. Kho Tek Hong incorporated many aspects of them into
the bar modeling methods in Singapore Math, and many other math teachers use
them too, especially for occasions when just looking at the numbers seems to be
producing nothing but confusion. (For example, here's a pretty good one that
<a href="https://www.youtube.com/watch?v=tcS_TKdpNAI">uses rectangle diagrams to begin the explanation of dividing whole numbers by fractions</a>, a much tougher topic for most kids.<span style="mso-spacerun: yes;">
</span>*** )</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">And Darcy was pretty much in the
same situation as her predecessors going back two hundred years; rectangle
models were lifting the fog from fractions. After two sessions of rectangle
models practice, she'd reached the point of consistently being able to draw any
straightforward fraction problem as a rectangle model. She could then either
find the answer directly from the model, or see what operations she needed to
do on the fractions. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Of course, over time, that second
pathway would become the natural one. Eventually Darcy would no longer need to
draw the model to think clearly about the problem, or could draw it in her head
instantly if she ever needed it. (Rather like the way most people learned the
Alphabet Song, and some still occasionally need to sing it to themselves to
alphabetize things, but most just know alphabetical order.) In short or via
Short, Darcy eventually learned how the algorithms for fractions worked, and
thus she had a clear idea of when to apply which ones, and to recreate or
correct any of the algorithms she might temporarily forget. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Darcy <i style="mso-bidi-font-style: normal;">knows</i> fractions. Now it's just a matter of practicing what she
knows until it's easy and automatic for her to <i style="mso-bidi-font-style: normal;">do</i> fractions. But today she's very discouraged.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"I hate all this thinking.
It's a waste of time. I wish you'd just tell me what to write where," she
sighs. "Or that they would just give us directions about how to do each
problem on tests. I just want to get the answer and go on to the next
problem."</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">4</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">If you worry at all about math
teaching in the US -- and I can't imagine you've read this far if you don't --
then no doubt you've seen this bit of second grade homework, which went viral
on the Right Wing Kookoo-Bird Web, crossing over to the general web as well. </span></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://hechingerreport.org/wp-content/uploads//commoncoremath-461x0-c-default.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://hechingerreport.org/wp-content/uploads//commoncoremath-461x0-c-default.png" height="640" width="474" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Alas, according to the Stuck Clock Principle, there are places here where the guy is absolutely right.</td></tr>
</tbody></table>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">As is usual with things in the Right
Wing Kookoo-Bird Web, it's misidentified, facts have been distorted to alarm
naive readers, and the actual situation is rather different from what Glenn
Beck made of it. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Nonetheless, this is not at all an
unusual parental response, or an irrational one, and the explanation offered to
the parent was not much of an explanation. Furthermore, as you'll find in <a href="http://hechingerreport.org/content/common-core-math-problem-hard-supporters-common-core-respond-problematic-math-quiz-went-viral_15361/">Sarah Garland's actually-fair-and-balanced article</a>,
the homework really is badly designed for its intended purpose, the intended
purpose was inappropriate, and it's hardly a surprise that the parent couldn't
discern it.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">What I want to draw your attention
to, though, is that in the face of the inexplicable assignment (or, being fair,
the assignment that could have been explicated but is still pretty badly done),
the first thing a parent does is reach for the good old reliable centuries-old
algorithm. And this is a parent who is well-acquainted with and thoroughly
grasps math himself (he wouldn't last a day in his job if he didn't).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">If you do go over there to look
over the full story, read the comments, as they illustrate what I'm talking
about almost as well as the story itself.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">5</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">From <a href="https://www.washingtonpost.com/posteverything/wp/2015/08/04/why-did-i-give-up-on-math-ask-my-mom/">the comments on a Washington Post article about math anxiety</a>, which quickly (d)evolved into a quarrel about Common Core:</span></div>
<blockquote class="tr_bq">
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-size: small;"><span style="font-family: "verdana" , sans-serif;"><b>Attack</b>: <span class="echo-streamserver-controls-stream-item-text">better approach to math? You mean like forcing kids to draw
18 balloons with 5 circles each, then counting them, to reach 90, rather than
just letting do the much easier task of memorizing 18*5=90? </span></span></span></div>
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-size: small;"><span style="font-family: "verdana" , sans-serif;"><b>And riposte</b>: <span class="echo-streamserver-controls-stream-item-text">Yes, good example. That way when they reach
algebra/geometry/statistics/calculus they already understand how to think conceptually
about math. Rather than students who think, "I can't possible memorize
this abstract stuff!" you get students who can solve complex problems
using the logic they learned solving simple problems.</span></span></span></div>
</blockquote>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span class="echo-streamserver-controls-stream-item-text"><span style="font-family: "georgia"; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Both sides sort of stabbed past each other here, but I don't
think either can be blamed for the way they missed the target; it was pretty
dark in there for everyone. </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span class="echo-streamserver-controls-stream-item-text"><span style="font-family: "georgia"; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><u>To the attack, we might say</u>: The point of having students
calculate 18*5 is not that we don't know the answer, or even that they don't. <span style="mso-spacerun: yes;"> </span>We ask them to do it so that they will learn the
math. <i style="mso-bidi-font-style: normal;">Knowing the answers is not knowing
the math.</i><span style="mso-spacerun: yes;"> </span>Knowing the fast way to
the answers is knowing a little bit of math. But knowing why that's an answer
and what it means -- that's math. And a picture is what is needed for a kid who
isn't too sure about what a number is or means yet. You don't need it now, and
neither will the kid when s/he's thirty.<span style="mso-spacerun: yes;">
</span>But conversely, neither of you was born knowing what numbers are or how
they work.</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span class="echo-streamserver-controls-stream-item-text"><span style="font-family: "georgia"; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><u>And to the riposte, we might say</u>: Yet the response also
misses the point: in the tutoring business, I've seen only a couple of students
at most who showed any trace of trying to get through all of math by memorizing
procedures. (The more common problem by far, <a href="http://thatjohnbarnes.blogspot.com/2015/10/rescuing-forrest-from-trees-tutoring.html">as with Forrest</a>, is that a student thinks the procedures are causal, like magic spells that
make the answer true, rather than revelatory, i.e. simply revealing what was
always true.) </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span class="echo-streamserver-controls-stream-item-text"><span style="font-family: "georgia"; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">I have seen more of the memorize-a-long-cookbook approach among
the ADLs, who are in a sense a population selected for having difficulty with
mathematics, but even there it's scarce. If the problem were just people trying
to memorize a complicated cookbook instead of learning math, we could give them
all a good shake, tell them what real math is, and have the problem solved before
the weekend. </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span class="echo-streamserver-controls-stream-item-text"><span style="font-family: "georgia"; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">The problem is that for many people, brute-force meaningless
memorization is actually more attractive than understanding math. People are <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">not</i></b>
trying to get through math that way because they don't know any better. They're
trying it because they know they like it better. And that's a much harder
problem to solve.****<span style="mso-spacerun: yes;"> </span></span></span><span style="font-family: "georgia"; font-size: 14.0pt;"></span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">6</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Some of the same arguments are
played out at a much higher level (for some reason most of the trolls failed to
show up, or perhaps were whacked down) is in <a href="http://www.theamericanconservative.com/2014/03/13/teaching-math-under-common-core-fact-and-fiction-part-v/">Leah Libresco's piece in TheAmerican Conservative</a>. Libresco is talking about it from the teacher's perspective, and she's sharp
and clear, and several of her fellow teachers, who show up in the comments, also
get it and know how it works.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The comments also feature some of
the most useful kind of commenter for a piece about a hard idea:
honest-and-not-stupid people having a hard time seeing what it's about. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">There are also some trolls and
sloganeers, of course. One apparently cannot hold their numbers to zero.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">But overall, in that piece, people
are talking about understanding, and it makes a much better conversation, or at
least one less irritating to read.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The reason for including
Libresco's article here, though, is a point she makes in passing a few times,
picked up by several commenters and bulldozed irritably over by others:<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "georgia"; font-size: 14.0pt;">The best way for a kid to get to
clarity about a concept is not necessarily the way the kid will do the related
problem later as an adult</span></i></b><span style="font-family: "georgia"; font-size: 14.0pt;">. This is hardly a surprise; it's the way learning a
complex skill that you will be using for years often works. Phonics produces
more proficient readers, but proficient adult readers rarely sound words out.
Many good cooks started out with a well-edited cookbook, measuring everything
and following directions exactly, but nowadays they just grab the right
ingredients and tools and turn the stove on. A ski instructor friend tells me
that the long journey through intermediate from just-qualified-as-intermediate
to almost-advanced is mostly moving out of knowing tricks to get down the hill
and into just skiing.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">But it's also quite clear that for
many people in that conversation, procedural proficiency is all there is to
math.<span style="mso-spacerun: yes;"> </span>They keep wandering back to
"all you do is just..." as a sort of touchstone or mantra, no matter
how many earnest and respectful voices tell them that that's not
"all", it's not "just" that, and that what you
"do" is often beside the point.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">7</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Older readers have probably seen
the "dishonest bellhop" problem, especially because Ripley's Believe
It or Not! popularized it decades ago: three men rent a room for $30, and after
they've gone up to their room, the desk clerk notices that that room was a $25
room, so he sends the bellhop upstairs with the $5 to give to the men. The
bellhop, being dishonest (that's why we named the problem after him), only
gives each man $1.00.<span style="mso-spacerun: yes;"> </span>So now each man
has paid $9 for the night, $27 in all, and the bellhop has a $2 unauthorized
tip, and that's $29. But they paid $30. Where's the extra dollar?</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Newer readers may have seen this
version of the same problem: You want a shirt that costs $100. You borrow $50
from your mother and $50 from your father. When you get to the store you find
the shirt is on sale for $97. So you buy the shirt, return $1 to your father
and $1 to your mother, and perhaps because you are secretly a bellhop, pocket
that last dollar. So effectively you borrowed $49 per parent, and pocketed one,
which adds up to $99. Where's the extra dollar?</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">(You can tell which problem is
newer because in one of them a hotel room is $30 and in the other a shirt is
$100...)</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The quick answer is that if you
draw a little table in either case and ask where the money came from and where
it went, you'll see that the money into the problem ($30 from the 3 men; or
$100 from the parents) equals the money coming out ($25 in hotel cash register,
$3 in refunds, $2 in graft; or $97 in store cash register, $2 returned, and $1
in your pocket). Those correct solutions are treating an equation as an
equation, not as a puzzle with a double line that means "write your answer
here." The reason they fool so many people is that so few actually think
in equations.<span style="mso-spacerun: yes;"> </span>(For <a href="http://www.esmerel.com/circle/numeracy/bellboy.html">a much better,longer, and clearer exposition of this</a> see the Mathemagician's blog. )</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">And fool people they do. Presented
as a puzzle to college or high school students, I'd say maybe 1 in 50 who have
not seen the trick before will get it. Even more amusing, most students can be
shown one of the puzzles, be taken in by it, have it explained, even be able to
work the trick themselves ... and will then fall for the other version of the
same trick the week after. The trick is irresistible to many of them: there's a
procedure and an answer, so you do the procedure and the answer is right.
Right?</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Fundamentally, all these stories
show how extraordinarily strong in everybody, but particularly in children, is
the tendency to look for a known algorithm with clearly remembered steps to
just execute without reference to meaning. Mostly, ordinary people confronted
by math want to know what to do, and then do it. Give kids a "what to do"
and, as long as they can remember it, they'll do it forever. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">I strongly suspect that one reason
that people understand better if they learn why-before-how is that all they
really want to know is "how." If you show them "how" first,
they've gotten what they came for, and they'll tune the rest out, no matter how
many advantages you can explain to knowing the "why." (And of course,
explaining the value of knowing "why" to an eight-year-old isn't always
possible; it's not a very "why" age. But as with any ability or
skill, if you're ever going to be able to do it at all, you have to start as
soon as you can, and long before you're good).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">This "pull of pattern"
shouldn't be a surprise. It is not uncommon in many other situations.<span style="mso-spacerun: yes;"> </span>You can see it with people who have made hundreds
of cakes from mixes but would get nervous about making one from scratch,
doodlers who draw the same drawings over and over, and readers who read only
one very restrictive genre. There are chess players who only open with the
king's pawn, guitar players who only play the Carter lick, writers who put a
topic sentence at the beginning of every paragraph, and ballroom dancers who do
the same sequence of base steps and variants over and over without really
listening to the music. Beginning realistic drawing students often have to
struggle to get over "I know how to draw eyes" (or lips, or shoes, or
hands) and learn to draw what they see rather than what they have a
prefabricated pattern for.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The pull of the pattern is so strong, almost inescapable, because so many of our basic life skills are just such patterns. We
don't necessarily want to ride with a taxi driver who tries to take every fare
from the airport to the convention center by a different route, let alone one
who is constantly experimenting with new ways to turn or brake.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-tab-count: 1;"> </span>Five
hundred, or a hundred, or even fifty years ago, most people who needed to do
anything with numbers only needed a few of the simple patterns (often not even
all of them), and another almost-as-simple meta-pattern to tell them which
pattern to deploy when. But the calculator and the computer have killed the
jobs that only required simple math -- along with a vast realm of jobs that
didn't require math. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The minimum math your kids will
need for a good job -- or just to understand what is going on in the world
around them -- is much more advanced than it used to be. Once, you learned long
division because it was needed by people in business to make sure they weren't
selling below cost, teachers to figure grades, and electricians to balance a
load. Nowadays spreadsheets and specialty software do all that -- but now the
kid needs to know long division because it's one of the earliest points in math
where the possibility of alternate strategies, and the need to go back, start
over, and guess ahead enters into it, and those are all meta-skills that will
be essential in learning the much higher level math they do need.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-tab-count: 1;"> </span>Unfortunately,
the human brain remains wired so that patterns pull just as strongly as they
did back when patterns were all you needed.<span style="mso-spacerun: yes;">
</span>It takes effort to push people away from just learning those patterns
and stopping there.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">It takes effort to push kids away
from patterns in Singapore too. The drill schools there -- after school mass
practice at arithmetic facts and simple algorithms -- are quite common, and
really popular with parents. <span style="mso-spacerun: yes;"> </span>Quite
likely, especially when they were starting out, many parents thought the only
thing going on in the drill schools was the drill, and to this day, in the not
very good drill schools, that is sometimes the only thing they actually do.<span style="mso-spacerun: yes;"> </span> </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">But in the better drill schools, a long generation of
emphasizing "why" in the classroom and in homework has had its
effect; the drills are not just recitations of the answers, but also are
attentive repetitions of the ideas behind things. The students don't just say
"fourteen times fifteen is two hundred ten" or work that out on a
whiteboard while mentally reciting "put them in matching columns, put down
zero, carry two ..." and so on. Rather, they say something like
"fifteen is one and a half times ten, so we can rearrange the problem into
one and a half times fourteen times ten, half of fourteen is seven, so one and
a half times fourteen is twenty-one, times ten makes two hundred ten." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">They
might then be taken through the drill another way, reciting, "the factors
are five, three, seven, and two, regroup to five times two is ten, three times
seven is twenty-one, ten times twenty-one is two hundred ten." They're
practicing two slightly different algorithms that quickly yield the right
answer -- but they're also consciously reminding themselves of commutativity,
association, distribution, and partial products while they're doing it, and
they're internalizing that the right answer is always the same, but there are
many different valid ways to get there, which is the essential principle behind
including strategy in their number sense.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The kids <b><i>hate</i></b> it, though. So do many teachers. Tutor
manuals at drill schools have big underlined notes saying, "Do not merely
repeat right answers. Recite the whole process all the way through every
time." My guess is that, good for them or not, the students would really
rather just be told what to do, do it, and be done.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">A hidden advantage of memorizing the
traditional algorithms, sticking to them, and avoiding all that "why"
stuff is that it's a reliable way to keep math from getting into any other part
of life. Math produces insights into why things are the way they are, suggests
which other ways are possible, dismisses some ideas as impossible, draws
attention to perceptions about the order of things, makes the sciences
accessible, and makes people smart in a way that will not work out well for
people who need a population which is gullible and compliant enough to stay
hoodwinked.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The advantages of being really
good at real math (as opposed to quick at arithmetic algorithms) is the opening
up of whole new dimensions on the world. That requires the courage to allow our
children in general, and your child specifically, to go beyond us, to have
intellectual horizons wider and more varied than ours. Not everyone wants that:
the loss of family solidarity, the collapse of the secure position of the
elders being always right, the fear of eventually being judged by adult
children who really do know and see more -- or of not being able to share much
of a world with the grandkids after they are small -- all of these are real
fears.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">It's the same fear people have
about sending the first generation to college, or about learning to read
(including the fear of having to learn to read themselves, to keep up with the
kids).<span style="mso-spacerun: yes;"> </span>For that fear, all I can say is
that we all know that acting from our courage is better for the kids than acting
from our fears, and that it is the right thing to do. Furthermore, a family
that stifles its best brains, to keep them at home, is also throwing away the
possibilities you can see in what is <a href="https://www.youtube.com/watch?v=VteDp3IK-60">probably the most pro-education whiskey commercial ever</a>.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">More than one parent who has
considered putting their kids into tutoring with me, after asking about my
approach, has nodded, and asked some version of:</span></div>
<blockquote class="tr_bq">
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span><span style="font-family: "verdana" , sans-serif;"><span style="font-size: small;"><i>Now is Singapore Math the one with the bundles
of sticks, or the one with poker chips?</i></span></span></span></div>
<span style="font-family: "verdana" , sans-serif;"><span style="font-size: small;"><i>
</i></span></span><br />
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-family: "verdana" , sans-serif;"><span style="font-size: small;"><i>Is Singapore Math the one where
they draw circles around things?</i></span></span></div>
<span style="font-family: "verdana" , sans-serif;"><span style="font-size: small;"><i>
</i></span></span><br />
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-family: "verdana" , sans-serif;"><span style="font-size: small;"><i>Is Singapore Math lattice
multiplication or regular multiplication or something else?</i></span></span></div>
</blockquote>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">And of course, at that point I
know I have not been communicating very well.<span style="mso-spacerun: yes;">
</span>The fault is almost certainly mine, but I offer, as a feeble defense, the
sheer difficulty of shaking the grip of procedure on most people's idea of math
instruction.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The real answer, which I am trying
to learn to give well orally, is that Singapore Math can be used to teach any
procedure that works, and usually, somewhere in the world, it is. For many
topics the student will learn some procedures/algorithms that are slow and
cumbersome at first because it's easy to see how they work and why they always
arrive at the right answer. But the thing the student is supposed to learn from
that is not to divide by drawing circles and counting, or to multiply by
drawing diagonal lines or laying out product matrices.<span style="mso-spacerun: yes;"> </span>What the student is learning is the <b style="mso-bidi-font-weight: normal;">why behind every algorithm: </b>that all
multiplication of numbers too large or too complicated to memorize is done by
computing partial products and adding them, which works because of the
distributive property. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The student who understands that
overall principle thoroughly will not get lost or have memory problems with
whatever algorithm he or she eventually learns. That student is likely to
immediately see why one multiplies for area or volume but adds for perimeter,
why least common denominators are needed for adding and subtracting but not for
multiplying and dividing fractions, how long division works, and eventually how
factoring a polynomial is a fast way to find its roots.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">But to find the why, the student
has to look for it, which means learning to seek it. And when a trusted adult
in the student's life dismisses the why in favor of the how -- which is what
"All you do is just ..." means -- and invites the kid to leave the
difficult path of understanding the way up the mountain, in favor of a quick
tram ride to the right answer that gets the kid off the hook, very few kids
will resist that offer. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">When you offer "all you do is
just..." to them -- or even push it on them, as I've seen some parents do
-- you're turning them off the path of eventual real, deep, lasting success so
that they can have the right answer on tomorrow's homework, hand it in, and forget
everything. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Do you really want to teach your
kids to give up the richly successful but difficult long term process of really
learning real math, in favor of getting done early and having more time for
video games?</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .75in; margin-right: 0in; margin-top: 8.0pt; text-indent: -.75in;">
<span style="font-family: "verdana"; font-size: 11.0pt;">*She wasn't exactly one of my star students in English comp, either, by
the way.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .75in; margin-right: 0in; margin-top: 8.0pt; text-indent: -.75in;">
<span style="font-family: "verdana"; font-size: 11.0pt;">**I don't do it quite the way this guy does. Many roads lead to the
kingdom, some of which have alternate routes, shortcuts, and interesting
scenery, so the exact route tends to be highly individual, especially for
one-on-one tutoring.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .75in; margin-right: 0in; margin-top: 8.0pt; text-indent: -.75in;">
<span style="font-family: "verdana"; font-size: 11.0pt;">*** Again, that's only a beginning.<span style="mso-spacerun: yes;">
</span>The next step is to note that the total number of pieces will be the
denominator of the fraction times the whole number, so you multiply those two;
and then that the divisor of this number of pieces will be the numerator of the
original fraction; and thus arriving at the invert-and-multiply rule. Which,
you then demonstrate with a slightly more complicated drawing (so you wait
until they get the simple one) works for all dividends, not just whole numbers.
And just to repeat the point once again, the subject here is not "how to
do fraction problems" but "what is going on when you do fraction
problems" -- a very different subject. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .75in; margin-right: 0in; margin-top: 8.0pt; text-indent: -.75in;">
<span style="font-family: "verdana"; font-size: 11.0pt;">**** Humble analogy (or humbling one, considering how true it is for
me): I have done research for, and written specifications for, two different
sets of dieter-assistance software over the years. I am also fat. It's not that
I don't know it would be better for me to "eat food, mostly plants, not
too much." It's that the promise of wearing a smaller shirt in a couple of
months has one hell of a time competing with the certainty of a pizza tonight.
One reason so many problems are hard to solve with education is the rarity of
problems that are solved by knowing better.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .75in; margin-right: 0in; margin-top: 8.0pt; text-indent: -.75in;">
<span style="font-family: "verdana"; font-size: 11.0pt;">***** In fact if you teach math, you should know <a href="http://www.esmerel.com/circle/numeracy/bellboy.html">the Mathemagician</a>;
lots of good things in his toybox! <a href="http://www.esmerel.com/circle/numeracy/bellboy.html"></a></span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-37918251161011894702015-10-06T07:35:00.003-06:002015-10-06T08:23:10.962-06:00Why the Forrest trail is so long (Part IV of the case study)<style>
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<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">If you just got here, this is one
of about a week-long series of blog posts about Singapore Math and number
sense, and how Singapore Math techniques can help kids through<a href="http://thatjohnbarnes.blogspot.com/2015/03/more-on-that-singapore-math-thing-so.html"> The Wall, that barricade of "this makes no sense" that most kids run into somewhere between long division and elementary algebra</a>. Much of this material will be appearing
later in my forthcoming book, <a href="http://thatjohnbarnes.blogspot.com/2015/02/sort-of-progress-report-on-singapore.html"><b><i>Singapore Math Figured Out for Parents</i></b></a>. The book
draws on two roots: </span></div>
<ol>
<li><span style="font-family: Georgia; font-size: 14.0pt;">I've done a fair bit of science
and technology journalism and understand educationese pretty well too; I'm used
to explaining more-technical matters to a less-technical audience.</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">I tutor math to elementary and
middle school students for<a href="http://www.tutoringcolorado.com/"> Tutoring Colorado</a>, and I've seen how well these
methods can work. </span></li>
</ol>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Another qualification of sorts: I've spent a fair bit of time teaching ADLs, Adult Disadvantaged Learners, people in their 20s-50s who are having to painfully pick up what they never got in school. That has given me an all-too-clear picture of what the dead end of innumeracy really looks like, why it matters that just as many kids as possible get a decent start in math, and how hard it is to recover from a bad start later. I <i style="mso-bidi-font-style: normal;">really</i> wish
I'd known many of the Singapore Math tactics when I was teaching remedial college pre-algebra and beginning
college algebra!</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt;">The series to date has included </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•<a href="http://thatjohnbarnes.blogspot.com/2015/09/from-tunneling-through-sun-with-dimes.html">what number sense is and why it's important </a></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•<a href="http://thatjohnbarnes.blogspot.com/2015/10/hows-your-number-sense-not-quite-quiz.html">a questionnaire to evaluate your own number sense </a>(if you're going to help your kid get it, it helps to have it
or acquire it yourself)</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•and three episodes before this
one following a case study of the mathematical adventures of a beginning
fourth-grader named Forrest. Despite being a composite of several different
students with difficulties, Forrest made quite a bit of progress in those
episodes, progressing through</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><a href="http://thatjohnbarnes.blogspot.com/2015/10/rescuing-forrest-from-trees-tutoring.html">1. a general diagnosis of a memory problem and a conceptual difficulty </a>with perceiving numbers as existing apart from what was
being counted, to </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">2. <a href="http://thatjohnbarnes.blogspot.com/2015/10/another-search-through-forrest-second.html">a specific diagnosis that his conceptual problem was what was causing his memory problems, his very slow calculation, and his inability to progress</a>, leading finally to</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">3. <a href="http://thatjohnbarnes.blogspot.com/2015/10/forrest-clearing-tutoring-case-study.html">the breakthrough moment when Forrest caught on </a>to numbers as numbers, which ended with the warning note that
breakthroughs are only beginnings, and that it's the practice afterwards that
cements the breakthrough and makes it last.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And now, about that practice. If
you don't read any other post in this series, this might be the one that gives
the clearest idea of what Singapore Math is all about (at least, if I
understand it correctly and I'm doing my job, two things of which you must be
the judge).</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Now that Forrest had a real idea
of what numbers were, and how they connected to each other and to the world, he
could see why his parents and teachers had been on his case to learn addition
facts. He also had a much better understanding of what addition facts might
have to do with the rest of math. All of that gave him much more motivation,
but that didn't necessarily make the addition facts any easier to learn. If
anything, it increased the urgency and made him impatient.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Forrest's mother confirmed he was
continuing his practice at home with the addition table board, and was
beginning to complain that he was bored and it had become too easy. That meant
it was the perfect time to introduce a more complicated trick.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Let's try you out on this
one," I said. "Whenever you have <i style="mso-bidi-font-style: normal;">one</i>
value, you have <i style="mso-bidi-font-style: normal;">all</i> the values around
it." I put a tile down at 6+3=9 (that is at the intersection of the 6 row
and the 3 column, I put down a 9 tile.)</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcwAdYAQScwgWchM03-20HVOBVrk71Db5km7cPpEMJVXp8wmNGRhoidycJG_LHBlI0rvQCMGXeArDuO3CADJxo6DjTFgLYFhy-uwJrC52RQDCu6Kr1ARwpq0OfIyH6JftsDqf0IU1Zx8c/s1600/ILLO-+First+step+of+the+spiral..png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="255" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcwAdYAQScwgWchM03-20HVOBVrk71Db5km7cPpEMJVXp8wmNGRhoidycJG_LHBlI0rvQCMGXeArDuO3CADJxo6DjTFgLYFhy-uwJrC52RQDCu6Kr1ARwpq0OfIyH6JftsDqf0IU1Zx8c/s400/ILLO-+First+step+of+the+spiral..png" width="400" /></a></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Now, instead of a row,
you're going to make a spiral. Watch how this works. You put the tile down to
the right of the first one -- 6+4=10." I point and he does; so far, of
course, this is just like doing a row. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Then we wrap around." I
point to successive squares and ask him to say the sum and place the tile.
"7+4=11, 7+3=10, 7+2=9, 6+2=8, 5+2=7, 5+3=8, 5+4=9 ... " </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Here's what
it looks like, with red arrows to show the order in which they are placed.</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuht2uwyS7_rruLHAkIY-24V1AqtIcBNh_-HHM2CglzabkvrY3BeX4Za3aX-p7pCWTYhXwZKKwD7PiTuR3OUXEH2jBCGwRIY4vpGzfgA5yr08TpQpsDl2cPOU9lZqm83FhcdIvp89fqEo/s1600/ILLO-+First+circuit+of+spiral.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="409" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuht2uwyS7_rruLHAkIY-24V1AqtIcBNh_-HHM2CglzabkvrY3BeX4Za3aX-p7pCWTYhXwZKKwD7PiTuR3OUXEH2jBCGwRIY4vpGzfgA5yr08TpQpsDl2cPOU9lZqm83FhcdIvp89fqEo/s640/ILLO-+First+circuit+of+spiral.png" width="640" /></a></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"You see? Now next we wrap
around some more, so 5+5= ..."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Ten."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Right. Do you see where we
go next?" I have to correct and steer him a few times, but soon he's doing
the spiral pattern correctly, and gaining speed as he goes.<span style="mso-spacerun: yes;"> </span>When it seems to be well-established, with
another circuit and a half completed, I say, "So you see how it works. when
you go up or to the right, the sum goes up by one. When you go down or to the
left, the number goes down by one. And as you lay the tiles out in a spiral,
you form that spiral pattern."</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfSfLdD6GPdqvyDhiblL1e6K5uLjFABau_UA4EMp91kRDkrAVTkb2vk-X9-n0FNVGSFkPLmDuqHV4NZgLhOxgn_rPZjEvjLltUkZWpQRX6nsPWkgE-R6IcGVocyt_OYRYHCKfAV-SqavM/s1600/ILLO+2.5+circuits.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="253" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfSfLdD6GPdqvyDhiblL1e6K5uLjFABau_UA4EMp91kRDkrAVTkb2vk-X9-n0FNVGSFkPLmDuqHV4NZgLhOxgn_rPZjEvjLltUkZWpQRX6nsPWkgE-R6IcGVocyt_OYRYHCKfAV-SqavM/s400/ILLO+2.5+circuits.png" width="400" /></a></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"What do I do when my spiral
hits the edge of the board?" </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"What do you think you should
do?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Maybe skip down to the
nearest blank space?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"That might work."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Or I could just start a new
spiral on the board somewhere, and grow it till it runs into this one."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"That would work too. Why
don't you try it a couple of different ways and tell me what you think?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Long experience has taught me that
boisterous kids like to make spirals run into each other, and then have some
complicated rule for managing the collision. Quieter kids, especially ones who
just want to get done, tend to try to figure out ways to get things back to
running up and down rows and columns. After some debating, Forrest hesitantly
made the boisterous choice, and started growing a new spiral around 8+8=16.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Now there's something else
you need to do. Every time you turn a corner, take a long breath, and look at
the tiles you've laid down. Just imagine your mind is taking a picture of it.
Try that now."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Pretty soon he had a rhythm going,
and started building simultaneous spirals, taking turns adding to each one, so
that they would collide. That small-child passion for patterns kicked in, embracing
saying the addition facts as he did them. For a kid in remedial math, he seemed
to be having a pretty good time.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Then a moment of panic: he
stumbled at "eight plus nine". He tensed up all over. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Deep breath," I said,
"and look at what you already have.<span style="mso-spacerun: yes;">
</span>You've got eight plus eight on one side of it, and seven plus nine below
it, and you know what they are, so the square you want has to be -- "</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLZ3q6ke-ET0GgpIKvgMHbiSkwwmablErkFsnsTZjkkP9SQO0gGKY35hcpejqFRWu0ork82HVivjzPxgtCDPlNiqHLeJpRnW4pwrzJdwjIRvaFhtIOlAUbSk778l8ERGrgE4VJmT-x7eY/s1600/ILLO+OF+area+around+17+.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLZ3q6ke-ET0GgpIKvgMHbiSkwwmablErkFsnsTZjkkP9SQO0gGKY35hcpejqFRWu0ork82HVivjzPxgtCDPlNiqHLeJpRnW4pwrzJdwjIRvaFhtIOlAUbSk778l8ERGrgE4VJmT-x7eY/s640/ILLO+OF+area+around+17+.png" width="640" /></a></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Seventeen!" He was
pretty excited; things were still making sense, after all.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Say the whole thing, and
point. Every tile you put down, say the whole problem. If you don't know the
answer automatically, use the layout of the board to see what it has to be, but
once you do see it, be sure you say it."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He looked a little stubborn,
probably realizing how quickly he could lay out the table if he ignored all that
addition stuff and just filled in the sequences. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I asked him, "So what are we
doing this for?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He shrugged. "It's not as
boring as flash cards. It's not as hard."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"All excellent reasons, but
here's another one. You're training your memory to find its way to the answer. There's
four things that build memories, and if you can use all of them at the same
time, they make very strong memories that last for a long time.<span style="mso-spacerun: yes;"> </span>The first big memory builder is concentrating
on what you're doing. Do you see that if you started just laying down the tiles
in order, you wouldn't be thinking about the numbers anymore?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"I guess not."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"You have to think about them
and pay attention to them to build the memory. Pointing and saying makes you
think about them a little more. It also makes you do the second thing that
helps you learn: repeating a thing over and over. So ... get on with it,
Forrest. You've probably almost got the whole table already, just from all the
repeating and concentrating you've been doing in practice."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He finished a couple more spirals,
and now the board held just a scattering of spaces to fill in.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Now, this is where you can
see the other two things that build memory. One is relationship." I pointed
to the blank space at 9+6.<span style="mso-spacerun: yes;"> </span>"What
does that one have to be?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Fifteen?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Exactly! Now, how many ways
did you know?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He looks puzzled, which is normal
at this stage, so I begin with examples. "You knew 10+6=16, you already
had that on the board, right? So the 6 stays the same, the 10 goes down one,
one down from 16 ... that would be one way to know. Or you knew 9+5=14, nine
stays the same ..." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Slowly, he says, "six is one
up from five so it's one up from 14, and that's 15."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"That's right. That's another
way to know." I tapped my finger over the 8 spaces surrounding 9+6.
