Thread: Ockham's Razor
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Old 06-16-2007, 08:26 PM
Metric Metric is offline
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Default Re: Ockham\'s Razor

You're missing Boro's (correct) point. Here's the prototype example:

Suppose you have a computer producing a string of output characters -- you don't know the program (input), but you do so far have the first 183,000 output characters. It just so happens that these 183,000 characters happen to be the first 183,000 digits of pi.

Now for the central question -- if you had to predict the next character (number 183,001), is it MORE LIKELY to be the next digit of pi, or a random character? What would you bet on, and why?

Keep in mind, there are plenty of possible programs that say "calculate the first 183,000 digits of pi, and then do something completely different," and given only the first 183,000 output characters, you can't distinguish between any of these and the much simpler program "calculate pi."

The fields of inductive inference, algorithmic probability, etc. were set up to answer this sort of question. And the answer turns out, not surprisingly, to be that "it is more probable that the next output character will be the next digit of pi." As such, they represent something of a rigorous justification for Ockham's razor, and makes Borodog's point -- that simpler explanations that fit the data equally well are typically more likely to be true.
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