Saturday, August 4, 2012

A short one for fun, with math

At the moment I'm drowning in half-finished blog posts as I keep having ideas and getting interrupted before I chew them to my satisfaction; one of the glories of Them There Interwebbical Things is that I don't have to chase after the biggest audience I can find, or any audience at all really, and just figure that the people who enjoy 3000-word Ramblers (tip of the hat to Mitch Wagner, who refers to many of my pieces as that) will find them here, and if that's not very many people, well, some of us are having fun and the rest of you will have to go find pictures of cute babies and cats and short punchy posts about whatever you like to be punched shortly about.

Anyway, having digressed, let me just point you to the following Tweet from Peter Aldhous:

We’ve travelled 560 million km. We’re right on target to fly through the eye of a needle. Target 3km * 12 km press conf

The question, of course, is just how proportionate that is.

So ... or sew ... 

A No. 5 sharp hand sewing needle (what most of us keep around for sewing on buttons and closing up small tears) is 0.8 mm thick. The eye of  a sharp is usually about 4/5 of its width, so that would be around 0.64 mm.   An average height middle-class American woman* is 1.648 m tall, and women's eye-to-fingertip length averages 46% of height, so proportionately, if we assume for some horrible reason that this poor crazy woman is threading the needle by raising the thread to her eye and then trying to hit the eye of the needle at arm's length, that thread tip is traveling 1184.5 times the width of the aperture that the sewing woman is so awkwardly trying to hit.** 

NASA's Curiosity, neglecting for the moment that it's traveling in an enormous curved orbit to do it, is traveling 560 million km to hit an aperture 3 km by 12 km.  To make the comparison to the needle a little better, a 3X12 rectangle has the same area as a circle with diameter of 6.77.***  So distance/aperture  is 560 million/6.77=82,714,513.  

You could look on that as NASA trying to hit a needle's eye, not at arm's-length, but at 69,830 arm's-lengths (which comes to about 53 kilometers, if the woman's arm length is the 758 mm I was using before).  Add to that that they're hitting it by throwing (rather than hand-guiding) about a quarter-circle of a curve.  Or you could look on it as the woman trying to thread a needle eye  (at arm's length, remember) that is  only about 9 nanometers wide (about the width of 25 calcium atoms laid out in a straight line).  

That's some sewing there, NASA. Maybe your department of metaphors should look for a metaphor that's about six orders of magnitude more incredible, because that's what you're doing.


*why a woman? why not? 
why middle class? because that's the point where early nutrition plays a minimal part.  
why American? Because although my country doesn't take particularly good care of its citizens, it keeps excellent, easily accessible records of the consequences of not taking care of them.

** a=aperture.  d=distance. a=0.64; d=46%*1648 (once you put both in millimeters); d/a=1648/0.64=1184.5.

*** Area=3X12=36=pi(r squared).  r=sqrt(Area/pi)=about 3.39 (staying at two digit precision).  diameter= about 6.77 (same precision)=aperture.  Why use the area?  Because that's what matters when you're trying to hit a target at a distance.  Why circularize?  Because that was what I was doing with the eye of the needle; d/a, distance over aperture, was the proportion of  the distance traveled by the thread tip to the diameter of the needle's eye.  If you want another number figured another way, cook it yourself (and I hope you do).