Reading the Comics, January 15, 2015: Electric Brains and Klein Bottles Edition
I admit I don’t always find a theme running through Comic Strip Master Command’s latest set of mathematically-themed comics. The edition names are mostly so that I can tell them apart when I see a couple listed in the Popular Posts roundup anyway.
Jimmy Hatlo’s Little Iodine is a vintage comic strip from the 1950s. It strikes me as an unlicensed adaptation of Baby Schnooks, but that’s not something for me to worry about. The particular strip, originally from the 7th of November, 1954 (and just run the 12th of January this year) interests me for its ancient views of computers. It’s from the days they were called “electric brains”. I’m also impressed that the machine on display early on is able to work out the “square root of 7921 x2 y2”. The square root of 7921 is no great feat. Being able to work with the symbols of x and y without knowing what they stand for, though, does impress me. I’m not sure there were computers which could handle that sort of symbolic manipulation in 1954. That sort of ability to work with a quantity by name rather than value is what we would buy Mathematica for, if we could afford it. It’s also at least a bit impressive that someone knows the square of 89 offhand. All told, I think this is my favorite of this essay’s set of strips. But it’s a weak field considering none of them are “students giving a snarky reply to a homework/exam/blackboard question”.
Joe Martin’s Willy and Ethel for the 13th of January is a percentages joke. Some might fault it for talking about people giving 110 percent, but of course, what is “100 percent”? If it’s the standard amount of work being done then it does seem like ten people giving 110 percent gets the job done as quickly as eleven people doing 100 percent. If work worked like that.
Steve Sicula’s Home and Away for the 13th (a rerun from the 8th of October, 2004) gives a wrongheaded application of a decent principle. The principle is that of taking several data points and averaging their value. The problem with data is that it’s often got errors in it. Something weird happened and it doesn’t represent what it’s supposed to. Or it doesn’t represent it well. By averaging several data points together we can minimize the influence of a fluke reading. Or if we’re measuring something that changes in time, we might use a running average of the last several sampled values. In this way a short-term spike or a meaningless flutter will be minimized. We can avoid wasting time reacting to something that doesn’t matter. (The cost of this, though, is that if a trend is developing we will notice it later than we otherwise would.) Still, sometimes a data point is obviously wrong.
Zach Weinersmith’s Saturday Morning Breakfast Cereal wanted my attention, and so on the 13th it did a joke about Zeno’s Paradox. There are actually four classic Zeno’s Paradoxes, although the one riffed on here I think is the most popular. This one — the idea that you can’t finish something (leaving a room is the most common form) because you have to get halfway done, and have to get halfway to being halfway done, and halfway to halfway to halfway to being done — is often resolved by people saying that Zeno just didn’t understand that an infinite series could converge. That is, that you can add together infinitely many numbers and get a finite number. I’m inclined to think Zeno did not, somehow, think it was impossible to leave rooms. What the paradoxes as a whole get to are questions about space and time: they’re either infinitely divisible or they’re not. And either way produces effects that don’t seem to quite match our intuitions.
The next day Saturday Morning Breakfast Cereal does a joke about Klein bottles. These are famous topological constructs. At least they’re famous in the kinds of places people talk about topological constructs. It’s much like the Möbius strip, a ribbon given a twist and joined back to its edge. The Klein bottle similarly you can imagine as a cylinder stretched out into the fourth dimension, given a twist, then joined back to itself. We can’t really do this, what with it being difficult to craft four-dimensional objects. But we can imagine this, and it creates an object that doesn’t have a boundary, and has only one side. There’s not an inside or an outside. There’s no making this in the real world, but we can make nice-looking approximations, usually as bottles.
Ruben Bolling’s Super-Fun-Pak Comix for the 13th of January is an extreme installment of Chaos Butterfly. The trouble with touching Chaos Butterfly to cause disasters is that you don’t know — you can’t know — what would have happened had you not touched the butterfly. You change your luck, but there’s no way to tell whether for the better or worse. One of the commenters at Gocomics.com alludes to this problem.
Jon Rosenberg’s Scenes From A Multiverse for the 13th of January makes quite literal quantum mechanics talk about probability waves and quantum foam and the like. The wave formulation of quantum mechanics, the most popular and accessible one, describes what’s going on in equations that look much like the equations for things diffusing into space. And quantum mechanical problems are often solved by supposing that the probability distribution we’re interested in can be broken up into a series of sinusoidal waves. Representing a complex function as a set of waves is a common trick, not just in quantum mechanics, because it works so well so often. Sinusoidal waves behave in nice, predictable ways for most differential equations. So converting a hard differential equation problem into a long string of relatively easy differential equation problems is usually a good trade.
Tom Thaves’s Frank and Ernest for the 14th of January ties together the baffling worlds of grammar and negative numbers. It puts Frank and Ernest on panel with Euclid, who’s a fair enough choice to represent the foundation of (western) mathematics. He’s famous for the geometry we now call Euclidean. That’s the common everyday kind of blackboards and tabletops and solid cubes and spheres. But among his writings are compilations of arithmetic, as understood at the time. So if we know anyone in Ancient Greece to have credentials to talk about negative numbers it’s him. But the choice of Euclid traps the panel into an anachronism: the Ancient Greeks just didn’t think of negative numbers. They could work through “a lack of things” or “a shortage of something”, but a negative? That’s a later innovation. But it’s hard to think of a good rewriting of the joke. You might have Isaac Newton be consulted, but Newton makes normal people think of gravity and physics, confounding the mathematics joke. There’s a similar problem with Albert Einstein. Leibniz or Gauss should be good, but I suspect they’re not the household names that even Euclid is. And if we have to go “less famous mathematician than Gauss” we’re in real trouble. (No, not Andrew Wiles. Normal people know him as “the guy that proved Fermat’s thing”, and that’s too many words to fit on panel.) Perhaps the joke can’t be made to read cleanly and make good historic sense.