It was a busy week — well, it’s a season for busy weeks, after all — which is why the mathematics comics pile grew so large before I could do anything about it this time around. I’m not sure which I’d pick as my favorite; the **Truth Facts** tickles me by playing symbols up for confusion and ambiguity, but **Quincy** is surely the best-drawn of this collection, and good comic strip art deserves attention. Happily that’s a vintage strip from King Features so I feel comfortable including the comic strip for you to see easily.

Tony Murphy’s **It’s All About You** (December 15), a comic strip about people not being quite couples, tells a “what happens in Vegas” joke themed to mathematics. The particular topic — a “seminar on gap unification theory” — is something that might actually be a mathematics department specialty. The topic appears in number theory, and particularly in the field of partitions, the study of ways to subdivide collections of discrete things. At this point the subject starts getting specialized enough I can’t say very much intelligible about it; apparently there’s a way of studying these divisions by looking at the distances (the gaps) between where divisions are made (the partitions), but my attempts to find a clear explanation for this all turn up papers in number theory journals that I haven’t got access to and that, I confess, would take me a long while to understand. If anyone from the number theory group wanted to explain things I’d be glad to offer the space.

Ryan Pagelow’s **Buni** (December 17), a pantomime strip, uses a chalkboard full of (gibberish) mathematical symbols to represent the study of interpersonal feelings. That isn’t by itself ridiculous, and the notion that Buni’s got a casual mistake that causes him to despair is a funny one. I just can’t help thinking this is the sort of thing to be worked out by a computer simulation is all, but I lean towards computer simulations for stuff is all.

Steve Sicula’s **Home And Away** (December 17) starts with a kid wondering why time seems to drag; her father’s answer is that a given amount of time, like a year, is a larger fraction of your life when young compared to when old. It’s a tempting theory; many of our senses measure differences between things by the ratio of their sizes rather than their absolute difference. In the famous analogy, it’s easy to tell a five-pound weight from a ten-pound one, but it’s difficult to tell a 50-pound from a 55-pound weight. It’s not hard to imagine that a year feels much longer when it’s one-eighth of your life than when it’s one-thirty-eighth.

I have some skepticism, though. It seems to me that time really feels like it’s dragging when you aren’t in a pattern, when there’s substantially different things to do and keep doing. Too much homogeneity lets time vanish for the same reason it’s hard to actually remember what happened on the commute in this morning: so little happens that demands your thinking that it’s hard to notice it. And it’s easier to keep doing new and challenging things as a kid, since it seems like part of adulthood is a matter of arranging tasks so they’re done to predictable patterns. So I don’t think there’s a simple explanation for why time would drag for a child and fly for her parent.

Tom Toles’s **Randolph Itch, 2 am** (December 17, rerun) is a kind-of appearance by Albert Einstein and his famous equation.

Ted Shearer’s **Quincy** (December 19, originally run October 6, 1975) shows Quincy talking about where he fits in his class’s rankings, and you do have to admit, he *is* right. Percentages, and percentiles, can offer a way to understand how a big set of data is distributed: the 50th percentile, for example, is a value which 50 percent of the data is less than (and 50 percent greater than). The 25th percentile is a value which 25 percent of the data is less than (and 75 percent greater than); the 75th percentile, sensibly, is a value which 75 percent of the data is less than (and 25 percent greater than). Looking at the percentiles can give you an idea whether the data is distributed normally (that’s a term of art here, meaning it follows a distribution that’s got great theoretical backing and turns up a *lot*) or whether it’s bunched up in ways that are peculiar or that indicate something might be up.

Alex Hallatt’s **Human Cull** (December 19) suggests that people asking for the allegedly impossible 110 percent should be marked for death. As I’ve mentioned before the idea of giving 110 percent is perfectly sensible if 100 percent means “a full normal effort” or “an effort meeting some expected standard”; as long as that’s not “the most that can possibly be given” there’s no logical problem in trying to get more than that. My objection to “110 percent” is its cliched nature, but I don’t think using a phrase without thinking about it justifies culling.

Brian Anderson’s **Dog Eat Doug** (December 20) tosses off a Jurassic Park reference and the mention of the mathematician in the book/movie, who talks a bit about chaos theory as a way of explaining dinosaur rampages. I’m skeptical that dinosaur rampages need mathematics to explain but I would expect I’d rather make it through one alive myself, so, I’ll go along with it.

