So last week there were only a handful of comic strips which mentioned mathematics in any detail. That is, that brought up some point that I could go on about for a paragraph or so. There were more that had some marginal mathematics content. I gather them here for the interested.
Gordon Bess’s Redeye rerun for the 7th mentions mathematics as the homework that the chief is helping his son with. It could be any subject, but arithmetic is easy to fit into one panel of comic strip. And it’s also easy to establish that the work is on a low level. The comic originally ran the 18th of February, 1973.
John McPherson’s Close to Home for the 11th mentions percentages. The joke’s built on doing a meaningless calculation. And a bit of convention, in which the label has been reduced to the point people could mis-read it. You just know this guy would tell the “scanner didn’t pick it up, it must be free” joke if he thought of it that fast.
Paige Braddock’s Jane’s World for the 11th is part of a sequence from 2002 in which Jane concludes the problems in her life came from the introduction of algebra. Her niece is having fun with algebra, a thing I understand. Algebra can be a more playful, explorative kind of mathematics than you get with, like, long division. For some people it’s liberating. This one’s a new tag, so I’m sure to be surprised that I have ever mentioned Jane’s World sometime in the future.
Wiley Miller’s Non Sequitur for the 11th presents a Sphere of Serenity. Or, as Danae’s horse points out, a Cube of Serenity. There are ways that the difference between a sphere and a cube becomes nothing. If the cube and the sphere have infinitely great extent, for example, then there’s no observable difference between the shapes. Or if we use certain definitions of distance then the sphere — as in, the points all an equal distance from a center — can be indistinguishable from a cube. That’s not what the comic is going for.
Today’s quartet of mathematically-themed comic strips doesn’t have an overwhelming theme. There’s some bits about the mathematics that young people do, so, that’s enough to separate this from any other given day’s comics essay.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 14th is built on a bit of mathematical folklore. As Weinersmith’s mathematician (I don’t remember that we’ve been given her name) mentions, there is a belief that “revolutionary” mathematics is done by young people. That isn’t to say that older mathematicians don’t do great work. But the stereotype is that an older mathematician will produce masterpieces in already-established fields. It’s the young that establish new fields. Indeed, one of mathematics’s most prestigious awards, the Fields Medal, is only awarded to mathematicians under the age of forty. I was cheated of mine. Long story.
There’s intuitive appeal in the idea that revolutions in thinking are for the young. We think that people get set in their ways as they develop their careers. We have a couple dramatic examples, most notably Évariste Galois, who developed what we now see as foundations of group theory and died at twenty. While the idea is commonly held, I don’t know that it’s actually true. That is, that it holds up to scrutiny. It seems hard to create a definition for “revolutionary mathematics” that could be agreed upon by two people. So it would be difficult to test at what age people do their most breathtaking work, and whether it is what they do when young or when experienced.
Is there harm to believing an unprovable thing? If it makes you give up on trying, yes. My suspicion is that true revolutionary work happens when a well-informed, deep thinker comes to a field that hasn’t been studied in that way before. And when it turns out to be a field well-suited to study that way. That doesn’t require youth. It requires skill in one field, and an understanding that there’s another field ready to be studied that way.
Will Henry’s Wallace the Brave for the 14th is a mathematics anxiety joke. Wallace tries to help by turning an abstract problem into a concrete one. This is often a good way to approach a problem. Even in more advanced mathematics, one can often learn the way to solve a general problem by trying a couple of specific examples. It’s almost as though there’s only a certain amount of abstraction people can deal with, and you need to re-cast problems so they stay within your limits.
Yes, the comments turn to complaining about Common Core. I’m not sure what would help Spud work through this problem (or problems in general). But thinking of alternate problems that estimated or approached what he really wanted might help. If he noticed, for example, that 10 + 12 has to be a little more than 10 + 10, and he found 10 + 10 easy, then he’d be close to a right answer. If he noticed that 10 + 12 had to be 10 + 10 + 2, and he found 10 + 10 easy, then he might find 20 + 2 easy as well. Maybe Spud would be better off thinking of ways to rewrite a problem without changing the result.
Wiley Miller’s Non Sequitur for the 15th mentions calculus. It’s more of a probability joke. To speak of a calculated risk is to speak of doing something that’s not certain, but that has enough of a payoff to be worth the cost of failure. But one problem with this attitude is that people are very, very bad at estimating probabilities. We have terrible ideas of how likely losses are and how uncertain rewards can be. But even if we allow that the risks and rewards are calculated right, there’s a problem with things you only do once. Or only can do once. You can get into a good debate about whether there’s even a meaningful idea of probability for things that happen only the one time. Life’s among them.
Bob Weber Sr’s Moose and Molly for the 16th is a homework joke. It does actually depend on being mathematics homework, though, or there’d be no grounds for Moose’s kid to go to the savings and loan clerk who’ll help with “money problems”.
