So a couple weeks ago one of the multi-state lotteries in the United States reached a staggering jackpot of one and a half billion dollars. And it turns out that “a couple weeks” is about the lead time most syndicated comic strip artists maintain. So there’s a rash of lottery-themed comic strips. There’s enough of them that I’m going to push those off to the next Reading the Comics installment. I’ll make do here with what Comic Strip master Command sent us before thoughts of the lottery infiltrated folks’ heads.
Bud Blake’s Tiger for the 28th of January (a rerun; Blake’s been dead a long while) is a cute one about kids not understanding numbers. And about expectations of those who know more than you, I suppose. I’d say this is my favorite of this essay’s strips. Part of that is that it reminds me of a bit in one of the lesser Wizard of Oz books. In it the characters have to count by twos to seventeen to make a successful wish. That’s the sort of problem you expect in fairy lands and quick gags.
Mort Walker’s Beetle Bailey (Vintage) from the 7th of July, 1959 (reprinted the 28th of January) also tickles me. It uses the understanding of mathematics as stand-in for the understanding of science. I imagine it’s also meant to stand in for intelligence. It’s also a good riff on the Sisyphean nature of teaching. The equations on the board at the end almost look meaningful. At least, I can see some resemblance between them and the equations describing orbital mechanics. Camp Swampy hasn’t got any obvious purpose or role today. But the vintage strips reveal it had some role in orbital rocket launches. This was in the late 50s, before orbital rockets worked.
Matt Lubchansky’s Please Listen To Me for the 28th of January is a riff on creationist “teach the controversy” nonsense. So we get some nonsense about a theological theory of numbers. Historically, especially in the western tradition, much great mathematics was done by theologians. Lazy histories of science make out religion as the relentless antagonist to scientific knowledge. It’s not so.
The equation from the last panel, , is a legitimate one. It describes the Laplace Transform of the function f(t). It’s named for Pierre-Simon Laplace. That name might be familiar from mathematical physics, astronomy, the “nebular” hypothesis of planet formation, probability, and so on. Laplace transforms have many uses. One is in solving differential equations. They can change a differential equation, hard to solve, to a polynomial, easy to solve. Then by inverting the Laplace transform you can solve the original, hard, differential equation.
Another major use that I’m familiar with is signal processing. Often we will have some data, a signal, that changes in time or in space. The Laplace transform lets us look at the frequency distribution. That is, what regularly rising and falling patterns go in to making up the signal (or could)? If you’ve taken a bit of differential equations this might sound like it’s just Fourier series. It’s related. (If you don’t know what a Fourier series might be, don’t worry. I bet we’ll come around to discussing it someday.) It might also remind readers here of the z-transform and yes, there’s a relationship.
The transform also shows itself in probability. We’re often interested in the probability distribution of a quantity. That’s what the possible values it might have are, and how likely each of those values is. The Laplace transform lets us switch between the probability distribution and a thing called the moment-generating function. I’m not sure of an efficient way of describing what good that is. If you do, please, leave a comment. But it lets you switch from one description of a thing to another. And your problem might be easier in the other description.
John McPherson’s Close To Home for the 30th of January uses mathematics as the sort of thing that can have an answer just, well, you see it. I suppose only geography would lend itself to a joke like this (“What state is Des Moines in?”)
Scott Adams’s Dilbert for the 31st of January mentions Zeno’s Paradox, three thousand years old and still going strong. I haven’t heard the paradox used as an excuse to put off doing work. It does remind me of the old saw that half your time is spent on the first 90 percent of the project, and half your time on the remaining 10 percent. It’s absurd but truthful, as so many things are.
Samson’s Dark Side Of The Horse for the 2nd of February (I’m skipping some lottery strips to get here) plays on the merger of the ideas of “turn my life completely around” and “turn around 360 degrees”. A perfect 360 degree rotation would be an “identity tranformation”, leaving the thing it’s done to unchanged. But I understand why the terms merged. As with many English words or terms, “all the way around” can mean opposite things.
But anyone playing pinball or taking time-lapse photographs or just listening to Heraclitus can tell you. Turning all the way around does not leave you quite what you were before. People aren’t perfect at rotations, and even if they were, the act of breaking focus and coming back to it changes what one’s doing.