There’s been a little rash of comics that bring up mathematical themes, now, which is ordinarily pretty good news. But when I went back to look at my notes I realized most of them are pretty much name-drops, mentioning stuff that’s mathematical without giving me much to expand upon. The exceptions are what might well be the greatest gift which early 20th century probability could give humor writers. That’s enough for me.
Mark Anderson’s Andertoons (March 27) plays on the double meaning of “fifth” as representing a term in a sequence and as representing a reciprocal fraction. It also makes me realize that I hadn’t paid attention to the fact that English (at least) lets you get away with using the ordinal number for the part fraction, at least apart from “first” and “second”. I can make some guesses about why English allows that, but would like to avoid unnecessarily creating folk etymologies.
Hector D Cantu and Carlos Castellanos’s Baldo (March 27) has Baldo not do as well as he expected in predictive analytics, which I suppose doesn’t explicitly require mathematics, but would be rather hard to do without. Making predictions is one of mathematics’s great applications, and drives much mathematical work, in the extrapolation of curves and the solving of differential equations most obviously.
Dave Whamond’s Reality Check (March 27) name-drops the New Math, in the service of the increasingly popular sayings that suggest Baby Boomers aren’t quite as old as they actually are.
Rick Stromoski’s Soup To Nutz (March 29) name-drops the metric system, as Royboy notices his ten fingers and ten toes and concludes that he is indeed metric. The metric system is built around base ten, of course, and the idea that changing units should be as easy as multiplying and dividing by powers of ten, and powers of ten are easy to multiply and divide by because we use base ten for ordinary calculations. And why do we use base ten? Almost certainly because most people have ten fingers and ten toes, and it’s so easy to make the connection between counting fingers, counting objects, and then to the abstract idea of counting. There are cultures that used other numerical bases; for example, the Maya used base 20, but it’s hard not to notice that that’s just using fingers and toes together.
Greg Cravens’s The Buckets (March 30) brings out a perennial mathematics topic, the infinite monkeys. Here Toby figures he could be the greatest playwright by simply getting infinite monkeys and typewriters to match, letting them work, and harvesting the best results. He hopes that he doesn’t have to buy many of them, to spoil the joke, but the remarkable thing about the infinite monkeys problem is that you don’t actually need that many monkeys. You’ll get the same result — that, eventually, all the works of Shakespeare will be typed — with one monkey or with a million or with infinitely many monkeys; with fewer monkeys you just have to wait longer to expect success. Tim Rickard’s Brewster Rockit (April 1) manages with a mere hundred monkeys, although he doesn’t reach Shakespearean levels.
But making do with fewer monkeys is a surprisingly common tradeoff in random processes. You can often get the same results with many agents running for a shorter while, or a few agents running for a longer while. Processes that allow you to do this are called “ergodic”, and being able to prove that a process is ergodic is good news because it means a complicated system can be represented with a simple one. Unfortunately it’s often difficult to prove that something is ergodic, so you might instead just warn that you are assuming the ergodic hypothesis or ergodicity, and if nothing else you can probably get a good fight going about the validity of “ergodicity” next time you play Scrabble or Boggle.