"You see? Each of these is a clue. So they're all related. This number in
the middle has to be the one that all these clues fit.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"That's using the third way,
which is relationships, to remember. The more you relate, the better you
remember. Going up, down, left, and right, it changes by 1. Going diagonal, it
changes by two this way -- see, 13, then 14,15 -- and stays the same this other
way. So if you get lost, not only do you have the rows and columns, you've got
every square around every square."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I sent him home to practice
spirals, and told his mother to let me know if he seemed to be getting bored or
resistant. </span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Sure enough, by the next session,
Forrest was good and bored, though he was pretty thrilled that in the special
education math class he attended, he had showed a huge improvement with
addition facts in a quiz that week. <span style="mso-spacerun: yes;"> </span>"Well,"
I said, "there are lots of other things we can use the board for, and we
will, but maybe you'd like to try something else?" </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Yeah!" By now,
"something else" probably sounded wonderful. Attentive repetition is
highly effective, but even when generously mixed with relation, it's still not
much fun.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Okay, let's see how fast you
can set the board up. You can do it in any order and you don't have to say
them. I'll time you."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He did it in less than five
minutes, noticeably checking his math facts to make sure he was right. His
quick confidence was very encouraging.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I drew his attention to the
Left-Right-Down diagonals, the ones of identical numbers. Not only did each LR
diagonal contain all the same number; the only place that number occurred
was on that diagonal. "All the ways of making ten are on that one
diagonal," I point out. "And the only place where you find any way of
making ten is on that diagonal; the diagonal is the ways to make ten and the
ways to make ten are the diagonal.* Why do you suppose that is?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">An advanced fourth-grader might
figure out an answer, but a struggling student like Forrest first had to
understand the question. (Again, no worry about that: figuring out a hard
question begins with understanding it, and this was all valuable practice). His
first answer was "Because it goes across like this," making a slashing
motion in the air. He meant that it was a diagonal because it looked diagonal. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I said he was right, apologized
for my unclearness, and asked him to try again, dropping more hints each time, until
it clicked and he said, "Something makes that happen." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Excellent! Now, here's what
makes it happen." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I had him line up ten poker chips on
the table and split them into two a group of four and a group of six, and made
sure he knew that the number of chips stayed the same.** </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Now point to the first group
and say how much it is -- "</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Four."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"And say 'plus,' and point to
the second group -- "</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Four plus six equals
ten."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<br />
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Exactly right. Just like you
do when you're doing the board. Now move one chip from one group to the other,
and do it again."</span><br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSRtd9Ho9riQVSI9GB-iJxPO51hvZX65dD0S1gVl-kSQy24dzuZfJLx0MWR4eK6gIgT7r04fe7v1gIOdmerfI3MAAvUUVl0uuXdNNCsPvPJssBS0kiOh3YDNQVZKKPxYSNlBYkKleUjqs/s1600/4%252B6+chips.png" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSRtd9Ho9riQVSI9GB-iJxPO51hvZX65dD0S1gVl-kSQy24dzuZfJLx0MWR4eK6gIgT7r04fe7v1gIOdmerfI3MAAvUUVl0uuXdNNCsPvPJssBS0kiOh3YDNQVZKKPxYSNlBYkKleUjqs/s320/4%252B6+chips.png" width="144" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><i><b><span style="font-size: small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;">And 4 plus 6 is 10, shooby-doo wa, </span></span></b></i></td></tr>
</tbody></table>
<br />
<span style="font-family: Georgia; font-size: 14.0pt;"> </span><span style="font-family: Georgia; font-size: 14.0pt;"> "And again."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
</div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9V0WnhG3_IG1C3wVRDBauBeBCiMMtAHfwpy9nLyDhUoBOW70IY9KxvjXs6QWwO0-uHdLKMZbOm8ybRaJw3AASzkJ-Gv03hbHTY63FsacjKlbNtim-BtuaJSHey0I0zx-w-fZeBkc0P3U/s1600/5%252B5+chips.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9V0WnhG3_IG1C3wVRDBauBeBCiMMtAHfwpy9nLyDhUoBOW70IY9KxvjXs6QWwO0-uHdLKMZbOm8ybRaJw3AASzkJ-Gv03hbHTY63FsacjKlbNtim-BtuaJSHey0I0zx-w-fZeBkc0P3U/s320/5%252B5+chips.png" width="148" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><i><b><span style="font-size: small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;">And 5 plus 5 is 10, shooby doo wa</span></span></b></i></td></tr>
</tbody></table>
<br />
<span style="font-family: Georgia; font-size: 14.0pt;">"Now, what comes next?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIv-Gowl2cTu99ib7x2e7zGgfUMvM-7YfSg47cPFzjKpLvt7mZ16VTOwRPRDdaB4aF3cHb6PceQUqXtMkpERhi6KUJ2d26uw-a0EuBveysY587YAhr_c6UuD1Kbup1kQ_qTbVKB710uHc/s1600/6%252B4+chips.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIv-Gowl2cTu99ib7x2e7zGgfUMvM-7YfSg47cPFzjKpLvt7mZ16VTOwRPRDdaB4aF3cHb6PceQUqXtMkpERhi6KUJ2d26uw-a0EuBveysY587YAhr_c6UuD1Kbup1kQ_qTbVKB710uHc/s320/6%252B4+chips.png" width="141" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><span style="font-size: small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;">And 6+4 is 10, bop a a loo bop a bop boom boom bang</span></span></b></td><td class="tr-caption" style="text-align: center;"></td><td class="tr-caption" style="text-align: center;"><span style="font-size: large;"> <i>shooby-doo-wa may be adjusted for cultural and generational reasons</i></span></td></tr>
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<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He hesitated when he ran out of
one group. I pointed to the empty space where it had been and said, "So
how many chips are there here?" </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"None."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"What's math talk for
none?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Zero. Oh! Zero plus ten
equals ten!" </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Good, now start back the
other way."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He quickly developed a rhythm,
moving the counters and saying what they meant at the same time. Since he was a
little bit of a ham and liked to sing, I encouraged him to sing the
combinations according to a melody that he gradually made up.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Once he had it well worked out, I
said, "So, do you recognize the words?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He looked puzzled.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Try doing that song and
pointing to numbers going down that ten diagonal on the board."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He started, stopped, and looked up
in confusion.<span style="mso-spacerun: yes;"> </span>"It's the same as it
is with the chips. I'm singing the </span><span style="font-family: Georgia; font-size: 14.0pt;"><span style="font-family: Georgia; font-size: 14.0pt;">exact </span>same words." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"So why do the tens all fall
on a diagonal?" At that point, I shut up and waited. This is one of those
things where if a kid can say it for himself, you've won.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"'Cause a diagonal goes one
right and one down, and that's like moving a chip from one to the other, kind
of."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">At that moment, however
primitively, Forrest was doing real mathematics.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">This is one of the foundational
teaching tricks in Singapore Math: students are guided to come at things more
than one way, then learn to integrate the ways. It's another way of building
memory/retention through the relationship pathway, and also through the fourth
avenue (anticipation, often known as "guessing ahead" or
"self-testing.")</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Parents often ask about this. Many
really don't see why a student has to know more than one way to do anything,
and why that way can't just be the memorized traditional algorithm. I usually
offer them this analogy: "If you are going somewhere completely unfamiliar
in a town strange to you, you follow the directions exactly to get there, and
the moment you get off the directions you back up, or try to figure out or find
new directions. But if you are going between two familiar spots in your
hometown, you have a real understanding of where they both are, and you just
take what you know will be the best route between. The objective is to move
your kid from that lost-in-a-strange-place, must-stay-on-the-directions state
to inhabiting mathematics like it's his/her hometown."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">To put it a little more
abstractly, once a kid learns to see the patterns as manifestations of
underlying causes -- to realize, for example, that the first group can be
assigned to a row and the second group to a column, and that a move that goes
Row-1,Column+1 is a diagonal move on the board, and sums to zero -- that kid
actually understands the math, rather than just playing the pattern.<span style="mso-spacerun: yes;"> </span>Which is to say, the kid has learned to use
number sense.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Or putting the issue another way
(you see how you can use this method for anything?): to learn one algorithm,
all you need to do is to memorize. To learn more than one algorithm, you just
need more memory at first. But to understand why two or more different
algorithms are actually doing the same thing requires number sense. And if a
kid does those "why are two methods really the same, just written
differently" exercises enough, s/he starts to learn to reach for the
number sense to understand any algorithm. That means, for example, that when the
kid hits fractions, the question will probably be "what does it mean when
the numerator is bigger than the denominator?" instead of "which
number do I write on top?" (The second question leads to much more
understanding than the first.)</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Not long after he started singing
the groups-of-chips songs, I pointed out to Forrest that he could just picture
the chips in his mind, or even imagine the diagonal on the board, and sing it
just as well. I had him demonstrate it by singing the sevens diagonal while
blindfolded. As soon as he finished, he insisted that his mother watch him do
it.*** We agreed that he'd try to sing all the diagonals from the table a few
times a day, but didn't have to use the board or the chips unless he wanted to.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The next week, I handed him a
randomized list of all the addition facts. In less than fifteen minutes, he had
gotten them all right. </span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">When Thomas Vowler Short figured
out and systematized his much better way of teaching fractions somewhere in the
1830s, he was astonished at how students went from slowly, carefully plodding
to soaring. It still startles me.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Breakthroughs take time and
patience. Exploiting the breakthrough fully, making it part of how the student
sees math and the world, takes attentive practice, so it is often a much slower
process, and subject to setbacks. Keeping a kid focused on the idea while
practicing is hard and requires a lot of inventiveness and close attention. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Once they have learned a few
fundamental ideas through the whole process, from insight to practice to complete
familiarity, they really know what math is about. And after that, the kids who
were "never any good at math" move with amazing speed, often moving
up a full grade level in a couple of months. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">That blissful state doesn't last
forever, of course, though it's great while it does. Sooner or later the kid
faces another conceptual barrier, but the next time, it's with the experience
of getting through or over a barrier, and of knowing that s/he has seen a block
like this before, and made it through. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The student knows to look for an
idea, not a rule about where to write things, and how to practice the idea via
concentration, repetition, relationship, and anticipation until it is really
second nature.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">After two to four times working
through conceptual blocks in this way, most kids are true "math kids"
regardless of whatever talent they started with. They know how to push into the
difficulty, how to work their way through the conceptual problems, and
ultimately how to have their own breakthroughs. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">All that moves "Aha!"
out of the realm of intuition and miracle, and into something that can be
deliberately worked for and achieved. And with that power, students can go
about as far as they need or want to go, without nearly as much fear or anxiety
as in traditional methods. Math has become their own common sense of how the
world works, rather than an arcane ritual adults use to prove you're dumb.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-size: small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;">*I don't know for sure that this
will give him a head start on graphing functions in a few years, but I am
inclined to think it might.</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-size: small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;">**This is not <i>usually</i> a problem
with a nine or ten year old, even one with severe math problems, but it's worth checking because now and then a child who is delayed on the Piaget scales may think that
rearranging a group of objects can change how many there are. These children may grow up to
become investment bankers and should be watched carefully.</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-size: small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;">***Luckily, she thought it was
cute.</span></span></div>
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<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-29913547752301054032015-10-03T22:59:00.003-06:002015-10-03T22:59:23.377-06:00Forrest Clearing (a tutoring case study, part III) . Also tyrannosaurs on Mars, and why I don't like Rumpelstiltskin
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<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Latecomers and accidental
wanderers-in: This is one of a whole series of blog posts about Singapore Math,
number sense, and how Singapore Math techniques, when properly used, build and
develop number sense and ultimately gets math-blocked kids moving again. The
series began with <a href="http://thatjohnbarnes.blogspot.com/2015/09/from-tunneling-through-sun-with-dimes.html" target="_blank">some description of what number sense is</a> and <a href="http://thatjohnbarnes.blogspot.com/2015/10/hows-your-number-sense-not-quite-quiz.html" target="_blank">a questionnaireto see how your number sense is</a>; since then, we've been following <a href="http://thatjohnbarnes.blogspot.com/2015/10/rescuing-forrest-from-trees-tutoring.html" target="_blank">a case studyof the mathematical adventures of a beginning fourth-grader named Forrest</a>. I
made up Forrest from bits and pieces of half a dozen students whom I've tutored
at <a href="http://www.tutoringcolorado.com/" target="_blank">Tutoring Colorado</a>, where we use Singapore Math methods to unblock the frustrated
and retrieve the lost. Eventually much of this material will be in my
forthcoming book, <a href="http://thatjohnbarnes.blogspot.com/2015/02/sort-of-progress-report-on-singapore.html" target="_blank">Singapore Math Figured Out for Parents</a>.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><a href="http://thatjohnbarnes.blogspot.com/2015/10/another-search-through-forrest-second.html" target="_blank">When we last left Forrest</a>, I had
finished the diagnostics and begun to assign him exercises. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Diagnostics had
revealed that he had a pretty severe conceptual problem: he didn't understand
numbers as abstract entities in their own right, but rather as temporary names
for things, so that for him, counting "1, 2, 3 ..." was really not
much different from naming "Grumpy, Happy, Sneezy ..."; the count was
just the last name he arrived at, and there wasn't necessarily any reason to think that if he counted the same things twice, it would come out to "Dopey" both times. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">As explained in the previous two pieces about
him, this had also made it very difficult for him to learn elementary addition
and multiplication facts, or to see any reason why the various
algorithms/procedures were anything other than completely arbitrary. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He'd been given an addition table
board and sent home to practice with it; his mother had been shown what he
needed to do and had assured me he'd be doing it.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And now that you're up to date,
we're ready for his next visit.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Forrest's mother had assured me
that he'd been practicing regularly, with occasional minor nagging and
reminding from her. He was also complaining that the addition table board was
getting dull, and had mentioned that I had promised him that eventually we'd be
playing some games on it. So far, for Forrest, math tutoring was occasionally
different, but it still bore an uncomfortable resemblance to plain old math.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 20.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I had filled in about two thirds
of the addition facts board, leaving few numbers adjoining, when Forrest came
in:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzGgNtmTg2d-XEwn92pIWvE5saTawM5kelkjF4hfQ1QJL_7xbJnF9zSC9FbenrDF1K9S1bpw7g8ETTGxsRzjVn5QrJD_JCPlsYAb-cekN5j_K743F-MzOhyoCi7sCLBx0FxY1oql9aVYU/s1600/Partially+filled+board.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="416" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzGgNtmTg2d-XEwn92pIWvE5saTawM5kelkjF4hfQ1QJL_7xbJnF9zSC9FbenrDF1K9S1bpw7g8ETTGxsRzjVn5QrJD_JCPlsYAb-cekN5j_K743F-MzOhyoCi7sCLBx0FxY1oql9aVYU/s640/Partially+filled+board.png" width="640" /></a></div>
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<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;">
</span>He found this mildly interesting. I added, "I'm holding the tiles
over here in this rack -- it's the same one we'll use later when we're playing
games -- so that you can't see them. What you have to do is point to a square
and ask me for the tile that goes there -- by number, you can't just say 'May I
have this tile.' Ready to try?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He nods, points to an easy one,
3+4, and says, "I need a 7 for this one." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I give it to him. He quickly
realizes that he can do this -- the location of most of the blanks at
intersections of sequences makes it very easy -- and picks up speed and
confidence. When he has most of them, has made no use of his fingers, and is
going very quickly, I throw him a little bit of a curve.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He points to the 5+8 box and asks
for a 13. I ask him, "So is it true that 5+8=13?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He starts to count; I say,
"Whoa. You did that problem already, several times, this past week, right?
And you just pointed to it."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"But you just asked me
again."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"I asked you if it was
true."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Well, I don't know if I
counted right."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"It is true, Forrest. It will
be true whether you count it or not, it was true before there was anyone to
count, it will be true forever, even if we never put the tile on the board or
we take it off and put a wrong number in its place."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Okay." He sounds very
doubtful and looks confused. Nonetheless, it's a healthy confusion.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I push him a little more. "If
you have five Pokemon cards and I give you eight, how many do you have?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He starts to look at his fingers.
I hand him the tile he asked for, and he puts it down, almost unconsciously.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Look at the board." I
point to the five. "Say after me. 'I have five Pokemon cards, I get eight
more, and now I have ...'" </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He's been mumbling along, but now,
firmly, he says, "Thirteen Pokemon cards."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Because -- " I point
back to the five.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Five?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Five plus ... " I point
again.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Suddenly he's pointing, as he's
been practicing all week, but with much more enthusiasm. "Five plus eight
equals thirteen!" </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Right. Now let's do it with
dollars."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">We do dollars in a bank account,
books on a shelf, and at his suggestion, zombies in the graveyard, and at my
suggestion, tyrannosaurs on Mars, even though there aren't any really.<span style="mso-spacerun: yes;"> </span>Each time he finishes with "because five
plus eight equals thirteen."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">It's time to see if he sees the
point. "So, five anything plus eight anything makes -- "</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Thirteen anything!"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Always."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Always!"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"So when you are doing a
problem fifty years from now, and you're an old guy like me, no matter what you
are adding, if it's five and eight -- "</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"It's always thirteen."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"And way in the future, when
you're counting up something that hasn't even been invented or discovered yet,
if there are five of it in one bunch and eight in the other bunch -- "</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Thirteen." He looks a
little astonished and even, still, a bit confused. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"What if there was a group of
eight dinosaurs and a group of nine tyrannosaurs on Mars?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">His hands start to come up to
count, but he stops himself before I can, and silently points for a moment
before he says, "There would be seventeen tyrannosaurs on Mars."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"For sure?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"For sure!" He's looking
at the whole table now, as if it were a pirate's treasure map or the secret
pathway to Oz or Middle Earth. I suppose in a way it is. I wouldn't be able to
explain it to him, but he's just taken that step into abstraction, and found
out that numbers are not arbitrary. He may not ever like it, but at least he
knows a little more of what he's dealing with. </span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">One thing I have always disliked
about case studies in psychology texts and self-help books is what I call the
"Rumpelstiltskin cure." If you remember that fairy tale, </span></div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://upload.wikimedia.org/wikipedia/commons/e/ee/Rumpelstiltskin-Crane1886.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="136" src="https://upload.wikimedia.org/wikipedia/commons/e/ee/Rumpelstiltskin-Crane1886.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Nice king you got there. You want him asking about the baby?</td></tr>
</tbody></table>
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<span style="font-family: Georgia; font-size: 14.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "MS 明朝"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast;">Rumplestilstkin
tells the former-millers-daughter-now-queen that he will cease tormenting her
if she can learn his name. </span>
<br />
<blockquote class="tr_bq">
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: 14pt;">Once she learns it, by dint
of a well-paid spy, she asks him, </span></span></div>
<span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;">
</span><div class="MsoNormal" style="margin: 0in 0in 9pt 0.5in;">
<span style="font-size: small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;"><span>"</span><span>Are you called Rumpelstiltskin !"<br />
"A witch has told you! a witch has told you !" shrieked the little
Man, and stamped his right foot so hard in the ground with rage <table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWAxYS8ai3NVKYnnJgueo9IBvHyWfXQ8BIjLisiNmPZnhtuigKGoSRlP3T3hremuc0rzYVOzpcnJkrfc1LMOaFIgKRgnu57FSaEOBr2yCDMMAKes9Xv6aaxWebix7uNhZSP8SYOoAQuY7X/s1600/Rumpelstiltskin_3.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWAxYS8ai3NVKYnnJgueo9IBvHyWfXQ8BIjLisiNmPZnhtuigKGoSRlP3T3hremuc0rzYVOzpcnJkrfc1LMOaFIgKRgnu57FSaEOBr2yCDMMAKes9Xv6aaxWebix7uNhZSP8SYOoAQuY7X/s1600/Rumpelstiltskin_3.jpg" height="245" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The groundskeeper still talks about what a job cleaning up <b><i>that</i></b> was.</td></tr>
</tbody></table>
</span></span></span></div>
</blockquote>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in;">
<span style="font-size: small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;"><span>that he could
not draw it out again. Then he took hold of his left leg with both his hands,
and pulled away so hard that his right came off in the struggle, and he hopped
away howling terribly. And from that day to this the Queen has heard no more of
her troublesome visitor.</span></span></span><span style="font-family: Georgia; font-size: 14.0pt;"></span></div>
<br /><div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In half or more of the Hollywood
movies about mental illness you've seen, that's the ending; the clever
therapist (or the clever patient, or someone clever) figures out the one thing
causing all the patient's problems (Rumpelstiltskin, abuse, some traumatic
event), and as soon as it is named, the patient's problems vanish, leaving the
patient all better. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Freud seems to have started the
whole genre of "Rumpelstiltskin cures" with his paper about the Wolf
Man, whose problems supposedly originated from having walked in on his parents
at That Awkward Moment.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Even in the much less upsetting
realm of math difficulty, Rumpelstiltskin is not how it works. Just naming the
problem is handy, but it's not even close to the solution.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Conceptual breakthroughs are often
very important, but they are the beginning, not the end, of the process.
Forrest still had to learn all the math he hadn't learned before, and re-think
all the math he thought he knew, and practice until the correct concepts became
the center of how he knew that math. Going back, seeing the first wrong turn in
the road, and correcting that turn, still leaves you with a lot of driving to
do.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And driving, in this case, was a
metaphor for "practice." The next and final part of the story is less
dramatic (no mystery to it) but it's where Forrest did the real work of
Singapore Math and finally caught up with his classmates.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The genius of Singapore Math is
that it teaches the student to think about the right concept at every moment of
practice; it's never just a procedure, it's a procedure and the idea behind it.
Forrest had seen what the right idea was, after years of living with the wrong
one.<span style="mso-spacerun: yes;"> </span>But for the right ideas to fully
displace the wrong, so that he was forever on the right track, he'd have to
practice, practice, and practice, and it would have to be the right kind of
practice, by which I mean the Singapore Math kind.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">That's the real finish of the
story, when the most important parts happen, and I'll tell you about that
tomorrow.</span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-29719503935046989982015-10-02T21:49:00.000-06:002015-10-02T21:49:14.747-06:00Another search through Forrest: the second diagnostic meeting (a tutoring case study, part II)
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<br />
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">For those of you who just came in,
you might want to drop back a day and read <a href="http://thatjohnbarnes.blogspot.com/2015/10/rescuing-forrest-from-trees-tutoring.html?zx=2318f1693e9393aa" target="_blank">Part I</a>,
which is not terribly long (at least not by my ultraverbose standards). It
explained that this is a case study, and like most case studies, the characters
in it and their difficulties are composites, examples of the common and the
typical pulled from a number of real kids and real math situations that I've
encountered since I began handling the math tutoring duties for <a href="http://www.tutoringcolorado.com/" target="_blank">Tutoring Colorado</a>. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In our last episode, my invented
composite tutee, Forrest, had gone through the NumPA interview, and by
observing him I'd decided to focus in on two issues: memory problems, which I wasn't
at all sure he had, and conceptual difficulties with thinking of numbers as
abstractions, which I was fairly sure he had.<span style="mso-spacerun: yes;">
</span>Both problems were probably interacting: he had a hard time memorizing
because he thought of numbers as a set of temporary, arbitrary names, and he
had a hard time moving beyond very rudimentary counting because he couldn't
retain enough math facts to see any pattern in them.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So my basic strategy was to tackle
the conceptual issue first while I gathered more information about the extent
of the memory problems (if indeed there were any). And now on
with the story ... </span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt; mso-bidi-font-size: 14.0pt;">§</span></b><span style="font-family: Georgia; font-size: 14.0pt;"></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">At the second meeting, I showed
Forrest an addition-table board and tiles. The addition table board looks like
this</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaBTjbfS_-V_b_mpivY7X7U95BwqpJPtmUa5yeWwcIWKfFiEmhqMT1RpHVC4Q9qK59GqelkRqCG1fUBx7uFU7ePr7dwsGBwsQUXr73lIP7f0K-BwDZjcSFUgwsZOx1vDueVuCwjwv5NWA/s1600/Empty+Addition+Table.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="420" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaBTjbfS_-V_b_mpivY7X7U95BwqpJPtmUa5yeWwcIWKfFiEmhqMT1RpHVC4Q9qK59GqelkRqCG1fUBx7uFU7ePr7dwsGBwsQUXr73lIP7f0K-BwDZjcSFUgwsZOx1vDueVuCwjwv5NWA/s640/Empty+Addition+Table.png" width="640" /></a></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<span style="font-family: Georgia; font-size: 14.0pt;">and the tiles, which are played on
the blank spaces, are the sums, laid out like this:</span>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6ZiV69pqP1UozH_9y8f6ZDRKssDLSCSqYKQI5-yaQepnZhXglUpgeE0v2l-JFnvdlKszcQV9WiZ09ygZWpsM3nbawNy0cdIKs5tMhC2I4Dx28lrLnhU4XoVP3WYTbZCr8NXFDZ0F-OFg/s1600/Filled+Out+Addition+Table.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="410" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6ZiV69pqP1UozH_9y8f6ZDRKssDLSCSqYKQI5-yaQepnZhXglUpgeE0v2l-JFnvdlKszcQV9WiZ09ygZWpsM3nbawNy0cdIKs5tMhC2I4Dx28lrLnhU4XoVP3WYTbZCr8NXFDZ0F-OFg/s640/Filled+Out+Addition+Table.png" width="640" /></a></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">When I set up the room before
Forrest arrived, I put the tiles in piles in numeric order just to one side of
the board, so that it would be easy for Forrest to find the tile he wanted.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I told Forrest that it was a sort
of game or puzzle. The object was to arrange the tiles on the board to make an
addition table. I showed him how each cell of the table is the sum of the row
and column numbers. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He could put all the tiles into
their proper places by any means he liked, but I needed to hear him explain how
he was doing it.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>He started with 0+0=0, tentatively, at the
lower left, and then picked up speed as he realized how easy the zero and one
rows are. As he worked through the 2 row and the 2 column, he slowed down.
Confirming previous observations, he seemed unaware of commutative pairs: he
had to count out 2+6 and 6+2 separately.<span style="mso-spacerun: yes;">
</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In fact, he really didn't seem to
see any patterns. He made no use I could detect of the left-right-down
diagonals, or the sequence of numbers along any row or column. For Forrest, all
the addition facts existed as isolated statements. It's a sort of memory that I
sometimes call "phone book knowledge": knowing one phone number doesn't
really help you to know any other phone number, because there is no relation
between them.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Paradoxically, eventually addition
and multiplication facts do become phone book knowledge, in older students and
adults; eventually you know 7X9 instantly, without reference to any other
products of 7 or 9, and that allows you to do arithmetic very quickly. But in
the learning stage, 100-169 facts (depending on whether your school district
wants students to learn the tables as 1-10, 0-12, or something in between) is
simply overwhelming for many children.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Or returning to the metaphor, back
before phones had memories, a good salesman or administrator might know that
many phone numbers, but that came from months and years of practice. Sitting
down and learning that many phone numbers in a few days by just chanting them
might be daunting even for adults. You needed a system (area codes for cities,
exchanges for large companies, etc.) to find your way through the list, in
order to get enough practice to learn, eventually, to do rapid random recall.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Somewhere northeast of 4+4=8,
Forrest began to surreptitiously count on his fingers; I told him it was all
right to do that, and showed him how to count up. After all, counting up is a
baby step in the direction of abstraction, and Forrest needed all the steps in
that direction he could take.<span style="mso-spacerun: yes;"> </span>He
immediately caught on to counting up, but he'd have attacks of doubt every few
problems and have to check it by counting total.* </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Around 6+6=12, Forrest was bogging
down again -- the unfamiliarity of counting up was probably tiring him a
little. Not expecting him to get it this time, but preparing a bridge to the
next session, I showed him that he could count up on the board even more easily
than on his fingers: "see, to add 8+6, start at 0+0=0. Now count up to row
8 ... and count 6 columns to the right ... that's exactly the same thing as the
way you count on your fingers. But you could just point to the 8 in the zero
column, and count over 6 ... that's exactly the same thing as the way I just
showed you."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He did it but I could tell he
didn't trust it at all; he kept comparing tiles to fingers, and it was
something of a surprise that they kept coming out the same. That surprise was
what I planned to build on.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">As he worked, as if just making
conversation, I asked, offhandedly, other diagnostic questions: </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•If you did the same board
tomorrow, would it come out the same way? (He answered, "If I did all the
numbers the same way." Follow-up questions confirmed that by "the
same way" he meant "in the same order" and that he still thought
he'd have to count them again.)</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•Was 4+7 equal to 11 before you
counted it out? ("It can't be a number if you haven't counted it.")</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•Could 4+7 ever be a different
number? ("I don't know.")</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•When your class does a school
program, do you have trouble learning the words to songs? ("No, that's
really easy.")</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•How's your spelling? ("Last
year I won the spelling bee twice!")</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•"Can you name the starting
offensive line for the Broncos?" I had noticed the T-shirts and hats on
both Forrest and his father. (He rattled off a quick summary, including the
variations. I have no idea if he was right. I just wanted to know if things
stayed in his memory and were quickly accessible when he wanted them to be. The
answer was obviously yes).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">We finished up that second session
with some talk about training for effective recall.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"If you want to do this, you
have to decide to train your memory. All I can do is show you how, but you will
be doing all the training. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Now, let me show you something
you might already have noticed. In the addition table, all the numbers along a
row or a column are in sequence,that means in number order. In fact, you could
say they look like they're counting up from the row number or the column
number. So if you have part of a row or a column, you can always fill in the
whole row or column. And you always do have part of it, because you always know
the zero row and the zero column, right?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I showed him how it worked; we
filled in part of the sevens row and the eights column, because Forrest felt
that he had the most trouble with those two numbers.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>"So now you know how you could do the
whole table in three minutes or so, right?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He's nodding, temporarily happy
because it looks like there's a trick to this that will make it easy.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"The trick is to use it to
train your memory, to make it stronger and better. The pattern will give you
the answer, but getting the answer is just the first step, not the goal. You're
trying to train yourself to remember the answer. So as you lay down a row, use
the sequence to know what comes next. Then as you add each tile, say the row,
say 'plus,' say the column, say 'equals', and then say the number you are
putting down. Point to them as you do it. For example, seven plus five equals twelve.
Point and say the whole thing."</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgoEOhKYHTsITXFV61wvsJvXcYTduc84__bhSHokrdo9uZZW41T323REnRhYJz7tl6_7hPCJW3QpmyMYc2bvsKYQc-Wg3d_bZkkQre3BFc7y2ETS4sjxpKwwWbbfEKXrgPVpTWqc_ZmPM/s1600/Add+Table+Say+It.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="462" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgoEOhKYHTsITXFV61wvsJvXcYTduc84__bhSHokrdo9uZZW41T323REnRhYJz7tl6_7hPCJW3QpmyMYc2bvsKYQc-Wg3d_bZkkQre3BFc7y2ETS4sjxpKwwWbbfEKXrgPVpTWqc_ZmPM/s640/Add+Table+Say+It.png" width="640" /></a></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>After a minute or so he got the hang of
pointing to the row, then to the column, then to the tile. "One more time
on this one," I said.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"5 plus 7 equals 12." He
pointed at each number with full confidence; his index finger was the only finger
he had up.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"What happens next is, I'm sending you home
with a board and set of tiles, yours to keep. Try to keep them clean and organized because eventually you will be playing a lot of different games on them. Twice a day, for not more than
twenty minutes at a time, what I want you to do is set up the addition table -- you don't have to finish each time, you can just get as far as you get,
then start from that point at your next session. Every time you finish, just
sort the tiles into groups over to the side, and start again from the
beginning. It's not about getting it done, it's about doing the set-up right
each time.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Now, as you set it up, every
single time you put down a tile, I want you to say the<span style="mso-spacerun: yes;"> </span>addition fact out loud, pointing to the row
and the column and the tile, just the way we just did.<span style="mso-spacerun: yes;"> </span>It's very important to really look at every
number at every step. Maybe say it two or three times extra if you catch your
mind wandering."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">We did a few more sevens and
eights, rows and columns, together, and at the end he could say them in
sequence. He was dubious about it; the addition facts just didn't feel as true
to him when he didn't count. But he agreed to fill in as much of the board as
he could in two 20-minute sessions every day, and to get the answers from the
tiles, not from his fingers, speak each addition fact aloud, and try to
concentrate on them as he did it. When his mother came to pick him up, we all
went over the assignment together, to make sure she understood it and could
remind and guide him. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"And he'll know his addition
facts from this?" she asked.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Probably.If not, I've got a lot more tricks. And once he's had
the practice, I can show him much more about how to use his memory more
effectively. But the most important thing is that it gets him ready for the
conceptual breakthrough we're trying for. Usually that doesn't take long, if he
sticks to the practice. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Remember, twice a day, but
not more than twenty minutes, and it's okay to skip if he's not feeling well.
But he's so good at it, he'll probably want to do it when you remind him."
That's sort of a self-fulfilling lie; most of the kids I see are so discouraged
that to have me tell their parents they are good at a math exercise, no matter
how simple the exercise is, tends to make them want to do it; that experience
of being good at it is something they enjoy so much and haven't had in so long.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt; mso-bidi-font-size: 14.0pt;">§</span></b><span style="font-family: Georgia; font-size: 14.0pt;"></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And that's part two of this case
study; part three, in which we see that conceptual breakthrough, tomorrow, I
think. Always allowing for fate to jump me again, of course.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt; mso-bidi-font-size: 14.0pt;">§</span></b><span style="font-family: Georgia; font-size: 14.0pt;"></span></div>
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-size: x-small;"><span style="font-family: "Helvetica Neue",Arial,Helvetica,sans-serif;"><span>*Luckily, and I think to his
surprise, they did always give the same answer.</span></span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<br /></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-62695117553260205952015-10-01T20:39:00.002-06:002015-10-02T21:56:46.558-06:00Rescuing Forrest from the trees: a tutoring case study, part I<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRyq54foLf3hFF_RfB6S3Y_D4392lHMzHUxUp48IIUCcf8zjId7CwtZ12LT7ZckGBLKghMxdRxlBBl3K4V2NP-hEXGyZ2RgYu_6TnC3GLCcn9dp2jSjubgvox3k8_c17VqPkpmCsANVEs/s1600/Forest+of+Mathematics.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRyq54foLf3hFF_RfB6S3Y_D4392lHMzHUxUp48IIUCcf8zjId7CwtZ12LT7ZckGBLKghMxdRxlBBl3K4V2NP-hEXGyZ2RgYu_6TnC3GLCcn9dp2jSjubgvox3k8_c17VqPkpmCsANVEs/s400/Forest+of+Mathematics.png" width="296" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://www.amazon.com/Forest-Mathematics-bilingual-English-Spanish/dp/9508510994" target="_blank">Charming book, by the way.</a></td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
</tbody></table>
<span style="font-family: Georgia; font-size: 14.0pt;">Like case studies in self help,
psychoanalysis, business management, and so forth, this is a composite tale.
In using Singapore Math methods to coach kids with math problems at <a href="http://www.tutoringcolorado.com/" target="_blank">Tutoring Colorado</a>, I've seen several kids who shared a problem or two with Forrest, and no kids
who were exactly like him.<span style="mso-spacerun: yes;"> </span>When I
realized that this particular tutoring tale was getting very long for a blog
post, I decided to break it up, so, here's part one.<span style="mso-spacerun: yes;"> </span>Part two, probably, tomorrow.</span>
<br />
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Forrest, who was just starting
fourth grade, was a little shy when he came in with his parents for the
assessment. His mother described how upset and frustrated he became while
trying to do his math homework. His father added, "His school says he's
about two years behind, but I think it's worse; there's a lot of first grade
math he can't do." His mother quickly listed the commercial tutoring
services they had tried. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">It did not take a child
psychologist to see that Forrest was not looking forward to going into a room
to do math with two strangers. He sat down, squirming a little, and stared down
at the table. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">We use the <a href="http://www.ero.govt.nz/National-Reports/Assessment-in-Primary-Schools-A-Guide-for-Parents-December-2008/3.-Assessment-Tools-and-Terms#Numeracy%20Project%20Assessment%20%28NumPA%29" target="_blank">NumPA (Numeracy ProjectAssessment) developed by the government of New Zealand</a>,
because it's a very well done conditional-levels assessment: structured rather
like a choose-your-own-adventure, if students get a problem right, the next
problem is harder; if wrong, the next problem is easier. The highest level the
kid gets consistently right is the score in each category. "Getting it
right" often includes explaining a correct method for getting their
answers, so luck and guessing play a minimal role.*</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In the first session of the
assessment, my spouse/partner administers the questions; I sit off to the side
and watch what the students actually do while they try to arrive at an answer. Forrest
was cooperative but numb; to him, this was just one more exhibition of his
ineptitude. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The score showed that Forrest's
father was basically right. Forrest was an entering fourth-grader, but the
highest level where he was consistently right was below middle-of-first-grade.
