Russell Standish wrote:

>Thanks for the rap! I sent my previous post before coming across this
>one. Yes your summary is correct. However section 4 goes on to show
>what sort of universe we expect to see ourselves in (ie the Multiverse
>we find ourselves in - its the best explanation I've come across yet
>for Quantum Mechanics), based on some pretty simple, and one would
>hope uncontroversial assumptions about what it means to be conscious.
>
>To go further on the measure problem would require attaching a
>particular property of our observed universe to the anthropic
>principle - eg why we find ourselves in 4D Minkowski
>spacetime. Tegmark has some speculations on this matter, but it
>doesn't go far enough.

Doesn't your scheme assume something like "one turing machine, one vote" 
though?  On the universal prior page you say:

"the natural measure induced on the ensemble of bitstrings is the uniform 
one, i.e. no bitstring is favoured over any other."

On the other hand, Michiel de Jong said:

"although there is no global measure (as in option 1), Solomonoff's 
universal prior allows us to make predictions _as_if_ there were one, 
because it approximates any candidate measure within O(1)."

When he says it "approximates any candidate measure", does this mean there 
is some general class of measures for which the universal prior is a "good 
enough" approximation in some sense?  Obviously not *all* measures would 
work, since I could pick a measure that was 100% concentrated on a 
particular bitstring and 0% on all the others, and that'd yield predictions 
quite different from those based on the universal prior.  Juergen 
Schmidhuber's paper goes into more detail on the class of measures that the 
universal prior is a "good enough" approximation for, right?  Maybe I need 
to go read that...

Anyway, it may be that for most "plausible" measures the universal prior is 
a good approximation, in which case using it is perfectly justified.  But it 
still seems that for a complete TOE we must address the measure problem in a 
more direct way, in order to rule out weird measures like the one I 
mentioned...using the universal prior might turn out to be a bit like 
"renormalization" in quantum field theory, i.e. a tool that's useful for 
making calculations but probably isn't going to be the basis of our final 
TOE.

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