A very peculiar favorite book
In that peculiar period of
my life when I went to graduate school to study things I was sort of interested
in, dropped out to make money doing R&D on things I really wasn't
interested in, and then returned to grad school to study things I actually was
interested in, I was fascinated with William Irwin Thompson’s
extended essay, At
the Edge of History: Speculations on the Transformation of Culture. At a guess, I re-read it ten times, but it may have
been twenty.*
The part of At the Edge
of History that I have reread the
most is a the fourth chapter, "Values and Conflict Throughout History."
It's typical Thompson, i.e. it begins in one small, narrow, interesting place,
rockets to a view of the whole world, and then gently deposits you back into
your world. As a child, I remember reading a kids-sf novel in which a mouse
finds himself sent up on a sounding rocket and becomes so enthralled with the
experience that he keeps trying to get the human scientists to pick him for
another ride (it was long ago, and the book was old then, written well before
Gagarin and probably before Sputnik. ) That's kind of what Thompson does to you
when he's on his game; there's a nifty little bit of intellectual cheese to
nibble on, right through this—CLANK. THUNDER. WHOOSH. OH MY GOD IT'S THE WHOLE
WORLD SPREAD OUT IN FRONT OF ME … and then forever after, you wish you could
see that again, and whenever the giants in the white coats come by, you jump
and dance and beg for another ride on the rocket.
Or if you're a much saner
mouse than I am, whenever you see that sadistic bastard in the white coat you
hide under something and hope he goes away. It's kind of a matter of taste and
temperament. Once I became one of those white coat guys, I was always looking
for mice who volunteered among my test subjects (or students, as I believe the
Human Services department prefers they be called).
In any case, Thompson's
"Values and Conflict Throughout History" leads off with an initial
reference to John Marshall's
famous ethnographic film The
Hunters, (the link is to a trailer – imdb here if you find The
Hunters more interesting than what
I'm going to talk about further on down, which I think is entirely likely), a
movie that we are lucky to have; Marshall, while quite young, gained the trust
and apparently the liking of some of the last true hunter-gatherers on Earth,
and was permitted to film four of them on a 13-day hunt in the early 1950s.
(That tribe have all long since been forced to give up their traditional way of
life; it's doubtful that there can ever be another movie like The Hunters for seeing how the whole human race lived until a
geologic eye blink ago).
The four men on the hunt,
Thompson argues, are not just any four dudes that were up for a hunt when they
called for volunteers. He dubs them the Headman, the Huntsman, the Shaman, and
the Clown, and argues that they represent four types that are fundamental to a
human society that is going to accomplish anything together (and bringing down
a giraffe by wounding it with a poisoned arrow and then tracking it till it
drops, days later, is quite an accomplishment!) He sees them as the cells of a
double, cross-cutting dichotomy:
|
Function
|
||
Operational |
Ideational
|
||
Social Position
|
High
|
Headman
|
Shaman
|
Common
|
Huntsman
|
Clown
|
By
"operational" Thompson seems to mean "getting stuff done day to
day" and by "ideational," relating to or working with
ideas/visions/dreams. So clockwise around those four, we have the High King,
the High Priest, the Low Comedian, and Working Joe.
Thompson goes into a
fascinating direction from that: he argues that larger and more complex
societies keep re-subdividing each of the four categories into further powers
of four, so that, for example, once there's an organized church, you replace
the Shaman with an organization that will have Bishops (operational-high),
Theologians (ideational-high), Mystics (ideational-low), and Scribes
(operational-low), or once the Huntsman has become the military, the huntsmen
subdivide Generals, General Staff, Warrior Heroes, and Common Soldiers.
As Thompson points
out, the Trojan War story embodies this very well: the Greeks have Agamemnon,
Odysseus, Achilles, and Ajax in those roles. We might without much violence to
the idea also say Kirk On the Bridge, Spock, Kirk While Beamed Down, and then
Bones/Scotty/Chekhov/Sulu/Uhura in a five-way split of the Warrior
Hero/Achilles gig.** Or Thompson doesn't say it, but if you've ever been in an
academic department, you will immediately recognize the Chairman, the Tenured
Theoretician, the Departmental Stalwart, and the Poor Bloody Grad Student.
