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> I have been looking through the archives on this list and cannot find =
> any clear arguments against the following challenge to Tegmark's =
> hypothesis ( 'Is the theory of everything merely the ultimate ensemble =
> theory?'):
>
> If our world can be equated to a mathematical structure which is related =
> by the physical laws that are apparent to us, then it can also be a far =
> more complex mathematical structure which explicitly specifies the =
> universe as it has evolved during our lifetimes (for example a phase =
> space specification of all the particle positions/momenta for a universe =
> coming into existence say in 1850, and happening to obey =
> classical/quantum-mechanical laws as required to convince us that the =
> universe does follow simple laws).
>
> Now there would seem to be far more different mathematical structures =
> where this type of scenario occurs (but with sufficient deviation from =
> 'normality' such that we would notice - the odd white rabbit scuttling =
> across a ceiling, for instance, to reuse an earlier example), than there =
> is of the relatively simple mathematical structure(s) that science =
> implies underlies our phenomenal world. So statistically we should be in =
> one of these 'contrived' universes. (This also happens to be the essence =
> of what I take to be John Leslie's position against Tegmark's - and =
> David Lewis's - hypotheses, though he has expressed it differently.)
>
> Perhaps I could play the role of devil's advocate for the moment, and =
> say that if no counter-argument can be found to this challenge, then =
> Tegmark's scheme must be rejected out of hand, because we see no =
> levitating rabbits. (I would also just like to say that I am =
> specifically addressing Tegmark's scheme described in the paper =
> mentioned above, and not any TOE entirely confined to a MWI of QM =
> (which, as a 1b category hypothesis would be vulnerable to the criticism =
> mentioned in his paper), nor Shmidhuber's 'Great Programmer' hypothesis =
> (which would seem to need to address a 'turtles all the way down' =
> accusation).)
>
> Does anyone happen to have an idea about how to respond to this =
> challenge to Tegmark's hypothesis?
This issue was discussed in depth in the thread "Why physical
laws?". A possible solution relates to giving greater measure to items with
smaller description. see "unlikely universes" thread (Schmidhueber)
I think this is an important problem, and I suspect the answer comes
down to the same sort of reasoning as Occam's razor. I don't think it
has been adequately resolved yet, but also don't believe it is an
effective counter argument to Tegmark's thesis.
Cheers
>
> Alastair
>
>
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> <DIV><FONT size=3D2>I have been looking through the archives on this =
> list and=20
> cannot find any clear arguments against the following challenge to =
> Tegmark's=20
> hypothesis ( 'Is the theory of everything merely the ultimate ensemble=20
> theory?'):</FONT></DIV>
> <DIV> </DIV>
> <DIV><FONT size=3D2>If our world can be equated to a mathematical =
> structure which=20
> is related by the physical laws that are apparent to us, then it can =
> also be a=20
> far more complex mathematical structure which explicitly specifies the =
> universe=20
> as it has evolved during our lifetimes (for example a phase space =
> specification=20
> of all the particle positions/momenta for a universe coming into =
> existence say=20
> in 1850, and <EM>happening</EM> to obey classical/quantum-mechanical =
> laws as=20
> required to convince us that the universe does follow simple =
> laws).</FONT></DIV>
> <DIV><FONT size=3D2></FONT> </DIV>
> <DIV><FONT size=3D2>Now there would seem to be far more different =
> mathematical=20
> structures where this type of scenario occurs (but with sufficient =
> deviation=20
> from 'normality' such that we would notice - the odd white rabbit =
> scuttling=20
> across a ceiling, for instance, to reuse an earlier example), than there =
> is of=20
> the relatively simple mathematical structure(s) that science implies =
> underlies=20
> our phenomenal world. So statistically we should be in one of these =
>
> 'contrived' universes. (This also happens to be the essence of what I =
> take to be=20
> John Leslie's position against Tegmark's - and David Lewis's - =
> hypotheses,=20
> though he has expressed it differently.)</FONT></DIV>
> <DIV> </DIV>
> <DIV><FONT size=3D2>Perhaps I could play the role of devil's advocate =
> for the=20
> moment, and say that if no counter-argument can be found to this =
> challenge, then=20
> Tegmark's scheme must be rejected out of hand, because we see no =
> levitating=20
> rabbits. (I would also just like to say that I am specifically =
> addressing=20
> Tegmark's scheme described in the paper mentioned above, and not any TOE =
>
> entirely confined to a MWI of QM (which, as a 1b category hypothesis =
> would be=20
> vulnerable to the criticism mentioned in his paper), nor Shmidhuber's =
> 'Great=20
> Programmer' hypothesis (which would seem to need to address a 'turtles =
> all the=20
> way down' accusation).)</FONT></DIV>
> <DIV> </DIV>
> <DIV><FONT size=3D2>Does anyone happen to have an idea about how to =
> respond to=20
> this challenge to Tegmark's hypothesis?</FONT></DIV>
> <DIV> </DIV>
> <DIV><FONT size=3D2>Alastair</FONT></DIV>
> <DIV> </DIV></BODY></HTML>
>
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Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 7123
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Sun Jul 04 1999 - 19:40:31 PDT