One of the comics from the last half of last week is here mostly because Roy Kassinger asked if I was going to include it. Which one? Read on and see.
Scott Metzger’s The Bent Pinky for the 24th is the anthropomorphic-numerals joke for the week. It’s pretty easy to learn, or memorize, or test small numbers for whether they’re prime. The bigger a number gets the harder it is. Mostly it takes time. You can rule some numbers out easily enough. If they’re even numbers other than 2, for example. Or if their (base ten) digits add up to a multiple of three or nine. But once you’ve got past a couple easy filters … you don’t have to just try dividing them by all the prime numbers up to their square root. Comes close, though. Would save a lot of time if the numerals worked that out ahead of time and then kept the information around, in case it were needed. Seems a little creepy to be asking that of other numbers, really. Certainly to give special privileges to numbers for accidents of their creation.
Wiley Miller’s Non Sequitur for the 25th is an Einstein joke. In a rare move for the breed this doesn’t have “E = mc2” in it, except in the implication that it was easier to think of than squirrel-proof bird feeders would be. Einstein usually gets acclaim for mathematical physics work. But he was also a legitimate inventor, with patents in his own right. He and his student Leó Szilárd developed a refrigerator that used no moving parts. Most refrigeration technology requires the use of toxic chemicals to actually do the cooling. Einstein and Szilárd hoped to make something less likely to leak these toxins. The design never saw widespread use. Ordinary refrigerators, using freon (shockingly harmless biologically, though dangerous to the upper atmosphere) got reliable enough that the danger of leaks got tolerable. And the electromagnetic pump the machine used instead made noise that at least some reports say was unbearable. The design as worked out also used a potassium-sodium alloy, not the sort of thing easy to work with. Now and then there’s talk of reviving the design. Its potential, as something that could use any heat source to provide refrigeration, seems neat. And everybody in this side of science and engineering wants to work on something that Einstein touched.
Mort Walker and Greg Walker’s Beetle Bailey for the 26th is here by special request. I wasn’t sure it was on-topic enough for my usual rigorous standards. But there is some social-aspects-of-mathematics to it. The assumption that ‘five’ is naturally better than ‘four’ for example. There is the connotation that some numbers are better than others. Yes, there are famously lucky numbers like 7 or unlucky ones like 13 (in contemporary Anglo-American culture, anyway; others have different lucks). But there’s also the sense that a larger number is of course better than a smaller one.
Except when it’s not. A first-rate performance is understood to be better than a third-rate one. A star of the first magnitude is more prominent than one of the fourth. This whether we mean celebrities or heavenly bodies. We have mixed systems. One at least respects the heritage of ancient Greek astronomers, who rated the brightest of stars as first magnitude and the next bunch as second and so on. In this context, if we take brightness to be a good thing, we understand lower numbers to be better. Another system regards the larger numbers as being more of what we’re assumed to want, and therefore be better.
Nasty confusions will happen when the schemes of thought collide. Is a class three hurricane more or less of a threat than a class four? Ought we be more worried if the United States Department of Defense declares it’s moved from Defence Condition four to Defcon 3? In October 1966, the Fermi 1 fission reactor near Detroit suffered a “Class 1 emergency”. Does that mean the city was at the highest or the lowest health risk from the partial meltdown? (In this case, this particular term reflects the lowest actionable level of radiation was detected. I am not competent to speak on how great the risk to the population was.) It would have been nice to have unambiguous language on this point.
On to the joke’s logic, though. Wouldn’t General Halftrack be accustomed to thinking of lower numbers as better? Getting to the green in three strokes is obviously preferable to four, and getting there in five would be a disaster.
Darby Conley’s Get Fuzzy for the 28th is an applied-probability strip. The calculating of odds is rich with mathematical and psychological influences. With some events it’s possible to define quite precisely what the odds should be. If there are a thousand numbers each equally likely to be the daily lottery winner, and only one that will be, we can go from that to saying what the chance of 254 being the winner is. But many events are impossible to forecast that way. We have to use other approaches. If something has happened several times recently, we can say it’s probably rather likely. Fluke events happen, yes. But we can do fairly good work by supposing that stuff is mostly normal, and that the next baseball season will look something like the last one.
As to how to bet wisely — well, many have tried to work that out. One of the big questions in financial mathematics is how to hedge bets. I write financial mathematics, but it applies to sports betting and really anything else with many outcomes. One of the common goals is to simply avoid catastrophe, to make sure that whatever happens you aren’t too badly off. This involves betting various amounts on many outcomes. More on the outcomes you think likely, but also some on the improbable outcomes. Long shots do sometimes happen, and pay out well; it can be worth putting a little money on that just in case. Judging the likelihood of those events, especially in complicated problems that can’t be reduced to logic, is one of the hard parts. If it could be made into a system we wouldn’t need people to do it. But it does seem that knowing what you bet on helps make better bets.