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Wednesday, December 01, 2021

What’s the ratio of boys to girls in a given town? Infiniti. *Evidence in hot-hand link

If someone with two children tells you they have a son born on a Tuesday, what’s the probability that their second child is a son? half, one third, or thirteen twenty-sevenths—the problem is under-defined.

Is there such a thing as a hot hand in basketball? Everyone knows that one: it’s an illusion! Actually, no, it’s not. There is such a thing (and it’s got nothing to with athletic hand temperature).

If your friend flips a coin three times, you ask whether she got any heads, and she replies, “yes, for instance: the second flip landed on heads,” is it a safe bet (over fifty percent) that the third flip was tails? Turns out it depends on what the flipper was thinking when she told you the second flip was heads.

So what gives? Why am I shouting counterintuitive math problems at you?

Several reasons, I suppose. First among them being that these sorts of things are delightfully interesting. They make you “huh” and re-read and scratch your head, and when you’re done, you understand something that other people don’t, and that’s a satisfying feeling (however selfish).

Perhaps more importantly, though, each of these problems is proof that the world doesn’t work the way we expect it to, and that’s a good thing! A world without surprise is a boring one, where grey men in grey suits walk around doing grey things for grey reasons—no color!  

I think it’s easy to look at our overwhelming lack of knowledge as a bad thing: we don’t know most things and some would argue we won’t know most things. That can be a frightfully isolating thought to consider. But it can also be a pleasant one—after all, it’s the reason there’s so much surprise in the first place. Life isn’t about having the answers to all the questions, it’s about being willing to ask the questions and look for the answers despite the obscurity of the search. So I say let’s continue surprising ourselves, maybe life will look a bit more colorful.

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