Reading the Comics, January 16, 2019: Young People’s Mathematics Edition

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.

Mathematician: 'Only young people do revolutionary mathematics. 20 is ancient. 15 is old. 10 is middle-aged.' Kid, holding up two fingers: 'Three is THIS MANY.' Mathematician: 'It's counter-intuitive, but we must accept it.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 14th of January, 2019. I have many essays inspired by something said in Saturday Morning Breakfast Cereal. You can find them at this link.

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.

Spud: 'Can you help me with this math problem?' Wallace: '10 + 12? It helps if you visualize real things. Say you have ten cans of E-Z Cheez and someone gives you twelve more ... how many cans of E-Z Cheez do you have?' Spud: 'I'm sweating.'
Will Henry’s Wallace the Brave for the 14th of January, 2019. I have only had a few chances to talk about Wallace the Brave so far, but the chances I’ve taken are at this link. (It and Breaking Cat News are the two recently-launched comics I’m most excited by.)

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.

Widow, to the party gathered at the gravesite: 'Needless to say, calculus wasn't his best subject.' The epitaph: 'It's a calculated risk, but you only live once!'
Wiley Miller’s Non Sequitur for the 15th of January, 2019. Essays mentioning Non Sequitur should appear at this link.

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.

Kid: 'Dad! Let's tackle my homework!' Moose: 'Later, son. I'm busy.' Kid goes to Westpork Savings and Loan. The bank clerk's sitting under a sign, 'Let us help you with your money problems.' Kid reads: 'If Farmer Smith sells wheat at $1.25 a bushel and Farmer Brown sells it at $1.30, how many bushels must each sell ... '
Bob Weber Sr’s Moose and Molly for the 16th of January, 2019. I haven’t had the chance to talk about Moose and Molly before. But now I have the tag, and will be putting essays mentioning it at this link.

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”.

I think there’s one more batch of comic strips to discuss this week. When I’ve published it, you should find the essay at this link. And then there’ll be Sunday again.


Reading the Comics, July 28, 2018: Command Performance Edition

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.

Check-out at Whole Numbers Foods. The cashier, 7, asks, 'We have great discounts! Are you a prime member?' The customer is an unhappy-looking 8.
Scott Metzger’s The Bent Pinky for the 24th of July, 2018. I’m curious whether the background customers were a 2 and a 3 because they do represent prime numbers, or whether they were just picked because they look good.

Tony Rubino and Gary Markstein’s Daddy’s Home for the 25th is an iteration of bad-at-arithmetic jokes. In this case there’s the arithmetic that’s counting, and there’s the arithmetic that’s the addition and subtraction demanded for checkbook-balancing.

Dad: 'Dang ... my checkbook doesn't balance again. That's happened more times than I can count.' Neighbor: 'See, that's why your checkbook doesn't balance.'
Tony Rubino and Gary Markstein’s Daddy’s Home for the 25th of July, 2018. I don’t question the plausibility of people writing enough checks in 2018 that they need to balance them, even though my bank has been sold three times to new agencies before I’ve been able to use up one book of 25 checks. I do question whether people with the hobby of checkbook-balancing routinely do this outside, at the fence, while hanging out with the neighbor.

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.

[ When Einstein switched to something a lot easier. ] (He's standing in front of a blackboard full of sketches.) Einstein: '*Sigh* ... I give up. No matter how many ways I work it out, the squirrels still get to the bird feeders.
Wiley Miller’s Non Sequitur for the 25th of July, 2018. In fairness to the squirrels, they have to eat something as long as the raccoons are getting into the squirrel feeders.

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.

General Halftrack, hitting a golf ball onto the green: 'FIVE!' Lieutenant Fuzz: 'You're supposed to yell 'fore'!' Halftrack: 'A better shot deserves a better number!'
Mort Walker and Greg Walker’s Beetle Bailey for the 26th of July, 2018. Mort Walker’s name is still on the credits, and in the signature. I don’t know whether they’re still working through comics which he had a hand in writing or drawing before his death in January. It would seem amazing to be seven months ahead of deadline — I’ve never got more than two weeks, myself, and even that by cheating — but he did have a pretty good handle on the kinds of jokes he should be telling.

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.

Bucky Katt: 'See, at first Whitey was giving me a million to one odds that the Patriots would win the World Series, but I was able to talk him down to ten to one odds. So, since it was much more likely to happen at ten to one, I upped my bet from one dollar to a thousand dollars.' Rob: 'Do you know *anything* about gambling?' Bucky: 'Duhhh, excuse me, Senor Skeptico, I think it was me who made the bet --- not you!'
Darby Conley’s Get Fuzzy rerun for the 28th of July, 2018. It originally ran the 13th of May, 2006. It may have been repeated since then, also.

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.

If you’ve liked this essay you might like other Reading the Comics posts. Many of them are gathered at this link. When I have other essays that discuss The Bent Pinky at this link; it’s a new tag. Essays tagged Daddy’s Home are at this link. Essays that mention the comic strip Non Sequitur should be at this link, when they come up too. (This is another new tag, to my surprise.) Other appearances of Beetle Bailey should be on this page. And other Get Fuzzy-inspired discussions are at this link.