Reading the Comics, October 7, 2014: Repeated Comics Edition


Since my last roundup of mathematics-themed comic strips there’s been a modest drizzle of new ones, and I’m not sure that I can find any particular themes to them, except that Zach Weinersmith and the artistic collective behind Eric the Circle apparently like my attention. Well, what the heck; that’s easy enough to give.

Zach Weinersmith’s Saturday Morning Breakfast Cereal (September 29) hopes to be that guy who appears somewhere around the fourth comment of every news article ever that mentions a correlation being found between two quantities. A lot of what’s valuable about science is finding causal links between things, but it’s only in rare and, often, rather artificial circumstances that such links are easy to show. What’s more often necessary is showing that as one quantity changes so does another, which allows one to suspect a link. Then, typically, one would look for a plausible reason they might have anything to do with one another, and look for ways to experiment and prove whether there is or is not.

But just because there is a correlation doesn’t by itself mean that one thing necessarily has anything to do with another. They could be coincidence, for example, or they could be influenced by some other confounding factor. To be worth mention in a decent journal, a correlation is probably going to be strong enough that it’s hard to believe it’s just coincidence, but there could yet be some confounding factor. And even if there is a causal link, in the complicated mess that is reality it can be difficult to discern which way the link flows. This is summarized in deductive logic by saying that correlation does not imply causation, but that uses deductive logic’s definition of “imply”.

In deductive logic to say “this implies that” means it is impossible for “this” to be true and “that” false simultaneously. It is perfectly permissible for both “this” and “that” to be true, and permissible for “this” to be false and “that” false, and — this is the point where Intro to Logic students typically crash — permissible for “this” to be false and “that” true. Colloquially, though, “imply” has a different connotation, something more along the lines of “this” and “that” have to both be false or both be true together. Don’t make that mistake on your logic test.

When a logician says that correlation does not imply causation, she is saying that it is imaginable for the correlation to be true while the causation is false. She is not saying the causation is false; she is just saying that the case is not proved from the fact of a correlation being true. And that’s so; if we just knew two things were correlated we would have to experiment to find whether there is a causal link. But finding a correlation one of the ways to start finding casual links; it’d be obviously daft not to use them as the start of one’s search. Anyway, that guy in about the fourth comment of every news report about a correlation just wants you to know it’s very important he tell you he’s smarter than journalists.

Saturday Morning Breakfast Cereal pops back up again (October 1) with an easier-to-describe joke about August Ferdinand Möbius and his rather famous strip, here applied to the old gag about walking to school uphill both ways. One hates to be a spoilsport, but Möbius was educated at home until 13, so this comic is not reliable as a shorthand biography of the renowned mathematician.

Eric the Circle has had a couple strips by “Griffinetsabine”, one on October 3, and another on the 7th of October, based on the Shape Singles Bar. Both strips are jokes about two points connecting by a line, suggesting that Griffinetsabine knew the premise was good for a couple of variants. I’d have spaced out the publication of them farther but perhaps this was the best that could be done.

Mikael Wulff and Anders Morgenthaler’s Truth Facts (September 30) — a panel strip that’s often engaging in showing comic charts — gives a guide to what the number of digits you’ve memorized says about you. (For what it’s worth, I peter out at “897932”.) I’m mildly delighted to find that their marker for Isaac Newton is more or less correct: Newton did work out pi to fifteen decimal places, by using his binomial theorem and a calculation of the area within a particular wedge of the circle. (As I make it out Wulff and Morgenthaler put Newton at fourteen decimal points, but they might have read references to Newton working out “fifteen decimal points” as meaning something different to what I do.) Newton’s was not the best calculation of pi in the 1660s when he worked it out — Christoph Grienberger, an Austrian Jesuit astronomer, had calculated 38 decimal places a generation earlier — but I can’t blame Wulff and Morgenthaler for supposing Newton to be a more recognizable name than Grienberger. I imagine if Einstein or Stephen Hawking had done any particularly unique work in calculating the digits of pi they’d have appeared on the chart too.

John Graziano’s Ripley’s Believe It or Not (October 1) — and don’t tell me that attribution doesn’t look weird — shares a story about the followers of the Ancient Greek mathematician, philosopher, and mystic Pythagoras, that they were forbidden to wear wool, eat beans, or pick up things they had dropped. I have heard the beans thing before and I think I’ve heard the wool prohibition before, but I don’t remember hearing about them not being able to pick up things before.

I’m not sure I can believe it, though: Pythagoras was a strange fellow, so far as the historical record is clear. It’s hard to be sure just what is true about him and his followers, though, and what is made up, either out of devoted followers building up the figure they admire or out of critics making fun of a strange fellow with his own little cult. Perhaps it’s so, perhaps it’s not. I would like to see a primary source, and I don’t think any exist.

The Little King skates a figure 8 that requires less tricky curving.
Otto Soglow’s The Little King for 29 February 1948.

Otto Soglow’s The Little King (October 5; originally run February 29, 1948) provides its normal gentle, genial humor in the Little King working his way around the problem of doing a figure 8.

Roger Cotes’s Birthday


Amongst the Twitter feeds I follow and which aren’t based on fictional squirrels is the @mathshistory one, reporting just what it sounds like. It noted the 10th of July was the birthday of Roger Cotes (1682 – 1716) and I knew there was something naggingly familiar about his name. His biography at the MacTutor History of Mathematics Archive features what surely kept him in my mind: that on Cotes’s death at age 34 Isaac Newton said, “… if he had lived we might have known something”. Given Newton’s standing, that’s a eulogy almost good enough to get Cotes tenure, even today.

MacTutor credits Cotes with, among other things, inventing the radian measure of angles; I’m wise enough, I hope, to view skeptically all claims of anyone uniquely inventing anything mathematical, although it’s certainly so that radian measure — in which you give an angle of arc, not by how many degrees it reaches, but by how long the arc is, in units of the radius — is extraordinarily convenient analytically and it’s hard to see how mathematicians did without it. People who advanced the idea and its use deserve their praise. (Normal people can carry on with degrees of arc, for which the numbers are just more pleasant.) As a bonus it serves as one of the points on which people coming into trigonometry classes can feel their heads exploding.

Cotes’s name also gets a decent and, if I have it right, appropriate amount of fame for what are called Newton-Cotes formulas. These are methods for “numerical quadrature”, the slightly old-fashioned name we use to talk about numerical approximations of integrals. In an introductory calculus class one’s likely to run across a couple of rules for numerical quadrature — given names like the Trapezoid Rule, Simpson’s Rule, Simpson’s 3/8ths rule, or the Midpoint Rule — and these are all examples of the Newton-Cotes formulas. Teaching the routine for getting all these Newton-Cotes formulas was, for whatever reason, one of the things I found particularly delightful when I taught numerical mathematics; some subjects are just fun to explain.

MacTutor also notes that from 1709 through 1713, Cotes edited the second edition of Newton’s Principia, and apparently did a most thorough job of it. It claims he studied the Principia and arguing its points with Newton in enough detail that Newton finally removed the thanks he gave to Cotes in the first draft of his preface. A difficult but correct editor is probably more pleasant to have when the project is finished.