Difference between revisions of "Locate the hypothesis"
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* [[Amount of evidence]]
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Revision as of 04:55, 30 September 2009
When the space of possible answers is large, it takes a large amount of evidence just to think of the correct answer - to promote it to your attention.
Suppose there's a million boxes, and only one of those boxes contains a diamond. And suppose that we have a locator device, which, waved over a box, always beeps if the box contains a diamond, and beeps with 10% probability if the box does not contain a diamond. Then a beep is a likelihood ratio of 10:1 in favor of the box containing a diamond, and the box has 1:1,000,000 prior odds of containing the diamond. If we run the locator over all the boxes, we would get 1 true positive and 100,000 false positives.
When the space of possibilities is large, it takes a large amount of Bayesian evidence just to locate the truth in hypothesis-space - to raise it to the level of our attention - to select it as one of a manageable number of alternatives to spend time thinking about individually.
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." This sounds like Einstein is defying the sovereignty of experiment - jumping to conclusions in advance of the experimental data. But since Einstein was in fact right, it would be extremely improbable for him to have been right just by jumping to conclusions. Einstein must have had enough rational evidence already in hand to locate General Relativity in theory-space.