And now I get caught up again, if briefly, to the mathematically-themed comic strips I can find. I’ve dubbed this one the trapezoid edition because one happens to mention the post that will outlive me.
Todd Clark’s Lola (May 4) is a straightforward joke. Monty’s given his chance of passing mathematics and doesn’t understand the prospect is grim.
Joe Martin’s Willy and Ethel (May 4) shows an astounding feat of mind-reading, or of luck. How amazing it is to draw a number at random from a range depends on many things. It’s less impressive to pick the right number if there are only three possible answers than it is to pick the right number out of ten million possibilities. When we ask someone to pick a number we usually mean a range of the counting numbers. My experience suggests it’s “one to ten” unless some other range is specified. But the other thing affecting how amazing it is is the distribution. There might be ten million possible responses, but if only a few of them are likely then the feat is much less impressive.
The distribution of a random number is the interesting thing about it. The number has some value, yes, and we may not know what it is, but we know how likely it is to be any of the possible values. And good mathematics can be done knowing the distribution of a value of something. The whole field of statistical mechanics is an example of that. James Clerk Maxwell, famous for the equations which describe electromagnetism, used such random variables to explain how the rings of Saturn could exist. It isn’t easy to start solving problems with distributions instead of particular values — I’m not sure I’ve seen a good introduction, and I’d be glad to pass one on if someone can suggest it — but the power it offers is amazing.