On Wed, Mar 07, 2007 at 04:30:57PM +1100, Stathis Papaioannou wrote:
> On 3/7/07, Jesse Mazer <[EMAIL PROTECTED]> wrote:
> 
> Russell Standish wrote:
> >
> > >
> > >Well there is a reason we don't observe them, due to observational
> > >selection effects tied to Occam's razor. This is written up in my "Why
> > >Occams Razor" paper. Nobody has shot down the argument yet, in spite
> > >of it being around on this list since 1999, and in spite of it being
> > >published since 2004.
> >
> > The basic problem I have with this proposal is the starting assumption,
> > where you say that the "natural measure induced on the ensemble of
> > bitstring
> > is the uniform one." This sort of assumption is made by a number of TOEs
> > including Schidhuber's, but it always seemed fairly arbitrary to me, not
> > much different in principle from assuming that the measure produced by the
> > laws of physics in our universe (which, under the MWI, will probably
> > include
> > some instances of every possible finite computation in some branch or
> > another) should be taken as a starting point. I posted on this issue in
> > one
> > of my first posts on this list:
> >
> >
> > http://groups.google.com/group/everything-list/browse_thread/thread/0d5915764b7f3e08/fc56caf79ce58750?#fc56caf79ce58750
> 
> 
> If a uniform measure leads to the world we see, isn't that empirical
> evidence that it is the correct one? A uniform measure, or no measure at all
> (which seems to me equivalent), isn't really as arbitrary as some specific
> measure from physics, which as you imply is what the whole everything idea
> is trying to avoid. Could the question in theory be settled by experiment,
> running the UD and counting the relative number of structures?
> 
> Stathis Papaioannou
> 

True, and this was the sense in which I adopted it for the
paper. 

However, I think there is an even better argument. By interposing
another suitable onto function (f:{0,1}*->{0,1}* say) between the
observer and the ensemble of strings, one can make the ensemble of
bitstrings have any measure one likes.

So by composing the observer function O(x) with f(x), we can perform
the treatment for an arbitrary measure as though the we had an
observer O(f(x)) observing strings selected from a uniform measure.

In short terms, one can write "Without loss of generality, assume a
uniform measure over the strings".

Whichever way you cut it, structure is still in the eye of the
observer :)

-- 

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A/Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics                              
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
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