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Emile comments on Open Thread, August 2010-- part 2 - Less Wrong
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After seeing the recent thread about proving Occam's razor (for which a better name would be Occam's prior), I thought I should add my own proof sketch:
Consider an alternative to Occam's prior such as "Favour complicated priors*". Now this prior isn't itself very complicated, it's about as simple as Occam's prior, and this makes it less likely, since it doesn't even support itself.
What I'm suggesting is that priors should be consistent under reflection. The prior "The 527th most complicated hypothesis is always true (probability=1)" must be false because it isn't the 527th most complicated prior.
So to find the correct prior you need to find a reflexive equilibrium where the probability given to each prior is equal to the average of the probabilities given to it by all the priors, weighted by how probable they are.
*This isn't a proper prior, but it's good enough for illustrative purposes.
Amusing exercise: find a complexity measure and a N such that "the Nth most complex hypothesis is always true" is the Nth most complex prior :)
:)
Equivalently, can you write a function that takes a string and returns true iff the string is the same as the source code of the function?
Anyone got some quining skills?
in Python:
...it's probably possible to make a simpler one.