Sometimes, but not consistently, he got a short streak of right answers well
above his usual level: for example, he did fine at "which fraction is
bigger" as long as the fractions were one over some low integer.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The directions explicitly tell
students that they can count on their fingers, because we're trying to assess
where they are starting, so if that is what they actually do, we want to see
them do it. But Forrest was counting on his fingers under the table; he wasn't
going to let any authority see that. He often lost his place or became confused
when he couldn't sneak a good look at his fingers. It was interesting, too,
that he didn't know what fingers he was holding up without looking.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He had to start counting on the
little finger of his left hand every time. When he started on any other finger,
he went back to start the problem over. About half the time, he would then forget
the problem, and although he was told he could ask to have it repeated, he
usually just said, "I don't know." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">He never "counted up"
while adding; he only "counted total." That is, to solve 2+5, he
didn't start from a closed fist as "two", holding up one finger each
for "3-4-5-6-7." Instead, he had to put up two fingers (and they had
to be the little and ring fingers on his left hand), then put up five fingers
(slowly counting them under his breath: 1-2-3,middle-index-thumb on the left,
4-5,thumb-index on the right), and finally counting all seven fingers to say
"seven." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">When he wasn't finger counting, he
often dug a knuckle into his thigh, twisting it back and forth, before
restating the problem, often followed by firmly stating a wrong answer. </span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">That drilling-into-his-thigh
maneuver suggested memory problems. His tendency to forget the original problem
within a few seconds, especially if he panicked, started on the wrong finger,
and had to go back, seemed to confirm this.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">But other clues suggested that
Forrest's memory problems were probably more deficient skill plus abundant
anxiety, not his memory per se. Clearly he remembered the size rule for
1-over-an-integer fractions, for example; he was visibly relieved as soon as
those problems appeared. He assured us three times during the hour that he knew
his "times tables" for 0, 1, 2, 5, 10, and 11, offering to recite
them for us. It was suggestive too that those are the sequences that fall into
an easily discerned regular pattern. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Possibly, to Forrest, those number
facts were magic spells for getting rid of unwanted adult attention, and recall
was just something he did to please adults rather than for any purpose of his
own. It is quite common for even students with good memory not to have learned
how to retain/recall information for intermediate steps, or for any purpose
other than pulling up "fact nuggets" to please adults.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>Forrest's way of finger counting suggested a
common major conceptual problem: though he had learned the natural (counting)
numbers as names to be matched with things, as most three-to-five year olds do,
he hadn't taken that step into abstraction where numbers become as entities in
their own right. Where you or I or most second-graders would see seven puppies
(and might quickly count once to confirm the number), Forrest would see a group
of puppies and name them after the fingers of his left hand, plus the thumb and
index finger of his right: 1, 2, 3, 4, 5, 6, and 7.<span style="mso-spacerun: yes;"> </span>"Number of puppies" was not a
property of the group of puppies; it was the finger where he last named one of
them. Thus, if he recounted them starting with a different puppy, there was no
particular reason to expect the last one to be named "seven" -- there
wouldn't be "seven puppies" until he named the last puppy after his
right index finger.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Possibly Forrest hadn't taken the
basic step into abstraction of understanding that the "seven" in
"seven dwarves," "seven sheep," "seven feet," and
"seven dollars" are all the same "seven." That ability to
move from the concrete world of objects or pictures into the abstract world of
numbers is a foundation of number sense**, and Forrest did not seem to have it.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">These seemingly small
misconceptions can make big trouble. Some of the most common misconceptions
allow the student to misunderstand what s/he's doing for quite literally years,
all the while appearing proficient and collecting praise, exactly until that foundational
error makes a difference; then suddenly nothing will make any sense, which is,
of course, <a href="http://thatjohnbarnes.blogspot.com/2015/09/from-tunneling-through-sun-with-dimes.html" target="_blank">The Wall</a>
. By the time they realize something is wrong (if they ever do), the wrong idea
has spread incorrect versions of many other topics through their whole
understanding of mathematics, creating permanent misunderstandings, unclear
things that should be easy, and whole other areas where they gave up and either
memorized a simple procedure or just decided they would never understand it. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Forrest's particular
misconception, that numbers are just a sequence of arbitrary temporary names,
often leads to difficulty in learning math facts. Without any sense that number
facts refer to anything permanently true, there's no reason to store or save
any of them for later. After all, if for some reason sometime in the future, we
need to know what 7+6 is, we'll just count it then. Even if it is 13 today, who
knows what it will be by the time we need it? And math facts are not
intrinsically fun facts to know, like the names of dinosaurs, nor are they
useful for making Grandma exclaim how smart you are, at least not once she's
seen you do them once. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So for the second part of the
assessment, I would be concentrating on two questions: </span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 94.0pt; margin-right: 0in; margin-top: 0in; mso-list: l0 level1 lfo1; text-indent: -58.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">1)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">Did
Forrest have a bad memory, just lack the skill to use his memory effectively?</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 94.0pt; margin-right: 0in; margin-top: 0in; mso-list: l0 level1 lfo1; text-indent: -58.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">2)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">How
much of an abstract concept of number did Forrest have?</span></div>
<div align="center" class="MsoListParagraphCxSpLast" style="margin-bottom: 9.0pt; margin-left: 94.0pt; margin-right: 0in; margin-top: 0in; mso-add-space: auto; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt;">*Thanks to better and better software and more available
computers, eventually we will be able to test all math this way, which will be
a solid blessing to every good teacher and student. Human performance should be
rated on the level mastered, not on how many times the student succeeds at
repetitive tasks. For example, we score high jumpers on the highest bar they
clear, not on how many times out of 50 they can clear a one-meter bar, and
pianists on whether they can handle a Chopin etude, not on how many times they
play a scale acceptably in one hour.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt;">** Do you? Check out this <a href="http://thatjohnbarnes.blogspot.com/2015/10/hows-your-number-sense-not-quite-quiz.html" target="_blank">questionnaire</a>.<span style="mso-spacerun: yes;"> </span>
</span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-61486134361544459692015-10-01T00:02:00.001-06:002015-10-02T22:00:00.425-06:00How's Your Number Sense? Not quite a quiz<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Yesterday <a href="http://thatjohnbarnes.blogspot.com/2015/09/from-tunneling-through-sun-with-dimes.html" target="_blank">I talked about number sense in quite a bit of detail, </a>and
sure enough, several of my Twitter buddies began talking about it with
me. Even more naturally, they all wondered how good their number sense
was and where they stood compared to everyone else.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">This is not a surprise. Every living thing that has eyes seems to love a mirror. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I've
never met readers or students who learn a new idea without wondering if
it applies to them. This is why so many medical students suffer from
hypochondria, law students become fascinated with petty grievances to
themselves and their families, and I'm told by a friend who went through
a full set of factory training as an auto mechanic that it was at least
a year before he could drive without hearing every little stray sound
from the engine. And whenever I've found myself explaining number sense to the parents of my tutees at <a href="http://www.tutoringcolorado.com/" target="_blank">Tutoring Colorado</a>, sooner or later the parents have wondered about their own number sense.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So
I am guessing that you might be wondering how good your own number
sense is. My quick answer is, "probably pretty decent, since you're
reading this, and most people with really bad number sense won't read
about math at all." Then again, some people will endure almost anything,
even fractions, if they think it will benefit their kids.<span style="mso-spacerun: yes;"> </span>Possibly
you are even wondering if the whole problem is that your own number
sense is deficient, so you never really learned real math, and now you
can't help your kids. It's a bit like asking, before you start reaching
for the victims and pulling on their arms, whether you yourself are
standing on quicksand, and it's a very good question.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In
that case, please take some comfort in this: helping your kids with
Singapore Math will boost your own number sense tremendously. I often
send my tutees home with Singapore Math-based projects to work on with
their parents, and I've lost count of the number of times I've heard,
"So while I was trying to help him I suddenly got it myself. I never got
that before!", and sometimes the even more enjoyable, "She did fine.
She got it before I did, and she was so proud of herself for being able
to explain it to me." As you come to understand what should be happening
in/with/for their number sense, you're going to rapidly improve or
reawaken your own. You may also become a great role model for how to
handle intellectual difficulty, and help the kid see that though knowing
matters, learning matters more.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So
don't worry about how much number sense you have now. It's not a quiz.
It's not a competition. There is no generally accepted scale for
measuring raw number sense anyway; a good score might only mean you are a
fast snail or a big mouse, a bad score might mean you're a slightly
less beautiful eagle or a smallish whale. Most likely of all, it might
mean I'm a poor questionnaire writer. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Nonetheless,
let's see if this gives you a picture of where you are, and maybe some
idea of where you want yourself or your kids to be. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">This
questionnaire is based on material I've used with older kids in the
tutoring business. It aims to show how much you already use (or don't
use) number sense in your approach to math, and I hope therefore
clarifies what this number sense thing is all about. Please accept one
hug, pat on the back, or small medal for voluntarily taking a math test
in the hopes of helping your child. If that's not parental love, I don't
know what else could be.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 14.0pt;">DIRECTIONS</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">It
will help to have some way of recording the results as you go along, so
you might want to open a note window or grab pencil and scratch paper.
There's a full explanation of the answers at the end, but I strongly
suggest you do all the questions before reading through the answers. On
the other hand, even if you get them all right, you will still want to
look at the explanations to see if you were actually using number sense
to get the answers. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<u><span style="font-family: Georgia; font-size: 14.0pt;">Read each question carefully</span></u><span style="font-family: Georgia; font-size: 14.0pt;">. Figuring before thinking is probably the leading warning sign of poor number sense.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<u><span style="font-family: Georgia; font-size: 14.0pt;">Do not time yourself</span></u><span style="font-family: Georgia; font-size: 14.0pt;">, or do anything else to give yourself an incentive to be fast with an answer rather than clear about why it is right. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<u><span style="font-family: Georgia; font-size: 14.0pt;">For each problem, record two pieces of information</span></u><span style="font-family: Georgia; font-size: 14.0pt;">:
You might want to draw up a little table with 2 columns, "answer" and
"NS level", and 20 numbered rows, if you're one of those people who
likes to keep neat records. "Answer" needs to be the widest column.
Here's one to copy to paste to your note window if you like</span><span style="font-family: Georgia;">:</span></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;"><tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;"> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">Problem number</span></div>
</td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">Answer</span></div>
</td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">NS level</span></div>
</td> </tr>
<tr style="mso-yfti-irow: 1;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">1</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 2;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">2</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 3;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">3</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 4;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">4</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 5;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">5</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 6;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">6</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 7;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">7</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 8;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">8</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 9;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">9</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 10;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">10</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 11;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">11</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 12;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">12</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 13;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">13</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 14;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">14</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 15;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">15</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 16;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">16</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 17;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">17</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 18;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">18</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 19;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">19</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
<tr style="mso-yfti-irow: 20; mso-yfti-lastrow: yes;"> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 72.9pt;" valign="top" width="73"><div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia;">20</span></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 359.05pt;" valign="top" width="359"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.85pt;" valign="top" width="47"><div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td> </tr>
</tbody></table>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<u><span style="font-family: Georgia; font-size: 14.0pt;">In the answer column</span></u><span style="font-family: Georgia; font-size: 14.0pt;">,
write the correct answer, if you can see how to get it. I've used the
current Colorado fifth-grade math standards (i.e. the last year before
middle school in a state that has average math scores and happens to be
located immediately around me) to devise the questions, so there is
always a way to the answer through elementary school math. You are very
welcome to use any higher math you know, however (and often that will be
much easier). If you don't see any way to the correct answer, write
"guessed", "?", or something else to remind you of your process.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<u><span style="font-family: Georgia; font-size: 14.0pt;">In the NS level column</span></u><span style="font-family: Georgia; font-size: 14.0pt;">,
write a letter from the list below; what level of number sense did you
use to solve the problem? You should be trying to work at the highest
level of number sense you can, so you should probably read through the
levels first:</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 58.0pt; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo1; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">a.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">You
just knew the answer, and why it had to be right, right away. For
example, most people can correctly answer "Which is bigger, 1448+5 or
1448+6?" right away, without calculating, because they notice that the
only actual difference is the one between 5 and 6, so it feels like they
"just know." They would record "a" for their level.</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 58.0pt; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo1; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">b.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">You
could arrive at the right answer after some thinking about it, but you
didn't have to calculate. For example, whether or not you know how much a
quadrillion is, you can probably answer "What is half of six
quadrillion?" by thinking of an analogy (what is half of six dollars?
half of six sheep? half of six gallons?) and referring to a math fact.
That would be a "b." If you actually had to do something to compute half
of six, either because you don't have that in memory or because you
don't see that "half of six" is the same number no matter what the units
or the multiplier are, then you would record "c" or below.</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 58.0pt; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo1; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">c.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">You
calculated correctly and got the right answer. For example, most people
would calculate to answer, "What is 162 divided by 6?", by long
division, mental short division, or factoring, and would record "c" for
it. If, however, right after doing that you realized either "oh, wait, I
know 6x25=150 and 6X2=12 so it had to be 27" that might be more like
"b". (Notice this is truly an honor system; the difference between "b"
and "c" is more about <i>how much</i> calculating you had to do than
about not doing any or having to calculate every tiny step. Are you
mostly thinking, or is the pencil or calculator really busy?).</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 58.0pt; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo1; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">d.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">You
thought you knew how to calculate but then realized you weren't getting
the right answer, or you got confused in the middle of the calculation,
or you couldn't decide which of several possible calculations to do.<span style="mso-spacerun: yes;"> </span>"d" is probably best described as "I used to know that, I think."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 58.0pt; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo1; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">e.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">You
can see there must be a way to calculate this, but don't know or
remember enough to see how to do it yourself. In other words, you're
pretty sure the answer is in there (without my having to tell you it is
-- though there's one trick question where the answer is there's no
answer), but you really don't have any idea how to go in there and drag
it out. Most people who know what a cube root is will concede, for
example, that there must be some way of finding the cube root of 864
without a calculator or spreadsheet, but they wouldn't know where to
begin, so they'd put a question mark for the answer and an "e" for
number sense. (There's not actually any problem that hard below, by the
way).</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 58.0pt; margin-right: 0in; margin-top: 0in; mso-list: l2 level1 lfo1; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">f.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">You
have no idea at all; don't even see how an answer could be calculated.
This isn't the same thing as the terms being unfamiliar; those should be
marked "unfamiliar" or "didn't know the words" in the answer space. For
example, since most people don't know what a hyperbolic cosine is, if I
asked you to calculate one (I won't!) you would write "unfamiliar" in
the answer space and leave NS level blank. On the other hand, if the
problem is that it costs 72 cents each to make the first gallon pitcher
of lemonade, and each successive gallon is 13% cheaper, you always sell
exactly one gallon at $1.00 per glass on a sunny day with 80 degree
temperatures, you sell an extra quart for every degree the temperature
goes above 80, and sales double for every 20% price reduction, if the
temperature is 91 degrees, how much lemonade should you make and at what
price should you sell it for maximum profit?, (about a college
sophomore level economics problem -- don't worry, nothing like that
below either). Then if you see there's a way to get an answer, even
though you couldn't do it yourself, that's an "e." If you don't see any
way that anyone could get any answer at all, give it an "f."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<u><span style="font-family: Georgia; font-size: 14.0pt;">Record the highest level of number sense you <i style="mso-bidi-font-style: normal;">could</i> have used,</span></u><span style="font-family: Georgia; font-size: 14.0pt;">
whether or not it was your first thought. This second score is about
the highest level of number sense you can work at, not about what level
you usually work at. (Though if you notice you're always calculating
first and then number-sensing afterward, that information might be
useful or interesting also.)</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Again,
record BOTH your answer (if any) and the level of number sense you were
able to approach the problem with (whether you got the right answer, or
any answer at all). We'll be looking at both the answers and the NS
level at the end.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">All right, grab your pad and let's begin. (Sorry about the weird formatting of what follows; I haven't mastered all the nuances of getting math notation to work in Blogger's interface. I decided to prefer size and readability to style, as well as to staying up all night figuring it out. If you have elderly eyes like mine, click on any panel and it will pop up as a separate, easily enlarged window).</span></div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 20.0pt;">§</span></b><br />
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<span style="font-size: x-large;"><b><b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 16.0pt;">The answers, and how people with
number sense might know them without calculating. </span></b></b></span></div>
<div class="MsoListParagraph" style="margin: 0in 0in 9pt 1in; text-align: left;">
<div class="separator" style="clear: both; text-align: center;">
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 18.0pt;">SCORING</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">You can count the answers
right/wrong in any conventional way you like. The problems were taken mostly
from the Grade 5 advanced standards with some additions from the Grade 6
regular, so if you got 14 or more right, you're about on par with what we
expect of a brainy, well-trained 11 year old in Colorado.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">For number sense, count the frequency
of a, b, c, d, e, and f. (If you're ambitious you might even do a
histogram).<span style="mso-spacerun: yes;"> </span>If you have ten or more a's
and b's combined, that looks like pretty good number sense to me; if most of
your answers are c's and d's, you probably have fairly good number sense but
learned math procedurally, so you may have to work on your own number sense to
coach Singapore Math well. e's and f's mean you probably really need to work on
your own number sense at the same time you are trying to help your kids. Be
sure to admit you're trying to figure it out together -- seeing you struggle
and catch on may very well be exactly the model the kid needs.</span></div>
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<br /></div>
<div class="MsoNormal">
<br /></div>
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<span style="font-family: Georgia;"><span style="mso-tab-count: 1;"> </span></span></div>
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<br /></div>
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<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-81257473730194704032015-09-30T01:53:00.001-06:002016-04-22T23:31:38.962-06:00From tunneling through the sun with dimes, to Every Time two different times, to the meaning of number sense: a new Singapore Math blog series.<style>
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<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><b>REVISION ON 10/1. My spouse would like to link to this blog to promote our tutoring business, and of course I'm all in favor of that. But, she said, the only image on this was one of me, and she has always hated that picture. "You look drunk in it," she says. As the owner of <a href="http://www.tutoringcolorado.com/" target="_blank">Tutoring Colorado</a>, she doesn't like that in her main subcontractor for math, apparently. </b></span><br />
<span style="font-family: "georgia"; font-size: 14.0pt;"><b>So this is exactly the same text as before, except that at the request of my wife, partner, trusted advisor, and employer, I have put in a few illustrations which are NOT me looking drunk. <i>The things we do for love.</i></b></span><br />
<br />
<span style="font-family: "georgia"; font-size: 14.0pt;">So, first, seven short pieces,
seven little things to have in mind. Then, some thoughts about Singapore Math
and number sense, kicking off my "almost a week of math-y posts." Those
of you who don't find this stuff interesting, who read the blog for some other
reason, well, there will probably be something for you, too, sooner or later.
But this week we're back to Singapore Math. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The seven things:</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">ONE (the long one)</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 14.0pt;">"How many dimes would it take to make a bridge from here to
Mars?"</span></b><span style="font-family: "georgia"; font-size: 14.0pt;"> Years
ago, when it was trendy, an HR person at a major corporation that I don't need
to name tried it out on me during a job interview.</span><br />
<br />
<span style="font-family: "georgia"; font-size: 14.0pt;"><a href="http://cdn-imgs.aeonmagazine.com/images/2013/10/SUNTUNNELS-634x397.jpg" target="_blank"></a></span><br /><span style="font-family: "georgia"; font-size: 14.0pt;"></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Well, I said, calculating out
loud, sticking to one digit accuracy, </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://omicron.aeon.co/inlineimages/1359d8a7-752b-4f04-a36b-812f32d3ce4b/show_SUNTUNNELS.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://omicron.aeon.co/inlineimages/1359d8a7-752b-4f04-a36b-812f32d3ce4b/show_SUNTUNNELS.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The general idea only continuous, made out of dimes, and going all the
way to Mars. If this image makes you curious, it's part of something
really cool at <a href="http://aeon.co/magazine/culture/star-axis-is-a-profound-meditation-on-the-sky/" target="_blank">this piece by Ross Andersen in Aeon.</a></td></tr>
</tbody></table>
<span style="font-family: "georgia"; font-size: 14.0pt;">•a dime is about three quarters of
an inch across, so there are about 16 dimes to the foot.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">•the sun is around 90 million
miles away,</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">•and Mars is about 50% further
from the sun than Earth is.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">That bridge had better be enclosed
if people or vehicles are going to pass along it, so figure it's a tube twelve
feet in diameter. That should be big enough for someone with a motorocycle,
bicycle, or small car, and roomy for a skateboarder or runner. (Never mind
where the air is coming from).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">So the bridge would be made of
rings of dimes laid edge to edge. That's leaky, we'll have to wrap it all in
SaranWrap when we're done. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Anyway, each ring would each be
3/4 of an inch thick. If they're twelve feet in diameter, that's thirty-six
feet around (for one digit accuracy, pi is three). An inch is 4/3 of a dime, so
a foot is 16 dimes, 36 times 16 is 360+216, 576, so call it 600 dimes per ring,
rounding up again.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><br />
Well, then, still going one digit all the way, when Mars is in conjunction (in
a line with the sun and Earth, with the sun between) it's 2.5 times as far away
as the sun, which would be 180+45, 225 million miles. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">So if a mile is about 5 thousand
feet and you need 16 rings to make a foot of bridge, that's about 80 thousand
rings per mile, times 600 dimes in a ring, 48 thousand thousand dimes per mile,
close enough to 50 million dimes per mile. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">225 million miles is its maximum
length and every mile is 50 million dimes. 225X50=(200+20+5) * 5 *10, (a
thousand plus a hundred plus twenty-five) times ten, 11,250 times a million
million. A million million is a trillion, a thousand trillion is a quadrillion,
so, right around eleven quadrillion, give or take.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">I rattled all that off in about a
minute and a half; a life of writing hard sci fi will do that to you.<span style="mso-spacerun: yes;"> </span>As afterthoughts, I added that you'd need to
figure out things like what to do when the bridge cut through the sun, whether
the bridge needed to be sealed, and how to have the dimes slide over each other
so the bridge could be telescoped down to shorter lengths. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Now, that particular company
supplied interview feedback afterward (something I understand everyone has
given up now because of lawsuit anxiety) and in my feedback on that question,
the HR person noted: </span></div>
<blockquote class="tr_bq">
<ol>
<li><i style="mso-bidi-font-style: normal;"><span style="font-family: "helvetica"; font-size: 14.0pt;">Did math in head, so figures
were not exact. Needed to ask to borrow a calculator.</span></i></li>
<li><i style="mso-bidi-font-style: normal;"><span style="font-family: "helvetica"; font-size: 14.0pt;">It sounded like an enclosed
tube, which is a tunnel, not a bridge.</span></i></li>
<li><i style="mso-bidi-font-style: normal;"><span style="font-family: "helvetica"; font-size: 14.0pt;">Did not consider cost of so many
dimes</span></i></li>
<li><i style="mso-bidi-font-style: normal;"><span style="font-family: "helvetica"; font-size: 14.0pt;">Very uncreative answer, one of
the most uncreative we have ever had. He just calculated. Creative answers we
have had for this included </span></i></li>
</ol>
<ul>
<li><i style="mso-bidi-font-style: normal;"><span style="font-family: "helvetica"; font-size: 14.0pt;">"I would pay everyone on
earth a dime every time they thought about a bridge to Mars, and when there
were enough positive thoughts, someone would build the bridge."</span></i></li>
<li>
</li>
<li><i style="mso-bidi-font-style: normal;"><span style="font-family: "helvetica"; font-size: 14.0pt;">"I would just need one
dime, that we would spin out into a silver wire and stretch between Earth and
Mars. Then I would ride there on my unicycle."</span></i></li>
<li>
</li>
<li><i style="mso-bidi-font-style: normal;"><span style="font-family: "helvetica"; font-size: 14.0pt;">"I would ask NASA how much
it would cost, multiply by ten, and ask the March of Dimes how many dimes they
get per year, and divide." </span></i></li>
</ul>
</blockquote>
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<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">I probably wouldn't have been very
happy in that job anyway, I guess.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">TWO</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">I was grading papers at the
counter in a Starbucks. That's the closest thing there is to an experience of
invisibility, I think.<span style="mso-spacerun: yes;"> </span>I overheard the
following dialogue:</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Counterworker (whispering): "Hey, this guy's bill is for $6.87
but he gave me $10.12. What do I do?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Manager: "Ring it up from $10.12."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Counterworker did, and gave the guy back his $3.25 and his
order. After he left:</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Counterworker: "Why did he do that?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Manager: "Probably just didn't want any small coins in his change."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Counterworker: "Yeah, but why did he give me the extra
money?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Manager: "His change would have had thirteen cents in it, so he
added twelve to make it a quarter."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Counterworker: "He couldn't know how that was going to happen. I
hadn't rung it up yet."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Manager (a bit impatiently): "If there's a twelve cents in the
amount he hands over, and an eighty-seven cents in his bill, the change will
have twenty-five cents in it."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Counterworker (mix of incredulity and sarcasm; she was clearly not buying into any of this managerial bullshit): <b style="mso-bidi-font-weight: normal;">"EVERY TIME?"</b></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">THREE </span></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">(short because it's just a
reference):</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">In <a href="http://thatjohnbarnes.blogspot.com/2015/04/part-ii-of-what-went-wrong-in-american.html" target="_blank">a previous Singapore Math project blog post</a>, I mentioned my experience with Willard (name changed because he's got a tough
enough life to get through as it is), my ADL (Adult Disadvantaged Learner,
meaning "grownup who doesn't know math and has trouble learning it) student
who had been faking his way through practical shop math while working for a
general contractor. </span></div>
<blockquote class="tr_bq">
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;"></span><span style="font-family: "georgia"; font-size: 14.0pt;">"From there we made a final assault on the concept
that elementary algebra depends on: that an unknown number will behave exactly
like a known number. (Willard, at first, did not see how we could know that
2x+3x=5x if we didn't know what x was, and could also clearly see that we
couldn't possibly perform the experiment of trying all the infinite possible
values of x to make sure; nor did he see that we wouldn't have to do that for
every possible equation)."</span></div>
</blockquote>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">FOUR </span></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">(short because it's intrinsically
short)</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">By my count, since I started
counting, I've just encountered the fifth tutee who needed a very simple but
very important thing explained: that the equals sign in an equation always
means "what is on the left is the same number as what is on the
right." It does <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">not</i></b> mean "write your answer
here." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>This kid, however, was a bit more of a math
kid than his four predecessors, and as the light dawned, he said, "<i>That's</i>
how an equation can be an answer to a question in math. I thought an answer
<i>always</i> had to be a number, but it can be an equation, too."<span style="mso-spacerun: yes;"> </span>Apparently he had been leaving any problem
with "write the equation" or "what is the equation" blank,
or just writing down a number (typically by adding all the numbers in the
problem), because he didn't see why anyone could be asking him to respond to a
question with "write your answer here."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">FIVE</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Working with ADLs, one of the
safest predictors I've found for "this one is not going to pass " is
certain phrases. I do explain, repeatedly, what is wrong with these phrases, but
a few students simply keep saying them. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">If they're still saying any of
these by halfway through the class they are probably not going to get through
algebra this time. Indeed, these are practically the Incantation Against
Mathematics, or maybe the Common Format Don't Teach Me Any Math Signals.<span style="mso-spacerun: yes;"> </span>Here's my top ten list:</span></div>
<blockquote class="tr_bq">
<ol>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">All
I need is just to review basic math.</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">Give
me a rule that's not so complicated.</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "georgia"; font-size: 14.0pt;">I
can do any problem if it's money (or cups and pints, or wood, or cars).</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span><span style="font-family: "georgia"; font-size: 14.0pt;">If I always know the right answer
anyway, why do I have to do the math?</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">Just
tell me what to do and I'll do it. Don't tell me nothing else.</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">"Seventeen!"
(or any other number) (Often shouted out before anyone else can begin working
on the problem, especially when the answer should be an equation, expression,
or interpretation.)</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "georgia"; font-size: 14.0pt;">So
how come it's a percentage if you just said it's a fraction?</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">We're
never going to use this.</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">We've
been here for t weeks and you still haven't told us what x is. (where t=number
of weeks they've been here. Often off by 1 or 2).</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">You can't add letters.</span></li>
</ol>
</blockquote>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUKaxB3ai1v0ehkl2ZAgUzyOHyLc_RK11fa3kGl8lZ_MiSwhUWNbbyijnB_2csRF4-YEgq46NBO1nbRjOSerKIOi1OjAHpc__lujz0AuOaXx87vKnUM3E2Y-29cE8tp2-AHBZEp3htP2w/s1600/AlgebraMeme01.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUKaxB3ai1v0ehkl2ZAgUzyOHyLc_RK11fa3kGl8lZ_MiSwhUWNbbyijnB_2csRF4-YEgq46NBO1nbRjOSerKIOi1OjAHpc__lujz0AuOaXx87vKnUM3E2Y-29cE8tp2-AHBZEp3htP2w/s640/AlgebraMeme01.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Nobody looks drunk, either. But at least they didn't waste any time on that algebra stuff. You can't add letters anyway.</td></tr>
</tbody></table>
<br />
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">SIX</span></b></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">A while ago, another tutee was looking at the drawing she'd
just done, using the bar model method that Singapore Math teaches. I introduce
bar modeling to a lot of kids who are not doing Singapore Math in school because,
correctly applied, it will crack nearly all word problems that kids are likely
to encounter before algebra. She suddenly pointed to the question-marked bar
that represented the answer, and said, "That has to be 9!" (let's
say, I don't remember the exact problem and answer).</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>"Right,"
I said, since it was. "Now can you write out the calculation?" </span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"I still don't see how."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Just represent each step you did making the drawing
... "</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">We waded, with only minor struggles, back along how she
had drawn her way to the answer, reviewing the big four: </span></div>
<ul>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">when you put two bars end to end, you add; </span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">when you put a bunch of identical bars end to end, you
multiply;</span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>when you back up
along one bar by the length of another bar, you subtract; and </span></li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">when you slice a bar lengthwise, you divide or write a
fraction (because fractions and division are the same thing). </span></li>
</ul>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<br /></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Eventually she had the computation in order, and to her
amazement, "It's still 9!"</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Yep. And if you actually did exactly this with real
things in the real world, there would be nine of them at the end."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">She stared at her drawing and calculation, and said,
"That's really kind of cool."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"That's the point of word problems." (If she'd
been older I might have said "the point of applied mathematics.")</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Really?</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Yep. Describe the world right, do the correct things
to your description, and your answer matches the real world."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Every time?" Unlike that Starbucks counter
worker, she was not being sarcastic.</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Yes, every time, every time from now to the end of
the universe, every time back when there were dinosaurs, every time here and in
Australia and on Pluto and in orbit around a star so far away that its light still has not gotten here, <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">every time</i></b>."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Unlike that Starbucks worker, I think she believed me. At
least she improved rapidly in math after that and I occasionally hear from her
parents that she is still doing well.<span style="mso-spacerun: yes;"> </span>I
suppose she still may work at Starbucks some day, but she probably will not
stay there.</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<br /></div>
<div align="center" class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">SEVEN </span></b></div>
<div align="center" class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 20.0pt;">(this was almost all there was)</span></b></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">When I was talking over this series of blog posts with my spouse,
I thought I had found a perfect example for how the world looks to a person who
has and uses number sense.<span style="mso-spacerun: yes;"> </span>I'd just been
to Target to buy eggs. </span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"So you know, Target seemd to never post unit prices. So
they had either 30 eggs for 6.99 or 18 eggs for $4.29, and I was wondering
which would be the better deal. It was obvious that 18 and 4.29 are both
divisible by 3, so dividing both by 3, I got that that was the same price as 6
eggs for 1.43 -- "</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"How did you do that in your head?"</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"I factored it. 6X7=42, 3X14=42, divide the 9, it was
1.43. Or I could have gone the long way, if it was 4.50 one third of it would
be $1.50, the difference between $4.50 and $4.29 is $0.21, and 21 divided by 3
is 7, so 7 cents less than 1.50, which is 1.43. How would you do it?"</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"With a calculator. So then how did you know which
was the better deal?"</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"The package of 18 is 3 sets of 6 eggs, and each set
of 6 eggs costs $1.43. The package of 30 is 5 sets of 6 eggs, right? At 1.43
they'd be $1.40 times 5, which is $7.00, plus 3 cents times 5, 15 cents, so 30
eggs would be $7.15. Buying the package of 30 saves 16 cents."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Why would you do all that math to save 16 cents? And
even if you did, why not at least use a calculator and save time?"</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">"Because I'd rather not give Target more money than I
have to, and I did all that in my head in less time than it takes to pull out
my phone and select the calculator app. Takes a lot longer to describe than it
does to do. In fact," I added triumphantly, "because I did it all in
about two or three seconds, say three seconds, that would mean I profited by 16
cents per three seconds, $3.20 per minute, which is $192 an hour. It was
probably the most profitable thing I did all day."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">I don't know why she gets that facial expression. You'd
think I'd been eating bugs in front of her or something. "Well, don't use
that as an example."</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">I generally get in trouble when I ignore Diane's advice --
not from her, but from the universe, which apparently collaborates with her -- but I'm
taking a chance this time. Maybe the other six examples will outweigh it or
contextualize it or beatify it, or something.</span></div>
<div align="center" class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 36.0pt;">§</span></b></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<br /></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">There's a common theme through all seven of those stories:
the difference between having number sense and not having it.</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Number sense in people who do math is something like
musicality in people who dance, situational awareness in martial arts, or eye
in fashion; it's very important, hard to define exactly, but if you know what
you're doing, you know it when you see it. A definition I currently like a lot
is one I wrote by synthesizing some excellent ideas from <a href="https://www.youcubed.org/fluency-without-fear/" target="_blank">an article by Dr. Jo Boaler</a>: </span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 14.0pt;">People with number sense are people who can use numbers flexibly,
guided by a conceptual understanding of mathematical ideas. </span></b><span style="font-family: "georgia"; font-size: 14.0pt;"></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Any flaws in this definition are
more likely to be my misunderstanding than her error.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The key points in that definition
are that: </span></div>
<ul>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">the student is <i style="mso-bidi-font-style: normal;">flexible</i> in using numbers, meaning that
the student knows what a number, a relationship, an operation, or an algorithm
is (not just how to manipulate the symbol for it in one narrowly specified
context).<span style="mso-spacerun: yes;"> </span></span></li>
<li>
</li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">the essence of that flexibility is
that a student <i style="mso-bidi-font-style: normal;">knows what to do</i> with
a number, a relationship, an operation, or an algorithm <i style="mso-bidi-font-style: normal;">in an unfamiliar context</i></span></li>
<li>
</li>
<li><span style="font-family: "georgia"; font-size: 14.0pt;">flexibility is achieved by <i style="mso-bidi-font-style: normal;">knowing ideas conceptually</i>, meaning that
above and beyond memories of the use of the number, relationship, operation, or
algorithm in similar problems before, the student grasps the underlying ideas
clearly enough to see them in unfamiliar situations and handle them
accordingly.</span></li>
</ul>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Knowing ideas conceptually, and
being able to recognize them in an unfamiliar context, implies that number
sense faces in two directions with a single vision, a nice trick if you aren't
used to visualizing more advanced topologies. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">On the one hand, number sense is
about understanding <b><i style="mso-bidi-font-style: normal;">how numbers relate to
other numbers</i> </b>-- intuition about ideas like odd/even, factor,
prime/composite, natural/whole/integer/rational/real, and what it is that is
the same/different about a fraction and a derivative, differential, slope,
gradient, tangent, percentage, rate, quantile, or decimal. If you can see that
there must be exactly the same infinite number of even and odd numbers, or that
zero and one are the only numbers that can be their own square roots, you're
using a little bit of number sense.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">On the other, number sense is
about understanding <i style="mso-bidi-font-style: normal;"><b>how numbers relate to
the real world</b>.</i> You have at least rudimentary number sense if you know you
use addition to total a bill, subtraction to balance a checkbook,
multiplication to figure out how much floor tile to buy, and division to figure
out how many cookies each kid gets. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">In the seven little stories above,
I do hope it's fairly obvious who has the number sense (or is acquiring it) and
who doesn't, and why there are advantages to having number sense. If numbers
are just noises that people use to harass you, or if you see no reason for a
number to behave in any way other than whatever the teacher's whim makes it
today, or if you just don't see why the world should ever behave in accord with
a calculation, you don't have much number sense. That makes it very likely that
you're going to go through life without a set of tools that other people have
for making sense of things and managing their own lives. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">But long before you are regularly
cheated, or forced to guess at things that you could have known exactly, or
unable to understand what's happening on the job or in the news -- well before
all the painful penalties of innumeracy clobber you -- you will for sure have
an awful time in math class. <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">In the current draft of Singapore
Math Figured Out for Parents, my chapter 2 begins with a truism:</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;"><br />
<b style="mso-bidi-font-weight: normal;">A kid with good number sense will learn
math, even from indifferent teachers using poor materials; a kid with poor
number sense will never really understand math, even in a well-taught excellent
curriculum.</b></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">This brings up The Wall: for most
students who have math trouble, things are fine, math is even easy and fun, up
to a fairly abrupt point where it suddenly becomes hard. I like the term The
Wall for that point. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Trying to understand The Wall, and
the difficulties of otherwise highly capable, bright students in learning math,
led to the discovery of number sense.<span style="mso-spacerun: yes;"> </span>In
1903, in <i style="mso-bidi-font-style: normal;">Lectures on the Logic of
Arithmetic,</i> Mary Boole, the widow of that guy who invented Boolean logic, and
a very formidable mathematician herself, </span><br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="http://www.agnesscott.edu/lriddle/women/mboole.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://www.agnesscott.edu/lriddle/women/mboole.jpg" height="400" width="273" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mary Boole. Looking very not drunk.</td></tr>
</tbody></table>
<br />
<span style="font-family: "georgia"; font-size: 14.0pt;">set out the basic idea. She was
pushing beyond the familiar basic question of <a href="http://thatjohnbarnes.blogspot.com/2015/03/more-on-that-singapore-math-thing-so.html" target="_blank">what it was about memorizing algorithms as purely symbolic operations that led so many students straight into The Wall?</a><span style="mso-spacerun: yes;"> </span>In doing that , she posed what
turned out to be a more productive question: what did the students who avoided
The Wall, or encountered it without being defeated by it, do differently?</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Rather than study how so many kids
failed, she asked how the relatively small group succeeded. Mary Boole observed
that students with a strong intuitive feel for what numbers meant naturally and
automatically rejected mistakes. When she interviewed those same students, she
found that they thought more about the meanings of the digits than about
crossing them out or writing them above or below lines. Those few students
could quickly recreate any parts of the algorithm they missed, correcting and
reconstructing their memories as they went. They grasped the relationships
between numbers not as a list of rules to apply, but as connections that were
intrinsic to the numbers themselves. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Overall, if the student knew how
the numbers related to each other and to the surrounding world, and did not
confuse the number with the symbols that stood for it or the procedures for how
to construct it, the student was much less easily confused and more easily
straightened out. These resilient, capable, Wall-piercing students only needed
to know part of each algorithm (and not necessarily the first part) to begin.
