Harry Potter and the Methods of Rationality

"You think I should just carry a big rock everywhere I go?"

Dumbledore gave Harry a serious look. "That might prove wise."

"Ah..." Harry said. It looked rather heavy. "I'd think the other students would tend to ask me questions about that."

"Tell them I ordered you to do it," said Dumbledore. "No one will question that, since they all think I'm insane." His face was still perfectly serious.

"Er, to be honest if you go around ordering your students to carry large rocks I can kind of see why people would think that."

"Ah, Harry," said Dumbledore. The old wizard gestured, a sweep of one hand that seemed to take in all the mysterious instruments around the room. "When we are young we believe that we know everything, and so we believe that if we see no explanation for something, then no explanation exists. When we are older we realise that the whole universe works by a rhythm and a reason, even if we ourselves do not know it. It is only our own ignorance which appears to us as insanity."

"Reality is always lawful," said Harry, "even if we don't know the law."

"Precisely, Harry," said Dumbledore. "To understand this - and I see that you do understand it - is the essence of wisdom."

"So... why do I have to carry this rock exactly?"

"I can't think of a reason, actually," said Dumbledore.

"...you can't."

Dumbledore nodded. "But just because I can't think of a reason doesn't mean there is no reason."

The instruments ticked on.

"Okay," said Harry, "I'm not even sure if I should be saying this, but that is simply not the correct way to deal with our admitted ignorance of how the universe works."

"It isn't?" said the old wizard, looking surprised and disappointed.

Harry had the feeling this conversation was not going to work out in his favour, but he carried on regardless. "No. I don't even know if that fallacy has an official name, but if I had to make one up myself, it would be 'privileging the hypothesis' or something like that. How can I put this formally... um... suppose you had a million boxes, and only one of the boxes contained a diamond. And you had a box full of diamond-detectors, and each diamond-detector always went off in the presence of a diamond, and went off half the time on boxes that didn't have a diamond. If you ran twenty detectors over all the boxes, you'd have, on average, one false candidate and one true candidate left. And then it would just take one or two more detectors before you were left with the one true candidate. The point being that when there are lots of possible answers, most of the evidence you need goes into just locating the true hypothesis out of millions of possibilities - bringing it to your attention in the first place. The amount of evidence you need to judge between two or three plausible candidates is much smaller by comparison. So if you just jump ahead without evidence and promote one particular possibility to the focus of your attention, you're skipping over most of the work. Like, you live in a city where there are a million people, and there's a murder, and a detective says, well, we've got no evidence at all, so have we considered the possibility that Mortimer Snodgrass did it?"

"Did he?" said Dumbledore.

"No," said Harry. "But later it turns out that the murderer had black hair, and Mortimer has black hair, so everyone's like, ah, looks like Mortimer did it after all. So it's unfair to Mortimer for the police to promote him to their attention without having good reasons already in hand to suspect him. When there are lots of possibilities, most of the work goes into just locating the true answer - starting to pay attention to it. You don't need proof, or the sort of official evidence that scientists or courts demand, but you need some sort of hint, and that hint has to discriminate that particular possibility from the millions of others. Otherwise you can't just pluck the right answer out of thin air. You can't even pluck a possibility worth thinking about out of thin air. And there's got to be a million other things I could do besides carrying around my father's rock. Just because I'm ignorant about the universe doesn't mean that I'm unsure about how I should reason in the presence of my uncertainty. The laws for thinking with probabilities are no less iron than the laws that govern old-fashioned logic, and what you just did is not allowed." Harry paused. "Unless, of course, you have some hint you're not mentioning."

"Ah," said Dumbledore. He tapped his cheek, looking thoughtful. "An interesting argument, certainly, but doesn't it break down at the point where you make an analogy between a million potential murderers only one of whom committed the murder, and taking one out of many possible courses of action, when many possible courses of action may all be wise? I do not say that carrying your father's rock is the one best possible course of action, only that it is wiser to do than not."