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Vladimir_Nesov comments on Description complexity: an apology and note on terminology - Less Wrong Discussion

13 Post author: cousin_it 10 November 2010 12:43AM

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Comment author: Vladimir_Nesov 10 November 2010 12:59:28AM 6 points [-]

Curiously, this means there's no object for which we have defined both "complexity" and "prior probability", which makes all arguments of the form "complexity is high => probability is low" automatically suspect.

This is an interesting pattern to keep in mind.

Comment author: Will_Newsome 28 December 2011 08:49:42PM 0 points [-]

bump

Comment author: endoself 28 December 2011 09:31:13PM 1 point [-]

The above is not as strong as it seems. It can be shown that on any given Turing machine, the prior probability of an equivalence class of programs is at most an O(1) factor greater than the part of that probability due to just the simplest program in the class.

Arguments can still be suspect if you don't know which program is the simplest. However, it is often possible to show that a program is probably the simplest; since there are many more complex programs than simple ones, a randomly drawn complex hypothesis is extremely unlikely to have a shorter equivalent.