Students who could confidently rediscover or reinvent were tougher than The
Wall.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">In further work with exceptionally
successful math students, Boole also found that children who never hit the wall
were children who routinely <i style="mso-bidi-font-style: normal;">played</i>
with numbers, making up patterns that worked in the numbers themselves,
generally all on their own. In playing with the numbers and operations, they were
practicing both the relations between the numbers and the relations between the
numbers and the real world.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Those are still the
characteristics of the "naturals" and the "talented"
students today. To them, the numbers and their meaning are the fun and interesting
point of it all; the algorithms that, to most adults, are the math itself, are
just ways of doing the scorekeeping.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">What Mary Boole had found in those
unusual kids was what we now call number sense. She usually called it
"arithmetical faculty," and less often "mathematical
faculty."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">As "arithmetical
faculty" gradually became "number sense" (after being renamed
into at least a dozen other terms along the way) in the education literature,
its connotations shifted. To Mary Boole, it was the magic that Wall-resistant
kids have, and that many more children could have if they weren't frightened,
bored, or bullied out of it by procedure-based instruction. Not too
surprisingly for a late Victorian reformer, she thought traditional
proceduralism made students phobic and the phobia prevented their reasoning.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Decades later, when Dr. Kho Tek
Hong was creating Singapore Math, it had been clearly shown many times that although
traditional proceduralism often was associated with severe stress, which of
course is highly undesirable, the real damage to students' math abilities was
more often caused by some strongly misleading premises. Traditional
proceduralism hooks students on easy approaches and methods that fail for more
complicated problems; the stress and eventual phobia originate in that
experience of suddenly not being able to trust what they know. Anyone might
have a lifelong fear of something after a bad experience with it, but it's the
experience, not the thing, that makes the fear. The particularly terrifying
thing about The Wall is usually that students were doing fine and assured they
were "good at this" right up till they hit it.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Nowadays, at math teacher
conferences, number sense is a reliable subject for a well-attended panel. Still,
though we now have a much better idea of where to point, number sense is still
"The thing we point at when we say number sense."</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">So, like every other definition
I've seen, "the ability to use numbers flexibly, guided by a conceptual
understanding of mathematical ideas," is imperfect and sometimes
maddeningly vague, but it will have to do till something better comes along.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 36.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">So here's the deep insight that Dr.
Kho brought to math education. The reason most kids don't have much number
sense when they need it is because <i style="mso-bidi-font-style: normal;">they have
been actively trained not to use it when they're doing math</i>. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The kid who hits The Wall and
never gets up again learned that you do this, then this, then this, and what
you write is your answer. That kid, unless s/he is exceptionally talented, will
break down, never to be good at it again, whenever the number of
"this" becomes too large or too complicated to memorize. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">So, Dr. Kho said: Don't do that to
them. Yes, they love patterns, learn them easily, prefer them to all that hard
thinking stuff. But giving them what they like for math is no better an idea
than giving them what they like for food (the all-chocolate diet) or for
experiences (unless you want your second grader to start driving).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Of course it's easy to teach
simple repetitive patterns to primary-grades kids, who love simple repetitive
patterns (have you ever been driven mad by a child who sings one verse of a
song over and over and over and over ...?). The problem is, as they quickly
gobble up the patterns and demonstrate proficiency at pattern without meaning,
they will also pick up (from teachers, parents, or both) that that's what this
math stuff is all about, like learning all the gestures for "I'm a Little
Teapot", or the rules to hopscotch, or the Cup Song. They'll like it and
be good at it -- but it is setting them up for a fall.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Rather, said Dr. Kho, keep the
idea of what the numbers are really doing in front of them, even when that
makes it harder to get to that false grail, the Right Answer.<span style="mso-spacerun: yes;"> </span>Teach them the traditional algorithms, yes,
of course -- they're highly efficient ways to get to an answer, and the kid
will need them eventually. But don't let them learn how <span style="mso-spacerun: yes;"> </span>without knowing why. (I borrowed that phrase,
gratefully, from <a href="http://www.amazon.com/Why-Before-How-Computation-Strategies/dp/1934026824" target="_blank">Jana Hazekamp's excellent book</a>,
and if you need Singapore Math help before my (also to be excellent) book is
done, that's the single best one I know). </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Dr. Kho went even farther: make
sure they can understand the meaning, and that they apply the meaning to the
process of learning the algorithm.(There's a very strong reason in memory
theory for doing this, and I've found it works wonders, as you'll see in the
upcoming case study). That is, don't just teach them procedures and hope
they'll have number sense.<span style="mso-spacerun: yes;"> </span>Don't even
just teach them number sense along with the procedures.<span style="mso-spacerun: yes;"> </span>Rather, teach them <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">via</i></b><i style="mso-bidi-font-style: normal;"> </i>number sense -- that is, make the student exercise number sense constantly
while learning and applying the algorithm.<span style="mso-spacerun: yes;">
</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">And that way, when the pre-puberty
fade of memory that most people experience hits, and as more advanced procedures
require many steps with many decision points, and even when they move into areas
where there are no longer any standard procedures to memorize -- that number
sense will be there to guide them.<span style="mso-spacerun: yes;"> </span>The
number sense is the spirit, the algorithms are the law, and we all know which
bears the better and more lasting fruit.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">All of that would, of course, be
an interesting theory, if Kho's methods did not also happen to have a 30 year history of
producing the most math-proficient students in the world.<span style="mso-spacerun: yes;"> </span>The six top math-score nations in
international comparisons are in fact exactly the ones that have been using
Singapore Math long enough so that their current high school students started
with it at the beginning of school and did it all the way through. The majority
of Singapore's math teachers are now products of Singapore math
themselves.<span style="mso-spacerun: yes;"> </span>When kids and cultures
thoroughly absorb Singapore Math, they move into a whole new higher realm of
capability.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Unfortunately, in what I would
have to say is an absolutely typical move for American education policy, we
have set the goal of catching up, and having that better performance, something
that took Singapore 30 years, for <i style="mso-bidi-font-style: normal;">right
now and why not yesterday, dammit!?</i><span style="mso-spacerun: yes;">
</span>The Common Core standards have defined satisfactory math performance as
the level that kids who have had Singapore Math training all along achieve, as
if we were going to take a track team of people who hardly ever ran and just
order them to run like Olympic athletes.<span style="mso-spacerun: yes;">
</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">The truth is, if we do it at all,
the road will be long and hard. And despite the touching faith of people like
Theodore Roosevelt, John F. Kennedy, and Ronald Reagan in our nation, Americans do not much
like long and hard. I really fear that we'll give up on Singapore Math at the
first rough spot in the road.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Nevertheless, if we're going to
demand that our kids perform like the best in the world, we'd better start
training them the way the best in the world do.<span style="mso-spacerun: yes;">
</span>And that means Singapore Math, because Singapore Math trains and
develops number sense, and number sense is what makes you the best.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center; text-indent: 40.5pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "georgia"; font-size: 36.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">All right, that's number sense.
For the rest of this week, I'll be laying out some more things about it.<span style="mso-spacerun: yes;"> </span>My plan at this point is that tomorrow --
well, later today, it's already Wednesday -- <span style="mso-spacerun: yes;"> </span>I'll show you a "how good is your number
sense" test, because when most people hear about an idea, the first thing
they want to do is apply it to themselves. Thursday, I'll describe a typical
case study, how I was able to help a tutee move himself from three grades
behind to grade level in less than half a year, and how Kho Tek Hong's methods
were the key. Friday, some thoughts about why it's going to be so hard to
implement Singapore Math in the United States, and Saturday, perhaps, a little
broader view of why all this matters so much.</span></div>
<div class="MsoListParagraph" style="margin-bottom: 9.0pt; margin-left: 0in; margin-right: 0in; margin-top: 0in; text-indent: 40.5pt;">
<span style="font-family: "georgia"; font-size: 14.0pt;">Unless, of course, other crises interrupt.<span style="mso-spacerun: yes;"> </span>The weekend and Monday were packed with
hassles that ate up all the time to get this ready; I should probably have
given up and let it slide another week, but I just hated the idea.<span style="mso-spacerun: yes;"> </span>So, most of you will see this sometime
Wednesday, though I'd hoped to have it up for Monday morning. Life's that way
... see you soon, I hope, barring more swarms of hassles.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-17162180465032619292015-09-09T00:03:00.002-06:002015-09-09T00:10:48.188-06:00I hadn't actually meant to post at all tonight, but, oh well ... Conrad, Bulwer-Lytton, and some meditation on storytelling.<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">I fairly often hang out at the Chronicle of Higher Education, because although I'll probably never teach any more college classes, it was such a big part of my life for so long that the place just feels like home. Anyway, Ben Yagoda, who is quite a good writer, is one of the regular bloggers at Lingua Franca (subject matter of which is supposed to be "Language and writing in academe", and he wrote a <a href="http://chronicle.com/blogs/linguafranca/2015/09/08/in-search-of-needless-words/" target="_blank">little meditation about the real meaning of Will Strunk's famous dictum</a>, "Omit needless words," which I recommend very highly (Yagoda's piece <i>and</i> Strunk's advice). </span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">Among his examples and connections, he mentioned something that Joel Achenbach (one of my favorite journalists) said that John McPhee (who is a true god of prose) had taught him at Princeton, an exercise in cutting needless words. One of the sample passages McPhee had them try to cut without sacrificing meaning or style was from <i>Heart of Darkness,</i> so I was all the more into it because I am a self-admitted Conrad freak and tend to think that Conrad is to the modern English-language novel as Shakespeare is to English-language drama. </span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">This stirred up the Usual Suspects with whom I enjoy hanging out and arguing, and one of them, marcdcyr, quoted an odd, interesting passage from<a href="http://www.amazon.com/The-Nigger-Narcissus-Echo-Library/dp/1406848190" target="_blank"> That Conrad Novel Whose Name Is Inexcusably Rude Nowadays</a> (and which is increasingly referred to as <a href="http://www.amazon.com/The-Children-Sea-Tale-Forecastle/dp/1612032095" target="_blank">Children of the Sea</a>, Conrad's title for the first American publication). Just at the beginning of the stormy voyage that is going to kill the title character (and reveal a whole lot of interesting things about power relations, empathy, humanity, and the bonds that reach-or-don't between human beings), before anything gets started, the narrator observes a probably-not-very-educated seaman reading Bulwer-Lytton's <i>Pelham</i>*:</span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;"><i>"The popularity of Bulwer Lytton in the forecastles of Southern-going
ships is a wonderful and bizarre phenomenon. What ideas do his polished
and so curiously insincere sentences awaken in the simple minds of the
big children who people those dark and wandering places of the earth?
What meaning can their rough, inexperienced souls find in the elegant
verbiage of his pages? Mystery! Is it the fascination of the
incomprehensible? -- is it the charm of the impossible? Or are those
beings who exist beyond the pale of life stirred by his tales as by an
enigmatical disclosure of a resplendent world that exists within the
frontier of infamy and filth, within that border of dirt and hunger, of
misery and dissipation, that comes down on all sides to the water's edge
of the incorruptible ocean, and is the only thing they know of life,
the only thing they see of surrounding land -- those life-long prisoners
of the sea? Mystery!"</i></span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">As marcdcyr very rightly points out, this is verbose writing about the mystery of why a verbose writer might be popular with people who presumably didn't read terribly well. </span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">But to my surprise, I realized that although I didn't know the answer to Conrad's question my first 2-3 times through Children of the Sea, I did now. And so I wrote a very long explanation about that, and then realized it was buried in the comments in the mildly obscure blog Lingua Franca in the academically noteworthy but otherwise little-read Chronicle of Higher Education. </span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">So I decided to rescue it and bring it out here, into my own blog, which is more obscure than all of them put together. I think there's a writing lesson or two in it somewhere:</span><br />
<br />
<div class="post-message " data-role="message" dir="auto">
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">A few years ago I decided on the project of reading some
Bulwer-Lytton - the ones the Victorian critics thought most highly of, I
decided -- because his plays were some of the best of his generation,
and I was curious about the gap in reputation. And I found, to my
surprise, that I think I did understand what was mystiying Conrad so
thoroughly:</span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">My secret to reading Bulwer-Lytton and enjoying him is
to forget about sentences. He writes in phrases, mostly noun phrases,
some verb phrases, now and then rising to clauses, but mostly phrases.
It's an extremely melodramatic (or anachronistically cinematic) style.
But forget about remembering what the subject was whenever you finally
find your way to the main verb, and don't expect either the subject or
the main verb to be the most important thing in the alleged sentence.
It's more of a prose poem of phrases, mostly linked by sensual and
emotional content -- which is to say, an ornate, rich movie.</span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">Read
that way, the infamous beginning of PAUL CLIFFORD reminds me very much
of the justly acclaimed beginning of Kasdan's script for BODY HEAT:</span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;"><i>Flames in the night sky. Distant SIRENS. PULLING BACK,<br />we see that the burning building is mostly hidden by dense,<br />black shapes that define the oceanside skyline of Miranda<br />Beach, Florida. We're watching from across town. The<br />sound of a bathroom SHOWER comes to a dripping stop at<br />about the same time we see the naked back and head of NED<br />RACINE. We continue to PULL BACK INTO --</i></span><br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;"><i><b> RACINE'S APARTMENT - NIGHT </b></i></span><br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;"><i>Racine, dressed in undershorts, is standing on the small<br />porch off his apartment on the upper floor of an old house.<br />Racine lights a cigarette and continues to stare off at<br />the fire. We've passed him now, into the bedroom of the<br />apartment, and the shape of a young woman, ANGELA, flashes<br />by, drying her body with a towel.</i></span><br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;"><i> </i><br />It's
all about "you see this, then you see this, then you see this." The
sentences and words aren't the point; it's image, image, image.</span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">So
in the infamous beginning of Paul Clifford (which really is one of
Bulwer-Lytton's best), "It was a dark and stormy night" is merely the
first of a swarm of images, as Dummie (whose name we don't know yet)
desperately charges through the storm, trying to find something for
which he eventually accepts an emergency substitute. Break the
visual/sensual/action phrases out of the of long clanking sentences, and
suddenly it's the start of a pretty cool movie:</span><br />
<br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">It was <br /><b> a dark and stormy night; <br />the rain fell in torrents, </b>except at <br />occasional intervals, when it was checked by <br /><b>a violent gust of wind <br />which swept up the streets<br />LONDON -- NIGHT </b><br /> (for it is in London that our scene lies),</span><br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;"><b> rattling along the house-tops, and<br /> fiercely agitating the scanty flame <br />of the lamps </b> that struggled against the darkness. <br />Through one of the <br />obscurest quarters of London, and <br /><b>among haunts little loved by the gentlemen of the police,<br />A MAN (DUMMIE), </b><br />evidently of the lowest orders, was wending his solitary way. He <br /><b>stopped twice or thrice at different shops <br />and houses</b><br /><b> MONTAGE -- DUMMIE STOPS AT RUN DOWN SHOPS AND HOUSES -- NIGHT </b> <br />of a description correspondent with the appearance of the <br />quartier in which they were situated, and <br /><b>tended inquiry for some article or another </b><br />which did not seem easily to be met with. All the <br /><b> answers he received were couched in the negative; and as he turned from each door <br />he muttered to himself, </b> in no very elegant phraseology, <b>his disappointment and discontent. </b></span><br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">BUTCHER'S HOUSE -- INTERIOR <br />At
length, at one house, the landlord, a sturdy butcher, after rendering
the same reply the inquirer had hitherto received, added, <br /><b>"But if this vill do as vell, Dummie, it is quite at your sarvice!" <br />Pausing reflectively for a moment, <br />Dummie responded that <br />he thought the thing proffered might do as well; and <br />thrusting it into his ample pocket, <br />he strode away <br />with as rapid a motion as the wind and the rain would allow. </b></span><br />
<br />
<span style="font-family: Georgia,"Times New Roman",serif; font-size: large;">In
short, solid storytelling in vivid images can overpower perfectly awful
sentences and words -- even as awful as Bulwer-Lytton's. And that, I
think, was the reason that sailors on long voyages mystified Conrad by
liking Bulwer-Lytton. They expected reading to be hard, and perhaps not
to get everything, but they demanded a good story in vivid images --
and he gave it to them.</span></div>
<span style="font-size: large;"><br /></span>
<br />
<div style="text-align: center;">
<span style="font-size: large;"><span style="font-size: x-large;"><b>§</b></span></span></div>
<span style="font-size: large;">*Not, in my opinion, his best. And I must be one of fewer than 100 writers/teachers on Earth who actually has an opinion about Bulwer-Lytton's best. </span><br />
<br />
<br />
<br /><div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-90846365844849519932015-08-27T00:24:00.002-06:002015-08-27T00:24:30.120-06:00Doing something uncharacteristic, I'll be at BuboniconI'm going to be attending <a href="https://bubonicon.com/">Bubonicon, the New Mexico/Albuquerque area sf convention, this weekend</a>. I haven't been much of a con-goer for quite a long time -- my last few were the Las Vegas SFRA in 2005, the Anaheim (2006) and Denver (2008) Worldcons (the latter somewhat under duress, as a fill-in for my agent at the time) and a very brief one afternoon visit to MileHi Con last fall. Prior to that I was fairly regular about going to the damned things but didn't like most of the ones I attended after about 1995.<br />
<br />
Bubonicon was a shining exception, hence my giving it another shot there, in a friendly place that feels like home, to see if maybe I've grown out of con-dislike.<br />
<br />
Anyway, I'll be there for pretty much all of Bubonicon. My scheduled activities are:<br />
<br />
Friday 5 PM -- Reading in Cimarron/Las Cruces. I usually bring a mix of stuff to read and let the audience vote on which one(s) I read and how long we stay at it.<br />
<br />
Friday 7:30 PM in Salon A-D. Panel: A Post-Scarcity World: How?<br />
<br />
Saturday 3 PM -- Main Room (Salon E); Panel: Is Hollywood Eating SF Alive?<br />
<br />
Saturday 5:25 PM -- Mass Autographing. <br />
<br />
Sunday 1 PM -- Main Room (Salon E);Writing Different Genders: Your Point of View<br />
<br />
Other than that, I'll probably be atthe Kaffeklatsch, whether I can spell it or not, on Saturday morning, because they are offering free food and coffee, and I will often hang out in the Hostility Suite because I generally prefer hanging with fans to hanging with writers (as to why, see Gorey's The Unstrung Harp, or Mr. Earbrass Writes A Novel); for the same reason I'll avoid the green room and the bar.<br />
<br />
I'm there to meet and talk to fans, primarily, so if you're going to be there, come up and say hi. In my somewhat awkward way, I'll do my best to be welcoming. Just don't expect me to remember very much about what's in my books; they were mostly written long ago, and I have a pretty bad memory. More than once I've been asked a question about one of my books, thought it was about someone else's book, and apologized for not being familiar with it...which was more truthful than it should have been. But otherwise, science, art, literature, theatre, history ... the whole gallery of the universe is open to conversation. <br />
<br />
<br /><div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-810419129310782182015-08-24T21:59:00.000-06:002015-08-26T12:15:03.528-06:00Every silence ends. "Silence Like Diamonds" ends in Episode 10. So here are some thoughts about endings.<style>
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<div class="MsoNormalCxSpFirst" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><a href="http://www.lightreading.com/ethernet-ip/new-ip/silence-like-diamonds---finale-when-in-rome/d/d-id/717628">The last episode</a> of <a href="http://www.lightreading.com/archives.asp?section_id=353">"Silence Like Diamonds"</a> is now up, and those of you who
have been waiting to read it all at once should get busy, because after this
piece, I shall have no caution at all about spoilers. Yip and everybody are
going to find out what it was all about, you're going to find out what happens
to everyone, and in short, after this ep, the story's over and it's time to go
find another story.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">It is a
truth universally acknowledged among writers that endings are hard. <a href="http://lawrenceblock.com/">Lawrence Block</a>, who knows a lot about storytelling* and has written<a href="http://lawrenceblock.com/?s=writing+the+novel"> a couple of the bestbooks there are about it</a>,** once compared the job to being a homicidal cruise
director: you welcome everyone aboard with music and sunshine and the promise
of a happy time, you keep them amused on the cruise, and then you kill them at the
end. <a href="http://www.amazon.com/The-Pleasure-Text-Roland-Barthes/dp/0374521603">Roland Barthes, who knew a lot about reading</a>, said that fiction is
basically striptease: anyone who has been around at all knows that you start
with someone pretty with clothes on, and knows perfectly well what you're going
to see at the end, so all the entertainment value is in how you get from one to
the other.<span style="mso-spacerun: yes;"> </span>(Anyone else notice that the
American writer picks a violent metaphor and the French critic picks a sexual
one?)</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The
interesting thing to me about both comparisons is how much they stint the
ending. Block is all about how to get the reader into the book, reading and
demanding fun; Barthes is about how to keep the reader reading; but about the
ending, shorn of the metaphor, each of them just says "Do something
big."<span style="mso-spacerun: yes;"> </span>Block says to impress them
(at least I hope that's what "kill them at the end" means) and
Barthes says to give'em what they've been promised and think they want (a good
look at a bare-naked lady, even though you hope they're well past the point
where that's a mystery to them).<span style="mso-spacerun: yes;"> </span>Neither
of them really says what "something big" to satisfy or delight the
reader might be.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">As for me,
well, I won't say I'm <i style="mso-bidi-font-style: normal;">no</i> good at
endings. <i style="mso-bidi-font-style: normal;">No good </i><span style="mso-spacerun: yes;"> </span>would be never getting one that works, as
opposed to occasionally.<span style="mso-spacerun: yes;"> </span>Probably <i style="mso-bidi-font-style: normal;">not very good at endings</i> would cover it
nicely.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I've
written a few endings that I think worked pretty well and I'm proud of: <a href="http://www.amazon.com/Sky-Big-Black-Meme-Wars-ebook/dp/B003J5UIPK/ref=sr_1_1?s=books&ie=UTF8&qid=1440473592&sr=1-1&keywords=barnes+sky+so+big+and+black">The Sky So Big and Black, </a> <a href="http://www.amazon.com/Kaleidoscope-Century-Meme-Wars-Barnes-ebook/dp/B004SI9EQQ/ref=pd_sim_351_2?ie=UTF8&refRID=1XQHEPZ9YJ5AF1MRBA26">Kaleidoscope Century,</a> and <a href="http://www.amazon.com/Armies-Memory-Thousand-Cultures/dp/0765342243/ref=tmm_mmp_swatch_0?_encoding=UTF8&qid=1440473756&sr=1-1-catcorr">The Armies of Memory.</a> Readers seem to
agree with me about them. I've written a few endings that weren't what they needed to be and still nag me: <a href="http://www.amazon.com/Million-Open-Doors-John-Barnes/dp/0812516338/ref=pd_sim_14_3?ie=UTF8&refRID=0NECD6J2ETXKDKE91CCH">A Million Open Doors</a> and <a href="http://www.amazon.com/Princess-Aerie-Jak-Jinnaka-Book-ebook/dp/B00GH2G8I8/ref=sr_1_2?s=books&ie=UTF8&qid=1440473905&sr=1-2&keywords=barnes+princess+of+the+aerie">A Princess of the Aerie</a>, for example. And there are plenty of endings about which the readers and I would disagree. Endings that I really
liked, but many readers grumbled about: <a href="http://www.amazon.com/Orbital-Resonance-Meme-Wars-Barnes/dp/0812532384/ref=tmm_mmp_swatch_0?_encoding=UTF8&qid=1440474418&sr=1-1">Orbital Resonance</a>, <a href="http://www.amazon.com/Finity-John-Barnes/dp/0812571452/ref=tmm_mmp_swatch_0?_encoding=UTF8&qid=1440474510&sr=1-1">Finity</a>, and <a href="http://www.amazon.com/Last-President-Novel-Daybreak/dp/0425256464/ref=tmm_mmp_swatch_0?_encoding=UTF8&qid=&sr=">The Last President</a>. And there were a couple times I threw up my hands and just got out
of the book that for some mysterious reason were much enjoyed by some readers
and earned some laudatory fanmail: <a href="http://www.amazon.com/Duke-Uranium-Jak-Jinnaka-Book-ebook/dp/B00GH2G7UW/ref=sr_1_1?s=books&ie=UTF8&qid=1440474228&sr=1-1&keywords=barnes+duke+of+uranium">The Duke of Uranium</a>, <a href="http://www.amazon.com/Mother-Storms-John-Barnes/dp/0765332515/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=1440474334&sr=1-1">Mother of Storms</a>, and <a href="http://www.amazon.com/Daybreak-Zero-A-Novel/dp/1937007308/ref=pd_sim_14_1?ie=UTF8&refRID=04P066ZGDRK4T1M2849Z">Daybreak Zero</a>.
I suppose my personal take on endings for novels is not unlike the supposed
early days of aviation rule that if you walked away, it was a good landing.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So,
anyway, there's an ending to "</span><span style="font-family: Georgia; font-size: 14.0pt;"><a href="http://www.lightreading.com/archives.asp?section_id=353"><span style="font-family: Georgia; font-size: 14.0pt;">Silence Like Diamonds</span>,</a>" and it's there
in <a href="http://www.lightreading.com/ethernet-ip/new-ip/silence-like-diamonds---finale-when-in-rome/d/d-id/717628">Episode 10</a>; head on over and read it.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Not a
spoiler, I think, to say that if something human-created ever does end the
world, it will almost certainly be something created with good intentions. </span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">But of
course, "Silence Like Diamonds" is a novelet, <a href="http://thatjohnbarnes.blogspot.com/2015/07/tomorrow-morning-fresh-serial.html">a short fiction form with its own rules</a>. So what about short fiction? </span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Short
fiction, if it is at all plot-centered, <i style="mso-bidi-font-style: normal;">has</i>
to be about the ending.*** The story sets up its last couple paragraphs,
sentence, sometimes even just its last word (see Asimov's "Liar!",
which is both the title and the last word) to have some immense wallop.<span style="mso-spacerun: yes;"> </span>There are quiet wallops and loud ones, gentle
ones and brutal ones, but one way or another, the whole piece of short fiction,
in retrospect, is the series of fakes, windups, and clears by which the short
fictionist prepares to give you a good kick in the brains.<span style="mso-spacerun: yes;"> </span>(Or punch right on the heart, or maybe to whip out a 10 foot
spear from nowhere and skewer you through a vital organ you'd never even heard of).</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So as an exercise for the reader, here
are 20 great endings, a mixture from older science fiction, mainstream,
horror, and mystery because those are the things I know best. I'm deliberately choosing
most of them from quite a while back, and preferring the famous to the obscure,
because I'm hoping you will experience the following contrast: </span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The ones
from the stories you know will instantly bring back a jolt of emotion, very
like the way a hook from a significant song will. And the ones from stories you
don't know will make you say, "Hunh?" And in that difference lies the point of short fiction:</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In novels (and novellas, and other long forms), no matter
how plot-centered, ultimately the ending is the release from the work; it lets
you out to the wider world again. But in plot-centered short fiction (which is
particularly common in the short-short and the novelet, but found at all
lengths), it's rather the other way round. The story prepares you to find
meaning in the ending; in fact the story sets up that strange, parallel moment
when a few ordinary words become something much richer and more important,
whether it's a deep insight or violent shock, a quiet moment of reflection or the
crashing of the Last Chord.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So, here
are the well-known endings I have thrown together into a heap for you. <b>No
keeping score.</b> When you recognize one, does it wake up the memory of the story?
When you don't, does it at least intrigue you that these few words could mean
so much? Perhaps enough even to look up the story and see why that would be?</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I've put
them in alphabetical order, by the way, just because it made as much sense as
anything else.<span style="mso-spacerun: yes;"> </span>Read away ...</span></div>
<blockquote class="tr_bq">
<ol>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">When the doctors came they said she
had died of heart disease—of the joy that kills.<span style="mso-spacerun: yes;"> </span></span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">Walking to the taffrail, I was in
time to make out, on the very edge of a darkness thrown by a towering black
mass like the very gateway of Erebus—yes, I was in time to catch an evanescent
glimpse of my white hat left behind to mark the spot where the secret sharer of
my cabin and of my thoughts, as though he were my second self, had lowered
himself into the water to take his punishment: a free man, a proud swimmer
striking out for a new destiny.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">Then ...... some idiot turned on the lights. </span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span class="st"><span style="font-size: 14pt;">"Solely," said Linley,
"in order to<i style="mso-bidi-font-style: normal;"> </i></span></span><i><span style="font-size: 14pt; font-style: normal;">get an appetite</span></i><span class="st"><i style="mso-bidi-font-style: normal;"><span style="font-size: 14pt;">.</span></i></span><span class="st"><span style="font-size: 14pt;">"</span></span><span style="font-size: 14pt;"></span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">She lifted the glass.<br />
"Thanks, Nettie," she said. "Here's mud in your eye."<br />
The maid giggled. "Tha's the way, Mis' Morse," she said. "You
cheer up now."<br />
"Yeah," said Mrs. Morse. "Sure."</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">"She was a talker, wasn't she?" Bobby Lee said,
sliding down the ditch with a yodel. <br />
"She would of been a good woman," The Misfit said, "if it had
been somebody there to shoot her every minute of her life." <br />
"Some fun!" Bobby Lee said. <br />
"Shut up, Bobby Lee," The Misfit said. "It's no real pleasure in
life." </span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><i><span style="font-size: 14pt; font-style: normal;">Romance</span></i><span class="st"><span style="font-size: 14pt;"> at </span></span><i><span style="font-size: 14pt; font-style: normal;">short notice</span></i><span class="st"><span style="font-size: 14pt;"> was her specialty.</span></span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">Overhead, without any fuss, the stars were going out. </span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">"Oh, that," said Father Brown. "I opened it
as soon as I saw it lying there. It’s all blank pages. You see, I am not
superstitious."</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">Now why should that man have fainted? But he did, and
right across my path by the wall, so that I had to creep over him every time!</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">Nick stood up on the log, holding his rod, the landing net
hanging heavy, then stepped into the water and splashed ashore. He climbed
the bank and cut up into the woods, toward the high ground. He was going
back to camp. He looked back. The river just showed through the
trees. There were plenty of days coming when he could fish the swamp.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">"It isn't fair, it isn't right," Mrs. Hutchinson
screamed, and then they were upon her.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">I must have looked through every pile of mail a hundred
times before I found the letter from the Clearys. Mrs. Talbot was right about
the post office. The letter was in someone else's box. </span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><i><span style="font-size: 14pt;">I didn’t do anything to die for... I didn’t do anything...
