Reading the Comics, September 6, 2015: September 6, 2015 Edition

Well, we had another of those days where Comic Strip Master Command ordered everybody to do mathematics jokes. I’ll survive.

Don Trachte’s Henry for the 6th of September, 2015.

Don Trachte’s Henry is a reminder that arithmetic, like so many things, is easier to learn when you’re comfortable with the context. Personally I’ve never understood why some of the discs on pool scoring racks are different colors but imagine it relates to scoring values, somehow. I’ve encountered multiple people who assume I must be good at pool, since it’s all geometry, and what isn’t just geometry is physics. I’ve disappointed them all so far.

Tony Rubino and Gary Markstein’s Daddy’s Home uses arithmetic as an example of joy-crushing school drudgery. It could’ve as easily been asking the capital of Montana.

Scott Adams’s Dilbert Classics, a rerun from the 29th of June, 1992, has Dilbert make a breakthrough in knot theory. The fundamental principle is correct: there are many knots that one could use for tying shoelaces, just as there are many knots that could be used for tying ties. Discovering new ones is a good ways for knot theorists to get a bit of harmless publicity. Nobody needs them. From a knot-theory perspetive it also doesn’t matter if you lace the shoe’s holes crosswise or ladder-style. There are surely other ways to lace the holes, too, but nobody needs them either.

Maria Scrivan’s Half Full uses a blackboard full of mathematical symbols and name-drops Common Core. Fifty years ago this same joke was published, somewhere, with “Now solve it using the New Math” as punchline. Thirty years from now it will run again, with “Now solve it using the (insert name here)” as punchline. Some things are eternal truths.

T Lewis and Michael Fry’s Over The Hedge presents one of those Cretan paradox-style logic problems. Anyway, I choose to read it as such. I’m tickled by it.

And to close things out, both Leigh Rubin’s Rubes and Mikael Wulff and Anders Morgenthaler’s WuMo did riffs on the story of Newton and the falling apple. Is this truly mathematically-themed? Well, it’s tied to the legend of calculus’s origin, so that’s near enough for me.

Fibonacci’s Biased Scarf

Here is a neat bit of crochet work with a bunch of nice recreational-mathematics properties. The first is that the distance between yellow rows, or between blue rows, represents the start of the Fibonacci sequence of numbers. I’m not sure if the Fibonacci sequence is the most famous sequence of whole numbers but it’s certainly among the most famous, and it’s got interesting properties and historical context.

The second recreational-mathematics property is that the pattern is rotationally symmetric. Rotate it 180 degrees and you get back the original pattern, albeit with blue and yellow swapped. You can form a group out of the ways that it’s possible to rotate an object and get back something that looks like the original. Symmetry groups can be things of simple aesthetic beauty, describing scarf patterns and ways to tile floors and the like. They can also describe things of deep physical significance. Much of the ability of quantum chromodynamics to describe nuclear physics comes from these symmetry groups.

The logo at top of the page is of a trefoil knot, which I’d mentioned a couple weeks back. A trefoil knot isn’t perfectly described by its silhouette. Where the lines intersect you have to imagine the string (or whatever makes up the knot) passing twice, once above and once below itself. If you do that crossing-over and crossing-under consistently you get the trefoil knot, the simplest loop that isn’t an unknot, that can’t be shaken loose into a simple circle.

Knot Theorist

This scarf is totally biased. That’s not to say that it’s prejudiced, but that it was worked in the diagonal direction of the cloth.

My project was made from Julie Blagojevich’s free pattern Fibonacci’s Biased using Knit Picks Curio. The number of rows in each stripe is according to the numbers of the Fibonacci sequence up to 34. In other words, if you start at the blue side of the scarf and work your way right, the sequence of the number of yellow rows is 1, 1, 2, 3, 5, 8, 13, 21, 34. The sequence of the blue stripes are the same, but in the opposite direction. The effect is a rotationally symmetric scarf with few color changes at the edges and frequent color changes in the center. As I frequently tell my friends, math is beautiful.

If my geekiness hasn’t scared you away yet, here’s a random fun…

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A Summer 2015 Mathematics A To Z: knot

Knot.

