[Piers]

Ockham's Razor is a useful rule of thumb for simplifying decision-making.

But however useful Ockham’s razor might be in practise it is instructive to observe that it is almost always wrong. There will always be a more complicated model that is more accurate, but which is likely lost amongst the uncountable number of plausible but incorrect more complicated models.

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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."


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The model that the computer will continue outputted the first n digits of pi means that its next output will be the n+1th is a good assumption to make in practise. However it is also clearly false. At some point, with 100% certainty the computer will not output the next digit of pi. Either because it not programed to, a power cut, a bug in the program, the expanding sun finally engulfs the earth and the computer, some hardware anomaly or someone just turning the computer off.