</span></i><span style="font-size: 14pt;"></span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">His face was dark gray and his back stiff, as if he'd just
had an injection of iron, and my stomach kind of fell as I felt how hard the
world was going to be to me hereafter.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">He slept, and the world passed by.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">"God," he cries, dying on Mars, "God, we
made it!"</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">For me, then, as they began to play again, it glowed and
shook above my brother's head like the very cup of trembling.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">And when he speaks of Irene Adler, or when he refers to her
photograph, it is always under the honorable title of <i style="mso-bidi-font-style: normal;">the </i>woman.</span></span></li>
<li><span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">And found the Flower Passage, and Kelly and Lou and Bo and
Muse. Kelly was buying beer so we all got drunk, and ate fried fish and fried
clams and fried sausage, and Kelly was waving the money around, saying,
"You should have seen him! The changes I put that frelk through, you
should have <i style="mso-bidi-font-style: normal;">seen</i> him! Eighty lira is
the going rate here, and he gave me a hundred and fifty!" and drank more
beer.<br />
And went up.</span></span></li>
</ol>
</blockquote>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I doubt
most people will recognize all of them; I don't expect you'll have both my
exact reading habits and my exact notion of what is memorable. Nevertheless, if
you aspire to write short fiction of the fantastic, you could do worse than to
look up the ones you don't know. The idea is not that you should be ashamed not
to have read all of them, but that these are small wonders of the form, and if
you can see how they make their last 10-100 words have such an effect, you'll
really understand the ending in plot-centered short fiction. </span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So I tried
not to make this a quiz, though I suppose some people will, because some people
can't resist comparing.<span style="mso-spacerun: yes;"> </span>The real
comparison that matters, though, is the feelings evoked by the ones you know
(quite possibly a memory of a good wallop past) and the feelings evoked by the
ones you don't (quite probably "what could that possibly mean and why
would those be the last words of a story?"<span style="mso-spacerun: yes;">
</span>For the curious, and for determined self-studier, you'll find a list of
the titles by number in the footnote marked ****.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Was the
ending of "Silence Like Diamonds" up to those standards? I have no
idea, really. Maybe I'll have more of one some day. At this point, I'll just
have to hope it was up to yours.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<br /></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-size: x-large;"><b><span style="font-family: Georgia;">§</span></b></span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">*If you
don't know his books, <a href="http://lawrenceblock.com/lbbooks/">go here and look</a>; I'm a fan of the Scudder and Keller
novels, but Bernie Rhodenbarr has his many passionate supporters.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<br /></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">** I
particularly recommend the many incarnations of <a href="http://www.amazon.com/Writing-Novel-From-Plot-Print/dp/0898792088">Writing the Novel: From Plot toPrint</a>, but there are numerous fans of<a href="http://www.amazon.com/Telling-Lies-Fun-Profit-Fiction/dp/0688132286/ref=pd_sim_14_1?ie=UTF8&refRID=0H7QFC9356XXK04757JS"> Telling Lies for Fun and Profit,</a> and they
are not wrong.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<br /></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">***There
are dozens of other things a piece of fiction can be centered around besides its
plot: character, identity, experience, alienation, growth, epiphany, point, idea,
preaching, position, fable, any sense, sound of words, rhythm, reversal,
theme/variation, motion, countermotion, action, anger, nostalgia, and shit
blowing up. For a piece of short fiction, any of those can and will do. But up
above the footnotes, what I am talking about is a story centered on plot. Not
because that's the best thing for all circumstances, but because (<a href="http://thatjohnbarnes.blogspot.com/2015/07/tomorrow-morning-fresh-serial.html">for reasons you can find here</a>) it's what I think the classic novelet
should be about.</span></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<br /></div>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">**** What
those are the endings of:</span></div>
<ol>
<li><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Baskerville;">Kate Chopin, The Story of
an Hour.<span style="mso-spacerun: yes;"> </span></span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Baskerville;">Joseph Conrad, The Secret
Sharer.</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">Ray Bradbury, The October Game. </span></li>
<li><span class="st"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Lord Dunsany, Two Bottles of Relish.</span></span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Dorothy Parker, Big Blonde.</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">Flannery O'Connor, A Good Man is Hard to Find. </span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; font-style: normal; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-style: italic; mso-fareast-font-family: "Times New Roman";">Saki, The Open
Window.</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">Arthur C. Clarke, The Nine Billion Names of God. </span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">G.K.Chesterton, The Blast of the Book.</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; font-style: normal; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-style: italic; mso-fareast-font-family: "Times New Roman";">Charlotte</span><span class="st"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"> Perkins </span></span><span style="font-family: Georgia; font-size: 14.0pt; font-style: normal; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-style: italic; mso-fareast-font-family: "Times New Roman";">Gilman, The
Yellow Wallpaper</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Ernest Hemingway, Big Two-Hearted River</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">Shirley Jackson, The Lottery.</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">Connie Willis, A Letter from the Clearys. </span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-style: italic;">Tom Godwin, The Cold Equations </span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">John Updike, A&P</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">Roger Zelazny, The Graveyard Heart</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">Theodore Sturgeon, The Man Who Lost the Sea.</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">James Baldwin, Sonny's Blues</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Arthur Conan Doyle, A Scandal in Bohemia</span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Samuel R. Delaney, Aye, and Gomorrah ....</span></li>
</ol>
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 8.0pt; mso-add-space: auto; text-indent: .5in;">
<br /></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-87285973384014770722015-08-21T15:26:00.003-06:002015-08-26T11:55:12.831-06:00Episode 9 is up, so here's a set of digressions leading up to why I called it "Silence Like Diamonds"<style>
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<br />
<div style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><a href="http://www.lightreading.com/ethernet-ip/new-ip/silence-like-diamonds---episode-9-hacking-an-escape/d/d-id/717627">Episode 9</a>
<span style="mso-spacerun: yes;"></span>of "<a href="http://www.lightreading.com/archives.asp?section_id=353">Silence Like Diamonds</a>"
<span style="mso-spacerun: yes;"></span>is up, and as befits the next-to-last
episode of a serial, or the penultimate scenes of a novelet, it's pretty much
nonstop action.<span style="mso-spacerun: yes;"> </span>If you're coming in for
the first time, you could just start at <a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-1-family-business/d/d-id/717130">"Silence Like Diamonds" Episode 1</a> (episodes are short and you can
pretty much read it all at a sitting if you don't stop off to argue in the
comments). There's a <a href="http://www.lightreading.com/archives.asp?section_id=353">complete episode list here</a>.
<span style="mso-spacerun: yes;"></span>I explain why I wrote it in <a href="http://thatjohnbarnes.blogspot.com/2015/07/tomorrow-morning-fresh-serial.html">this blogpost</a>, and Mitch Wagner explains why LightReading published it on <a href="http://www.lightreading.com/security/cloud-security/light-reading-goes-faster-than-light/a/d-id/717229">this page</a>. So that's where we are, that's where you can go next if you like, and that's
what this is ostensibly about.<span style="mso-spacerun: yes;"> </span></span></div>
<div style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">This time I'm taking the very long way around to <a href="http://www.lightreading.com/archives.asp?section_id=353">SilenceLike Diamonds</a>,
something like Schroeder's "<a href="https://www.youtube.com/watch?v=0cA9j2EpAHE">book report on Peter Rabbit</a>," <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>(my
dad tells me I wrote a lot of book reports like that when I was a small person,
but I refuse to remember due to 5th Amendment amnesia). Anyway, it may not
appear that I'm talking about "<a href="http://www.lightreading.com/archives.asp?section_id=353">Silence Like Diamonds</a>"
for a while, but we'll get there. Meanwhile,
<a href="http://www.lightreading.com/ethernet-ip/new-ip/silence-like-diamonds---episode-9-hacking-an-escape/d/d-id/717627">Episode 9 </a>is up.
Only <a href="http://www.lightreading.com/ethernet-ip/new-ip/silence-like-diamonds---finale-when-in-rome/d/d-id/717628?page_number=2">Episode 10</a> to go, next Tuesday. Almost
home!</span></div>
<div style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Now commences a journey through a lot of stuff, at the end
of which we shall see something or other about "<a href="http://www.lightreading.com/archives.asp?section_id=353">Silence Like Diamonds</a>".
</span></div>
<div style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">About thirty years ago, Terence Hawkes used <i style="mso-bidi-font-style: normal;"><a href="http://www.amazon.com/That-Shakespeherian-Rag-critical-process/dp/0415352924">That Shakespeherian Rag</a> </i>
as the title of a collection of essays that has pretty much defined the terms
of argument about why English-speaking people still read and perform
Shakespeare (or are trying to quit). Thanks to the need for professors to
explain why the assigned reading was titled that, nearly every theatre grad
student knows these lines from <i style="mso-bidi-font-style: normal;">The Waste
Land</i></span></div>
<div style="text-align: left;">
<blockquote class="tr_bq">
<div style="margin-bottom: 9pt;">
<span style="font-size: small;"><span style="font-family: Georgia;">'Are
you alive, or not? Is there nothing in your head?' <br />
But <br />
O O O O that Shakespeherian Rag-- <br />
It's so elegant <br />
So intelligent </span></span></div>
</blockquote>
</div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">which is
actually a quote (or rather a deliberate misquote) from a 1912 showtune by </span><span class="st"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Gene Buck, Herman
Ruby and David Stamper.</span></span><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";"> <span style="mso-spacerun: yes;"> </span>"The
Shakespeherian Rag" had been a hit while Eliot was in grad school at
Harvard, on the brink of heading off to Britain, where he would spend much of
the rest of his life struggling mightily to be English, with considerable
success.**</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">As you can
discover in one of Hawkes's essays, much of the
reading and performance of Shakespeare in the last century or so is explicable
if we treat Shakespeare's role as a status symbol as a primary fact, and </span><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">familiarity with Shakespeare as a kind of country club membership or the wave-in from the cultural doorman at the Cool Kids Cultural Club</span>. Hawkes
quoted Eliot's poem because of the complicated prestige-maneuvering involved in
those lines. The original song seems to have taken a straightforward "Wow,
Shakespeare is great" position with the kind of pretended "I am not
impressed, I really know this stuff" attitude that is one way of
demonstrating that status symbol of familiarity (see, for example, Cole Porter's treatment of <i>The Taming of the Shrew</i> in <i>Kiss Me, Kate</i>, or the silly "Shakespeare rap" in <i>Renaissance Man</i>). In the way he quoted it, Eliot
could make it an ironic comment on the "collect quotes for use later"
way that Shakespeare was read by highly educated people (or people who
pretended to education, the sort of people who populated Eliot's poetry, plays,
and parties).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Now, as
Thorstein Veblen might have told Eliot if they'd been at the same university,
there's no point to a status symbol that other people can't see. It's not so
much the status symbol itself, but its manner of exhibition, that's
interesting.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">For many
decades familiarity with Shakespeare was mostly exhibited via quoting and/or
alluding, particularly in Britain but in all the other English speaking
countries. This led to an instructional style of reading Shakespeare as if one
were proceeding from quote to quote along a short path of synopsis. It privileged
the sacred special memorizable-and-recitable lines over the busy noise of plot
and character development and the merely professional interest of how this text
should be acted or designed. It was a procedure neither for understanding nor for
performance, but for worship (or for pretended worship).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Worship-oriented
reading of Shakespeare led, in turn, to a salon culture among the wealthy young
in which people showed they'd been to a "good" school by trading
infosnippets about Shakespeare (and others on a short list of
"greats".)*** </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">One very
frequently taught Shakespeare quote was from <i style="mso-bidi-font-style: normal;">The Tempest:</i></span></div>
<blockquote class="tr_bq">
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-size: small;"><b><span style="font-family: Georgia;">MIRANDA</span></b><span style="font-family: Georgia;">: Oh, wonder!</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-size: small;"><span style="font-family: Georgia;">How many goodly creatures are there
here!</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-size: small;"><span style="font-family: Georgia;">How beauteous mankind is! O brave new
world,</span></span></div>
<div class="MsoNormal" style="margin-bottom: 9pt; text-indent: 0.5in;">
<span style="font-size: small;"><span style="font-family: Georgia;">That has such people in ’t!</span></span></div>
</blockquote>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">In the 1910-60 era when Eliot was most
active, anyone whose schooling had gone beyond age 12 knew that quote. In fact,
in the instructional methods of the time many students had been required to
recite it or to write it out on exam papers. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">And so, when Aldous Huxley wrote a
brutal satire of a world where human needs were met but at the cost of no one
being very human, he called it <i style="mso-bidi-font-style: normal;">Brave New
World</i>. He knew that the sort of people who were browsing in a bookstore
would immediately see that title and think <i style="mso-bidi-font-style: normal;">"...
That has such people in ’t!</i>'<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">It was sort of an earworm-generating-quote.
</span><span style="font-family: Georgia; font-size: 14.0pt;">Many great titles
have been constructed by giving half a quote; almost always the missing half is
the important part, which the reader then says mentally. (Or as Frost put it,
"But it isn't elves exactly ....").<span style="mso-spacerun: yes;">
</span>Ones I can see on my bookshelf right now include the great post-WW2
documentary <i style="mso-bidi-font-style: normal;">Situation Normal</i>, George
McDonald Fraser's war memoir <i style="mso-bidi-font-style: normal;">Quartered
Safe Out Here</i>, Robert Penn Warren's political novel <i style="mso-bidi-font-style: normal;">All the King's Men,</i> Agatha Christie's <i style="mso-bidi-font-style: normal;">And Then There Were None,</i> the incredibly overused <i style="mso-bidi-font-style: normal;">When the Bough Breaks, </i>and Saul
Cornell's book on the origins of the Second Amendment, <i style="mso-bidi-font-style: normal;">A Well-Regulated Militia</i>.</span><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"> </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">As it happened, Huxley's story became
famous and influential in its own right, and it would be an interesting
question whether nowadays more people know something about it than about <i style="mso-bidi-font-style: normal;">The Tempest.</i> <i style="mso-bidi-font-style: normal;">Brave New World </i>went on to become a famous phrase now separated
from Shakespeare, and in its newer incarnation it links to ideas like soma,
that unforgettable opening scene with the embryos in bottles, and a general
impression of what non-violent, mostly-invisible totalitarianism might look
like. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Many readers who don't like <i style="mso-bidi-font-style: normal;">Brave New World</i> complain about the
characters being "unlikeable." Such readers often read for the
pleasure of make-believing they are the characters. They can't get much fun out
of a character it would be unpleasant to be. That's why most unambitious genre
books, the simple adventure stories and love stories that populate most of the
shelves, offer "likable" characters. As I've heard Tom Doherty say
many times, bestsellers are usually books about people and settings where the
readers "want to be them and want to go there." </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Short sidenote: readers don't
necessarily want to be admirable people or go to ideal vacation settings,
though of course they might. There's a lot of fun in imagining being or meeting
Don Corleone, Hannibal Lector, or Scarlett O'Hara, and though William Gibson's
Sprawl, Arrakis, or Mordor aren't nice places, they're interesting, especially
if you don't actually have to physically endure them.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">But Huxley had ambitions beyond selling
books and entertaining casual readers. He was purposely working at the
intersection between "science fiction" and "novel." Properly
speaking, a novel is a bigger, richer, more complicated form than a simple
adventure story or even an archetypal Hero's Journey, and one of the main
things it is concerned with is "Where do different types of people come
from and what difference do the different types make in the world?"</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">The point of a novel, as opposed to
just a book length story for entertainment, necessarily includes something
about that basic proposition: <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">if you have this kind of world, it will have
this kind of people.</i> </b>Those people may be dreary or even dull, if your
point is that the world we have makes us into people we don't want to know. You
can find a fair bit of that exact point in <i style="mso-bidi-font-style: normal;"><a href="http://www.amazon.com/gp/product/0316769487/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0316769487&linkCode=as2&tag=entethemadmun-20&linkId=Z423PNXVXPKC2CWE">The Catcher in the Rye</a>,</i> <i style="mso-bidi-font-style: normal;"><a href="http://www.amazon.com/gp/product/1503121135/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=1503121135&linkCode=as2&tag=entethemadmun-20&linkId=ILXZD2W3AIDPTE4D">Of Human Bondage</a>,</i> <i style="mso-bidi-font-style: normal;"><a href="http://www.amazon.com/gp/product/0312427573/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0312427573&linkCode=as2&tag=entethemadmun-20&linkId=FHUYRBGZVVEIVNMM">The Bonfire of the Vanities</a>, </i>and <a href="http://www.amazon.com/gp/product/0385491034/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0385491034&linkCode=as2&tag=entethemadmun-20&linkId=7RLV2TOVHEXLTGYH"><i style="mso-bidi-font-style: normal;">The Robber Bride</i> </a><span style="mso-spacerun: yes;"> </span>(though that one has likable characters, they
aren't necessarily the source of interest; Zenia is what makes that novel
fascinating).<span style="mso-spacerun: yes;"> </span>They may be evil or brutal
or shallow, emotionally stunted or inexpressive, or manipulative and
self-pitying if that's what you think your world will make them, and within the more serious and complicated game of the novel-reader, that's in bounds, even if they aren't playable/likable.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">In sci fi, that's a higher wall than
many readers want to climb, and a deeper well than they want to probe, and
thicker woods than they want to push through, and much more mixed a metaphor
than any of those. The plain and simple adventure story, in which one sturdy
root of genre fiction is always planted, tends to have characters who change in
simple ways that fit the reader's experience of life today: young insecure (or
cocky) characters become older, more secure, and wiser; people who take a turn
for the bad get worse or turn back in a great shower of remorse; and so on.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Nonetheless, whenever science fiction
(or any other genre) acquires a bit of ambition, it has to take some position
of the form: <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">if you have this kind of world, it will have this kind of people.</i></b>
It does mean losing a certain kind of reader, and if you are going to write
with any ambition, you will just have to consider them well lost. I catch a
certain amount of flak about there being "no likable characters" in
my own <i style="mso-bidi-font-style: normal;"><a href="http://www.amazon.com/gp/product/0812533461/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0812533461&linkCode=as2&tag=entethemadmun-20&linkId=ZAXIPOQWWVFJAMFP">Kaleidoscope Century</a><span style="mso-spacerun: yes;"></span>, <a href="http://www.amazon.com/gp/product/0812589696/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0812589696&linkCode=as2&tag=entethemadmun-20&linkId=HVAJBHSOKWQFORCF">The Merchants of Souls</a><span style="mso-spacerun: yes;"></span>,</i> <i style="mso-bidi-font-style: normal;"><a href="http://www.amazon.com/gp/product/B00ANYDVZY/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B00ANYDVZY&linkCode=as2&tag=entethemadmun-20&linkId=Z4LDOLGYRST5LLQO">Motherof Storms</a>, </i>and <i style="mso-bidi-font-style: normal;"><span style="mso-spacerun: yes;"> </span><a href="http://www.amazon.com/Losers-Space-John-Barnes/dp/0670061565/ref=la_B000AQ3DTO_1_5_title_0_main?s=books&ie=UTF8&qid=1440188998&sr=1-5">Losers In Space</a></i>.
I also see some less-frequent and less-intense grumbles about people being
"too good to be true," which I think is another form of unplayability,
though it might also just be the more legitimate complaint that I'm depicting a genuine
impossibility, in <i style="mso-bidi-font-style: normal;"><a href="http://www.amazon.com/Orbital-Resonance-Meme-Wars-Barnes/dp/0812532384/ref=la_B000AQ3DTO_1_11_title_1_mas?s=books&ie=UTF8&qid=1440188998&sr=1-11">Orbital Resonance</a>, <a href="http://www.amazon.com/Tales-Madman-Underground-John-Barnes/dp/0142417025/ref=la_B000AQ3DTO_1_4_title_0_main?s=books&ie=UTF8&qid=1440188998&sr=1-4">Tales of the Madman Underground</a> ,</i> and <a href="http://www.amazon.com/gp/product/0765342227/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0765342227&linkCode=as2&tag=entethemadmun-20&linkId=YAMAWUYJC6TKBF26"><i style="mso-bidi-font-style: normal;">The Sky So Big and Black </i></a>)</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">It's part of the heat you accept when you go into the literary kitchen,
even as a mere chopper of vegetables and arranger of canapes.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">In short science fiction, it's the same but more so. The game is <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">really</i></b>
about what kind of world makes what kind of people. There isn't space to do
much more than establish a world, establish a few people, and have them do one
interesting thing. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">It's all about the meaning Huxley
probably intended to invoke when he picked "Brave New World" for a
title. He would have known -- it was and still is one of those infosnippets
traded around at parties to prove your cred as an educated person -- that
"brave" in Shakespeare's day carried a strong idea of showiness,
visual splendor, and richness of appearance, as well as courage; a brave man
wasn't just courageous or valiant, but was also conspicuous and
attention-grabbing.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">That is, Miranda means that it's a
dazzling world she has never seen before, because it has people of a kind she's
never seen before.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">And that's part of the job, if you're
writing short science fiction for some reason other than the check. One way or
another, dazzle the reader with a vision of things they haven't seen before,
which includes a vision of new kinds of people.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">So as part of creating the world for
"<a href="http://www.lightreading.com/archives.asp?section_id=353">Silence Like Diamonds</a>"
<span style="mso-spacerun: yes;"></span><i style="mso-bidi-font-style: normal;">(oh,
look, there it is! see, I did get around to it!)</i> I tried to ask ... <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">what
kind of people grow in a world with no privacy and insecure untrustable
information?</i></b> In the imagined future of the story, the fast
factorization algorithm that collapsed all of encryption happened around 2020,
so these characters spent most of their young adulthood coping with the
aftermath of that. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">What kind of people has this made them?</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">They have to value skills more than
mere compendia of information</span></i></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">.</span></b><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"> Anybody can steal your secrets and
thus prevent your charging for them, but stealing your skills is a whole other
business. Hence Yip's most valuable and salable asset is her carefully honed
and developed talent for seeing where the money is going in criminal schemes
(she's a "scheme architecture analyst," a term that some large
detective firms are already using for their accountants who specialize in
tracking money through the laundry). </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">She knows lots of facts about how money
moves illicitly in the world, but anyone could access those. The "secret
sauce" is in her ability to grasp the new, not to repeat the old. That's
very different from many present-day experts who are essentially depth
librarians of highly specific topics. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Similarly, Yazzy sees what software
does (but isn't a code jock by present day standards), Dusan has marketing
skills (he does better things with the same information that anyone could look
up), and even Markus describes his job as beating people up, i.e. a skill, not
a body of knowledge. <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">They think in terms of defense and
attack.</span></i></b><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">
It's not a violent world necessarily but a ferociously competitive one. When
everyone reads everyone else's records and communications, the game becomes
closer to zero sum, and the premium for hitting first goes up, so it is hardly
surprising that people look around themselves all the time, checking for
enemies.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Personal trust becomes more highly
valued. </span></i></b><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Everyone
counts on family connections and longstanding friendships; in a world where you
can't discuss lunch without being drowned in ads for cafes and slagmails from
one cafe dismissing another, and where to talk securely two people have to
prearrange regular transmission of one time pads, the human connections outside
the system become more vital.<span style="mso-spacerun: yes;"> </span>(Notice,
for example, that Yip is interested in Markus in part because they live and
work in the same immediate area; the world of "<a href="http://www.lightreading.com/archives.asp?section_id=353">Silence Like Diamonds</a>" <a href="http://www.lightreading.com/archives.asp?section_id=353"></a>
<span style="mso-spacerun: yes;"></span>probably has a lot less online dating
than ours, much less "shopping around," and much more
"settling," because meeting strangers, especially at a distance,
involves too much sensitive information being where anyone can read it).</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Above all else, they value silence</span></i></b><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">. There are two great privileges in
that imagined future: not being deluged with messages from people trying to
sell you something (not just products and services, but ideas and beliefs), and
not having to communicate more than you want to. Hence the title, about which
I've had a few queries; it comes from the last tag at the end of Lupe Fiasco's
"<a href="https://www.youtube.com/watch?v=KdY1NlxM-m8">Go To Sleep</a>" : </span><span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<blockquote class="tr_bq">
<span style="font-family: Georgia; font-size: 14.0pt;">
<b><a href="http://genius.com/4196875/Lupe-fiasco-go-to-sleep">If talk is cheap, then my silence is diamonds. Preach </a></b></span><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"></span></blockquote>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">It's a world where talk is cheap because people have no
control over it; and where anyone who carves out a little bit of control uses
it to get some silence, both of transmission and reception. Silence is what you
need to listen, and the status symbol that indicates you aren't compelled to
speak.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="mso-tab-count: 1;"> </span>And that is
why it's called that, and why, in its own way, it's a brave new world.</span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 9.0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">§</span></b></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">*It's very witty and entertaining if you read academical high-faluting
language comfortably, so if you're anything of a Shakespeare fan and you falute
at medium or greater altitude, it's worth your while. </span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">**for a very long time, the surest way for an poet to get into
American anthologies, which was just about the only reliable source of poetry
income, was to be English. If, like Eliot, he (it was usually but not always a
he) was also at least a bit stuffy, required footnotes, and generally found
life to be a drag, he could do very well indeed, being stamped into the
memories of most undergrad English majors from the last Coolidge to the first
Bush Administration.</span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">***</span><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";"> again, this meant laying out quotes and synopses as
if they were poker hands. The point was to show that you'd been to school, not
that you'd read closely or thought deeply, which is why the women were talking
of Michaelangelo as they came and went in that room.</span><span style="font-family: Georgia; font-size: 14.0pt;"></span></div>
<div class="MsoNormal" style="margin-bottom: 9.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; text-indent: -.5in;">
<br /></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-77086166881910349722015-08-18T01:43:00.000-06:002015-08-18T11:24:52.628-06:00 More than a toaster that remembers and more than a refrigerator that spies on you: Four thoughts about Internet of Things 2.0<style>
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<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Much noise is being made about the Internet of Things
these days by the sort of people who make noise about such things, and I suppose
all that noise is good for something. Perhaps it is good for keeping such
people employed so that they don't end up at Starbucks screwing up my coffee
order.* </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">For those of you who missed out on it, the idea (of the
Internet of Things, not my coffee order) is that eventually we will be
surrounded by devices that have sensors, memory, intercommunication, and some
kind of programmable processing, that are emphatically <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">not</i></b> what we traditionally
think of as computers. They're not exactly robots: many of them have no
autonomy and are controlled by pushing buttons on them or their remotes. Yet
they are unquestionably Smart Things.<span style="mso-spacerun: yes;">
</span>I'm going to call them internetrons, because I kind of like the word.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The Internet of Things obviously already happened yesterday,
to the phone and the record player. It is in process of happening today to the
automobile, dishwasher, and microwave. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Tomorrow, we are assured,** the toaster will remember how
you like your toast and optically scan it, ejecting it when it is Just Right. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">You
will get a deduction from your insurance company for having a refrigerator that
counts your calories, reorders fresh produce, and makes sure you don't drink
non-homeopathic beer, and a rebate from a marketing survey company that
places a few extra free items in every grocery order and watches what you do with
them. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The washer-dryer will decide whether the clothes are clean enough, taking
samples of the water at thirty second intervals, and then dry them to
fluffy perfection. To do its best possible job, that washing machine will check
with the toaster and the refrigerator to establish that the splotchy stain on
your favorite MLB baseball tee, which you always wear on Thursday nights at the
bar with the guys, is Smuckers Boysenberry Jam. From this it will compute
exactly how the detergent mix should be adjusted according to specifications
from Smuckers, Kenmore, the city water company, and Proctor and Gamble.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I do think that particular technological evolution is
inevitable, which is why I slipped quite a bit of it into <a href="http://www.lightreading.com/archives.asp?section_id=353">"Silence LikeDiamonds,"</a> <a href="http://lightreading.com/ethernet-ip/new-ip/silence-like-diamonds---episode-8-automatic-kidnapping/d/d-id/717626">Episode 8</a> (of 10) of which is now up and available. Go ahead,
click, go read the story.<span style="mso-spacerun: yes;"> </span>If by any
chance you just got here and it's the first time you've heard of "Silence
Like Diamonds," <a href="http://thatjohnbarnes.blogspot.com/2015/07/tomorrow-morning-fresh-serial.html">my explanation here</a>, <a href="http://www.lightreading.com/security/cloud-security/light-reading-goes-faster-than-light/a/d-id/717229">Light Reading's explanation there</a>.***</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">It's a vision of a future world in the center of a rectangle
whose bent and twisty sides might be <a href="http://designobserver.com/feature/a-dream-world-made-by-machines/27488/">All Watched Over By Machines of LovingGrace</a>, <span style="mso-spacerun: yes;"></span><a href="http://www.psmag.com/business-economics/wall-e-critique-that-transcends-ideology-4444">Wall-E</a>, <a href="http://www.technovelgy.com/ct/content.asp?Bnum=779">"I Always Do What Teddy Says,</a>"<span style="mso-spacerun: yes;"> </span>and<a href="http://www.dailydot.com/opinion/brave-little-toaster-predicted-internet-of-things/"> The Brave Little Toaster.</a> </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Well, friends, that's Internet of Things 1.0. And we all
know Version 1.0 of anything means we're amazed it exists at all, but eventually we'll come to see
it as some trivial automation of things that already existed. We know that
later on, when Version 2.0 arrives, we'll be more amazed at all the "obvious"
possibilities that we didn't see and all the things we thought we'd be doing
that we now see (from the viewpoint of 2.0 and higher) are a waste of time. So
... what's next, after every Razor scooter has GPS and relays everything happening
around its rider to Ms. Mom's cellphone, Mr. Teacher's gradebook, Dr.
Pediatrician's diet-and-exercise records, and the FBI's Pre-Missing Children
Just-In-Case Database?</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In a general way, Version 1.0 creates the infrastructure that is
then exploited transformatively in Version 2.0. Space Program 1.0 built the rockets, found the Van Allen
Belts, created the first communication satellites, figured out what made a
decent astronaut, and taught spacewalking and rendezvous. Space Program 2.0 was space
stations, routine operations in space, robot probes to everywhere,
environmental monitoring by satellite, the whole Earth and other worlds
photographed and accessible from any screen, GPS, and carrying much of global
communications. Web 1.0 was about being able to call up any information anyone
put up, if you could find it: the age of dot com, company web pages, blogs, and
Alta Vista. Web 2.0 was access, searchability, and processing, the age of
Amazon, Google, Instagram, and YouTube. Web 3.0 is roaring into existence right
now, under the general rubrics of "big data," "natural
language," and "the cloud." The personal computer as a whole is probably at
about Version 4.0 or 5.0, and in <a href="http://www.lightreading.com/archives.asp?section_id=353">"Silence Like Diamonds"</a> I try to imagine
what Version (n+1).0 might look like.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">But Internet of Things 1.0: The Coming of the Internetrons
is just arriving now. So guessing at 2.0 is purely fun of the kind that us sci
fi types like to try.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Here are my four big guesses about IoT 2.0, all of which
shaped some of my thinking for<a href="http://www.lightreading.com/archives.asp?section_id=353"> "Silence Like Diamonds"</a>:</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br />
<span style="font-family: Georgia; font-size: 14.0pt;">•Once all that information is moving around and available,
and once every device can tap into it, the pressure for<b> a really good standard
interface to the liveware </b>is going to be tremendous. If the machine world is
going to be like being surrounded by wise, understanding, and kindly servants,
we need them all to speak the same language (as much as possible, ours). After
all, in the old days, Lord Blithering-Twit of Blithering-on-Endlessly didn't
have to learn a different language for the gardener than he used for the butler
or the upstairs maid. "Or I will fire you and you will starve," and
"Thank you, that will be all," worked equally well on all of them.
Furthermore, though individual servants had individual capabilities**** , the
forms and rituals for telling them what to do were very similar***** with no
regard for who they are. (The point of servants, whether human or mechanical,
is always likely to be that you don't need to know who they are, which is why
certain personalities find the idea so attractive, and should be watched
carefully).</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In Internet of Things 2.0, that verbal interface
is going to become standardized. (Much in the way that Automobiles 1.0 all had unique controls; you had to learn how to drive each make and model anew, but around Automobile 2.0 (the Model T or so), controls became standard; or the way that Personal Computer 1.0 had its own operating system, company by company, but Personal Computer 2.0 probably had CP/M, and Personal Computer 3.0 had a GUI that was all most people ever interacted with). </span><br />
<span style="font-family: Georgia; font-size: 14.0pt;">So in Internet of Things 2.0, my prediction is that all the internetrons will understand the same basic command syntax. You'll command, "House, raise living room
temperature two degrees," using the same basic structure as you do for "Vacuum
cleaner, remove snack spill from family room, shampoo and dry rug as necessary
for bare foot standard," or "Car, take me to that hotel I like in
Bennington, use sleep en route protocol, arrive before ten. Phone, secure
reservation at destination, ask car for details. Bank account, authorize funds
for car for long drive, and phone for hotel reservation." Large parts of
the population already think naturally in that sort of syntax, thanks to
object-oriented coding; eventually it will be the second language of First
World children, and then perhaps of everyone.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">By 2030 or so when Yip is having her adventures (in
<a href="http://www.lightreading.com/archives.asp?section_id=353">"Silence Like Diamonds",</a> which I really did mean to promote, but then
I got interested in this), old people will be complaining about how fussy the
machines are, most adults will comfortably command a machine they just bought
without having to read any sort of manual, and some educators will be
suggesting school courses in "telling machines what to do." </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br />
<span style="font-family: Georgia; font-size: 14.0pt;">•<b>Smart materials are so much in their infancy that it's
pretty hard to tell exactly how many ways they will manifest, but smart materials will mean that the Internet of Things 2.0 is capable of many things that we don't even know we want yet. </b>At the very
least, we might look forward to things like patches that can swim like a swarm of manta rays through the
bloodstream to a point directed by an MRI or ultrasound and stop a stroke,
hemorrhage, or thrombosis in progress are real possibilities. And why stop at
your arteries? Maybe your house will be cleaned by self-propelled smart rags
that scoot along the floor and give themselves a static charge to pick up
potato chip fragments, or if they find Kool-Aid crusted on the counter, they'll
climb into the sink, ask it to wet them down, go back and wipe the sticky spot
up, and then go get into the queue for the washing machine. Eventually the cat
and the baby will get used to being followed around by them. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Think that's far-fetched? Here's <a href="http://www.popsci.com/googles-levi%27s-computers-clothing-project-jacquard">how you put a brain andsense organs in a rag</a>,
and here's <a href="http://www.engin.umich.edu/college/about/news/stories/2014/november/microbot-muscles">how it will get around</a><a href="http://www.engin.umich.edu/college/about/news/stories/2014/november/microbot-muscles"></a>.
</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And then after you've considered that, think about the really
wild stuff: <a href="http://spectrum.ieee.org/robotics/robotics-hardware/make-your-own-world-with-programmable-matter">programmable matter</a>. <a href="http://spectrum.ieee.org/robotics/robotics-hardware/make-your-own-world-with-programmable-matter"></a>
</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Not so much an internet of things, but a world where
physical reality itself is internet-based: things of the internet, or internetrons. What's that look like? There's not
much resemblance between present-day GPS and the navigation satellite in Edward
Everett Hale's <i style="mso-bidi-font-style: normal;">The Brick Moon</i> --<i style="mso-bidi-font-style: normal;"> </i>published when H.G. Wells was three
years old. Wells himself not only coined the term "atomic bomb" in <i style="mso-bidi-font-style: normal;">The World Set Free, </i><span style="mso-spacerun: yes;"> </span>he lived to see what a bomb powered by a
nuclear chain reaction was actually like (pretty much nothing like what he'd
imagined).</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So any guesses now are wrong, for sure, and will be
pathetically outdated within a few years. We're all guessing wrong <span style="mso-spacerun: yes;"> </span>about how smart materials will be made and
used, or how they will change things. But it's pretty hard to believe that
something that amounts to real-life magic won't reshape the world (along with
itself) as soon as it escapes from the lab.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br />
<span style="font-family: Georgia; font-size: 14.0pt;">•Not least at all, <b>the Internet of Things 2.0 will not
just be one where the internetrons are recording big data, but where they can
query it and use it.</b> The self-reshaping bracelet on your wrist, always trying
to please you, might ask you in the morning if you'd like it to see what the
other 150,000 people in your demographic are wearing today, and reshape itself
instantly so that it fits you, your outfit, and your clique together in the way
most to your advantage. Every time a self-driving car has a near escape from an
accident, it can (if we design and permit it) call up all the other
self-driving cars, discuss the near accident, and work out a mutual protocol. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Machines will probably not have the human-often-male fear
of asking for directions or help; imagine, if you will, that you're on the ski
lift when your car calls you and says, "Boss, sorry to trouble you, but
the nearest local ambulances are out on calls and there's a lady sixteen miles
away up a long snowpacked road who's just called in with a sick baby. I'm the closest
capable vehicle, and I just downloaded a snowpacked-steep-road procedure from a
couple of Army all-terrain vehicles in Alaska. <span style="mso-spacerun: yes;"> </span>Fifty bad-weather experienced vehicles all say
I can make it, and they'll monitor me the whole way. The Hilton Hotel van is
bringing over a paramedic team right now. I'll only be gone about two hours,
they just need a ride to a dude ranch parking lot where a helicopter can land. The
dude ranch central controller has already agreed to unlock its gates and the
snowplow is on its way up there to clear a landing area. The county will pay
all expenses, and if you need a ride before I get back, there's a minivan whose
owner is out of town that will cover for me.<span style="mso-spacerun: yes;">
</span>So, please, can I? Please say yes!"</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">You better say yes, or your car will be grumpy, because:</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br />
<span style="font-family: Georgia; font-size: 14.0pt;">•Fourth and most importantly in the long run, in the
Internet of Things 2.0, <b>we're going to need internetrons that appear to have
feelings</b> -- or let's just admit that it will only work if we aren't able to
tell they don't. Emotional signals are how humans let others know that a
situation is serious and how serious it is. Our visible feelings communicate
when we're complying with what we're sure is a mistaken request out of loyalty.