It’s a common joke that mathematicians shun things that have anything to do with the real world. You can see where the impression comes from, though. Even common mathematical constructs, such as “functions”, are otherworldly abstractions once a mathematician is done defining them precisely. It can look like mathematicians find real stuff to be too dull to study.

Knot theory goes against the stereotype. A mathematician’s knot is just about what you would imagine: threads of something that get folded and twisted back around themselves. Every now and then a knot theorist will get a bit of human-interest news going for the department by announcing a new way to tie a tie, or to tie a shoelace, or maybe something about why the Christmas tree lights get so tangled up. These are really parts of the field, and applications that almost leap off the page as one studies. It’s a bit silly, admittedly. The only way anybody needs to tie a tie is go see my father and have him do it for you, and then just loosen and tighten the knot for the two or three times you’ll need it. And there’s at most two ways of tying a shoelace anybody needs. Christmas tree lights are a bigger problem but nobody can really help with getting them untangled. But studying the field encourages a lot of sketches of knots, and they almost cry out to be done out of some real material.

One amazing thing about knots is that they can be described as mathematical expressions. There are multiple ways to encode a description for how a knot looks as a polynomial. An expression like contains enough information to draw one knot as opposed to all the others that might exist. (In this case it’s a very simple knot, one known as the right-hand trefoil knot. A trefoil knot is a knot with a trefoil-like pattern.) Indeed, it’s possible to describe knots with polynomials that let you distinguish between a knot and its mirror-image reflection.

Biology, life, is knots. The DNA molecules that carry and transmit genes tangle up on themselves, creating knots. The molecules that DNA encodes, proteins and enzymes and all the other basic tools of cells, can be represented as knots. Since at this level the field is about how molecules interact you probably would expect that much of chemistry can be seen as the ways knots interact. Statistical mechanics, the study of unspeakably large number of particles, do as well. A field you can be introduced to by studying your sneaker runs through the most useful arteries of science.

That said, mathematicians do make their knots of unreal stuff. The mathematical knot is, normally, a one-dimensional thread rather than a cylinder of stuff like a string or rope or shoelace. No matter; just imagine you’ve got a very thin string. And we assume that it’s frictionless; the knot doesn’t get stuck on itself. As a result a mathematician just learning knot theory would snootily point out that however tightly wound up your extension cord is, it’s not actually knotted. You could in principle push one of the ends of the cord all the way through the knot and so loosen it into an untangled string, if you could push the cord from one end and if the cord didn’t get stuck on itself. So, yes, real-world knots are mathematically not knots. After all, something that just falls apart with a little push hardly seems worth the name “knot”.

My point is that mathematically a knot has to be a closed loop. And it’s got to wrap around itself in some sufficiently complicated way. A simple circle of string is not a knot. If “not a knot” sounds a bit childish you might use instead the Lewis Carrollian term “unknot”.

We can fix that, though, using a surprisingly common mathematical trick. Take the shoelace or rope or extension cord you want to study. And extend it: draw lines from either end of the cord out to the edge of your paper. (This is a great field for doodlers.) And then pretend that the lines go out and loop around, touching each other somewhere off the sheet of paper, as simply as possible. What had been an unknot is now not an unknot. Study wisely.

Reading the Comics, June 16, 2015: The Carefully Targeted Edition

The past several days produced a good number of comic strips mentioning mathematical topics. Strangely, they seem to be carefully targeted to appeal to me. Here’s how.

Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. (June 12) is your classic resisting-the-world-problems joke. I admit I haven’t done anything at this level of mathematics in a long while. I’m curious if actual teachers, or students, could say whether problems with ridiculous numbers of fruits actually appear in word problems, or if this is one of those motifs that’s popular despite a nearly imaginary base in the real world.

Dan Thompson’s Brevity (June 13) is aimed very precisely at the professional knot theorist. Also, mathematics includes a thing called knot theory which is almost exactly what you imagine. For a while it looked like I might get into knot theory, although ultimately I wasn’t able to find a problem interesting enough to work on that I was able to prove anything interesting about. I’m delighted a field that so many people wouldn’t imagine existed got a comic strip in this manner; I wonder if this is what dinosaur researchers felt when The Far Side was still in production.