If you're a science
fiction or fantasy writer, there's a lot of potential for figuring out
imaginary societies on this basis, and if you're not but you write fiction,
it's also a quick way to come up with a cast. I've used it off and on for all
kinds of things.
But the most
interesting thing of all to me is something Thompson says very early on in his
essay:
This
model of four seems to be a persistent one; it recalls the rule of four in the
Indian caste system, Plato, Vico. Blake, Marx, Yeats, Jung, and McLuhan . So
many people look out at reality and come up with a four-part structure that one
cannot help but think that it expresses the nature of reality and/or the
Kantian a priori pure categories of the understanding. But whether the [four
part] structure exists in reality or is simply a projection of the categories
of the human mind, is, of course, the traditionally unanswerable question of
science. Since the mind is part of nature, we make a mistake when we imagine
that the act of perception is through a window in which we are on one side and
nature on the other. We are in nature, so there is no reason that subjectivity
and objectivity should be so dissonantly arranged; it is more than likely that
the key in which the nerves and the stars are strung is the same.
And there's my
jumping off point; in the decades since I first read that, I've encountered at
least a dozen other major theories underlain by a quadripartite division, and
have seen that same splitting into four crop up over and over. And whether this
is a case of a kind of theory for which I have a fetish, or it is actually a reflection
of reality, despite what Thompson says, is not a completely unanswerable
question; it's just not answerable with the kind of certainty that we have
about, e.g., the atomic weight of vanadium or the range of possible dates for
the birth of Genghis Khan. Rather, it's a question that demands a plausible
answer —and I think I have one.
And hence the
question at the top of this piece: Why is the world four?
Quadripartite
divisions abound.
Modern politics
often uses the basic division of Radical, Liberal, Conservative, Reactionary,
which you can draw like this:
|
Basic orientation
|
||
Left |
Right
|
||
Position about existing order
|
Preserve
|
Liberal
|
Conservative
|
Overthrow
|
Radical
|
Reactionary
|
Aristotle said there
were four causes of anything —by cause he meant ways of explaining them:
|
With regard to information source
|
||
Theory/descriptive |
Observation/ empirical
|
||
With regard to time
|
Static
|
Formal
|
Material
|
Dynamic
|
Final
|
Efficient
|
and for those of you
who slept through humanities class, essentially formal means by definition,
material means by ingredients or substance, efficient means by process that
brings it about, and final means by purpose.
The Four Gospels fit
into a double dichotomy:
|
Main concern about Jesus
|
||
Biography |
Nature
|
||
Audience
|
Jews
|
Mark
|
Matthew
|
Gentiles
|
Luke
|
John
|
as do the four
seasons:
|
Days are
|
||
Longer than nights |
Shorter than nights
|
||
Days are
|
Lengthening
|
Spring
|
Winter
|
Shortening
|
Summer
|
Autumn
|
as do the four
Beatles
|
Personality
|
||
Amiable doofus |
Troubled genius
|
||
Main musical position in group
|
Musician/backup
|
Ringo
|
George
|
Composer/lead
|
Paul
|
John
|
Northrop Frye
divided up literature into four forms:
|
Plot
|
||
Change or reversal |
Mood or expression
|
||
World seen as fundamentally
|
Friendly to people
|
Comedy
|
Romance or pastoral
|
Hostile
|
Tragedy
|
Satire or anatomy
|
Medieval and
Renaissance physicians believed we were governed by four Humors, or fluids:
|
Essential temperature
|
||
Hot |
Cold
|
||
Essential mood
|
Positive
|
Blood
|
Phlegm
|
Negative
|
Choler (Yellow Bile)
|
Melancholy (Black Bile)
|
When four guys set
out to rescue Princess Leia, they take along:
|
Led by
|
||
Profit |
The Force
|
||
Authority
|
Gives orders
|
Han Solo
|
Obi-wan Kenobi
|
Takes orders
|
Chewbacca
|
Luke Skywalker
|
And when four guys
(and a whole lot of men in tights) set out to oppose the wicked usurper and
serve the true king, they are
|
Physical Type
|
||
Small and fast |
Big and strong
|
||
Mental Type
|
Shrewd
|
Robin Hood
|
Friar Tuck
|
Impulsive
|
Will Scarlet
|
Little John
|
And of course this
would all be incomplete if I didn't at least mention the ancient four elements:
|
Temperature
|
||
Hot |
Cold
|
||
Moisture
|
Wet
|
Earth
|
Water
|
Dry
|
Fire
|
Air
|
I have no doubt at
all that I'll be getting some mail reminding me of all the ones I left out,
too.