Phil Frank and Joe Troise’s **The Elderberries** (December 20) does the usual jokes about lotteries being a tax (or in this case, a fine) on people who don’t know their mathematics. And, yes, at a cost of (say) a dollar and a chance of payoff of (say) one in 180 million, you can expect to lose money playing for any lottery jackpot … well, of less than 180 million dollars, anyway. Above that and the problem starts getting complicated since the expectation value — what you would expect to get per-drawing if you played a large number of these drawings for the same jackpot — can become positive, even though you still have essentially no chance of winning. The implication seems to be that it makes sense, on average, to play only when the jackpot is big enough; but to get a big enough jackpot requires an enormous number of people to play, which no one should do unless everyone does. And that doesn’t take into account the chance of multiple people having the winning numbers, which becomes more likely the greater the number of people playing *is*.

Steve Sicula’s **Home And Away** (December 21) pops in again with the dad talking “math stuff” with the kids, namely, probability. Betting and gambling seems a pretty solid way to teach mathematics to kids; a good portion of probability was created *by* gamblers, or at least people who wanted to understand gambling, and while some of them might have been motivated by the love of pure knowledge (or come around to it as they worked), a fair number of them were looking for a way to make money in ways that are easy or impressive. Besides that practical attraction, gambling problems also offer an immediacy and accessibility to problems: you don’t have to be a very abstract thinker to get what’s being asked about throwing a pair of dice, or drawing cards from a deck, and even if you don’t get it offhand, it’s easy to get dice or cards or poker chips from the convenience store and work it out by hand.

Mikael Wulff and Anders Morgenthaler’s **Truth Facts** (December 21) offers a set of jokes about statistics and their presentation; one in four of them is the joke that’s always made about statistics, but the others are pretty amusing.

Marty Links’s **Emmy Lou** (December 22, originally run December 17, 1962) plays on the word “square” having different meanings in different contexts and it caused me to look up where the definition of square as a non-hip guy comes from. Wikipedia seems to be of the opinion that the term grew from the 1940s to 1960s to refer to people who can’t think outside the box, which does make clear why the boxy square would be referenced, but it also seems to be of the opinion that the square is the one implied by the conductor’s hand movements during four-beat rhythms. Wikipedia needs to be edited by people with some understanding of paragraph structure.

Missy Meyer’s **Holiday Doodles** mentions that the 22nd of December is National Mathematics Day in India; this is surely because on this day in 1887 the phenomenal mathematician Srinivasa Ramanujan was born. Ramanujan is famous for his astounding work in number theory, and the legend of his discovery by and partnership with Godfrey Harold Hardy. The formula that the date nut bread is holding (look at the cartoon, you’ll understand), “V – E + F = 2”, is a mathematically famous one, although it comes from Leonhard Euler. It states that, for a solid shape with flat faces, and no holes or discontiguous parts or anything like that, the number of vertices (the corners) minus the number of edges (the connections between vertices) plus the number of faces (the flat surfaces between edges) will equal 2.

That formula was first proved by Leonhard Euler, and it’s a remarkable formula that in some ways can be credited as starting topology, the study of what you can know about shapes. The funny thing is I’m not aware of anything Ramanujan did that particularly connects to topology, but Meyer may have just wanted something which was clearly a mathematical formula, and needed one that would read cleanly in the space available. Ramanujan’s work, unfortunately for the purposes of comic art, tends to involve rather long formulas and some arcane functions, by which I mean functions you never even hear of in high school. Something has to give, although Meyer could have used “1729 = 1^{3} + 12^{3} = 9^{3} + 10^{3}”, evoking the famous-among-mathematicians taxicab anecdote.

(Other mathematicians perpetually overshadowed by Ramanujan’s birth would be Johann Pfaff, Pierre Bonnet, Evgraf Fedorov, Dmitri Egorov, and Vladimir Fock, by the way, though I admit I only recognize Pfaff’s name among them, for a construct known as the “Pfaffian”, which gets used when you study some kinds of matrices, and for “Pfaffian systems”, which turn up in differential equations.)

There’s a lot to like here.

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Aw, thank you. Glad you do.

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For the first time I can appreciate your descriptions as the comic about dragging time is not available anymore. I once read there is a whole subfield of psychology dedicated to investigating these effects – e.g. why we feel that time starts to ‘fly’ as we age. If I recall correctly one explanation was that it is the number of interesting and new events per period that define our subjective impression of the the ‘speed of time’. So when you life has become more of a routine there are less of those events.

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It’s not available? That’s strange and a little worrisome since that comic was from a site that I thought left links up and functional indefinitely.

I should have realized that there are people who study why time seems to pass so quickly as we age, and I just didn’t think of it or think to look up what psychology bloggers might have to say about it. (Well, I don’t have time to read even an introductory book about the subject.) But there are probably several contributing causes and that a year is a diminishing fraction of one’s lifespan-to-date is surely just one, and the number of surprising and novel events is probably another one, and I shouldn’t be surprised if they reinforce one another.

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