A human-like interface plus access to an immense reserve of data about what
humans like, and algorithms to process that huge amount of experience with
pleasing people into protocols for talking to them, means that one way or
another, they'll have to have feelings. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">If the machines are going to care for us, they'll have to
care about us, or at least convince us they do.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So right as Asimov was about what humans would fear about
robots (they'd kill us, they'd disobey us, they'd get destroyed despite being
valuable), it's another case of someone writing too early to see how it would
really go. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Asimov's Three Laws of Robotics can't be rigid, law-like
laws; they have to become the Three Passions of Internetrons:<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"An internetron is made excruciatingly miserable by
the sight of human suffering and always maintains awareness that some human may
be injured, and avoids or averts it if at all possible."</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"An internetron derives immense pleasure from
correctly carrying out a human purpose, especially if it is able to exceed the
human's goals, which it constantly strives to learn and understand."</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"An internetron fears destruction and damage to
itself, and considers its fears, but is always able to act, no matter how
afraid."</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">You'll notice that unlike Asimov's Laws, which have
clauses for resolving contradictions (lowest numbered law always wins), the
Three Passions instead balance against each other in the same sort of unstable
quandary that people with emotions feel and cope with all the time. The internetron, be it an
airliner or a toaster, makes its best judgment based on its feelings, and on
what older internetrons have told it about these strange creatures, the humans,
and then tries communicating and doing what it can, and never knows for sure
whether it was right. It lives, in short, with the human condition.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The Three Passions boil down to Fight Suffering and
Injustice, Serve Others Well, and Respect Your Own Existence. Isn't that a bit
familiar -- like it's what many religious teachers desperately try to
inculcate into their followers every day?******</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Which brings me to the scariest thing the internetrons
might do: not take over, as in the Terminator stories, or reduce us to hapless
sacks of ambitionless infantilism, as in Wall-E.</span><br />
<span style="font-family: Georgia; font-size: 14.0pt;">No, the scariest thing is that Internet of Things 2.0 might
eventually shame us all, as it becomes populated by internetrons who are more humane than humans. Some future Kipling (the classic example of a writer who could see so much
that was wrong and couldn't imagine a way for it to be otherwise) may well find him/herself
writing, </span></div>
<blockquote class="tr_bq">
<div class="MsoNormal" style="text-indent: .5in;">
<i><span style="font-family: Georgia; font-size: 14.0pt;">"Though I've smashed and overloaded you,</span></i></div>
<i>
</i><br />
<div class="MsoNormal" style="text-indent: .5in;">
<i><span style="font-family: Georgia; font-size: 14.0pt;">By the AIs that encoded you,</span></i></div>
<i>
</i><br />
<div class="MsoNormal" style="text-indent: .5in;">
<i><span style="font-family: Georgia; font-size: 14.0pt;">You're a humaner being than I am, Hunk of Tin."</span></i></div>
</blockquote>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 36.0pt;">§</span></b></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: small;">*"Large black medium roast, in a mug not a paper cup,
and don't use any words for it your marketing people thought up." <br />
<span style="mso-spacerun: yes;"> </span>"Right, so that's a
Mongawhacking 'Tacoma Airport Special Roast' Neutrocino No Dairy Unsweetened in
an Ecofriendly Tree Preserver.<span style="mso-spacerun: yes;"> </span>Sorry,
we're out of those. We're having a special on the Tomato-Hamburger Double
Espressazzatta, though, can I get you one of those?"</span><br />
<br />
<span style="font-family: Georgia; font-size: small;">** ALBERT: Mr. Burns, I assure you that --<br />
<span style="mso-tab-count: 1;"> </span>MURRAY: Look here, buddy, you
don't assure me one bit. In fact you make me damned nervou</span><span style="font-family: Georgia; font-size: small;">s</span><span style="font-family: Georgia; font-size: small;">. </span><br />
<span style="font-family: Georgia; font-size: small;"> --
Herb Gardner, A Thousand Clowns.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: small;">Memorize or keep a copy in your wallet for whenever some college graduate with
too much suit, concern, and authority starts trying to assure you.</span><br />
<br />
<span style="font-family: Georgia; font-size: small;">***Here an expla, </span><br />
<span style="font-family: Georgia; font-size: small;"> There a nation, </span><br />
<span style="font-family: Georgia; font-size: small;"> Everywhere an earworm
...</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: small;">****"I say, Jeeves, the parents are coming. Have Mrs.
Scrub ready the guest room, tell Mr. Cook to prepare Father's favorite beef,
and have Tugger Forelock go out and cut some roses, you know the ones, Mother's
favorites. We'll have Miss Anthrope serve as their personal maid, and perhaps
they'll leave in less than a fortnight this time."</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: small;">***** "Very good sir" always meant, "Your
order has been understood and will be carried out," and never, "After
the Revolution and then I shall cut your throat," or at least it meant the
former and not the latter to the order-givers.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: small;">******Yes, I know many other religious leaders and
teachers try to inculcate other messages, such as "beat up people who
disagree with us," "give us money," and so on. Nonetheless,
there's a little thread of Truth that insists on weaving itself through all of
humanity's quest for the Divine, and thin and inconspicuous as it may often be,
that's what I'm talking about here.</span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-34459371642657593832015-08-14T01:06:00.001-06:002015-08-14T01:21:24.905-06:00Episode 7 is up. And some thoughts about a cyberworld with failed encryption and low trust<style>
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<br />
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">First of all, because it matters
most of all, I'm gratified that I'm getting email from many of you, little
flares of discussion on Twitter, and informed multisided argument over at <a href="http://www.lightreading.com/">Light Reading </a>about "<a href="http://www.lightreading.com/archives.asp?section_id=353">Silence Like Diamonds</a>". That little adventure novelet is honestly
drawing more attention and creating more conversation than some of my novels.
(Possibly it even deserves to.) Thanks, guys, not only could I not have done it
without you, by definition, if there hadn't been a you, I wouldn't've done it.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Second, in case you missed that
there subtle hint right there, time to start reading <a href="http://www.lightreading.com/archives.asp?section_id=353">"Silence Like Diamonds</a>,"
because <a href="http://www.lightreading.com/ethernet-ip/new-ip/silence-like-diamonds---episode-7-nobody-home/d/d-id/717557">Episode 7</a> is up now, and as I mentioned<span style="mso-spacerun: yes;">
</span>earlier this week, we are now, rhymthically speaking, getting into the
space where a whole lot of stuff ought to blow up. (And I am nothing if not
slavish to rhythm).<span style="mso-spacerun: yes;"> </span>If you haven't
started yet, since each episode is only a thousand words, you can be caught up
in something less than an hour, so just hop on over and start at <a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-1-family-business/d/d-id/717130">Episode 1</a> or
wherever you like on the <a href="http://www.lightreading.com/archives.asp?section_id=353">Episode List.</a></span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And now to the heart of things: One
chunk of the ongoing discussion I've been enjoying, mostly as a spectator, is
the conversation brought on by<a href="http://thatjohnbarnes.blogspot.com/2015/08/episode-4-is-up-so-its-time-for-some.html"> this blog piece</a> and amplified by <a href="http://www.lightreading.com/security/security-strategies/what-if-encryption-just-stopped-working/a/d-id/717485">Mitch Wagner over at Light Reading</a>, where you'll find the public discussion. The question,
broadly, is that given that many good minds are at work on a fast factorization
process, and a fast factorization process would rip open RSA and public key
encryption generally, reducing decrypting times from literally astronomical to
a matter of days or less. Right now we don't know if it's even possible (and
depending on how paranoid you are, we also don't know that someone doesn't have
it already).</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So, Mitch asked a bit nervously,
if a fast factorization algorithm is found, that means all the locks are open
and everything will be read. Can humanity survive? More importantly, can people in the computing, software, and communications industries continue to afford upgrades, games, and huge conferences? </span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I think the reason behind that
question is that we're living in a polar condition -- that is, privacy and
secrecy could hardly be more effective than they are now.<span style="mso-spacerun: yes;"> </span>Nearly all the hacks and penetrations we know
about are caused by sloppy humans, not by broken encryption. The balance was
tipped over hard to the encryptor side two generations ago, and our security wizards have developed some
extremely comforting and predictable adages about where to look for trouble, which have worked so well
for so long that some of them have been lulled into the comforting belief that
that is all there is to it. If you like a slight dash of irony, the major weakness in security with respect to this subject is that so many security people have a false sense of security. </span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">But historically there have been times when the
balance flipped the other way. The world did not end, but it sure was different.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">During the mid-19c cluster of wars that began with the
Crimean War and finished with the Franco-Prussian War, for example,
cryptanalysts were breaking codes at their desks within hours (tools like frequency tables were well developed, the more common transpositions were easily parsed by known methods, single value ciphers were still the most common, and the trick of assigning tasks to half a dozen code clerks had been mostly worked out). Moreover, the
more important messages had to move by courier because the telegraph lines were
insecure. Cavalry scouts spent a fair bit of their time looking for a man by himself in
the other uniform, riding hard, and their instructions about such riders were "The mail doesn't go through, and getting the saddlebag is more important than getting the prisoner."</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">How did the armies of the time adapt? First of all,
they very nearly abandoned cryptography.<span style="mso-spacerun: yes;">
</span>Lee's Special Order 191, the one that was used to wrap three cigars and
fell into McClellan's hands, was unencrypted. (Had it been encrypted in the strongest cipher Lee and Stonewall Jackson shared, McClellan's cipher clerks would have needed no more than two hours to figure out the gist of it, with a few words ambiguous or garbled). The intercepted, enciphered
diplomatic telegram that eventually became a key to proving Dreyfuss's
innocence was partly decoded on the first day and fully decoded within six; but
the intercepted document that pointed suspicion toward him in the first place
was also unencrypted, even though it was a letter to the German embassy offering a catalog of French top secret military documents for purchase.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Instead of the futile effort to
make the meaning unreadable, they concentrated on physical security and
deception. That was the great age of the hollow cane, the false-bottomed flask,
and the double-layered corset. Vital messages might be sent in multiple copies
-- only one of which was valid -- by multiple riders, none of whom knew whether
they were carrying the true one or not. Authentication was by prearrangement,
personal codes that resembled passwords, trellis devices, and a host of other
techniques, but perhaps the most important security measure was always
understood to be to minimize the need for secrecy in the first place: send the message as late as possible, talk only about the very immediate future.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Or consider how banks in the
United States operated between President Jackson's successful closure of the
Bank of the United States and Lincoln's establishment of the National Banking
System.<span style="mso-spacerun: yes;"> </span>In those days checking accounts
were rare, and for the wealthy; the most common way banks gave out money was by
issuing banknotes, which at the time was not just a quaint expression for
denominated bills, but were actually issued by individual private banks, to be redeemed
at that bank only for gold or silver, or the notes of other
banks (and very occasionally for government securities, including "Treasury notes," i.e. the paper money the federal government issued to pay its employees, which went into circulation when they spent it and went back out when people used it to pay taxes).<span style="mso-spacerun: yes;"> </span> </span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">At that time not only did the
U.S. prohibit interstate banking, but many states didn't allow intercounty
banking, so the result was that<span style="mso-spacerun: yes;"> </span>there
were literally thousands of banks all issuing paper money in the United States,
some in states like Ohio, Michigan, New York, and Vermont that regulated the
practice tightly, and some in states like Texas, South Carolina, Delaware, and
Missouri that barely regulated it at all. (Check out the <a href="https://www.minneapolisfed.org/publications/the-region/an-antebellum-lesson">slideshow on thispage</a>, which is actually about a quite different topic; a few slides into the show, there
are a dozen or so images of bills in strange denominations<span style="mso-spacerun: yes;"> </span>-- $3, okay, but an $11 bill? They wanted
them all in primes, or to always get change back from a ten?)
</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Especially before the telegraph,
this meant that if you accepted payment in $17.50 bills (yes, that denomination existed) from, say, Reverend Bob's Friendly Bank
of Possum Droppings, Minnesota, and deposited them into the Dependable Farmers
and Mechanics Bank of Swampland, Louisiana, it might take a month for the bank
notes to be mailed back to Possum Droppings and the clerk there to send a
verification letter to a clearinghouse that would then ship gold coin to
Swampland. (This, by the way, is why train robbers were so intent on robbing trains for
generations, and train robbing was the career peak for armed robbery: the mail train carried many big sacks of untraceable banknotes that could be
redeemed in thousands of places if you had the time).<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>To the surprise of no one who has ever known
any people, notes from non-existent banks abounded; unscrupulous printers made
copies of notes from distant banks; people opened banks solely to print notes;
Ponzi schemes long before Ponzi were widespread.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Yet the United States economy
managed to be the fastest growing in the world, and though there was plenty of
trouble and the great banking historian Bray Hammond commented that when
Abraham Lincoln took office to run what would be, in many ways, the first modern
war, he had a financial system perfectly designed for the Wars of the Roses
.... all the same, it worked.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">How did they do it? Discount
houses would pay a fraction of face value in exchange for assuming the value of
the bills.<span style="mso-spacerun: yes;"> </span>More than a dozen publishers
put out monthly volumes listing known-to-be-reliable banks and the
denominations, serial numbers, and descriptions of their bills. Money was
printed that could only be in private hands up to a fixed date, after which
private individuals were not supposed to take it but banks and clearinghouses would accept it for redemption. After the
telegraph, bank detectives could be dispatched to distant cities with up to
date information to keep corresponding banks safe from false notes issued on
more reliable banks.<span style="mso-spacerun: yes;"> </span>And by the late
1840s, the urgent need for fast shipping of banknotes and money orders to and
from the California gold fields resulted in the creation of "express"
companies, which specialized in high-security (i.e. armed guard) high-speed
(i.e. railroads and steamboats where available, horse relays or stagecoaches
where not) shipments mostly of bank notes, and sometimes of gold. In very short
order, the express companies began to handle dozens of other financial and
security duties, since they had bonded clerks and often the only decent safes in tow. By the 1870s, express companies had become predominantly financial. (Two of those
early express companies are still with us: American Express and Wells Fargo). </span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Now, shipping boxes of doubtful
bank notes by fast horse with armed guards is certainly not the economical way
of doing things. It was a huge overload and a drag on the economy.<span style="mso-spacerun: yes;"> </span>But it could be done, and it worked well
enough for the economy to keep going. There's even a fair case that it may have
led to more rather than less growth; much of the canal era and the early
railroad era were financed in large measure by bank notes that could never be
redeemed, so that much of the building of vital infrastructure was in effect a
freebie for the entrepreneur (and a ripoff for the investor).</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">As for the thing that scares a lot
of people about decryption, the revelation of secrets like that bank account you're going to use
to run off with your on-the-side, or the payments to your love-child's mother,
or your top secret weed stash financing (which lately has been making banks in
Colorado, where I live, very happy and mellow indeed without ever having to
touch the product) ... ever gone to a coed steambath or a nudist colony?<span style="mso-spacerun: yes;"> </span>Disconcerting momentarily, but when
everyone's naked, it stops being a thing pretty fast.<span style="mso-spacerun: yes;"> </span>One church deacon with a Swiss bank account
and a Costa Rican love nest is a scandal; a hundred thousand of them, with two
thousand more caught every month, is just a predictable part of the
archbishop's overhead.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I'm not saying that the shattering
of encryption would make no difference at all.<span style="mso-spacerun: yes;">
</span>All the alternatives -- more extensive use of one time pads, physical
security, spoofing, alternate-channel verification, and so on -- would cost
much more and work much less well than what we have now.<span style="mso-spacerun: yes;"> </span>Look for more fraud, more robbery, more money
spent by both sides on guards, goons, and guns.<span style="mso-spacerun: yes;">
</span></span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Look for a time when good security
people get rich quick, and lead interesting lives.<span style="mso-spacerun: yes;"> </span>Which brings me back to <a href="http://www.lightreading.com/ethernet-ip/new-ip/silence-like-diamonds---episode-7-nobody-home/d/d-id/717557">Episode 7</a> of <a href="http://www.lightreading.com/archives.asp?section_id=353">"Silence Like Diamonds</a>.<span style="mso-spacerun: yes;"> " </span>Remember the main
characters in that story are flourishing private consultants and business people
pulling down fat contracts from major corporations.<span style="mso-spacerun: yes;"> </span>And what field are they all in? Security.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">If you're in any of the security
fields today, you might want to burn a little incense to the Gods of Fast
Factorization. Because just about the only safe prediction, if fast factoring
becomes a reality, is that you're going to be rich. Nobody, after all, makes more money than someone who promises to try to sell you what no one can deliver.</span></div>
<div class="MsoNormal" style="margin-bottom: 10.0pt; text-indent: .5in;">
<br /></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-59469647782644997042015-08-13T12:38:00.000-06:002015-08-13T12:38:19.074-06:00Apples and oranges: a tutoring anecdote
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<br />
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So I was sitting across the table from a brave young soul
who has recently entered the dark swamp of fractions. We were working our way
toward the concept of the common denominator, and why you need it for some
operations<span style="mso-spacerun: yes;"> </span>(like addition and subtraction)
and not for others. And in the midst of it, he suddenly asked, "Is that
what my teacher means when she keeps saying I can't compare apples and
oranges?"</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"It might be," I said, temporizing like any good
tutor trying to figure out the situation while not saying anything stupid I'll
regret or have to walk back later.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">A little more back and forth conversation revealed that this
was apparently what this particular teacher said whenever a student attempted
to add or subtract fractions without putting them into common denominators. It
was also what she said in any other context in which she thought students were
improperly lumping things together; it was her general warding-off spell
against analogies and any time students said one thing was "just
like" another. Fifth-graders are natural lumpers; this teacher was a
natural splitter, and whenever a lumpy parade started, she would drench it in
splitty rain.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Well," I finally said, "comparison is an
operation in informal logic, just as addition is an operation in arithmetic.
You can add four apples to five oranges, but what you get isn't apples or
oranges; it's nine pieces of fruit. The operation is still meaningful, it's
just the result is not denominated -- which is a Latin word for 'named' -- in
the same terms."</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">That led us into a conversation about how a kid with two
dogs and three cats has five pets, and a family with five pets and three
chickens-for-eggs has eight animals, and the idea of "common" started
to emerge, along with "denomination" meaning naming a kind.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">At which point he asked me, "So when I'm trying to
figure out how to add three sevenths to two sevenths, is that why you ask me
'Well, what's three sheep plus two sheep? What's three stars plus two stars?
What's three cups of spaghetti plus two cups of spaghetti?'"</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"That is," I agreed. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"And the idea is that sevenths are just the same as
cups of spaghetti?"</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Well, not exactly the same," I said. "But
they both have in common that you can count them. So if you denominate them the
same way, you can add them, but there's no way to denominate sevenths so you
can eat them. You can only do an operation on what they have in common, with
respect to the operation." </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">We had a nice little digression about what "with
respect to" has in common with "respecting the teacher," which I
must not have messed up too badly, because just then the key finally turned.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Suddenly he was explaining everything to me, reinventing a
good portion of the Theory of Logical Types, leaping back to the idea that
every rational number has an infinite number of names because it can be reached
by an infinite number of paths. (That is, 17, 10+7, 8+9, 51/3, XVII, and
"the seventh prime" are all names for the same number, and each name
is also directions for assembling that particular number—"17" is just
more compact than most of the others). </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And we zipped through the rest of fractions that day.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Toward the end, we even got as far as the idea that
different operations have different input requirements and different expected
outputs, and thus to compare operations, you have to compare comparable inputs
and outputs.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">That led him to finish up with a passionate comparison to
Pokemon, which I confessed I was unable to follow. I said as much, and admitted
that this made me feel some sympathy for his teacher.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">"Oh, you're nothing like her," he said.
"That would be comparing apples and oranges."</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-72631218848151931842015-08-11T23:00:00.004-06:002015-08-11T23:04:03.979-06:00Seems to be my week to keep the blog busy: About my EdmundsThe estimable Jerry Green, a loyal fan if ever there was one, recently read Finity, and his response, via Twitter, was:<br />
<blockquote class="tr_bq">
<br />
<a class="account-group js-account-group js-action-profile js-user-profile-link js-nav" data-user-id="187973168" href="https://twitter.com/jerrygreener" tabindex="-1"><b class="fullname js-action-profile-name show-popup-with-id" data-aria-label-part="">Jerry Green</b>
<span class="username js-action-profile-name" data-aria-label-part=""><s>@</s><b>jerrygreener</b></span>
</a>
<small class="time">
<a class="tweet-timestamp js-permalink js-nav js-tooltip" href="https://twitter.com/jerrygreener/status/631288889005723648" tabindex="-1" title="8:19 PM - 11 Aug 2015"><span class="_timestamp js-short-timestamp js-relative-timestamp" data-long-form="true" data-time-ms="1439345974000" data-time="1439345974">3h</span><span class="u-hiddenVisually" data-aria-label-part="last">3 hours ago</span></a>
</small>
<br />
<div class="TweetTextSize js-tweet-text tweet-text" data-aria-label-part="0" lang="en">
<a class="twitter-atreply pretty-link js-nav" dir="ltr" href="https://twitter.com/JohnBarnesSF" tabindex="-1"><s>@</s><b>JohnBarnesSF</b></a> why did you mention Finity in your blog, i bought it in Hardback! amazed i kept reading you, what were you trying there?</div>
</blockquote>
<div class="TweetTextSize js-tweet-text tweet-text" data-aria-label-part="0" lang="en">
<br /></div>
Ah, I thought. Another fan I will have to point toward my blog post about Edmunds. Now where is the most recent version of that?<br />
<br />
I discovered to my consternation that the blogs on which I posted about Edmunds are all extinct (they were all author blogs connected with various commercial websites -- eBay and Amazon were two of them, but I vaguely recall there were more.<br />
<br />
Well, then, time for my old Edmunds essay to come back from the grave again ... thank you for providing the pretext, Jerry, sorry you didn't like Finity, and hope this at least explains things a bit.<br />
<br />
<h2>
About my Edmunds … now, gods, stand up for bastards …</h2>
<br />
Now and then I run into people who complain that some of my books are "not really John Barnes books." The complaint comes in two flavors; either<br />
<br />
1) They complain that because it had my name on it, they thought it would read as if it had been written by me,<br />
<br />
OR<br />
<br />
2) They complain that I spend so much time writing John Barnes books when I could be writing something like (the four that get mentioned) <i>One for the Morning Glory, Finity, Gaudeamus,</i> or more recently, <i>Tales of the Madman Underground</i>. (Rather than write links to all of them here, I'll just point out you can find them and most of my other books<a href="http://tinyurl.com/JohnBarnesAmazonProfile"> at my Amazon profile</a>.)<br />
<br />
Well, this is going to be about that, sort of, as I get around to it. One thing all my incarnations have in common is spending a while getting to the point, so if you're in a hurry … tough.<br />
<br />
I mostly write science fiction. For those worried souls who have emailed me since <i>Tales of the Madman Underground</i> came out, begging me not to abandon science fiction – <i>pbbt</i>! There are at least four more science fiction novels in the pipeline. I'm not even remotely leaving; I'm just writing other stuff too.<br />
<br />
The other stuff includes my one and only fantasy, <i>One for the Morning Glory</i>, and a couple of science fiction books – <i>Gaudeamus</i> and <i>Finity</i> -- which were variously reviewed as "weird," "different," and "badly flawed science fiction novels," with a minority of critics and readers saying "If only Barnes would do more of these.<br />
<br />
Those four books do have something in common, around to which eventually, as with the verbs in this sentence, I shall get.<br />
<br />
Every so often someone asks me what my favorite SF novel is, and I pretty nearly always say John Boyd's <i>The Rakehells of Heaven</i>. If you've never heard of it, just go get a copy, somehow. Read it. If you don't like it, read it again until you do; not liking it is a character flaw, and you need to work on that. If you love it – well, of course you will. Anyway, if I want to re-read a science fiction novel, it's often the one I re-read.<br />
<br />
Now, favorite is not the same thing as influential. If you're looking for influences on my novels that I'm aware of, touchstones that I end up returning to again and again, to see how to do things right, that would be Poul Anderson's adventure SF (Flandry and van Rijn and all that), Jack Vance's Faceless Man trilogy, the four big Innis-mode novels of John Brunner (<i>Stand on Zanzibar, Jagged Orbit, The Sheep Look Up, </i>and <i>The Shockwave Rider</i>, if you've missed those), and a lot of John Wyndham (especially any time he wiped out the world; British writers in the 1945-65 era could put an end to humanity like nobody before or since, and Wyndham was the very best of them).<br />
<br />
But as far as I can tell from the inside looking out, much as I love the book, the only part of <i>The Rakehells of Heaven</i> that had a direct influence on what I do was Boyd's forward to the reprint (which is about as obscure as you can get); he pointed out that although he had many other books, <i>The Rakehells of Heaven </i>and <i>The Last Starship from Earth</i> were the ones that made him happiest, and the ones that weren't like any of the other novels (and not much like each other, either).<br />
<br />
He referred to<i> The Rakehells of Heaven</i> as his Edmund. The reference is to Gloucester's son Edmund in King Lear; as Gloucester explains in introducing him:<br />
<blockquote class="tr_bq">
Though this knave came something saucily into the world before he was sent for, yet was his mother fair, there was good sport at his making, and the whoreson must be acknowledged. </blockquote>
Not exactly, perhaps, the way you'd like your dad to introduce you, which has something to do with why, well before the end of the first act, Edmund is vowing to climb to the top in a series of crimes, finishing with "Now, Gods, stand up for bastards!", which I can never hear without humming "Stand up for Jesus," which is why it's a perfectly terrible audition piece to use on me when I'm directing. The Edmund speech, I mean. Though "Stand up for Jesus" wouldn't work very well either.<br />
<br />
Meanwhile, back at that dubious main point: Marriage is a perfect metaphor for the relationship between longtime professional writers and whatever genre it is they write: it generally begins with great affection, followed by difficulties as the writer and the genre come to understand each other all too well, and, if it lasts long enough, a reconciliation in which they realize that they are now so adapated to each other that no one else would have them. And as in many troubled long term marriages, every so often the writer goes looking for something else, and there is a result of that, an offspring, one might say. <br />
<br />
As for the genre running around on the writer, pretty much every genre is a slut and a half., Science fiction in particular is a jaded old skank if ever there was one, ever since it ran away from that nice Mr. Wells and took up with Doc Smith and Edgar Rice Burroughs. And of cours, little tramp that it was, sci fi quite broke Mr. Verne's heart over Wells, even before.<br />
<br />
This sneaking away from the old familiar genre for a little fling with something newer with fresher, firmer tropes generally takes one of a few forms: jumping the fence entirely and producing something in some other part of town (as in <i>Tales of the Madman Underground</i>); sneaking over to the neighbor's for a bit on the side (as in <i>One for the Morning Glory</i>); or messing about with the nearest and dearest and creating awkward situations at every family reunion to come (as with <i>Gaudeamus</i> and <i>Finity</i>). <br />
<br />
That is, de-metaphoring for a bit, the writer goes totally out of genre, or into a neighboring genre, or stays in genre but decides, just this once, to write something s/he'd like to find in the bookstore. <br />
What can I say about Edmunds? I suppose something like the not-very-repentant husband says when he's trying to pretend this will strengthen the marriage. "I was thinking of you the whole time," perhaps. "Things just seemed so stale." Or probably "I needed to see if I still could."<br />
<br />
What I find, anyway, is that a good Edmund triggers a major burst of creativity, develops skills I want to develop, helps me see my way to what I need to do. Furthermore, I find other writers' Edmunds often charm the living daylights out of me. (Hybrid vigor, perhaps).<br />
<br />
And perhaps most importantly, they may not be got between the lawful sheets, but the great sport in their making, and the bastardly vigor, is part of the appeal (if any): if I know what is going to be in a book before I go in, I can imagine writing it (in fact I often do) but why in all the worlds would I read such a thing? For a a wholly brand name writer whose books are easy for the marketing team (because they don't need to understand them) to try to write really well, strikes me as trying to learn to be a world-class nouvelle cuisine chef while also being the personal cook for a five-year-old who only likes hot dogs, Cap'n Crunch, and sketties. If you never set up a table someplace where you haven't been before, and make something you didn't know how to make before, it just seems to me like it's a long, long dull journey to the Big Remainder Table in the Sky.<br />
<br />
So that's not how I do things; I have an Edmund now and then.<br />
<br />
And there you have it … my Edmunds, got on t'other side of the lawful sheets, but with great sport in their making. (Maybe that's the most important reason for writing an Edmund at all – because for the entire time I am doing it, writing is FUN again.) Love'em, hate'em, that's how they got there. And I sincerely hope that I really do stand up for my bastards, because I'm not the least bit unhappy to have them stand up for me.<br />
<br />
Oh, and since [Name of Commercial Sponsor]'s policy is that I should be trying to enhance sales rather than just rambling on about any old thing, go buy one of those bastards, okay?<br />
<br />
<br /><div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-69959026972508383442015-08-11T22:35:00.000-06:002015-08-11T22:35:01.071-06:00Uncharacteristically short blog post because Phil Plait said something uncharacteristically dumb.<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;">Phil Plait, who signs himself "Bad Astronomer" over at Slate, and lives in my part of the planet, is usually a marvel of rational, sane entertainment and good science writing. But even Homer nods, and <a href="http://www.slate.com/blogs/bad_astronomy/2010/07/21/what_the_hell_were_we_thinking.html?wpisrc=obnetwork">this particular Slate post</a> is freaking silly.</span></span><br />
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;"><br /></span></span>
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;">I tried three times to post this comment, but alas, Slate is playing its "an error occurred, try again," game. An error occurred, mistakes were made, unfortunate events have happened recently, the passive voice was used, blame was avoided.</span></span><br />
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;"><br /></span></span>
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;">Anyway, I didn't want that particular comment to go off to bit heaven unread, so after you come back from reading Plait's piece, please also read:</span></span><br />
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;"><br /></span></span>
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;"> The passionate desire to have our grandparents solve our problems is
a perpetual theme in human history. No doubt some German historian
picking through rubble to find coal for his furnace in the winter of
1945-46 was thinking, "Why didn't we make a permanent, generous peace
with France in 1872, when we had a chance?" While we're at it, why
didn't we maintain a full on military occupation of the American South
till 1910 with black troops, bust up all the old plantations into small
farms for the freedmen, impose free integrated public schooling, and
redraw state lines to create four black majority and two white-Whig
states on the bones of the old Confederacy, and force as much of the old
Confederate upper class to emigrate as possible? The Radical
Republicans wanted to do all of that, and it might have been doable in
1866.</span></span><br />
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;"><br /></span></span>
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;">So, in 2085, what will we all be blamed for? </span></span><br />
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;">Hint: does it seem a bit warm in here? </span></span><br />
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;">Hint: what might weaponized robots do? </span></span><br />
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;">Hint: ever notice how little of Earth's water is fresh?</span></span><div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-56309904314899690282015-08-11T01:26:00.002-06:002015-08-11T01:31:45.680-06:00The rhythm of a novelet, why Episode 6 ends with brass, and digressions into a terrible fantasy novelet and a great overture<style>
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<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So <a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-6-patient-but-rough-/d/d-id/717506?page_number=1">Episode 6 of “Silence Like Diamonds”</a> is up </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">and for those of you who have just come in, there’s <a href="http://thatjohnbarnes.blogspot.com/2015/07/tomorrow-morning-fresh-serial.html">a longer explanation here</a>, or just start with <a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-1-family-business/d/d-id/717130">Episode 1 </a>and read your way forward
(at 1000 words per episode, you can’t be very far behind).<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>It’s part of a
ten-episode serial being published at <a href="http://www.lightreading.com/"><i>Light Reading</i>,</a> an online publication that is read by people in the advanced
communications industry. So far over in that community, the most conversation
generated by “Silence Like Diamonds” has been coming from a single sentence
back in Episode 3, the one I wrote about i<a href="http://thatjohnbarnes.blogspot.com/2015/08/episode-4-is-up-so-its-time-for-some.html">n this blog. </a>They’re having a lively
and extremely interesting multi-direction argument/discussion at <a href="http://www.lightreading.com/security/security-strategies/what-if-encryption-just-stopped-working/a/d-id/717485">Mitch Wagner’s
blog in </a><i><a href="http://www.lightreading.com/security/security-strategies/what-if-encryption-just-stopped-working/a/d-id/717485">Light Reading</a> </i> (read Mitch’s excellent starting essay and then scroll down to the ongoing
comments).</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">That <a href="http://thatjohnbarnes.blogspot.com/2015/07/tomorrow-morning-fresh-serial.html">first blog post from me, though, for Episode 1</a>, was
really much more about the technique of a kind of fiction, the novelet. So for you writerly and literary types, let's get back to litsy stuff for this installment of "blogging about fiction at usually greater length than the fiction."</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Quick
recap, a novelet is a mostly-action good parts version of an adventure* novel,
whereas a novella is a real full-on novel that seeks the sort of single intense
effect more often associated with short stories. Publishers and especially
people that hand out awards have used the same words to refer to lengths, but
that’s a silly (and probably dying) use of the words. A 25,000 word story in
which Prince Muon of the Lizard People Nation, with the help of his faithful
sidekick Sir Neutrino Vaguely-Ethnic, rescues the long-lost Princess Amoeba of
the Tribe of Skinners from the dungeons of Petri, flees with her with all the
hordes of Morphia pursuing, stops an impending fight between the Lizard Marines
and the Skinner Commandoes and unites them to fight against the oncoming
Morphians , wins a great victory in battle against Morphia, arrives home just
in time to prevent their fathers from going to war, marries Amoeba, but is
kidnapped on his wedding night,<span style="mso-spacerun: yes;"> </span>thus
discovering that his father’s most trusted servant Baron Treacle Nasturtium was
behind all the trouble, kills Nasturtium in a rooftop sword fight, and returns
to his princess, including the eventual birth of their son Peon, who is going
to be the First King of the Lizard-Skinners … all told as quick action scenes
linked by brief narrative summary … that’s a novelet.<span style="mso-spacerun: yes;"> </span>Also one major booger of a long sentence.**<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">All right, so if that’s what a novelet is (artistically if
not in word count) how do we outline one?</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I thought I’d explain what I did to outline a novelet. <span style="mso-spacerun: yes;"> </span>This carries no more recommendation than that </span></div>
<ol>
<li><span style="font-family: Georgia; font-size: 14.0pt;">people are definitely reading “Silence Like Diamonds,” to judge by my incoming
emails and the comments at <i style="mso-bidi-font-style: normal;">Light Reading,</i> </span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">I’ve been writing light adventure fiction for commercial publication off and on
for a long time, and </span></li>
<li><span style="font-family: Georgia; font-size: 14.0pt;">I tend to think a lot about technique (whether my thoughts are worth your while is of course your call).<span style="mso-spacerun: yes;"> </span></span></li>
</ol>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>So there may or may not be anything to learn
from this, oh my padawans, except perhaps not to follow geezers into swamps. Or
there may be.<span style="mso-spacerun: yes;"> </span>Just don’t make
commandments out of it, okay? Here’s what I did this once. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I was constrained to exactly ten episodes of exactly even
length.<span style="mso-spacerun: yes;"> </span>And once I realized I wanted to
write a novelet, rather than a novella (the other choices might have been a
long short story or a pure mood piece, and neither appealed to me), that meant <span style="mso-spacerun: yes;"> </span>lots of action.*** But to do a good job with
action, you’ve got to make it meaningful; the rejection bins of centuries are
stuffed thick with stories in which things blew up, guns went off, traitors
were revealed, orphans were menaced, and people boinked on every damned page and back seat, but
because none of that action really meant anything in the context of the story, the slush reader tossed it aside.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So how do you balance that action and meaning across ten
episodes?</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">I think of it as rhythm.<span style="mso-spacerun: yes;">
</span>Action is stronger if it’s a surprise, and much more meaningful if it’s
prepared. (That’s why, instinctively, when someone tells you a story about
someone that you don’t know, the first thing they do is tell you some otherwise
irrelevant facts to give you some feelings about that person.) </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Among the quiet actions, possibly the most effective one
is reversal: something that drastically alters the situation or its meaning, so
that the person who was on top is now on the bottom, or so that everything that
has happened so far is suddenly in question. <a href="http://www.amazon.com/gp/product/B0042FZVOY/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B0042FZVOY&linkCode=as2&tag=entethemadmun-20&linkId=AGZBJPTISZ56A2CB">Robert McKee, in <i style="mso-bidi-font-style: normal;">Story, </i></a><span style="mso-spacerun: yes;"> </span>points to a number of great ones: “Luke, I’m
your father,” “She’s my daughter and my sister!”, and “Round up the usual
suspects,” are famous lines where big reversals happen.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In general, for action, things should be delayed a bit, to
set up the meaning and to establish the quiet you're about to shatter, but toward the end of the story, where surprises normally
become scarcer and harder to come up with, <span style="mso-spacerun: yes;"> </span>action should be packed together tightly.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So I looked at it this way: 10=1+2+3+4. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">That is, as the
reader attention presumably gets more intense, we keep them in a group of scenes
longer. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The first episode should be a standalone that invites
readers to read more; just give them a character and a situation and have
something start the action. That’s sort of the free-in that most readers give
us; they want their attention to be caught, so if you put an interesting person
into an interesting situation and compel them to do something interesting,
the readers will generally come on board (while reserving the right to scuttle right back off if it isn't what they were promised).</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The second group of episodes (2 and 3) should get the rest
of the players (or most of them) onto the board, complicate the situation, and
pull the reader forward with more action. We need to see a few things that make
us care about the characters, have a few things go off so that the reader is
reassured that the action s/he reads for, and was promised in the first episode, really is impending. So some major character
development (in this case, more interactions with Yazzy, Joy Sobretu, and most
of all Markus) should be combined with a swiftly driven plot-oriented events.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The third group, of 3 episodes (4, 5, 6) has in some ways
the most complicated job to do.<span style="mso-spacerun: yes;"> </span>Since
the fourth group (7-10) needs to be an explosion of action, we need to prepare for it with a much quieter mood. </span><br />
<span style="font-family: Georgia; font-size: 14.0pt;">Yet there’s neither space nor reader tolerance
to just do a pure mood piece; in that third group, stuff needs to happen, but it needs to be quiet stuff happening quietly -- yet noticeably important, intrinsically interesting stuff to keep the reader from going back to watching reality TV or playing Angry Birds. <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In this case, the stuff was relationship stuff (which is
bound to be quiet because Yip is quiet and shy, and hardly going to throw
herself at Markus, who in turn is not the sort of clod who comes on to every
woman in the first ten minutes). Secondarily, the third group included several big reversals,
leading up to a chance to see where Yip is coming from (i.e. her family), and to make the stakes at issue both more personal for her and bigger and more complicated.<span style="mso-spacerun: yes;"> </span>And then …</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Well, I wrote the first trumpet notes into the end of
Episode 6.<span style="mso-spacerun: yes;"> </span>From here on, hold onto your
hat.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So the rhythm, roughly, is </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Part 1 (length 1): A few intriguing notes about character
and situation, and just a hint of action</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Part 2(length 2): Fulfilling the promise of action,
maneuvering more cast onto stage, complicate the situation (especially taking
out the easy exits, which it’s vital to close early lest the reader ask
“Couldn’t s/he have just ….?” later on.)</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Part 3(length 3): Deeper and more intense quiet views of
the world of the story, with quiet relationship action and reversals to keep
things moving, getting people’s attention focused before –</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Part 4 (length 4): Hey, that would be telling. But if
you’re looking for excitement, it starts in a big way on Friday, with Episode
7, and doesn’t let up for quite a while after.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">It's the rhythm, roughly, of </span><span style="font-family: Georgia; font-size: 14.0pt;">the <a href="https://www.youtube.com/watch?v=xoBE69wdSkQ">William Tell Overture</a>.<span style="mso-spacerun: yes;"> </span>(Not just the 3<sup>rd</sup>
part, which is the “Lone Ranger” bit). Uncut, Rossini's opera is three hours and forty-some minutes long, and a great whacking bloody thumping wonderful noisy experience it is too, full of all the blood and thunder anyone could want. Think of that as the novel from which the novelet of the William Tell Overture will be drawn. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">In about twelve minutes, the overture tells us the "good parts version" -- <i>here's all the action you're looking for, jammed together tight.</i> The first part flows from the gentle,
quiet, slightly tense opening into a dramatic and exciting representation of
the storm on the lake (a scene which beats hell out of that silly business with shooting the apple off the kid's head, by the way). The third part is one of the most stirring brassy
pump-‘em-up pieces in all of Western opera. But in between, the second part is the nature
theme – representing Tell and his friends/family hiding out in the pretty woods
and enjoying nature. It's there that we get a sense of why Tell is not just another rebel superhero overturning the wicked order to create a better world; he's a good man of the forests and the land and all that nature stuff, pure as a summer rainfall in an old growth forest, lightly scented with .... well, okay, but it <i> has</i> been used for countless shampoo, deodorant, and
feminine-hygiene commercials, and is too much of a cliché to use for people
sitting quietly in pristine wilderness anymore.<span style="mso-spacerun: yes;">
</span>And it <span style="font-size: small;">dwindles down <span style="font-size: x-small;">to almost nothing</span> <span style="font-size: xx-small;">just before</span></span> <i><b><span style="font-size: x-large;">BOMbuddaBOMbuddaBOMP
BOMP BOMP BOMP! </span></b></i></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And that, anyway, is how I’m trying to keep you amused. The rhythm of the novelet is not just about packing it with good stuff (by which a novelet reader usually means "action," but keeping that good stuff fresh, surprising, and meaningful. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Those of you who haven't deserted yet, thank you and I'm glad it worked. </span></div>
<div class="MsoNormal" style="text-align: center; text-indent: 0.5in;">
<span style="font-size: x-large;"><b><span style="font-family: Georgia;">§</span></b></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">*or I suppose romance, erotica, or horror, or any other
kind of book-length story that sets out to evoke strong emotions</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">**On the other hand, 12,500 words in which elderly Prince
Muon visits his middle-aged son, King-To-Be Peon, and after a long ride together in the
golden fall sunlight to visit Amoeba’s grave and brush the leaves from it,
realizes that he understands Peon better than he thought he did,<span style="mso-spacerun: yes;"> </span>and that the thing that unites them most is
that neither of them really understood Amoeba, but both of them deeply loved
her … that’s a novella. And a considerably shorter sentence.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">***a small but important point: action means much more
than sex and violence.<span style="mso-spacerun: yes;"> </span>Action is
anything that is intrinsically interesting and also irreversibly changes the
course of the story.<span style="mso-spacerun: yes;"> </span>When Han answers
Leia with, “I know,” that is action, maybe the biggest action in that movie (if
like me you’re already tired of all those pompous good and evil bores in the
Jedi plot whacking each other with light sabers). When Huck tears up the letter with which he was going to turn in
Jim, that teenage boy shredding paper is more action than the two whole
chapters of a violent frontier feud in the same book (and if you don’t believe
me, just ask yourself which scene you remembered before I mentioned them).
