In 1919, Sir Arthur Eddington led expeditions to Brazil and to the island of Principe, aiming to observe solar eclipses and thereby test an experimental prediction of Einstein’s novel theory of General Relativity. A journalist asked Einstein what he would do if Eddington’s observations failed to match his theory. Einstein famously replied: “Then I would feel sorry for the good Lord. The theory is correct.”

It seems like a rather foolhardy statement, defying the trope of Traditional Rationality that experiment above all is sovereign. Einstein seems possessed of an arrogance so great that he would refuse to bend his neck and submit to Nature’s answer, as scientists must do. Who can know that the theory is correct, in advance of experimental test?

Of course, Einstein did turn out to be right. I try to avoid criticizing people when they are right. If they genuinely deserve criticism, I will not need to wait long for an occasion where they are wrong.

And Einstein may not have been quite so foolhardy as he sounded . . .

To assign more than 50% probability to the correct candidate from a pool of 100,000,000 possible hypotheses, you need at least 27 bits of evidence (or thereabouts). You cannot expect to find the correct candidate without tests that are this strong, because lesser tests will yield more than one candidate that passes all the tests. If you try to apply a test that only has a million-to-one chance of a false positive (~ 20 bits), you’ll end up with a hundred candidates. Just finding the right answer, within a large space of possibilities, requires a large amount of evidence.

Traditional Rationality emphasizes justification: “If you want to convince me of X, you’ve got to present me with Y amount of evidence.” I myself often slip into this phrasing, whenever I say something like, “To justify believing in this proposition, at more than 99% probability, requires 34 bits of evidence.” Or, “In order to assign more than 50% probability to your hypothesis, you need 27 bits of evidence.” The Traditional phrasing implies that you start out with a hunch, or some private line of reasoning that leads you to a suggested hypothesis, and then you have to gather “evidence” to confirm it—to convince the scientific community, or justify sayin...

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