Rather than wait to read today’s comics I’m just going to put in a fresh entry going over mathematical points raised in the funny pages. This one turned out to include a massive diversion into the wonders of the ancient Roman calendar, which is a mathematical topic, really, although there’s no calculations involved in it just here.
Bill Hinds’s Cleats (March 7, rerun) calls on one of the common cultural references to percentages, the idea of athletes giving 100 percent efforts. (Edith is feeling more like an 80 percent effort, or less than that.) The idea of giving 100 percent in a sport is one that invites the question, 100 percent of what; granting that there is some standard expectable effort made, then, even the sports reporting cliche of giving 110 percent is meaningful.
Cleats continued on the theme the next day, as Edith was thinking more of giving about 79 percent of 80 percent, and it’s not actually that hard to work out in your head what percent that is, if you know anything about doing arithmetic in your head.
Jef Mallet’s Frazz (March 14) was not actually the only comic strip among the roster I normally read to make a Pi Day reference, but I think it suffices as the example for the whole breed. I admit that I feel a bit curmudgeonly that I don’t actually care about Pi Day. I suppose that as a chance for people to promote the idea of learning mathematics, and maybe attach it to some of the many interesting things to be said about mathematics using Pi as the introductory note the idea is fine, but just naming a thing isn’t by itself a joke. I’m told that Facebook (I’m not on it) was thick with people posting photographs of pies, which is probably more fun when you think of it than when you notice everybody else thought of it too. Anyway, organized Pi Day events are still pretty new as Internet Pop Holidays go. Perhaps next year’s comics will be sharper.
Jenny Campbell’s Flo and Friends (March 15) comes back to useful mental arithmetic work, in this case in working out a reasonable tip. A twenty-percent tip is, mercifully, pretty easy to remember just as what’s-her-name specifies. (I can’t think of the kid’s name and there’s no meet-our-cast page on the web site. None of the commenters mention her name either, although they do make room to insult health care reform and letting students use calculators to do arithmetic, so, I’m sorry I read that far down too.) But as ever you need to make sure the process is explained clearly and understood, and Tina needed to run a sanity check on the result. Sanity checks, as suggested, won’t show that your answer is right, but they will rule out some of the wrong ones. (A fifteen percent tip is a bit annoying to calculate exactly, but dividing the original amount by six will give you a sixteen-and-two-thirds percent tip, which is surely close enough, especially if you round off to a quarter-dollar.)
Steve Breen and Mike Thompson’s Grand Avenue (March 15) has the kids wonder what are the ides of March; besides that they’re the 15th of the month and they’re used for some memorable writing about Julius Caesar it’s a fair thing not to know. They derive from calendar-keeping, one of the oldest useful applications of mathematics and astronomy. The ancient Roman scheme set three special dates in the month: the kalends, which seem to have started as the day of the new moon as observed in Rome; the nones, when the moon was at its first quarter; and the ides, when the moon was full.
But by the time of Numa Pompilius, the second (traditional) King of Rome, who reformed the calendar around 713 BC, the lunar link was snapped, partly so that the calendar year could more nearly fit the length of the time it takes to go from one spring to another. (Among other things the pre-Numa calendar had only ten months, with the days between December and March not belonging to any month; since Romans were rather agricultural at the time and there wasn’t much happening in winter, this wasn’t really absurd, even if I find it hard to imagine living by this sort of standard. After Numa there were only about eleven days of the year unaccounted for, with the time made up, when it needed to be, by inserting an extra month, Mercedonius, in the middle of February.) Months then had, February excepted, either 29 or 31 days, with the ides being on the fifteenth day of the 31-day months (March, May, July, and October) and the thirteenth day of the 29-day months.
For reasons that surely made sense if you were an ancient Roman the day was specified as the number of days until the next kalend, none, or ide; so, for example, while the 13th of March would be the 2nd day before the ides of March, II Id Mar, the 19th of March would be recorded as the the the 14th day before the kalend of April, or, XIV Kal Apr. I admit I could probably warm up to counting down to the next month event, but the idea of having half the month of March written down on the calendar as a date with “April” in it leaves me deeply unsettled. And that’s before we even get into how an extra month might get slipped into the middle of February (between the 23rd and the 24th of the month, the trace of which can still be observed in the dominical letters of February in leap years, on Roman Catholic and Anglican calendars, and in the obscure term “bissextile year” for leap year). But now that you see that, you know why (a) the ancient Romans had so much trouble getting their database software to do dates correctly and (b) you get to be all smugly superior to anyone who tries making a crack about the United States Federal Income Tax deadline being on the Ides of April, since they never are.
(Warning: absolutely no one ever will be impressed by your knowledge of the Ides of April and their inapplicability to discussions of the United States Federal Income Tax. However, you might use this as a way to appear like you’re making friendly small talk while actually encouraging people to leave you alone.)
Tom Horacek’s Foolish Mortals (March 17), an erratically-published panel strip, calls on the legend of how mathematicians “usually” peak in their twenties. It’s certainly said of mathematicians that they do their most important work while young — note that the Fields Medal is explicitly given to mathematicians for work done when they were under forty years old — although I’m not aware of anyone who’s actually studied this, and the number of great mathematicians who insist on doing brilliant work into their old age is pretty impressive.
Certainly, for example, Newton began work on calculus (and optics and gravitation) when he was about 23, but he didn’t publish until he was about fifty. (Leibniz, meanwhile, started publishing calculus his way at about age 38.) It’s probably impossible to say what Leonhard Euler’s most important work was, but (for example) his equations describing inviscid fluids — which would be the masterpiece for anybody not Euler — he published when he was fifty. Carl Friedrich Gauss didn’t start serious work in electromagnetism until he was about 55 years old, too. The law of electric flux which Gauss worked out for that — which, again, would have been the career achievement if Gauss weren’t overflowing with them — he published when he was 58.
I guess that I’m saying is that great minds, at least, don’t necessarily peak in their twenties, or at least they have some impressive peaks afterwards too.