The more complex an explanation is, the more evidence you need just to find it in belief-space. (In Traditional Rationality this is often phrased misleadingly, as “The more complex a proposition is, the more evidence is required to argue for it.”) How can we measure the complexity of an explanation? How can we determine how much evidence is required?

Occam’s Razor is often phrased as “The simplest explanation that fits the facts.” Robert Heinlein replied that the simplest explanation is “The lady down the street is a witch; she did it.”

One observes that the length of an English sentence is not a good way to measure “complexity.” And “fitting” the facts by merely failing to prohibit them is insufficient.

Why, exactly, is the length of an English sentence a poor measure of complexity? Because when you speak a sentence aloud, you are using labels for concepts that the listener shares—the receiver has already stored the complexity in them. Suppose we abbreviated Heinlein’s whole sentence as “Tldtsiawsdi!” so that the entire explanation can be conveyed in one word; better yet, we’ll give it a short arbitrary label like “Fnord!” Does this reduce the complexity? No, because you have to tell the listener in advance that “Tldtsiawsdi!” stands for “The lady down the street is a witch; she did it.” “Witch,” itself, is a label for some extraordinary assertions—just because we all know what it means doesn’t mean the concept is simple.

An enormous bolt of electricity comes out of the sky and hits something, and the Norse tribesfolk say, “Maybe a really powerful agent was angry and threw a lightning bolt.” The human brain is the most complex artifact in the known universe. If anger seems simple, it’s because we don’t see all the neural circuitry that’s implementing the emotion. (Imagine trying to explain why Saturday Night Live is funny, to an alien species with no sense of humor. But don’t feel superior; you yourself have no sense of fnord.) The complexity of anger, and indeed the complexity of intelligence, was glossed over by the humans who hypothesized Thor the thunder-agent.

To a human, Maxwell’s equations take much longer to explain than Thor. Humans don’t have a built-in vocabulary for calculus the way we have a built-in vocabulary for anger. You’ve got to explain your language, and the language behind the language, and the very concept of mathematics, before you can st...

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