Reading the Comics, April 2, 2016: Keeping Me Busy Edition
After I made a little busy work for myself posting a Reading the Comics entry the other day, Comic Strip Master Command sent a rush of mathematics themes into the comics. So it goes.
Chris Browne’s Hagar the Horrible for the 31st of March happens to be funny-because-it’s-true. It’s supposed to be transgressive to see a gambler as the best mathematician available. But quite a few of the great pioneering minds of mathematics were also gamblers looking for an edge. It may shock you to learn that mathematicians in past centuries didn’t have enough money, and would look for ways to get more. And, as ever, knowing something secret about the way cards or dice or any unpredictable event might happen gives one an edge. The question of whether a 9 or a 10 is more likely to be thrown on three dice was debated for centuries, by people as familiar to us as Galileo. And by people as familiar to mathematicians as Gerolamo Cardano.
Gambling blends imperceptibly into everything people want to do. The question of how to fairly divide the pot of an interrupted game may seem sordid. But recast it as the problem of how to divide the assets of a partnership which had to halt — say, because one of the partners had to stop participating — and we have something that looks respectable. And gambling blends imperceptibly into security. The result of any one project may be unpredictable. The result of many similar ones, on average, often is. Card games or joint-stock insurance companies; the mathematics is the same. A good card-counter might be the best mathematician available.
Tony Cochran’s Agnes for the 31st name-drops Diophantine equations. It’s in the service of a student resisting class joke. Diophantine equations are equations for which we only allow integer, whole-number, answers. The name refers to Diophantus of Alexandria, who lived in the third century AD. His Arithmetica describes many methods for solving equations, a prototype to algebra as we know it in high school today. Generally, a Diophantine equation is a hard problem. It’s impossible, for example, to say whether an arbitrary Diophantine equation even has a solution. Finding what it might be is another bit of work. Fermat’s Last Theorem is a Diophantine equation, and that took centuries to work out that there isn’t generally an answer.
Mind, we can say for specific cases whether a Diophantine equation has a solution. And those specific cases can be pretty general. If we know integers a and b, then we can find integers x and y that make “ax + by = 1” true, for example.
Graham Harrop’s Ten Cats for the 31st hurts mathematicians’ feelings on the way to trying to help a shy cat. I’m amused anyway.
And Jonathan Lemon’s Rabbits Against Magic for the 1st of April mentions Fermat’s Last Theorem. The structure of the joke is fine. If we must ask an irrelevant question of the Information Desk mathematics has got plenty of good questions. The choice makes me suspect Lemon’s showing his age, though. The imagination-capturing power of Fermat’s Last Theorem as a great unknown has to have been diminished since the first proof was found over two decades ago. It’d be someone who grew up knowing there was this mystery about xn plus yn equalling zn who’d jump to this reference.
Tom Toles’s Randolph Itch, 2 am for the 2nd of April mentions “zero-sum games”. The term comes from the mathematical theory of games. The field might sound frivolous, but that’s because you don’t know how much stuff the field considers to be “games”. Mathematicians who study them consider “games” to be sets of decisions. One or more people make choices, and gain or lose as a result of those choices. That is a pretty vague description. It covers playing solitaire and multiplayer Civilization V. It also covers career planning and imperial brinksmanship. And, for that matter, business dealings.
“Zero-sum” games refer to how we score the game’s objectives. If it’s zero-sum, then anything gained by one player must be balanced by equal losses by the other player or players. For example, in a sports league’s season standings, one team’s win must balance another team’s loss. The total number of won games, across all the teams, has to equal the total number of lost games. But a game doesn’t have to be zero-sum. It’s possible to create games in which all participants gain something, or all lose something. Or where the total gained doesn’t equal the total lost. These are, imaginatively, called non-zero-sum games. They turn up often in real-world applications. Political or military strategy often is about problems in which both parties can lose. Business opportunities are often intended to see the directly involved parties benefit. This is surely why Randolph is shown reading the business pages.