Today’s mathematical-comics blog should get us up to the present. Or at least to Monday. Yes, I’m aware of which paradox of Zeno this evokes. Be nice.
Scott Adams’s Dilbert Classics for the 11th of September is a rerun from, it looks like, the 18th of July, 1992. Anyway, Dilbert has acquired a supercomputer and figures to calculate π to a lot of decimal places, to finally do something about the areas of circles. The calculation of the digits of pi is done, often on home-brewed supercomputers, to lots of digits. But the calculation of areas, or volumes, or circumferences or whatever, isn’t why. We just don’t need that many digits; forty digits of pi would be plenty for almost any calculation involving measuring things in the real world.
It’s actually a bit mysterious why the digits of pi should be worth bothering with. It’s not yet known if pi is a “normal” number, and that’s of some interest. In a normal number every finite sequence of digits appears, and as often as every other sequence of digits just as long. That is, if you break the digits of pi up into four-digit blocks, you should see “1701” and “2038” and “2468” and “9999” and all, each appearing roughly once per thousand blocks. It’s almost certain that pi is normal, because just about every number is. But it’s not proven. And if there were numerical evidence that pi wasn’t normal that would be mathematically interesting, though I wouldn’t blame everybody not in number theory for saying “huh” and “so what?” before moving on. As it is, calculating digits of pi is a good, challenging task that can be used to prove coding and computing abilities, and it might turn up something interesting. It may as well be that as anything.
Steve Breen and Mike Thompson’s Grand Avenue for the 11th of September is a “motivate the word problem” joke. So is Bill Amend’s FoxTrot Classics for the 14th (a rerun from the same day in 2004). I like Amend’s version better, partly because it gives more realistic problems. I also like that it mixes in a bit of French class. It’s not always mathematics that needs motivation.
J C Duffy’s Lug Nuts for the 11th of September is another pun strip badly timed for Pi Day.
Ruben Bolling’s Tom The Dancing Bug gave us a Super Fun-Pak Comics installment on the 11th. And that included a Chaos Butterfly installment pitting deterministic chaos against Schrödinger’s Cat. The Cat represents one (of many) interpretations of quantum mechanics, the “superposition” interpretation. It’s difficult to explain the idea philosophically, to say what is really going on. The mathematics is straightforward, though. In the most common model of quantum mechanics we describe what is going on by a probability distribution, a function that describes how likely each possible outcome is. Quantum mechanics describes how that distribution changes in time. In the superpositioning we have two, or more, probability distributions that describe very different states, but (in a way) averaged together. The changes of this combined distribution then become our idea of how the system changes in time. It’s just hard to say what it could mean when the superposition implies very different things, like a cat being both wet and dry, being equally true at once.
Julie Larson’s Dinette Set for the 12th of September is about double negatives. It’s also about the doomed attempt to bring logic to the constructions of English. At least in English a double negative — “not unwanted”, say — generally parses to a positive, even if the connotation is that the thing is only a bit wanted. This corresponds to what logicians would say. A logican might use “C” to stand in for some statement that can only be true or false. Then, saying “not not C” — an “is true” gets implicitly added to the end of that — is equivalent to saying “C [is true]”. My love, the philosopher, who knows much more Spanish than I do has pointed out that in Spanish the “not not” construction can intensify the strength of the negation, rather than annulling it. This causes us to wonder if Spanish-speaking logic students have a harder time understanding the “not not C” construction. I don’t know and would welcome insight. (Also I hope I have it right that a “not not” is an intensifier, rather than a softener. But I suppose it doesn’t matter, as long as the Spanish equivalent of “not not wanted” still connotes “unwanted”.)
Dan Collins’s Looks Good On Paper for the 12th of September is a simple early-autumn panorama kind of strip. Mathematics — particularly, geometry — gets used as the type case for elementary school. I suppose as long as diagramming sentences is out of fashion there’s no better easy-to-draw choice.
David L Hoyt and Jeff Knurek’s Jumble for the 14th of September is an abacus joke. For folks who want to do the Jumble themselves, a hint: the second word is not “Dummy” however appealing an unscramble that looks.
Stephen Beals’s Adult Children for the 14th builds on the idea of what if the universe were made wrong. And that’s expressed as a mathematics error in the building of the universe. The idea of mathematics as a transcendent and even god-touching thing is an old one. I imagine this reflects how a logically deduced fact has some kind of universal truth, that a sound argument is sound regardless of who makes it, or considers it. It’s a heady idea. Mathematics also allows us to say some very specific, and remarkable, things about the infinite. This is another god-touching notion. But we don’t have sound reason to think that universe-making must be mathematical. Mathematics can describe many aspects of the universe eerily well, yes. But is it necessary that a universe be mathematically consistent? The question seems to defy any kind of empirical answer; we must listen to philosophers, who can at least give us a reasoned answer.
Tom Thaves’s Frank and Ernest for the 14th of September depicts cave-Frank and cave-Ernest at the dawn of numbers. It suggests the symbol 1 being a representation of a stick, and 0 as a stone. The 1 as a stick seems at least imaginable; counting off things by representing them as sticks or as stroke marks feels natural. Of course I say that coming from a long heritage of doing just that. 0, as I understand it, seems to derive from making with a dot a place where zero of whatever was to be studied should appear; the dot grew into a loop probably to make it harder to miss.