Reading the Comics, October 5, 2015: Boxes and Hyperboxes Edition
I’ve got more mathematically-themed comic strips than this to write about, but this should do for one day’s postings. Motley did give me the puzzle of figuring out whether the character’s description of a process could be made sensible, which is a bit of extra fun. Boxes and cubes come up in three of the comics, too.
John McPherson’s Close to Home for the 3rd of October drops in the abacus as a backup for the bank’s computers. It’s a cute enough idea. Deep down, I admit, I’m not sure that an abacus would be needed for most of the work a teller has to do during a temporary computer outage, though. Most of the calculations to do would be working out whether there’s enough money in the account to allow a given withdrawal. That’s database-checking, really. Also I’m not sure that’s a model of abacus that’s actually been made, but if I understood what was wanted, then in some ways wasn’t the artwork successful?
Larry Wright’s Motley Classics for the 3rd of October is a rerun from the same day in 1987. Debbie gives the terribly complicated instructions on how to calculate a tip. I’m not sure how tip-calculating got to the pop culture position of “most complicated thing people do with mathematics that isn’t taxes”. Probably that it is a fairly universal need for mathematics that isn’t taxes (and so seasonally bound) explains it. I think she’s describing a valid algorithm, though, if we make some assumptions about her pronouns.
Suppose we start with the price P. Double that and move the decimal one place over, to the left I suppose, and we have 0.20 times P. Suppose that this is the first answer. If we divide this first answer by four, then, this second answer will be 0.05 times P. And subtracting the second answer from the first is, indeed, 0.15 times P, or fifteen percent of the original price. While correct, though, it’s still a lousy algorithm. Too many steps, too much division, and subtraction is a challenge. Taking one-tenth the price plus half a tenth would be numerically identical and less challenging. Taking one-sixth the price would be a division, yes, but get you to near enough fifteen percent with only one move.
Mark Pett’s Lucky Cow for the 4th of October, another rerun, shows off one of the silly semantic-equation games that mathematics majors sometimes play. Forgive them. There’s a similar argument which proves that half a ham sandwich is greater than God. It all amounts to playing on arguments which might (not always!) be correct in form but have things with silly meanings plugged into them.
Stephan Pastis’s Pearls Before Swine for the 4th of October gives Pig the chance to panic. It’s another strip about the difference between what “positive” and “negative” mean in inference testing, and so in medical testing, versus the connotations of “good” and “`bad” they have. I’ve explained this before, in other Reading the Comics essays, so I’ll spare the whole thing. But in short, “positive” in this case means “these test results are so far away from normal values that it strains plausibility to think it’s normal”. “Negative” means “these test results are not so far away from normal values as to strain plausibility to think it’s normal”.
Geoff Grogan’s Jetpack Jr for the 5th of October draws a hypercube as the box little alien Jetpack Junior arrived in. Well, these are some of the common representations of how a four-dimensional cube would look in our three-dimensional space (and that, rendered on a two-dimensional screen). The difficult-to-conceptualize part is that in the cube, seen in the middle third of the strip, every one of the red lines is the same length, and is perpendicular to all its neighbors. The triptych of shapes are all the same four-dimensional cube, too, just rotated along different axes by different amounts.
All my old links to play with hypercube rotations seem to have expired or turn out to be Java applets. Here’s a page that offers a couple of pictures, though. It has a link to an iOS app that should let people play with rotating a four-dimensional hypercube. Might enjoy it. I think this is the first time Jetpack Jr as such has got around here. It used to run as Plastic Babyheads from Outer Space, with a silly overarching story about aliens with plastic baby heads, ah, invading. I don’t think that made the Reading the Comics roster, though, unless some of the aliens mentioned pi, which they might have done.
Charles Brubaker’s Ask A Cat for the 5th of October I think is another debuting strip around here. It’s about the problem of Schrödinger’s Cat, a thought-experiment designed to show we don’t really understand what the conventional mathematical models of quantum mechanics mean. In at least some views, the mathematics of quantum mechanics suggests we could have an apparently ridiculous result: something big, like a cat, that we expect should work like a classical-physics entity, behaving instead like a quantum-mechanical entity, with no definable state. The problem has been with us for eighty years and isn’t well-answered, but that happens. Zeno’s paradoxes have been with us three thousand years and are still showing us things we don’t quite understand about divisibility and continuity.
Anthony Smith’s Learn to Speak Cat for the 5th of October is a completely different cat comic strip that I think is making a debut here. This is more a matter of silly symbolic manipulation than anything serious, though.
Tom Toles’s Randolph Itch, 2 am from the 5th of October is a rerun from 1999. And it shows a soap-bubble cube. Soap bubbles allow for some neat mathematics. They act like animate computers working out the way to enclose a given volume with the least surface area. A web site written by Dr Michael Hutchings at the University of California/Berkeley describes some of the mathematical work involved. Surprising to me is that it was only in the 1970s that the “double bubble conjecture” was proven. That’s a question about how to cover a given volume using two bubbles. The answer is what you might get from playing with soap bubble wands, but it took about a century of working on to prove. Granting, mathematicians did other things with their time, so it wasn’t uninterrupted soap-bubble work. Hutchings includes some review of the field as it existed in the early 2000s, and lists three open problems. The first of them is one that’s understandable even without knowing more mathematical lingo than what R3 is. (And folks who’re hanging around here know that by now.) Also it has pictures of soap bubbles, which are good for a lazy Friday morning.