Russell Standish wrote:
> In my approach (which didn't have this technical nicety), the ensemble
> of descriptions obeyed a uniform distribution.
I grab the opportunity to point out that there is no such thing as a
uniform distribution on infinitely many things. For example, there is
no uniform distribution on the natural numbers.
Uniform distributions that seem so natural in the finite case do not
even make sense in the general case. The natural distributions on the
possible universes are all nonuniform!
To deal with infinities one might think of using measures instead of
distributions. Measures do not assign probabilities to individual elements
but to sets of them. For example, assign measure 2^-n to all bitstrings
with a common prefix of size n. As n grows this measure goes to zero
very quickly - and renders unlikely any finite beginning or future of
any universe history, including the regular and describable ones.
Luckily, there are more natural and more plausible measures
that do not necessarily vanish as history size grows:
http://www.idsia.ch/~juergen/toesv2/node15.html
Juergen Schmidhuber
Received on Thu Mar 29 2001 - 01:53:30 PST