Reading the Comics, November 20, 2014: Ancient Events Edition

I’ve got enough mathematics comics for another roundup, and this time, the subjects give me reason to dip into ancient days: one to the most famous, among mathematicians and astronomers anyway, of Greek shipwrecks, and another to some point in the midst of winter nearly seven thousand years ago.

Eric the Circle (November 15) returns “Griffinetsabine” to the writer’s role and gives another “Shape Single’s Bar” scene. I’m amused by Eric appearing with his ex: x is practically the icon denoting “this is an algebraic expression”, while geometry … well, circles are good for denoting that, although I suspect that triangles or maybe parallelograms are the ways to denote “this is a geometric expression”. Maybe it’s the little symbol for a right angle.

Jim Meddick’s Monty (November 17) presents Monty trying to work out just how many days there are to Christmas. This is a problem fraught with difficulties, starting with the obvious: does “today” count as a shopping day until Christmas? That is, if it were the 24th, would you say there are zero or one shopping days left? Also, is there even a difference between a “shopping day” and a “day” anymore now that nobody shops downtown so it’s only the stores nobody cares about that close on Sundays? Sort all that out and there’s the perpetual problem in working out intervals between dates on the Gregorian calendar, which is that you have to be daft to try working out intervals between dates on the Gregorian calendar. The only worse thing is trying to work out the intervals between Easters on it. My own habit for this kind of problem is to use the United States Navy’s Julian Date conversion page. The Julian date is a straight serial number, counting the number of days that have elapsed since noon Universal Time at what’s called the 1st of January, 4713 BCE, on the proleptic Julian calendar (“proleptic” because nobody around at the time was using, or even imagined, the calendar, but we can project back to what date that would have been), a year picked because it’s the start of several astronomical cycles, and it’s way before any specific recordable dates in human history, so any day you might have to particularly deal with has a positive number. Of course, to do this, we’re transforming the problem of “counting the number of days between two dates” to “counting the number of days between a date and January 1, 4713 BCE, twice”, but the advantage of that is, the United States Navy (and other people) have worked out how to do that and we can use their work.

Bill Hind’s kids-sports comic Cleats (November 19, rerun) presents Michael offering basketball advice that verges into logic and set theory problems: making the ball not go to a place outside the net is equivalent to making the ball go inside the net (if we decide that the edge of the net counts as either inside or outside the net, at least), and depending on the problem we want to solve, it might be more convenient to think about putting the ball into the net, or not putting the ball outside the net. We see this, in logic, in a set of relations called De Morgan’s Laws (named for Augustus De Morgan, who put these ideas in modern mathematical form), which describe what kinds of descriptions — “something is outside both sets A and B at one” or “something is not inside set A or set B”, or so on — represent the same relationship between the thing and the sets.

Tom Thaves’s Frank and Ernest (November 19) is set in the classic caveman era, with prehistoric Frank and Ernest and someone else discovering mathematics and working out whether a negative number times a negative number might be positive. It’s not obvious right away that they should, as you realize when you try teaching someone the multiplication rules including negative numbers, and it’s worth pointing out, a negative times a negative equals a positive because that’s the way we, the users of mathematics, have chosen to define negative numbers and multiplication. We could, in principle, have decided that a negative times a negative should give us a negative number. This would be a different “multiplication” (or a different “negative”) than we use, but as long as we had logically self-consistent rules we could do that. We don’t, because it turns out negative-times-negative-is-positive is convenient for problems we like to do. Mathematics may be universal — something following the same rules we do has to get the same results we do — but it’s also something of a construct, and the multiplication of negative numbers is a signal of that.

Goofy sees the message 'buried treasure in back yard' in his alphabet soup; what are the odds of that?

The Mickey Mouse comic rerun the 20th of November, 2014.

Mickey Mouse (November 20, rerun) — I don’t know who wrote or draw this, but Walt Disney’s name was plastered onto it — sees messages appearing in alphabet soup. In one sense, such messages are inevitable: jumble and swirl letters around and eventually, surely, any message there are enough letters for will appear. This is very similar to the problem of infinite monkeys at typewriters, although with the special constraint that if, say, the bowl has only two letters “L”, it’s impossible to get the word “parallel”, unless one of the I’s is doing an impersonation. Here, Goofy has the message “buried treasure in back yard” appear in his soup; assuming those are all the letters in his soup then there’s something like 44,881,973,505,008,615,424 different arrangements of letters that could come up. There are several legitimate messages you could make out of that (“treasure buried in back yard”, “in back yard buried treasure”), not to mention shorter messages that don’t use all those letters (“run back”), but I think it’s safe to say the number of possible sentences that make sense are pretty few and it’s remarkable to get something like that. Maybe the cook was trying to tell Goofy something after all.

Mark Anderson’s Andertoons (November 20) is a cute gag about the dangers of having too many axes on your plot.

Gary Delainey and Gerry Rasmussen’s Betty (November 20) mentions the Antikythera Mechanism, one of the most famous analog computers out there, and that’s close enough to pure mathematics for me to feel comfortable including it here. The machine was found in April 1900, in ancient shipwreck, and at first seemed to be just a strange lump of bronze and wood. By 1902 the archeologist Valerios Stais noticed a gear in the mechanism, but since it was believed the wreck far, far predated any gear mechanisms, the machine languished in that strange obscurity that a thing which can’t be explained sometimes suffers. The mechanism appears to be designed to be an astronomical computer, tracking the positions of the Sun and the Moon — tracking the actual moon rather than an approximate mean lunar motion — the rising and etting of some constellations, solar eclipses, several astronomical cycles, and even the Olympic Games. It’s an astounding mechanism, it’s mysterious: who made it? How? Are there others? What happened to them? How was the mechanical engineering needed for this developed, and what other projects did the people who created this also do? Any answers to these questions, if we ever know them, seem sure to be at least as amazing as the questions are.