Reading the Comics, June 20, 2015: Blatantly Padded Edition, Part 1

I confess. I’m padding my post count with the end-of-the-week roundup of mathematically-themed comic strips. While what I’ve got is a little long for a single post it’s not outrageously long. But I realized that if I split this into two pieces then, given how busy last week was around here, and how I have an A To Z post ready for Monday already, I could put together a string of eight days of posting. And that would look so wonderful in the “fireworks display” of posts that WordPress puts together for its annual statistics report. Please don’t think worse of me for it.

John Graziano’s Ripley’s Believe It or Not (June 17) presents the trivia point that Harvard University is older than calculus. That’s fair enough to say, although I don’t think it merits Graziano’s exclamation point. A proper historical discussion of when calculus was invented has to be qualified. It’s a big, fascinating invention; such things don’t have unambiguous origin dates. You can see what are in retrospect obviously the essential ideas of calculus in historical threads weaving through thousands of years and every mathematically-advanced culture. But calculus as we know it, the set of things that you will see in an Introduction To Calculus textbook, got organized into a coherent set of ides that we call that, now, in the late 17th century. Most of its notation took shape by the mid-18th century, especially as Leonhard Euler promoted many of the symbols and much of the notation that we still use today.

John Graziano’s Ripley’s Believe It or Not is still a weird attribution even if I can’t think of a better one.

Hector D Cantu and Carlos Castellanos’s Baldo (June 18) reminds us that all you really need to do mathematics well is have a problem which you’re interested in. But what isn’t that true of?

J C Duffy’s The Fusco Brothers (June 18) is about the confusion between what positive and negative mean in test screenings. I’ve written about this before. The use of positive for what is typically bad news, and negative for what is typically good news, seems to trace to statistical studies. The test amounts to an experiment. We measure something in a complicated system, like a body. Is that measurement consistent with what we might normally expect, or is it so far away from normal that it’s implausible that it might be just chance? The “positive” then reflects finding that whatever is measured is unlikely to be that far from normal just by chance.

Larry Wright’s Motley (June 18, rerun from June 18, 1987) uses a bit of science and mathematics as a signifier of intelligence. In the context of a game show, though, “23686 π” is an implausible answer. Unless the question was “what’s the area of a circle with radius 23683?” there’s just no way 2368 would even come up. I suspect “hydromononucleatic acid” isn’t at thing either.

Mark Parisi’s Off The Mark (June 18) is this week’s anthropomorphic numerals joke.

Arnold is sparring with a kangaroo. Told to outsmart him, Arnold recites the Pythagorean Theorem. He gets clobbered.
Bud Grace’s The Piranha Club for the 19th of June, 2015.

Bud Grace’s The Piranha Club (June 19) is another strip to use mathematics as a signifier of intelligence. And, hey, guy punched by a kangaroo, what’s not to like? (In the June 20 strip the kangaroo’s joey emerges from a pouch and punches him too, so I suppose the kangaroo’s female, never mind what the 19th says.)


Looking to Euler

I haven’t forgotten about writing original material here — actually I’ve been trying to think of why something I’ve not thought about a long while is true, which is embarrassing and hard to do — but in the meanwhile I’d like to remember Leonhard Euler’s 306th birthday and point to Richard Elwes’s essay here about Euler’s totient function. “Totient” is, as best I can determine, a word that exists only for this mathematical concept — it’s the count of how many numbers are relatively prime to a given number — but even if the word comes only from the mildly esoteric world of prime number studies, it’s still one of my favorite mathematical terms. It feels like a word that ought to be more successful. Someday I’ll probably get in a nasty argument with other people playing Boggle about it.

Apparently, though, Euler didn’t dub this quantity the “totient”, and the word is a neologism coined by James Joseph Sylvester (1814 – 1897). That’s pretty respectable company, though: Sylvester — whose name you probably brush up against if you study mathematical matrices — is widely praised for his skill in naming things, although the only terms I know offhand that he gave us were “totient” and “discriminant”. That b^2 - 4ac term in the quadratic formula which tells you whether a quadratic equation has two real, one real, or two imaginary solutions, was a name (not a concept) given by him, and he named (and extended) the similar concept for cubic equations. I do believe there are more such Sylvester-dubbed terms, just, that we need a Wikipedia category to gather them together.

I’m amused to be reminded that, according to the St Andrews biographies of mathematicians, Sylvester at least one tossed off this version of the Chicken McNuggets problem, possibly after he’d worked out the general solution:

I have a large number of stamps to the value of 5d and 17d only. What is the largest denomination which I cannot make up with a combination of these two different values.