Steve Sicula’s Home and Away (June 14) name-drops the New Math, though the term’s taken literally. The joke feels anachronistic to me. Would a kid that age have even heard of a previous generation’s effort to make mathematics about understanding what you’re doing and why? New Math (admittedly, on the way out) was my elementary school thing.

Mark Litzler’s Joe Vanilla (June 15) tickles me with the caption, “the clarity of the equation befuddles”. It’s a funny idea. Ideally, the point of an equation is to provide clarity and insight, maybe by solving it, maybe by forming it. A befuddling equation is usually a signal the problem needs to be thought out some more.

Lincoln Pierce’s Big Nate: First Class (June 16, originally run June 11, 1991) is aimed at the Mathletes out there. It throws in a slide rule mention for good measure. Given Nate’s Dad’s age in the 1991 setting it’s plausible he’d have had a slide rule. (He’s still the same age in the comic strip being produced today, so he wouldn’t have had one if the strip were redrawn.) I don’t remember being on a competitive mathematics team in high school, although I did participate in some physics contests. My recollection is that I was an inconsistent performer, though. I don’t think I had the slightly obsessive competitive urge needed to really excel in high school academic competition.

And Larry Wright’s Motley Classics (June 16, originally run June 16, 1987) is a joke about using algebra in the real world. Or at least in the world of soap operas. Back in 1987 (United States) soap operas were still a thing.

Reading the Comics, March 10, 2015: Shapes Of Things Edition

If there’s a theme running through today’s collection of mathematics-themed comic strips it’s shapes: I have good reason to talk about a way of viewing circles and spheres and even squares and boxes; and then both Euclid and men’s ties get some attention.

Eric the Circle (March 5), this one by “regina342”, does a bit of shape-name-calling. I trust that it’s not controversial that a rectangle is also a parallelogram, but people might be a bit put off by describing a circle as a sphere, what with circles being two-dimensional figures and spheres three-dimensional ones. For ordinary purposes of geometry that’s a fair enough distinction. Let me now make this complicated.

Reading the Comics, April 27, 2014: The Poetry of Calculus Edition

I think there are enough comic strips for another installment of this series, so, here you go. There are a couple comics once again using mathematics, and calculus particularly, just to signify that there’s something requiring a lot of brainpower going on, which is flattering to people who learned calculus well enough, at the risk of conveying a sense that normal people can’t hope to become literate in mathematics. I don’t buy that. Anyway, there were comics that went in other directions, which is why there’s more talk about Dutch military engineering than you might have expected for today’s entry.

Mark Anderson’s Andertoons (April 22) uses the traditional blackboard full of calculus to indicate a genius. The exact formulas on the board don’t suggest anything particular to me, although they do seem to parse. I wouldn’t be surprised if they turned out to be taken from a textbook, possibly in fluid mechanics, that I just happen not to have noticed.

Piers Baker’s Ollie and Quentin (April 23, rerun) has Ollie and Quentin flipping a coin repeatedly until Quentin (the lugworm) sees his choice come up. Of course, if it is a fair coin, a call of heads or tails will come up eventually, at least if we carefully define what we mean by “eventually”, and for that matter, Quentin’s choice will surely come up if he tries long enough.

Reading The Comics, May 20, 2012

Since I suspect that the comics roundup posts are the most popular ones I post, I’m very glad to see there was a bumper crop of strips among the ones I read regularly (from King Features Syndicate and from gocomics.com) this past week. Some of those were from cancelled strips in perpetual reruns, but that’s fine, I think: there aren’t any particular limits on how big an electronic comics page one can have, after all, and while it’s possible to read a short-lived strip long enough that you see all its entries, it takes a couple go-rounds to actually have them all memorized.

The first entry, and one from one of these cancelled strips, comes from Mark O’Hare’s Citizen Dog, a charmer of a comic set in a world-plus-talking-animals strip. In this case Fergus has taken the place of Maggie, a girl who’s not quite ready to come back from summer vacation. It’s also the sort of series of questions that it feels like come at the start of any class where a homework assignment’s due.