Wednesday, August 3, 2011

Parsimony, Explained Like You're Five has a great new community called r/ExplainLikeImFive, where you can ask questions and get informative yet simple answers. This is useful not only for people who want to learn tough concepts without fear of judgment, but also for the explainers themselves: nothing tests the depth of your understanding on a topic like having to break it down so thoroughly that a 5-year-old gets it.

Recently someone asked for an explanation of Occam's razor. Below is my answer (and if it's not obvious how it pertains to this blog, just replace "monsters" with any instance of the supernatural).

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You know those bumps you hear sometimes when you go to sleep at night? Let's try out a few ways of explaining them.

Maybe your parents are making those noises when they close a door or bump into a wall. Or maybe those noises are from the house settling. When the air gets cooler at night, the wooden beams in the ceiling contract, which causes them to make little bumping sounds.

Or maybe there are monsters lurking in your closet, rapping on the walls, letting you know they're waiting for the right time to strike.

Bump. Bump. Bump.
Sorry, didn't mean to scare you.

Anyway, the point is that the "parents" and "wooden beams" explanations are better than the "monsters" explanation because they're more parsimonious, which you can think of as a fancy word for simple. Really, though, it's more than that: parsimonious explanations need less assumptions, less complicated extra stuff added on to have everything make sense.

True, the wooden beam explanation is more "complicated" in the normal sense, and it's "simpler" in the normal sense to just say "monsters did it" and leave it at that. But it turns out the opposite is true when you really look closely.

You can do experiments to find out that wood really does expand when it gets colder. But what about those monsters? Your parents checked the closet for you before they turned out the lights, so how exactly did they get in there, anyway? Hmm. Maybe they're invisible, and your parents just didn't see them. But then the next night you can have them feel around in there, too. Well, maybe the monsters can make themselves solid or unsolid at will. Now you've finally made everything in your explanation fit. But look at what you've had to do: you've had to assume not just monsters, but two pretty unlikely things about those monsters. It turns out that this explanation was more complicated after all.

Occam's razor says that all else being equal—that is, if all the other conditions (e.g. whether your parents are home) stay the same, and if the explanations are equally good in all other ways—more parsimonious explanations are more likely to be right. And this makes perfect sense: every bit you add onto your explanation can only make the odds of it being true go down, not up—just like the odds of rolling three 6s in a row on a die is lower than the odds of rolling two 6s in a row.

This idea is useful in pretty much any case where you need to choose between explanations: science, history, and even everyday life. It's a cornerstone of rational thinking. You've probably used it many times without even realizing it, but now that you understand it, you can apply it even more often and more carefully, and get results that are more likely to lead you to the right answer.

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