Now …. why? Why
is the world four?
Here's my guess:
Notice that that
four is always a double dichotomy. So to completely describe one of these
foursomes, you need to record:
4 cells, plus
2 dichotomies.
Now, a basic
principle ever since Alan Turing is that you can't think about something or
solve problems related to it unless you have an empty bin or register to move
the thoughts in or out of, so if you're going to think about a foursome, you
also need
1 empty register
(basically your scratch pad).
4+2+1 = 7.
Number of ideas most
people can hold in the head at one time: 7. Some below-average but not actually
disabled people go down to 5 —and don't think very clearly and get lost when
they try. Some very bright people go up to 9, which is to say they can work
with three empty registers and therefore work very fast.
I think that double
dichotomy—two splits of the world into two categories—is the most complex
idea we can easily hold in our heads and operate on all at once. For anything
more complex we have to add registers somehow—writing down, memorizing and
moving things in and out of memory consciously, etc. So the answer is
The world is four
because that's as complex as we can get in our heads all at once, and to be
useful, an idea has to not overflow our heads; and the best ideas tend to be
more complex.
And that has a few
interesting applications. Suppose a species of aliens is kind of dumb and all
they can handle is one dichotomy; that would be 2 cells, 1 dichotomy, and 1
empty register, or 4.
It seems to me
that's about as smart as most dogs and cats I've known; they can act on a
single category (good people/bad people, people who kick me at the dinner
table/people who drop food, etc.) and they can move people between them, or
align with one side or other. (To dogs and cats we might also add ferrets and
perhaps some voters).
And what if we go
the other way? A triple dichotomy requires
8 cells
3 dichotomies
1 empty register
or the ability to
hold 12 things in mind. Would such a being see us the way we do dogs? i.e. nice
enough, sometimes surprisingly smart, but, well, you know. Still a dog.
In general the
formula is that where the number of dichotomies is d, the number of registers
required to have one of these ideas about it is 2d+d+1. Supposing
you had an alien for whom d was = 5; they would have 38 registers. Would we be
able to talk to them at all?
Anyway, many
interesting things fit into these foursomes, and the foursomes have interesting
properties all their own. That's why I've numbered this blog entry as Part 0. I know I'll
be back to cases and points of interest about this topic, many times, though
probably rarely will I write two of these back to back.
And now that you know what I mean when I
write Why is the world four?
you can either sensibly hide under the food dispenser, or hop around and see if
I will send you up in a rocket.
* Nowadays At the Edge
of History seems to be most widely
available
as part of a double volume published by the Lindisfarne Institute, which
Thompson helped to found, if you find yourself so curious you have to look for
it. Even that edition was twenty years ago, and I was afraid that when I opened
the book again —I hadn't done so in four or five years —the magic might finally
have faded. But when I sat down to review it for this essay, before I quite
knew what I had done, an hour and a half had gone by and I had read about fifty
pages, so I would say that for at least one person, the old magic is still
there.
** Yes, that makes Kirk while
beamed down the Clown. See how well this works?