Tuesday, January 11, 2005

A Technical Explanation

Eliezer Yudkowsky has once again written a most entertaining article about probability theory. It's titled A Technical Explanation of a Technical Explanation, and it's a lot less dry than it sounds. This essay is filled with all sorts of fun quotes like this one which made me chuckle:

If someone is wrong on yes-or-no questions 99% of the time, we can get 99% accuracy just by inverting the responses. Anyone that stupid would be smarter than I am.

To summarize the article in a shortened form would not only violate the spirit of the article, but would not do the article justice. I shall do so anyway.

Suppose you have two theories about a certain phenomenon. You are going to perform an experiment that will help you identify which one of the two theories is more likely to be correct. The first theory is bold and predicts a high probability of some specific outcomes, and a low probability of all other outcomes. The second theory is timid and vague and predicts only that the outcome of the experiment will probably be in some broad range, but is not much less probable even outside that range. Well, probability theory favors the bold. If the bold theory's predictions are met in the experiment, the bold theory should then be regarded as much more likely to be correct than the vague theory. This is true even when the experimental result is consistent with the predictions of both theories.

It's a gamble. If your theory makes a bold prediction, your theory can be discredited if the experiments don't go your way. On the other hand, if your specific predictions are borne out by experiment, your theory receives a lot of credit.

Life is a bit like the casino game Keno (it's like Bingo). In Keno, you get a bigger payoff if you make a more specific prediction. For example, you can bet that all the numbers to be drawn will appear on the right side of the board. However, the payoff is bigger if you bet on exactly which numbers they will be - a more specific prediction.

Now, imagine that there was actually some method to figure out what numbers would likely show up in the next round based on the numbers in the last round. In the Keno game of life, the method is called science, and it's how you ought to play the game.

If your theory of life is too vague and can't be disproven, you can't reliably win, you can only get lucky.

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