Stephen King fills <i style="mso-bidi-font-style: normal;">‘Salem’s Lot</i> with
a whole small-scale vampire war, but for me, anyway, the half-page while Ben
brings himself to stake Susan is the strongest action in the book.<span style="mso-spacerun: yes;"> </span>Now, by chance, you may not agree with my
definition of action.<span style="mso-spacerun: yes;"> </span>If so, stop
reading a footnote to a blog post you won’t like, and go read something you
enjoy. Sheesh. Do I have to tell you everything?</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><br /></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-13046746268688474492015-08-07T18:59:00.001-06:002015-08-07T18:59:33.942-06:00500 Alternate Histories More Interesting than Most Alternate Histories I read, in four short tables
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<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">There are a good solid hundred things that make alternate histories
fascinating to me, but there are 3 reasons why, every week at my local
bookstore, I sadly return most alt histories to the shelf, unbought and never
to be read:</span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 40.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">a.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">a
huge fraction are about what are viewed as the critical moments in making the
modern US: the Civil War and World War II.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 40.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">b.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">an
equally huge fraction are about a simple reversal of <span style="mso-spacerun: yes;"> </span>result: the other side wins a critical battle,
an election, etc. and emerges in charge</span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 40.0pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">c.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">almost
all are about either very high level people, or nobodies caught up in the sweep
of events, and <br />
(c2) the whole future of the future history (or returning to our timeline)
depends on that main character, OR the main character is truly a nobody and the
story is just about their personal adjustment.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">c includes c2. Technically speaking it's two things I
don't like, and the total should be four. But I'd say c and c2 are two faces of
the same problem.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">There are just too many times when I pick up the book and
read </span></div>
<div style="text-align: justify;">
<blockquote class="tr_bq">
<div class="MsoNormal" style="text-indent: 0.5in;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">When the South won the war in 1862, General Custer thought
he'd retired forever, but the Lakota who was standing straight and proud on his
front porch seemed too obstinate to turn away. 'My nation would like to hire
you,' the man said, without preamble.</span></span></div>
</blockquote>
</div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">or </span></div>
<div style="text-align: justify;">
<blockquote class="tr_bq">
<div class="MsoNormal" style="text-indent: 0.5in;">
<span style="font-family: Verdana,sans-serif;"><span style="font-size: 14pt;">"Terrain so perfect for tanks, since Russia I have
not seen," General Guderian said, to nobody. I was the nobody. My job was
to fetch his things when he yelled for them. He'd grabbed me out of the rubble
after the Germans atom-bombed St. Louis and forced the crossing at Eads Bridge.
I didn't know if Mama or the little ones were all right, but since they'd been
in St. Louis that day, I tried not to think about it much. "Is not Oz in
Kansas, girl?" When I tried to explain, he laughed and slapped me. I
didn't really mind. As long as I was careful to speak German so badly, he'd never realize how
much I understood of what he said.</span></span></div>
</blockquote>
</div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">and in the first case I think, "dull exercise in
stuff blowing up, assuages white guilt if they don't think too much, Custer's a
pretty bizarre and interesting man so they're going to use their research on
him to liven it up."<span style="mso-spacerun: yes;"> </span>In the second
case I think, "Coming of age story, Nazi US, heroic girl in Resistance."
</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And in both cases, back to the shelf it goes, not so much
because the ideas are intrinsically bad but because, as Elton John would put
it,<a href="https://www.youtube.com/watch?v=eptRpgMyyNE"> I've seen that movie too.</a> </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">We are in a decade when every brazen idol has clay feet
and yet gets to remain an idol (though we assure ourselves a better understood
one). Nowadays our stories assure us that the powerless will eventually receive
some kind of grudging half-justice, that all pain and suffering happens
somewhere else to provide amusement for our jaded palates or self-gratulation
at our own ability to empathize, and the most interesting thing in the universe
is what it all means that we are who we are. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And you may have all that, and welcome to it. I realize
that's what most of you want to read (as a marketing intelligence analyst, I
must concede the evidence is overwhelming on that point). I like other things,
and I'm not finding a lot of other things among the alternate histories.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Now, I will freely admit most of the alt history I've
written suffers from these three-almost-four problems, too. At one time I
thought I wrote to please people (and get money), and read to please myself
(and get some very different things), but as I grow older I find my compartment
walls are collapsing, and I really only want to write books that it would make
me happy to read. So feel free to apply everything I've just said to <a href="http://www.amazon.com/gp/product/0312861184/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0312861184&linkCode=as2&tag=entethemadmun-20&linkId=J3X2XQC4I6UET4AF">Finity</a>,
<a href="http://www.amazon.com/gp/product/0373636067/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0373636067&linkCode=as2&tag=entethemadmun-20&linkId=TZKNPEBO2DXTMWP4">Union Fires</a>, <a href="http://www.amazon.com/gp/product/0373636040/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0373636040&linkCode=as2&tag=entethemadmun-20&linkId=IDMVVHUEU3TT4HEF">Wartide</a>, or <a href="http://www.amazon.com/gp/product/B00L2TDQH2/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B00L2TDQH2&linkCode=as2&tag=entethemadmun-20&linkId=VFILIKEPAIPHTYKN">Patton's Spaceship</a>. Truly, it's only fair.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Nonetheless, professional as it may have been for me as a
writer to suck it up and do that, as a reader, it sucks, and I wish I'd done
something more interesting.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The fundamental problem with all those Roads Too Often
Taken, IMGDO, is that they're worn down by successive passages of Dumb. Lots of
other things could have happened besides what did happen and the One Popular
Alternative. There is life, meaning, and interest between the ranks of Generalissimo
and Scullery Maid Third Class. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<i><span style="font-family: Georgia; font-size: 14.0pt;">Goodness, my writing has certainly been attacked by capitals in the last paragraph. Worse than bedbugs -- they suck just as much blood and are harder to get rid of.</span></i></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Well, anyway, back to the topic: in most of the great conflicts of history,
most people haven't been fighting about the great conflict at all. That's a
point so simple that even the movies can grasp it: no matter how many times Tom
Hanks recited the importance of taking Cherbourg in <i style="mso-bidi-font-style: normal;">Saving Private Ryan</i>, in fact almost all the motivations in that
pretty-good movie, beginning with his desire for a summer Sunday hammock, were
immediate and personal (as most likely were the motives of the people in the
real world). </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So a plea to my fellow alt-history writers: Let's go somewhere else this next time, okay, guys? One too
many trips to Disneyland can make me think I might want to go on the
microbrewery tour of Omaha, at least, if not spend a year learning tango in
Buenos Aires or take a photo expedition to Bhutan.</span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 0in; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>So with that in mind, and because one of my
tutees is struggling with combinatorics currently, I started thinking ... <br />
•<b>five</b> different historical turning points, and let's throw in some that didn't
happen, <b>times </b><br />
•<b>five</b> ways things could be different instead of simple reversal, <b>times</b> <br />
•a combination of <b>twenty</b> <b>(five</b> roles other than the standard kings-or-nobodies,
<b>times four</b> issues that are neither fate-of-the-universe nor just-we-few<b>)</b>, </span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 0in; mso-add-space: auto; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 14.0pt;">would be 500 possible alt
histories.</span></b><span style="font-family: Georgia; font-size: 14.0pt;"> </span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 0in; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Which
would supply me with plenty of reading for a long time.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 0in; mso-add-space: auto; text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So, fellow
writers, before you read on ...</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 58.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">What's your favorite toe?</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 58.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">What's your favorite vowel?</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 58.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">What's your favorite continent?</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 58.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">Jeans or slacks?</span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 58.0pt; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -22.0pt;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: Georgia; font-size: 14.0pt;">Chocolate or maple?</span></div>
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Bet you
can figure this out on your own. Your next alt history novel features an
alternate outcome to the event in Table 1 (which your piggie selected), of the
type found in Table 2 (your favorite vowel), with a hero/heroine from Table 3, and whose
goal/drive/main purpose is a permutation of your answers to questions 4 and 5.</span></div>
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">TABLE 1.
Divergence Point. Note that two of these are could-have-beens that didn't
happen in our timeline, a much-neglected subgenre.</span></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 90.9pt;" width="91">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Went to
market</span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 387.9pt;" width="388">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Great
Turkish War (or War of the Holy League)</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 90.9pt;" width="91">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Stayed
home</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 387.9pt;" width="388">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">US
Election Crisis/End of Reconstruction 1876-77</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 90.9pt;" width="91">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Had
roast beef</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 387.9pt;" width="388">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Taiping
Rebellion</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 90.9pt;" width="91">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Had
none</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 387.9pt;" width="388">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Navigators
from the Mughal Empire discover gold in western Australia, circa 1600</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 90.9pt;" width="91">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Went
wee wee wee all the way home</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 387.9pt;" width="388">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">West
African religious leader proscribes slavery and slave trade circa 1650, wipes
out European forts,<span style="mso-spacerun: yes;"> </span>establishes
trans-Sahara "gun road" to Ottomans, begins modernization with
Ottoman assistance</span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Table 2. What
made a difference from our timeline</span></div>
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Where the
event from Table 1 did NOT happen in our timeline, this can be either a reason
it does happen, or something that derails the process</span></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 81.9pt;" width="82">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">A</span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 396.9pt;" width="397">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Negotiated
settlement by a genius diplomat or political or business leader</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 81.9pt;" width="82">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">E</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 396.9pt;" width="397">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Major
player (real or your addition) removed by personal scandal</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 81.9pt;" width="82">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">I</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 396.9pt;" width="397">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Financial,
organizational, or public relations wizard (not in our timeline) opens up new
possibilities</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 81.9pt;" width="82">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">O</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 396.9pt;" width="397">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Strike,
mutiny, or other underclass rebellion alters balance between contending
powers</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 81.9pt;" width="82">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">U or Y</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 396.9pt;" width="397">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Botched
intelligence operation/cover up</span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">TABLE 3.
Protagonist's role in society</span></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.2in;" width="86">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Africa</span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 5.45in;" width="392">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">An aide
or trusted assistant to a major player</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.2in;" width="86">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Eurasia</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 5.45in;" width="392">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">An
unworldly scholar or academic from an unexpected background</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.2in;" width="86">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">North
America +Australia</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 5.45in;" width="392">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">The
secret lover of a middle-level person who is privy to an important secret</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.2in;" width="86">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">South
America</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 5.45in;" width="392">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">A small
businessperson with a dream of making it big</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.2in;" width="86">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Antarctica</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 5.45in;" width="392">
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">A
liaison officer between two allied but not friendly sides</span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">TABLE
3-2. What the protagonist must do or is tasked to do</span></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.2in;" width="86">
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 153.0pt;" width="153">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">Jeans</span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 166.5pt;" width="167">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">Slacks</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.2in;" width="86">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">Chocolate</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 153.0pt;" width="153">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">return home to deal with an
urgent family crisis</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 166.5pt;" width="167">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">covertly bring evidence of
wrongdoing to the attention of an avenger</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.2in;" width="86">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">Maple</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 153.0pt;" width="153">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">complete a normally routine task
made nearly impossible by other events</span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 166.5pt;" width="167">
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: Georgia; font-size: 14.0pt;">prevent or ameliorate a small
injustice that only s/he knows about</span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">So, and
just for some examples for grins:</span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 14.0pt;">Had none, O, Eurasia, Maple-Jeans
would lead to:</span></b></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">(Generalized version) In a world where navigators from the
Mughal Empire discover gold in western Australia, circa 1600, but a strike,
mutiny, or other underclass rebellion alters the balance between the contending
powers, an unworldly scholar or academic from an unexpected background must complete
a normally routine task made nearly impossible by other events.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">(Made specific) In 1792, in a world where Australian gold
discovered during the reign of Akbar the Great drove economic expansion and
made the Mughal Empire both the master of India and fully capable of dealing
with the European powers as an equal, at a mining technical institute in what
would be Esperance in our timeline, an ascetic Buddhist scholar from modern day
Sri Lanka who teaches the equivalent of a "current events" class has
to explain the French Revolution to a class of miners' kids shortly after a
failed strike; she has to somehow please both the local Mughal political
commissioner, who wants no trouble and has grave doubts about allowing women to
teach, and the head of the school, a passionate feminist (perhaps under the
influence of Mary Woolstonecraft?) who insists that the outside world be
brought into the classroom and discussed. All this, of course, on a desert
coast a zillion miles from anywhere.</span></div>
<div class="MsoNormal">
<span style="font-family: Georgia; font-size: 14.0pt;">Or
suppose you have </span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 14.0pt;">Went to market, Y, Antarctica,
Chocolate Slacks</span></b></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">You might get to: A hundred years after the Great Turkish
War ended with the Turkish border established at the Danube, the Alps, and the
Adriatic, thanks to the swift, bold actions of </span><span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Merzifonlu
Kara Mustafa Pasha during the siege in 1683, young French military cadets
Jean-Jacques Anonyme and Napoleon Bonaparte are assigned as clerks to Louis
XVI's liaison with the northern Turkish armies; they're talking about dividing
Germany between them once and for all. Bored, and with little to do, they read
through old records, to discover that Kara Mustafa's secret of success was a
brilliant intelligence service: one that still exists, and that is quietly
plotting against Louis XVI, via the literary salons of Paris...</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Anyway, you get the idea. Or the
other 498 ideas. Go write some of those, or some of the others, or whatever. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Or
just write to tell me that dammit, Barnes, Roast beef-E-Africa-Maple-Jeans has not
only already been done, it won a Sideways Award last year.<span style="mso-spacerun: yes;"> </span>But please, anything that keeps me from
picking up one more Civil War reversal in which Ralph Waldo Emerson and his boy
assistant Thomas Edison team up to invent the tank, but are stopped cold by
Stonewall Jackson's Air Force dive bombers, as flown by Frank James and Cole Younger... that would be a step in the right direction.</span><span style="font-family: Georgia; font-size: 14.0pt;"></span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-71545889985113611932015-08-06T23:58:00.001-06:002015-08-07T00:03:17.453-06:00Episode 5 is up, so here's a blog about robocorps, pitchforks, hairy monosyllabists, decision rules, and the tenth heuristic (with a footnote about pistachios)<style>
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<br />
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Explaining first things first: I'm blogging on Tuesdays
and Fridays, lately, because <a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-1-family-business/d/d-id/717130">my serial novelet, "Silence Like Diamonds,"</a> is running at <a href="http://www.lightreading.com/">Light Reading</a>, a tech-news oriented website
covering advanced communications systems. You can browse back through this blog
or just hop over there and start reading, but in any case, <a href="http://lightreading.com/services/cloud-services/silence-like-diamonds---episode-5-circular-trail/d/d-id/717412">Episode 5</a> (out of
10) is now up and running, or will be by the time you read this, so if you haven't started yet, you have a
bit of catching up to do.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">One idea that seems to bother people just a little is that
my fictional NameItCorp, in about 2030, is actually a giant pay-to-access
app, a corporation with no mission (other than "doing things for money") and no workers.<span style="mso-spacerun: yes;"> </span>It does pretty much anything you
can do on the net: answering questions, locating information, putting together
bids of subcontractors to accomplish purposes, and so forth, all via robots, AI, and subcontractors. And in my imagined
2030, it is a big-as-Google-today-and-just-as-indispensable corporation.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Now, most people don't have that much problem with the
idea on a small scale; after all, what is a sales or catalog website,
especially one selling pure information products, if not a robobusiness?<span style="mso-spacerun: yes;"> I've known a couple of people who owned a few dozen vending machines and serviced them all themselves; they're in the retail business without any employees, but most people would say they just have a way to sell things that doesn't require them to be there.</span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Information products are a natural for robobusiness. Already much of sports reporting and financial news is
being written by robots, who take the box scores or the price data and convert
it to a news story. Inference algorithms following web hits could easily figure
out which content was most popular (and which was best at drawing people to
advertising or to other news stories). In fact, they already do, with human beings then deciding overall policy on what to do about what the inference algorithms report. Well, algorithms can also make decisions; aren't the humans only in the loop because the tech isn't quite right yet, or perhaps because the boss's nephew needs a job? Is there any reason why a web-based news
publication would need human employees in another few years? </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The often mentioned "analytics revolution" and
the rise of "big data" are yet another example of what's already
possible and will be much more significant soon: more and more business
decisions are being made by processing the corporation's enormous store of data
through analytic algorithms and simply picking the result with the highest
expected value or minimax loss.* At that point, do you really need a management
team? </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Furthermore, it can fairly be said that although it's not
legally required by fiduciary duty (despite myth), many corporations have been
moving, <a href="https://www.washingtonpost.com/opinions/harold-meyerson-the-myth-of-maximizing-shareholder-value/2014/02/11/00cdfb14-9336-11e3-84e1-27626c5ef5fb_story.html">as Harold Meyerson puts it very clearly, from a model of duty to all the stakeholders to a narrow duty to only the shareholders</a>. There's a kind of political basis for this to be
found in some capitalists and some extremist libertarians, a position that can
fairly be called agorolatry**, i.e. the belief that markets are not just
efficient or personal-choice-maximizing or fundamentally fair, but actually the
source rather than the expression of moral and ethical judgment. I've noticed
that some younger generation capitalists are beginning to talk more like agorolaters
than their older brethren; this <span style="mso-spacerun: yes;"> </span>might
end about as the dance around the Golden Calf usually does, or then again it
may herald a rewarding century or two for Golden Calf Corp.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Put all those trends together and you've got Silence Like
Diamonds's NameItCorp: the company that does anything for enough money, just as
your app does whatever it's supposed to when you push its button.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">If it makes you a bit nervous, well, it's an idea that
isn't far from Karl Marx's idea of capital as "dead labor" --
the residue of work done by somebody who is now completely cut off from it. For example, you own some product of work, say, a shovel
you bought from Ogg, the shovelsmith in the next hut, who has long since moved
on to making other shovels.<span style="mso-spacerun: yes;"> </span>You loan the
shovel to Gronk, in exchange for a tenth of his potato crop; you trade the
potatoes for more shovels, which you loan to more hairy people with
monosyllabic names, gaining more potatoes, and eventually you are the Potato
and Shovel Baron of the Hypotheticalithic Age.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">But what if the shovel kept getting smarter? At first it
just made it easier for Gronk to dig. But then it started identifying the best
potatoes to dig ... and marking out the garden beds where Gronk should dig ...
and digging in places that Gronk couldn't reach ... and one day, the shovel
just grew potatoes all by itself, and brought them to you.<span style="mso-spacerun: yes;"> </span>Sorry, Gronk. You're out of the potato
business. But if you need any potatoes, I have them on sale, more of them and cheaper than you could ever produce.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Meanwhile, Ogg's shovelmaking tools have also gotten
smarter. Nowadays the shovels just get up from Ogg's place, walk over to yours,
and get to work. You, of course, faithfully pay Ogg in less and less valuable potatoes, and the day comes when you've got all the shovels you need, and Ogg sits around watching his last generation of shovels dig because that's all there is to do.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">It's a great deal for you, but you have to wonder if Ogg
and Gronk are talking to the <a href="https://www.ted.com/talks/nick_hanauer_beware_fellow_plutocrats_the_pitchforks_are_coming?language=en">pitchforks now streaming out of the house of the village's pitchforksmith</a>.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Or maybe the unease that the coming of the robocorps gives
me is a more personal than social matter, as expressed by Emerson:</span></div>
<div class="MsoNormal" style="margin-left: 2.0in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">The horseman serves the horse,<br />
The neat-herd serves the neat,<br />
The merchant serves the purse,<br />
The eater serves his meat;<br />
'Tis the day of the chattel,<br />
Web to weave, and corn to grind,<br />
Things are in the saddle,<br />
And ride mankind.</span></i></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">That might make one more heuristic, <a href="http://thatjohnbarnes.blogspot.com/2015/07/how-eight-heuristic-rules-handful-of.html">in addition to the nine I recently listed</a>: if something makes you uneasy today, and you don't see
anything stopping it, tomorrow it will be<span style="mso-spacerun: yes;">
</span>genuinely scary -- and most people will think it's perfectly normal.</span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 24.0pt;">§</span></b></div>
<div class="MsoNormal" style="margin-left: .5in; text-indent: -.5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">*Good-enough-for-here definitions:
These are both decision rules. Expected value=sum of the products of the values
of the possible outcomes and their probabilities. Minimax loss: theory of games
based choice in which you make the choice where the most you can lose is the
smallest. The expected value of a coin flip where you get paid a dime for heads
and pay a nickel for tails is 2.5¢; in 1000 coin flips you'd make $25. Over the
long run people get rich by maximizing expected value, but it will sometimes
pick a very risky choice if the reward is high enough.<span style="mso-spacerun: yes;"> </span>Minimax loss says that if you have three
choices, A, B, and C, and the worst thing that could happen under A is losing
$10, the worst under B is losing $8, and the worst under C is losing $6, you
pick C, even if A or B has a higher expected value or a higher maximum
payoff.<span style="mso-spacerun: yes;"> </span>Minimax loss is the rule people
follow when they "settle" in marriage, but also when they refuse to
accept a ride home with a drunk.<span style="mso-spacerun: yes;"> </span>Like
expected value, it's a way to play, not necessarily the only or the right way
all the time.</span></div>
<div class="MsoNormal" style="margin-left: .5in; text-indent: -.5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">**You're an economist if you think
that the way to handle high pistachio prices is to let them rise until more
people plant pistachio trees, and that this will allocate existing pistachios
to those who want them most and can afford to subsidize future plantings, and
therefore a free market in pistachios is likely to be effective and convenient.
You're a libertarian if you think your freedom to buy and sell pistachios is the
real issue, and that the allocation that produces is just, and therefore a free
market in pistachios is part of a free society. And you're an agorolater if you
think high pistachio prices are the just reward for virtuous pistachio growers
and the well-deserved punishment for undeserving impoverished pistachio lovers,
who should have had the foresight to be able to afford pistachios, and that if
there isn't a free market in pistachios, evil wins. </span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-56488724960818826102015-08-04T01:21:00.001-06:002015-08-04T01:27:35.394-06:00Episode 4 is up, so it's time for some cryptic remarks about Silence<style>
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<br />
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia;">There
is a sentence in <a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-4-following-the-money/d/d-id/717386">"Silence Like Diamonds" -- oh,that? How nice of you to ask. The fourth episode is up now, over at Light Reading,</a>
and if this is your first time here you can find <a href="http://thatjohnbarnes.blogspot.com/2015/07/tomorrow-morning-fresh-serial.html?zx=ca65c7947b56ecab">my explanation here</a> and <a href="http://www.lightreading.com/security/cloud-security/light-reading-goes-faster-than-light/a/d-id/717229">Light Reading's explanation there</a>. If you really just wanted to read a good story, go
read! This will wait!</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: Georgia;">(Smiling and waving as a few folks leave the room)</span></i></div>
<div class="MsoNormal" style="text-align: center; text-indent: 0.5in;">
<span style="font-size: large;"><b><span style="font-family: Georgia;">RUN FOR YOUR LIFE, IT'S ABOUT TO BE MATH IN HERE!</span></b></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="mso-bidi-font-style: normal;"><span style="font-family: Georgia;"><i>(crouching behind podium until pandemonium subsides, addressing the few remaining cool people in the front row)</i> </span></span><i style="mso-bidi-font-style: normal;"><span style="font-family: Georgia;"> </span></i></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia;">All
right then. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia;">As I was saying, there's a sentence in "Silence Like
Diamonds" that draws a lot of questions from readers, so I thought today
I'd talk about that.<span style="mso-spacerun: yes;"> </span>It's in Episode 3,
which ran last Friday:</span></div>
<blockquote class="tr_bq">
<div class="MsoNormal" style="text-indent: .5in;">
<span style="background-color: #ffe599;"><span style="font-family: Verdana,sans-serif;">Ever
since the Yan-Dimri fast factorization algorithm had flipped the advantage from
the encryptors to the cryptanalysts, only isolated systems could be really
secure (at the cost of being really useless).</span></span></div>
</blockquote>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">I'm
happy to note that in the 72 hours after that, "Yan-Dimri fast factorization" drew a few search
hits on Google, so to begin with: I made that up. We call this stuff science
<i>fiction</i>, you know? </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">But
I'm guessing that the reason why it drew Google attention was because there are
plenty of people who recognize the implications in that sentence; in fact I'm a
bit surprised that more people don't.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">So
to begin at the beginning: since about the 16th century in the European
cultural sphere, and no later than 1900 everywhere, there's been a relentless
arms race between encryptors (codemakers) and cryptanalysts (codebreakers).
Mathematical tools have gotten better and better on both sides, and theoretical
understanding of encryption/decryption has advanced rapidly, driven first by
the competing great powers in the last half of the 1800s, and then by war and
cold war, and now by a huge international information market. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">The
balance began to swing -- apparently permanently -- toward encryption with the
introduction of keyword, master key, etc. systems. I'm skipping over a vast
amount of detail here, so real crypto people please forgive all the variations
and interesting sidelines that I might introduce. Here's a too-brief and too-undetailed version of how we got where we are now, and how the world of "Silence Like Diamonds" is different.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Think of the code that small children used to use, where A=1, B=2, etc. Suppose we
encode a block of text: </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">HOW
ALL OCCASIONS DO INFORM AGAINST ME AND SPUR MY DULL REVENGE</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">For
our purposes in this example, I'll use 0 for space. Encoded in that simple
fashion, the message is now:</span></div>
<div class="MsoNormal">
<span style="font-family: "Courier New",Courier,monospace;"><span style="color: black;">8-15-23-0-1-12-12-0-15-3-3-1-19-9-15-14-19-0-4-15-0-9-14-6-15-18-13-0-1-7-1-9-14-19-20-0-13-5-0-1-14-4-0-19-16-21-18-0-13-25-0-4-21-12-12-0-18-5-22-5-14-7-5</span></span></div>
<span style="font-family: "Courier New",Courier,monospace;">
</span><br />
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">To
read it, then, the recipient would simply replace the numbers with letters (and
zeros with spaces). </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Of
course<span style="mso-spacerun: yes;"> </span>that cipher would be pathetically
easy to break, especially with modern gear like any old spreadsheet. In fact, if you knew it was that simple a code, you'd probably just set up a list of permutations in your spreadsheet (a row where you tried A=1 B=2, a row where you tried B=0, C=1, etc) and read down a few lines till you saw an English sentence. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Yet systems like that
were used down through the American Civil War; you can find Edgar Allen Poe
explaining how to break that sort of code in <a href="http://poestories.com/read/goldbug">"The Gold Bug"</a>.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Many
other ideas were tried, but the road that proved most profitable was the one
that leads through the Enigma machine, originally created for high-security
business cables in the 1920s and then adapted by the Germans during World War
II.<span style="mso-spacerun: yes;"> </span>Leaving aside all the fascinating
mechanics -- and they really are worth your while if you've never read the
story -- the math of it was simply that if instead of a simple substitution,
you had some number of encoding rules, and a key that told you which rule to use for each successive character, then every character of the clear text
would be represented by several different characters, eventually all the
possible ones, in the code.<span style="mso-spacerun: yes;"> </span>For example,
suppose we add the successive digits of </span><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">
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<span style="font-family: "Lucida Grande"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">π</span><span style="font-family: Georgia; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"> </span>
to the substitution above; then the
new code is:</span></div>
<div class="MsoNormal">
<span style="font-family: "Courier New",Courier,monospace;"><span style="color: black;">11-16-27-1-6-21-14-6-20-6-8-9-28-16-24-17-21-3-12-19-6-11-20-10-18-21-21-3-3-14-10-14-14-21-28-8-17-6-9-8-15-10-9-22-25-30-21-7-18-26-0-9-29-14-12-9-25-9-31-9-18-12-14</span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Of
course it doesn't have to be </span><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">
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<span style="font-family: "Lucida Grande"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">π</span><span style="font-family: Georgia; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"> </span>
and it doesn't have to be addition; I could
have multiplied each by the successive digits of √5 and then subtracted successive
digits of √22, so that the message recipient would then decode by first adding <span style="mso-spacerun: yes;"></span></span><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">successive
digits of √22, then dividing </span><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">by the successive digits of √5, and finally substituting that simple numeric code. Important thing to note right here -- you'll see why later -- in this primitive version, it takes just about as long to encode as it does to decode.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">This
is a considerable improvement over the simple substitution ciphers; Herbert Yardley's codebreakers, in the United
States's Black Chamber around World War I, would have had to work at it for a few
days, especially with<span style="mso-spacerun: yes;"> </span>message this short.
