As promised, I’ve got a fresh round of mathematics-themed comic strips to discuss, something that’s rather fun to do because it offers such an easy answer to the question of what to write about today. Once you have the subject and a deadline the rest of the writing isn’t so very hard. So here’s some comics with all the humor safely buried in exposition:

Allison Barrows’s PreTeena (September 24, Rerun) brings the characters to “Performance Camp” and a pun on one of the basic tools of trigonometry. The pun’s routine enough, but I’m delighted to see that Barrows threw in a (correct) polynomial expression for the sine of an angle, since that’s the sort of detail that doesn’t really have to be included for the joke to read cleanly but which shows that Barrows made the effort to get it right.

Polynomial expansions — here, a Taylor series — are great tools to have, because, generally, polynomials are nice and well-behaved things. They’re easy to compute, they’re easy to analyze, they’re pretty much easy to do whatever you might want to do. Being able to shift a complicated or realistic function into a polynomial, even a polynomial with infinitely many terms, is often a big step towards making a complicated problem easy.

Thom Bluemel’s Birdbrains (September 26) tosses one of the other common puns of mathematics, one which Max Garcia’s Sunny Street would do again come the second of October. I think I’d give Birdbrains the edge in this contest of identical punchlines since it’s got a more dynamic drawing and the added dollop of oddness which is a “math clown”.

Steve Moore’s In The Bleachers also competes for the coveted “gets the details right” imaginary trophy for me in calling up a correct version of Schrödinger’s Equation, the one which describes how the probability of a particle evolves in time. I couldn’t help noticing, too, that the hapless football player who slacked on quantum physics was named “Mr Landau”, since Lev Davidovich Landau was one of the giants of quantum mechanics (and a winner of the Nobel Prize in Physics, for the study of superfluids and explaining the strangeness of liquid helium) as well as coauthor of General Physics, which will take you from mechanics to thermodynamics to chemistry in under 400 pages. I don’t know whether Steve Moore has a background in mathematics or physics that might make him aware of Lev Landau’s work, or whether he picked a name arbitrarily that worked out well. (Moore’s turned up here before for making throwaway jokes that were right, so he’s at least consistent in putting this work in.)

Steve Borman’s Little Dog Lost (September 29) at first doesn’t seem to have much mathematical content: it’s the Lost Dog and a squirrel arguing about whether the dog is on the inside or the outside of a fence. This is one of those pieces of topology, though, that raises a question anyone might understand: what information do you need to tell which side of a boundary you’re on? Some recreational mathematics puzzles will show that you can say whether a particular dot is inside or outside of a tangle, provided some necessary assumptions are satisfied, just by drawing a line from your given point to any spot that’s definitely outside and counting how many boundaries one crosses getting to the definitely-outside portion. Part of the work of Moritz Pasch, recently mentioned around here, was about putting on a logically rigorous basis the concept of splitting a plane into separate pieces, which is pretty much the Lost Dog’s problem.

Jonathan Lemon’s Rabbits Against Magic (September 30) jokes about doing a full turn, and about whether 180 or 360 degrees is a complete turn. Usually when I see this joke it’s in the context of someone slightly clueless claiming they’d changed their mind and done a full 360 degree turn, which allows someone to nitpick the claim.

Harley Schwadron’s 9 to 5 (October 5) does a wiseacre-schoolchild joke, about how negative numbers would just lead to “budget deficits and subprime mortgages”. Schwadron may have just been clowning around, but historically, one of the big ways of understanding what negative numbers *were* was to think of them as debts, and their usefulness in accounting helped drive them from the field of suspicious-looking exotic mathematical constructs to reasonably familiar and useful tools.

Gene Weingarten, Dan Weingarten, and David Clark’s Barney and Clyde (October 6) — I have *got* to make a macro for that credit — is another wiseacre-schoolchild joke, although this one built around a more sophisticated subject and one that defies any quick answer. Cynthia asks whether it’s the case that mathematics isn’t real, since one can reasonably argue that most of the things one studies in mathematics don’t exist: the circles or right angles in geometry, for example, are idealized abstractions based on circle-ish figures and roughly perpendicular objects that we see; and it’s hard enough to say what exactly “two” is — as opposed to specific instances “two apples” or “two people” or “two feet of rope” — before we get into, say, .

But then *anything* studied is an abstraction to some extent, whether we study analytic functions, or the Renaissance, or the Mississippi River. You can accuse the first two of being constructions of the human mind, but the Mississippi River seems to be fairly real, at least until you start thinking carefully about just what you mean by the name given it. And it’s very difficult to say that something like mathematical constructs which correspond so well and so tightly to the real world aren’t something real. But this is a difficult subject, and one that involves much deeper and more thoughtful philosophical inquiry than I’m able to adequately share.

dro-mo (October 8), a pantomime comic, is a little bit baffling — they all are — at least until you recognize that it’s a duel of shapes in two, three, and ultimately four dimensions. I’m not sure I can say where exactly the laugh is, but there’s a smile to be had at least.

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