Reading the Comics, December 23, 2015: Richard Thompson Christmas Trees Edition


Richard Thompson’s Cul de Sac for the 19th of December (a rerun, alas, from the 18th of December, 2010) gives me a name for this Reading the Comics installment. Just as in a Richard’s Poor Almanac mentioned last time he gives us a Christmas tree occupying a non-Euclidean space. Non-Euclidean spaces do open up the possibility of many wondrous and counterintuitive phenomena. Trees probably aren’t among them, but I don’t know a better shorthand way to describe their mysteries. And if you’re not sure why so many people say this was the greatest comic strip of our still-young century, look at little Pete in the last panel. Both his expression and the composition of the panel are magnificent.

Tom Toles’s Randolph Itch, 2 am for the 21st of December is a rerun. And it’s one that’s been mentioned around here as recently as August. I don’t care. It’s still a good funny slapstick joke. The kicker at the bottom is also a solid giggle.

Richard Thompson’s Poor Richard’s Almanac for the 21st of December justifies my theme with its Platonic Fir. The Platonic Ideals of objects are, properly speaking, philosophical constructs. If they are constructs, anyway, and not the things that truly exist, and yes, we must be careful what we mean by ‘exist’ in this context. But Thompson’s diagram shows this Platonic Fir drawn as a mathematical diagram. That’s another common motif. Mathematical constructs, ideas like “triangles” and “circles” and “rotations”, do suggest Platonic Ideals quite closely. We might be a bit pressed to say what the quintessence of chair-ness is, the thing all chairs must be aspects of. But we can be pretty sure we understand what a triangle is, apart from our messy and imperfect real-world approximations of a true triangle. When mathematics enthusiasts speak of the beauty of pure mathematics it does seem like they speak of the beauty of approaching Platonic Ideals.

John Graziano’s Ripley’s Believe It or Not for the 21st of December continues its Rubik’s Cube obsession. Graziano spells Rubik correctly this time.

Don Asmussen’s Bad Reporter panel for the 23rd of December does a joke that depends on the idea of getting to be “more than infinity”. Every kid has run into the problem of trying to understand “infinity plus one”. The way we speak of “infinity” we can’t really talk about getting “more than infinity”. But we are able to think meaningfully of ways to differentiate sizes of infinity. There are some infinitely large sets that, in a sensible way, are bigger than other infinitely large sets. That’s a fun field of mathematics. You can get to interesting questions in it without needing much background or experience. It’s almost ideal for pop-mathematics essays and if you don’t believe me, then look at how many results you get googling for “Cantor’s Diagonalization Argument”. It’s not an infinite number of results, but it’ll get you quite close.

Brian and Ron Boychuk’s Chuckle Brothers for the 23rd of December is the anthropomorphic-numerals joke for this time around.

Mark Litzler’s Joe Vanilla for the 23rd of December is built on the idea that it’s absurd to develop an algorithm that could predict earning potential, hairline at 50, and fidelity. It sounds silly at first glance. But if we’ve learned anything from sabermetrics it’s that all kinds of physical traits can be studied, and modeled, and predicted. With a large and reliable enough data set, and with a mindfully developed algorithm, these models can become quite good at predicting things. The underlying property is that on average, people are average. If we know what is typical, and we have reason to think that “typical” is not changing, then we can forecast the future pretty well based on what we already see. Or if we have reason to expect that “typical” is changing in ways we understand, we can still make good forecasts.

Reading the Comics, April 6, 2015: Little Infinite Edition


As I warned, there were a lot of mathematically-themed comic strips the last week, and here I can at least get us through the start of April. This doesn’t include the strips that ran today, the 7th of April by my calendar, because I have to get some serious-looking men to look at my car and I just know they’re going to disapprove of what my CV joint covers look like, even though I’ve done nothing to them. But I won’t be reading most of today’s comic strips until after that’s done, and so commenting on them later.

Mark Anderson’s Andertoons (April 3) makes its traditional appearance in my roundup, in this case with a business-type guy declaring infinity to be “the loophole of all loopholes!” I think that’s overstating things a fair bit, but strange and very counter-intuitive things do happen when you try to work out a problem in which infinities turn up. For example: in ordinary arithmetic, the order in which you add together a bunch of real numbers makes no difference. If you want to add together infinitely many real numbers, though, it is possible to have them add to different numbers depending on what order you add them in. Most unsettlingly, it’s possible to have infinitely many real numbers add up to literally any real number you like, depending on the order in which you add them. And then things get really weird.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips (April 3) is the other strip in this roundup to at least name-drop infinity. I confess I don’t see how “being infinite” would help in bringing about world peace, but I suppose being finite hasn’t managed the trick just yet so we might want to think outside the box.

Continue reading “Reading the Comics, April 6, 2015: Little Infinite Edition”

Reblog: Lawler’s Log


I don’t intend to transform my writings here into a low-key sports mathematics blog. I just happen to have run across a couple of interesting problems and, after all, sports do offer a lot of neat questions about probability and statistics.

benperreira here makes mention of “Lawler’s Law”, something I had not previously noticed. The “Law” is the observation that the first basketball team to make it to 100 points wins the game just about 90 percent of the time. It was apparently first observed by Los Angeles Clippers announcer Ralph Lawler and has been supported by a review of the statistics of NBA teams over the decades.

benperreira is unimpressed with the law, regarding it as just a restatement of the principle that a team that scores more than the league average number of points per game will tend to have a winning record in an unduly wise-sounding phrasing. I’m inclined to agree the Law doesn’t seem to be particularly much, though I was caught by the implication that the team which lets the other get to 100 points first still pulls out a victory one time out of ten.

To underscore his point benperreira includes a diagram purporting to show the likelihood of victory to points scored, although it’s pretty obviously meant to be a quick joke extrapolating from the data that both teams start with a 50 percent chance of victory and zero points, and apparently 100 points gives a nearly 90 percent chance of victory. I am curious about a more precise chart — showing how often the first team to make 10, or 25, or 50, or so points goes on to victory, but I certainly haven’t got time to compile that data.

Well, perhaps I do, but my reading in baseball history and brushes up against people with SABR connections makes it very clear I have every possible risk factor for getting lost in the world of sports statistics so I want to stay far from the meat of actual games.

Still, there are good probability questions to be asked about things like how big a lead is effectively unbeatable, and I’ll leave this post and reblog as a way to nag myself in the future to maybe thinking about it later.

Ben Perreira

Lawler’s Law states that the NBA team that reaches 100 points first will win the game. It is based on Lawler’s observations and confirmed by looking back at NBA statistics that show it is true over 90% of the time.

Its brilliance lies in its uselessness. Like NyQuil helps us sleep but does little to help our immune systems make us well, Lawler’s Law soothes us by making us think it means something more than it does.

Why is it so useless, one may venture to ask?

Lawler2

This is a graphical representation of Lawler’s Law. Point A represents the beginning of a game. This team (which ultimately wins this game) has roughly a 50% chance of winning at that point. As the game goes on, and more points are scored, the team depicted here increases its chance of victory based on the number of points it has scored. Point B…

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