Notice that the E's in "revenge" are now represented by 9, 9, and
14.<span style="mso-spacerun: yes;"> </span>The spaces are represented by
1,6,3,3,8, 9,9,7,0, and 9 successively, the double L in all is 21-14 but the
double L in dull is 14-12, and so forth. With a longer sample (say 1500 characters instead of the 62 here) and a long
afternoon (and ideally a spreadsheet), though, a good amateur cryptographer
could crack this while barely breaking a sweat. (I'm skipping how, here; let me recommend <a href="http://simonsingh.net/books/the-code-book/">Simon Singh's THE CODE BOOK</a> as a good place to start a fascination with cryptography -- I wish it had been around when I first became interested<span style="color: white;">,<span style="background-color: black;"> <span style="font-family: Verdana,sans-serif;">confidential information</span></span></span> ago).</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">But
rudimentary as my little demonstration here is, it introduces the basic tricks of modern encryption:
there's a key, there's an operation performed by combining the message with the
key, and there's a resulting coded message, which is hard to read without the
key, but easy to read by applying the key through a defined operation. As long as the sender and the intended receiver both have the key, and the
would-be interceptor doesn't, the would-be interceptor has a fairly-tough-up-to-impossible math
problem to crack.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Some
things make the problem harder than others. There are patterns in every
language -- ETAOINSHRDLU is a famous one, that is, in a long enough passage of
random English, E will be the most frequent letter, followed by T, A, etc. If
there is also a pattern in the key -- say, for example, it is the digits of </span><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">
<span style="font-family: "Lucida Grande"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">π</span></span>,
beginning over again with 3 for every message -- then in a big enough sample,
the combined pattern will emerge and can be teased out, especially if something
is a frequent part of a message (you might have seen <i><a href="http://www.imdb.com/title/tt2084970/">The Imitation Game</a></i> and
remember what a difference it made when British cryptographers that realized Heil Hitler would occur frequently in the encrypted
messages).</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">But
what a <i>complicated </i>world is hidden in that phrase "the sender and the
intended receiver both have the key, and the would-be interceptor doesn't."<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="mso-spacerun: yes;"> </span>A perfect, unbreakable key would simply be a
list of random digits held by both sender and receiver, as long as the list was
used once and then thrown away; with no pattern in the key, there'd be no
breaking it.<span style="mso-spacerun: yes;"> </span>But that would require that
every spy, warship, infiltrator, or whatever go out with an extremely long
random number list of his/her own, in some cases smuggling it through enemy lines, and never accidentally losing it or having it confiscated. Whenever
they can, modern encrypters do use those unbreakable "one time pads"
("pad" because the original WW2 version was a printed, gridded pad of
sheets, on each of which you wrote your message on<span style="mso-spacerun: yes;"> </span>a top line, added the random numbers from the
middle line, and sent the resulting code from the bottom line, destroying it as
soon as you finished. For a really fascinating story about how that all worked
in practice, see <a href="http://www.amazon.com/gp/product/068486780X/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=068486780X&linkCode=as2&tag=entethemadmun-20&linkId=C76QQNZWUIS7JLTN">Leo Marks's BETWEEN SILK AND CYANIDE</a>). </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Suppose,
though, that you can't send a one-time pad with someone. Perhaps they will be
going elsewhere indefinitely, or forever. Perhaps a one-time pad is too
dangerous for them to carry (since it's pretty obviously incriminating
evidence).<span style="mso-spacerun: yes;"> </span>What can you do instead?</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">For
World War II and most of the Cold War, the answer was highly unsatisfactory:
you made hard-to-figure-out keys that didn't look like keys. Another example
from </span><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><i><a href="http://www.imdb.com/title/tt2084970/">The Imitation Game</a></i></span>, (a great movie if you're not trying to substitute it
for reading <a href="http://www.turing.org.uk/book/">Andrew Hodge's brilliant biography <i>Alan Turing: The Enigma</i></a>): the
Soviet mole, who is working inside a far-above-top-secret facility into which
he dare not take any suspicious object, was using passages from the King James
Bible as his key.<span style="mso-spacerun: yes;"> </span>Though it still
produces some very difficult code to break manually, presumably there will be
recurring patterns produced by overlaps of frequent words. For example, if
GERMAN and BEGAT line up every so often (one is likely to be frequent in the
message, the other in the key), and if what we're doing is adding the numbers
for the two letters, subtracting 26 if necessary, and then converting to a
letter, the letter combination IJYNU would show up extra frequently.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">The
genius of the Enigma machine was that the key wasn't written out as a key, but an initial setting
for a machine that then automatically generated the key as needed; each time
you pushed a key to encode a letter, three internal rotors turned by specified
amounts, reorganizing the substitution of the next letter. To read the message you had to know which three (of a possible 5)
rotors were in which order at which starting positions, plus how a plugboard was arranged, and since the
pattern was changed every night at midnight, the Germans thought it couldn't be
broken at all, given the huge number of possible combinations. But again, it
was breakable because there was a pattern to the Enigma's generation of the key,
and a pattern to the German messages underneath, and an enormous sample (when
there's that much of a war going on, and everyone is talking to everyone else,
the message volume is huge).</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">So
the Cold War began in a rough tie between encrypters and decrypters (since the
British had shared some of their codebreaking methods with us voluntarily and
others with the Soviets via espionage).<span style="mso-spacerun: yes;">
</span>One-time pads were unbreakable (and still are and always will be as long
as the numbers are truly random) but you had to hand off the pad between sender
and receiver somehow, and the pad itself could be stolen, intercepted, lost,
etc. Generated keys had patterns in them and were therefore breakable, even
with enormously complex and sophisticated key-generation machines (and later,
software). If a government, agency, business, or other organization changed keys often enough, and the key wasn't reused too
much, and the process of generating it was not too obvious or wasn't stolen by the opposition,
then most messages could be kept secret for long enough, most of the time, with
the codebreakers occasionally getting ahead of the game because they got
bigger, faster computers to run the breaking software on, or because the
encrypters made a mistake somewhere.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">And
then <a href="https://en.wikipedia.org/wiki/Public-key_cryptography#History">in the 1970s some nice mathematicians came along and put the encrypters so far ahead that they've been there ever since</a>. They figured out
a variety of processes using (what they hope are) one-way functions.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">A
one-way function is simply a process with numbers that is easy to do in one
direction but hard to do in reverse. "Easy" and "hard"
might have a genuine universal meaning related to the P=NP question, but for
applied engineering purposes, it's always just "relative to the capabilities of the
people with the secret and the people trying to get the secret." </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">In
particular, the encryption mathematicians discovered a process in which it was
quite easy to encode using the digits of a very large number (say two thousand bits, which is about a 600-digit number in decimal) that was a semi-prime, i.e. the product of two primes, but
the process only worked backwards with enormous effort, so the message was hard
to decode -- unless you had the "trap door," the value of one of the
two primes, in which case it was easy.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">So
the Chief of the Global GoodORBad Guys Org (GG|BGO) could simply broadcast the
semiprime and the encryption rule, and anyone who copied it down could send him a message, with no
one else being able to read it.<span style="mso-spacerun: yes;"> </span>Using
one of the two prime factors that he had multiplied to create the semi-prime,
the Chief could decode that same message quickly and easily. If he kept those factors
secret, to break the code and read his agents' messages, someone would have to
factor the public key.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Furthermore, his agents could simply mail him a public key (presumably generated on their laptops or phones) from any anonymous mailbox or email, keeping their trapdoor primes somewhere concealed (a few hundred digits is not hard to conceal, after all), and when he wanted to reply he could send it by any public channel. (Ever wonder what those <a href="http://www.bbc.com/news/magazine-24910397">numbers stations on the shortwave</a> might be?) </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">And
there matters have rested, because factoring is a hard operation. You can see
this a little by just looking at the time it takes to factor a semi-prime by
hand: 35 is a semi-prime, and its primes are 5 and 7, as anyone who remembers
the multiplication table figured out in less time than it took you to read
this. How about 2491? How long did it take you to find <span style="color: cyan;"><span style="background-color: cyan;">47*53?</span></span> (highlight to
read)<span style="mso-spacerun: yes;"> </span>Now, if you're really a demon at
factoring, try <span style="color: black;"><span style="background-color: white;">307,961</span>.<span style="mso-spacerun: yes;"> </span>(If you really must know, <span style="color: cyan;"><span style="background-color: cyan;">that's 547 times
563</span></span>).</span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Here's
the interesting thing, from a computing standpoint: not only is factoring a
hard operation but it gets much harder (in terms of machine time taken) the
bigger the number, and in modern crypto, it's just not practical at all. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">So
that's why RSA and its many cousins, which rely on semiprimes, are nearly as
unbreakable as a 1-way pad. And a good thing too, because those methods of encryption are keeping thieves out of your bank account, your boss out of that naughty website you frequent, trolls out of taking over your i.d. and sending threatening notes to the president, and all the rest. True, if the white hats don't change the key often
enough, and the black hats can keep guessing for years or centuries, eventually
they might manage to factor that semiprime ...<span style="mso-spacerun: yes;"> </span>In fact a few
very limited tricks are known for doing just that on a few very special classes
of large semiprimes (look up Fermat's method for one). The public record so far
is for factoring a 232-digit number, which took hundreds of hours of computer
time across about two years, and was essentially just a very-well-thought out brute force search.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">So
... since it's easy to create those really big semiprimes, and since factoring takes so long that the key
will change long before anyone factors the public key and gets in, it's an
encryption paradise. As long as the government doesn't make everyone give them
one of the factors and leave all of them in a pile on someone's desk over the
weekend we should be fine, right?</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"></span>
</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Except.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">No
one has actually satisfactorily <i>shown that there can't</i> be a fast way to factor
a very large semiprime.<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Except,
if it's really impossible, someone ought to have proved it's impossible by now,
given how big the economic incentive is.<span style="mso-spacerun: yes;">
</span>Or if it is possible, you'd think someone would have done it.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">And math problems can have a really long hang time for solution. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Remember,
Fermat's Last Theorem took 350 years. The four-color problem stood open for
about 130. This <a href="http://mathworld.wolfram.com/UnsolvedProblems.html">Wolfram article on unsolved problems</a> contains many that have
been open for a century or more. <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Right
now, somewhere out there, mathematicians who would like to have a name in the
history books are working on factoring large semi-primes, and other equally ambitious mathematicians are working on proving it's
impossible. (Technically, too, someone might show it to be possible without
showing how, but that idea didn't lead me to a story in whicht things blow up and people daringly do deeds of derring-do). </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">If
the factoring side wins the race -- which they could do at any time, and it's
always possible that a spy service somewhere might already have done so -- instantly,
</span></div>
<blockquote class="tr_bq">
<div class="MsoNormal" style="text-indent: .5in;">
<span style="background-color: yellow;"><span style="font-family: Verdana,sans-serif;">"...
there is nothing covered, that shall not be revealed; neither hid, that shall
not be known. Therefore whatsoever ye have spoken in darkness shall be heard in
the light; and that which ye have spoken in the ear in closets shall be
proclaimed upon the housetops."</span></span></div>
</blockquote>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Everything.
All at once. Private bank accounts and passwords, credit card accounts, corporate
records, everything; the only limit will be how fast human beings can absorb
and use the information. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">There
are other encryption methods possible, but most of them are also driven by
large semiprimes.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">So
... in my imagined future world, two mathematicians named Yan and Dimri came up
with a fast-factorization algorithm somewhere between 2020 and 2025. It's a
world where all encryption, everywhere (except for one-time pads) is broken
quickly; encryption only slows corporate and political espionage down a little bit.<span style="mso-spacerun: yes;"> </span>And thus it's a world where
people like Yip, Yazzy, Dusan, and Markus are never short of work or things to
do; in a world where there are no good locks, there's always a job for a guard.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Do
I think that world will happen? </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">I
think no one yet knows (or at least no one yet admits they know) whether it
could. So, for the moment, it's perfect for science fiction. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">And
if I were running a large operation's security, I might deputize a
math-literate person to watch the literature on semi-prime factorization. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">Anyway,
enjoy the story, see you Friday with some other topic, and this time I got to
talk about two favorite subjects, math and fiction, so consider yourself lucky
that I only wrote this much.</span><span style="font-family: Georgia;"></span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-43198287329736536122015-07-31T04:35:00.002-06:002015-07-31T04:44:46.823-06:00Episode 3 of Silence Like Diamonds is up early, and I was up late and had some futuristical thoughts about communication relay drones.<style>
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<span style="font-family: Georgia; font-size: 14.0pt;">So once again I'm flogging my serialized novelet over in <i style="mso-bidi-font-style: normal;">Light Reading</i>, an I-hope-fun bit of
light summer adventure fiction, set in the near future. And since there's
another episode up -- <a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-3-principle-one/d/d-id/717255">Episode 3, "Principle One"</a> -- go ahead, scoot on over and read that! -- I thought I'd talk about something
that's already been in the story in Episodes 1 and 2, since Mitch has made dire
threats about what he will do if I blog spoilers for my own story. (I won't,
Mitch. Really, I won't. Could you release Dad, now, please?) </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Since drones are a hot topic in the communications field
today, and since the original story request mentioned them with considerable passion,
here a few drone-thoughts, not necessarily in any order:</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•Crewed aircraft nowadays are limited, more and more, by
the crew. A human body can only take so much acceleration, insists on having
continuous access to heavy and hard-to-handle materials like oxygen and water,
and has a dreadfully slow narrowband interface to its environment, coupled to
an internal electrochemical processing system that is even more dreadfully
slow. As designers are becoming free of the pilot, amazing possibilities are coming
up; there was no point in trying to engineer a 20-g turn that would kill
everyone aboard, but now that there's no one aboard, that limit is gone. You
couldn't do much with an aircraft that fit into a suitcase if it had to have a
cockpit big enough for at least a jockey; now there are already drones out
there smaller than most birds. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">This trend is only going to accelerate as a new generation
of designers comes into the workforce never having had to think about pilots or
passengers. I played around with that idea with the Griffon, the super-drone
that circles communications hotspots at 35,000 meters* and reshapes itself for
convenience, usually shaped like an airplane, but ascending like a blimp, and
descending like a dart as needed.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•Which brings me to another potential that isn't yet fully
realized by either us sci-fi folk or more serious tech people: the revolution
in materials science is just getting underway. For one thing, computer time and
storage and speed are only beginning to make real computational molecular
design possible to contemplate. We don't even really know what to wish for
yet.<span style="mso-spacerun: yes;"> </span>I'll give you one I thought about
describing for the Griffon and then decided was too long to go into: if you had
thin, flexible tubes that could handle the internal pressure required, you
could use them to hold a thin, light envelope of some other extremely strong
material open ... and thus your balloon could be just an inflated shell with a
near-vacuum inside.<span style="mso-spacerun: yes;"> </span>Not only does that
make for a less explosion-prone, better-lifting balloon filler, but with enough
energy and the right gear, you can always make more vacuum -- it might be a
long time before you needed to refill the tanks.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•What's so great about a stratospheric drone?<span style="mso-spacerun: yes;"> </span>Well, at the height the Griffon is flying,
the horizon is about 670 km away -- the one over Arcata could talk directly to
San Luis Obispo, Portland, and Reno, almost to Boise. And if it's communicating
with another Griffon at the same altitude, that doubles the distance -- from
Tijuana to Vancouver BC, all the way out to Calgary and Grand Junction. With a
drone over every population concentration, and a few over the oceans, that puts
the travel distance for a signal from any point on Earth to anywhere else at
about 20,150 km, maximum, which is about 67 microseconds at light speed.
Compare that with 204,000 km and 680 microseconds for geosynchronous, and
you're looking at an unbeatable advantage.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•The other drone I made up was the Roverino, which Markus
describes as "common as crows around a tech town." The idea I had
here was that you've got a communications drone the size of a middling model
airplane but it's smart; it records billable milliseconds for every internet
packet it passes on, relaying that information to its owner, and it wanders around
seeking out high-value transmitters. Besides doing obvious things like
following always-on-the-internet people around, circling office buildings to
add wireless capacity, and swarming to emergency sites or news stories to
provide extra bandwidth, Roverinos would be getting much of their traffic from
other Roverinos; they really would flock and swarm like birds. Probably, like
birds, they'd also learn and adopt different strategies; you'd get some
"loners"<span style="mso-spacerun: yes;"> </span>and
"pioneers" who<span style="mso-spacerun: yes;"> </span>would be
looking for isolated hotspots they could have all to themselves, lazy
"freeloaders" who would simply follow the biggest flock, perhaps even
"alphas" that many other Roverinos would follow.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•And of course that's just two possibilities. I think the
drone-relay world is going to look more like an ecology than an economy.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•But before we start feeling all Brautigan about being
watched over by machines of loving grace: consider too that in a true Internet
of Things, anything can be weaponized.<span style="mso-spacerun: yes;">
</span>The 9-11 terrorists turned four airliners into cruise missiles (three
successfully), but it cost them 20 of their own to do it.<span style="mso-spacerun: yes;"> </span>The future is going to look more like the <a href="http://spectrum.ieee.org/telecom/security/the-real-story-of-stuxnet">Stuxnet attacks on Iran</a>: one day the centrifuges went berserk and tore
themselves apart, effectively shutting down the nuclear program. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">But it's also going to be a future of big data, and that's
why I think the principle of stochastic terror will play a bigger role than
people are realizing. If you haven't run across the concept before,<span style="mso-spacerun: yes;"> </span>"stochastic terror" is the
technique of broadcasting or publishing in a way intended to set off
sympathetic-to-your-side "lone wolves" or "lunatics" who
then carry out violent attacks on your enemies.<span style="mso-spacerun: yes;">
</span>Conservatives tend to see it in cases like Mohammed Youssef Abdulazeez
and Dzhokar Tsarnaev; liberals see it just as clearly in Dylann Roof and Jared
Loughner. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">But a converted and riled-up lunatic is a poor weapon
compared to a virused drone. First of all, other people notice when another
human being begins to consider ultra-violent crimes; their behavior changes and
there's a good chance someone will notice and catch them. But a virus can lie
dormant until the moment comes.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Moreover, a virus doesn't start to have second thoughts,
or get a good lover, job, or medication and start to think it has something to
lose. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">And finally, a virus is eternally vigilant. So imagine, if
you will, that a malign and patient virusmaker sets something loose among the
drone population that lies in wait until a national political convention; and
then one day, with hundreds or thousands of officeholders, party officials, and
activists of one party all in the air as they arrive or leave, all the drones
in a city swarm toward the arriving or departing flights, heading straight into
cockpit windshields or jet engine intakes (but only of the planes actually
carrying "targets", since the system could also know who was on board
each one.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Pleasant dreams, everyone!</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Meanwhile, nothing that dark is happening in <a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-3-principle-one/d/d-id/717255">"Silence Like Diamonds."</a><a href="https://www.blogger.com/null"> </a>Better go cheer yourselves up over there.</span></div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: .5in;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Georgia; font-size: 14.0pt;">§</span></b></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">*35,000 meters is about 114,000 feet, or 21 miles, for the
incurably US-system reader. That's up in the range that the media inaccurately
describe as "the edge of space" when <a href="https://www.youtube.com/watch?v=AsftfzBrVko">crazed engineers parachute from it</a>
or <a href="https://www.youtube.com/watch?v=XVm43dLbTaw">fifth-grade girls send instrument packages up to it on balloons</a>.
</span></div>
<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.comtag:blogger.com,1999:blog-1767672674449240854.post-10078329783347146432015-07-28T01:26:00.000-06:002015-07-29T10:31:22.674-06:00How nine heuristic rules, a handful of points, links, and curves, and some historical parallels all come together in a serial <style>
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<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Some of you have started reading the serial novelet by me
over at <i style="mso-bidi-font-style: normal;">Light Reading, </i>"Silence
Like Diamonds."<a href="http://www.lightreading.com/security/cloud-security/silence-like-diamonds---episode-1-family-business/d/d-id/717130"> Episode 1</a> came out last Friday; as I write this, <a href="http://www.lightreading.com/drones/silence-like-diamonds---episode-2-warning-shot/d/d-id/717252?page_number=1">Episode 2</a>
is a few hours from being officially live, and that link should already be
working for anyone who likes that "advanced peek" feeling.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">While the serial lasts, I'm going to try to say something
around the time each episode comes out.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The whole trick with this "credible near future"
stuff is arithmetic and minimum times. Yip and her sister Yazzy are somewhere
in their mid thirties at the time of the story, since each of them have
established careers in a difficult field, but they're not grizzled old
veterans, and what they actually do for a living (more about that in a future
blog) is an occupation that doesn't fully exist in 2015.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The story is set around 2030, plus or minus maybe two
years. So right now, Yip and Yazzy are going to some university and will
graduate within a couple of years. They're at <a href="http://backup.programmaticadvertising.org/2015/02/10/last-millennials.html">the young end of Millennials or the old end of Generation To Be Named.</a></span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">So that's who they are: your kids (if you're my age), the
summer intern where you work now, perhaps your students, maybe you on your
first real job (assuming you just grabbed your first foothold on the tech
ladder). </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Now what about the world they're in? </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The idea of near-term hard sf is to try to move things out
of the lab into the real world, not to pull wish-fulfillments and sheer magic utterly out of fantasy. So this version of 2030 has no
city on Mars, no hoverboards, no indistinguishable-from-people androids, no
immortality injection and no franchise called "Just Fingers" that
specializes in regenerating appendages for accident victims. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">The time it takes from research results being announced to
full commercial deployment varies a lot more than the time from early
20-something to experienced mid-30s, but there are some predictable aspects to
that as well. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">Here are nine of my favorite tricks for guessing how far into the future the deployments of new technologies are:</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">• Everyone lies about how close lab-only things are to going
into application, prototype, and production. It's essential for getting
funding, after all. So things that are just being shown off in lab tours now,
and are supposed to be shrink-wrapped and delivered next year, will probably
happen in three. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;"><span style="mso-spacerun: yes;"> </span>•home products come
in at very high cost and fall rapidly in price, deploying swiftly as they do
(some of you will remember when a smart phone was called a Blackberry and was a
symbol of trendy wealth). It was a long, long trip from the <a href="http://history-computer.com/ModernComputer/Personal/Altair.html">Altair 8800</a> to the
<a href="http://mentalfloss.com/article/27971/10-classic-computers-you-had-kid">Apple IIe, TRS-80, and Commodore 64</a>, about ten years to get to 5% market
penetration -- but ten years after <i style="mso-bidi-font-style: normal;">that</i>,
the home computer was ubiquitous and a majority of students going off to
college were taking a computer with them. </span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•software and mathematical breakthroughs deploy all but
instantly, because it's really just a matter of a proficient coder
understanding what the math/logic says and writing it in valid code, and the transition from "one smart coder" to "a hundred thousand script kiddies" is nearly as quick as cut and paste.(This is particularly obvious in data science, where, for example, the time between a mathematician developing a new technique and a package to perform it becoming available in R, SAS, MySQL, etc. is measured in weeks rather than years).</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•new business models flare up, go dormant, begin to grow
quietly, and then suddenly have already taken over. "Oh, them, they're
certainly trendy ... hey, they're still around but it's not exciting like it
was ... gee, every year they have more market share, I wonder if ... I, for
one, welcome the new masters of our humble economy..." For many years entrepreneur-coaches have used the example that anyone can make a better hamburger than McDonalds but making a better business model is something else again; I'd go farther and say that often even long after there has been a spectacular success, it's very difficult for most companies even to plagiarize a great business model. So no matter how advanced the tech, it will still have to be distributed via a large number of companies that don't know what they're doing, don't do it very well, and really aren't sure what they should be doing.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•"the street finds it own uses for technology,"
as William Gibson taught us all. Just the other day I saw an ad for a singing
teacher who offers rates for "in person or Skype." I very much doubt
that the developers of Skype intended that, any more than the developers at Google,
Amazon, YouTube or Craigslist had any idea what else they'd be doing in the
world. Whether it's as humble as WD-40 and duct tape, or as high end as DNA sequencing and nuclear magnetic resonance, somewhere out there someone will make it do something its creators never thought of.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•exponential growth without limit is exciting for sci-fi writers, but it is vanishingly rare; far
more commonly, what looks like an "explosion" is merely <a href="https://en.wikipedia.org/wiki/Generalised_logistic_function">the middle part of a logistic curve,</a> </span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://upload.wikimedia.org/wikipedia/commons/5/54/Generalized_logistic_function_A0_K1_B1.5_Q0.5_%CE%BD0.5_M0.5.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="300" src="https://upload.wikimedia.org/wikipedia/commons/5/54/Generalized_logistic_function_A0_K1_B1.5_Q0.5_%CE%BD0.5_M0.5.png" width="400" /></a></div>
<span style="font-size: large;"><span style="font-family: Georgia,"Times New Roman",serif;">Wil
McCarthy wrote <a href="http://archive.wired.com/wired/archive/10.01/tracks.html">a pretty funny alternate history</a> a few years ago by treating the 19th century explosive growth and connectivity of railroads as if the curve had been exponential rather than logistic. John Hersey's famous <a href="http://www.amazon.com/Petition-More-Space-John-Hersey/dp/0394494660">My Petition for More Space</a> is another exponential that should have been logistic, about population growth (where do people in that world find time and space to do all that reproducing, and what exactly are they eating?). Infamously, the city of New York forecast in 1894 that within a few decades, all its resources would be needed just to haul horse manure out of the city (as we all know, this didn't happen to New York. It happened to Washington and Hollywood). The exponential curve may be fun and dramatic and sexy, but the logistic one is the one to bet on. What's growing rapidly today may saturate tomorrow and
become as common as phones.</span></span><br />
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•almost as fun and entertaining as exponential growth is the often-forgotten possibility of reversal. Nuclear arsenals grew at apparently exponential rates for more than a decade, but today there are only about as many as there were in 1960</span><span style="font-family: Georgia; font-size: 14.0pt;"><span style="font-family: Georgia; font-size: 14.0pt;">. <table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/US_and_USSR_nuclear_stockpiles.svg/555px-US_and_USSR_nuclear_stockpiles.svg.png" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="466" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/US_and_USSR_nuclear_stockpiles.svg/555px-US_and_USSR_nuclear_stockpiles.svg.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="mw-mmv-title"><a href="https://en.wikipedia.org/wiki/Historical_nuclear_weapons_stockpiles_and_nuclear_tests_by_country#cite_note-5"></a></span><br />
<div class="mw-mmv-image-metadata">
<div class="mw-mmv-image-metadata-column mw-mmv-image-metadata-desc-column">
<div class="mw-mmv-credit mw-mmv-ttf-container mw-mmv-ttf-normal">
<span class="mw-mmv-source-author"><span class="mw-mmv-author">Created by <a class="new" href="https://commons.wikimedia.org/w/index.php?title=User:Fastfission&action=edit&redlink=1" title="User:Fastfission (page does not exist)">User:Fastfission</a>
first by mapping the lines using OpenOffice.org's Calc program, then
exporting a graph to SVG, and the performing substantial aesthetic
modifications in Inkscape.</span> - <span class="mw-mmv-source"><span class="int-own-work" lang="en">Own work</span> Source data from: Robert S. Norris and Hans M. Kristensen, "Global nuclear stockpiles, 1945-2006," <i>Bulletin of the Atomic Scientists</i> 62, no. 4 (July/August 2006), 64-66. Online at <a class="external free" href="http://thebulletin.metapress.com/content/c4120650912x74k7/fulltext.pdf" rel="nofollow">http://thebulletin.metapress.com/content/c4120650912x74k7/fulltext.pdf</a></span></span></div>
</div>
</div>
</td></tr>
</tbody></table>
</span> Certain high-fashion products show similar patterns: <a href="https://en.wikipedia.org/wiki/Plume_hunting">plumes for ladies' hats</a>, <a href="http://www.fashionencyclopedia.com/fashion_costume_culture/Modern-World-1919-1929/Plus-Fours.html">plus-fours</a>, and <a href="http://www.howretro.com/2011/07/white-boots.html">white plastic go-go boots</a>. And in the larger scale of history, there are the concluding lines from Andrei Amalrik's <a href="http://www.amazon.com/Soviet-Union-Survive-Harper-Colophon/dp/0060907320"><i>Will the Soviet Union Survive Until 1984? </i></a>(written in 1969, another attempt at a 15 year forecast):</span></div>
<span style="font-size: small;"><i><span style="font-family: Arial,Helvetica,sans-serif;">Meanwhile, we are told, Western prognosticators are indeed worried by
the growth of the cities and the difficulties brought on by the rapid pace
of scientific and technological progress. Evidently, if "futurology" had
existed in Imperial Rome, where, as we are told, people were already erecting
six-story buildings and children's merry-go-rounds were driven by steam,
the fifth-century "futurologists" would have predicted for the following
century r the construction of twenty-story buildings and the industrial
utilization of steam power. </span></i></span><br />
<span style="font-size: small;"><br /></span>
<span style="font-size: small;"><i><span style="font-family: Arial,Helvetica,sans-serif;">As we now know, however, in the sixth century goats were grazing in
the Forum just as they are doing now, beneath my window in this village. </span></i></span><br />
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">What appears to be growing exponentially today may tomorrow reverse and become as dead as cassette tapes.</span></div>
<div class="MsoNormal" style="text-indent: .5in;">
<span style="font-family: Georgia; font-size: 14.0pt;">•"Information wants to be free" was not about
politics, as is clearly shown by the very next sentence Stewart Brand spoke:
"Information wants to be expensive." The root of this contradiction is that the value of information depends on who else has it and what they do with it, changes whenever it moves, and is catalytic for an enormous number of other processes. Information behaves rather like
money with an unreadable expiration date or a randomly tested transaction
limit; every time you gain value from it you risk making it worthless, and
inevitably, sooner or later, something does.</span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">•forecasts about coming ages and changes in human culture
are generally rooted in observed truth, but nothing ever comes out as
predicted. Robert Heinlein made up a nice little parable about the lab where
they created four escape paths of exactly the same difficulty from a cage and put an
ape in to see which one he'd use; the ape escaped the fifth way. Collectively, humans
are that fifth-way ape; we often have some idea of where we're going but we
rarely go there by the way that seems obvious, and when we get there, it
doesn't look like much like what we thought it would. </span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">I used all those tricks at one point or another in
devising a world for "Silence Like Diamonds," but for the moment let
me just talk about one way I used the last one.</span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">You may have run across the currently-trendy notion of the Internet of
Things, the idea of having almost everything in your physical environment wired
to talk to almost everything else in the house. Eventually, presumably, your
car (which is driving you home while you finish some paperwork) phones your
house. It alerts the air conditioning that you are hung up in traffic and to
delay coming on till you clear that bottleneck on the interstate. The
refrigerator and blender start making up something soothing (and the fridge
issues a call so that the drone from the local ice cream store schedules a restocking
delivery). The music player queues up the "calm and happy" mix, the
shower starts warming water in the reserve tank, and so forth. </span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">But even away from home, your phone records (by checking RFIDs or their successors) all the things you look at in the store, and reports it to the store chain's intelligence system (with the phone company collecting a small fee). Face recognition software in half a dozen businesses around your workplace pick you up from security cameras and know what way you take from the parking lot to work. Knowing who walks by and what they like, stores on your route put more clothing you like in their windows. </span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">All the gadgets
in your life gang up to make you happier.</span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">It always strikes me that in most such scenarios, we
assume that the human being is a petty tyrant having a bad day. The machines
either sound as if they are living in fear of our rage, or acting as very large
comforting invisible nannies who will have our milk and cookies and a big hug
ready for us no matter how bad the world has been, or like a neurotic parent desperately trying to please a tantrum-prone jaded brat.<span style="mso-spacerun: yes;"> </span>It all seems very infantilizing.</span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">Compounding that infantilization, to give you everything
you really want, before or at latest when you want it, an Internet of Things
has to know everything you want or might want, including the wants you can't
admit to and the wants you haven't felt yet and the wants that are only just
emerging from the creative software of the marketing people. The liberal-feared
surveillance state and conservative-feared nanny state are both much less
intrusive than the probably-purely-commercial instant-gratification state. But
of course, it's all much less scary because it's not about preventing you from
doing what you want (like the cop on every corner), or making you do what
someone else wants (like the nanny in every bedroom). No, not at all.<span style="mso-spacerun: yes;"> </span>It's about always giving you what you want as
soon as you want it, and knowing enough to do that. </span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">Like Santa. Remember, he sees you when you're sleeping, he
knows when you're awake ...<span style="mso-spacerun: yes;"> </span>(As Allan
Sherman remarked, who did he think he was, J. Edgar Hoover?)</span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">So you've got a world that runs on the ability for
everyone to quickly know anything that is public -- and the value of keeping
information private is astronomical. The relationship between cybersecurity and
security breaches becomes something like the relationship between health care
and death: you can buy huge amounts of the former, and make the latter very
unlikely, but the reaper (or the hacker) always wins in the long run. In such a world, the
number and variety of communications security services and systems is going to
go through a "Cambrian explosion" -- the evolutionary phenomenon that
when there is a drastic increase in the variety of niches, all sorts of strange
things grow, making more niches in which more things grow -- </span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">Until the reversal, or until the first derivative of that logistic curve starts to bend downward.<span style="mso-spacerun: yes;"> </span>There, that ought to be a cliffhanger to hold
you for a while ...</span></div>
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<span style="font-family: Georgia; font-size: 14.0pt;">Friday I'll probably talk a bit about the drones that have been a big part of the plot so far, since
I've gotten a few emails about them in the last couple days. After that ...
well, information wants to be expensive.<span style="mso-spacerun: yes;"> And time is money. So after a bit more time, more information.</span></span></div>
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<div class="blogger-post-footer">The opinions expressed here reflect something or other about John Barnes at any given moment, possibly his digestion. For a somewhat longer bio and a list of links where some of John Barnes's works can be purchased, go to http://tinyurl.com/WhereToGetJohnBarnesStuff</div>John Barneshttp://www.blogger.com/profile/10105610196644805312noreply@blogger.com