Hello Fabien
I guess I don't think of that as a test of a physical theory. Any theory, even
a mystical religious one, could be ruled out by another theory being found to
be true.
What I was thinking of was a test that would falsify Tegmark's idea that every
mathematically consistent universe exists. If it were shown that there is only
one possible universe with self-aware beings in it (this one), that would be
consistent with Tegmark's idea (although he obviously contemplates that there would
be a range of possible universes). To falsify his hypothesis would require
that we show there is a mathematically consistent universe, different from this
one, with self-aware beings which does not exist. But this is either trivial
under the usual meaning of "exists" (if it's not in this universe it doesn't
exist) or it's impossible under Tegmark's definition in which "exists" just
means "is mathematically consistent". So Tegmark's idea seems rather empty of
physical content; though it may be suggestive of research directions (as was
positvism in the early 1900's).
For example, Tegmark claims his TOE makes two predictios. First, the
mathematical structure describing our world is the most generic one that is
consistent with our observations. Now suppose I come up with a mathematical
sturcture describing our world. Then you come up with one which also describes
our world but which is more generic than mine. Does that mean Tegmark's
prediction failed. No! it just means I used more axioms than necessary and
Godel's theorem already guarantees that if your system is consistent and
describes our world there are infinitely many other mathematically consistent
systems which reproduce all the theorems of your system plus some more and hence
also describe our world.
Second, Tegmark's TOE predicts that our observations are the most generic ones
that are consistent with out existence. I'm not sure what this means because I
can't think how (sets of) observations can be put into a partial order except
maybe by size - which doesn't seem to capture the idea of "more generic". Is
the smaller set the more generic? or the larger? And how can we compare "our
observations" to someone else's to see whose is more generic, when their isn't
anyone else by definition.
On 11-May-00, Fabien BESNARD wrote:
>
> -----Message d'origine-----
> De : Brent Meeker <meekerdb.domain.name.hidden>
> À : Fabien BESNARD <Fabien.BESNARD.domain.name.hidden>
> Date : jeudi 11 mai 2000 04:28
> Objet : Tegmark's big TOE
>
>
>> Hence, it seems pointless to say the mathematics describes the
>> behavoir of some "stuff" --- it just IS. This is essentially a
> philosophical
>> argument. I'd like to know if it is possible to test this theory - even in
>> principle.
>>
>> Brent Meeker
>
>
> I agree that this is essentially a philosophical argument, but it can be
> ruled out by experience and by the advancement of science : for instance, if
> one day we find that all the physical constants have a determinate value
> which is fixed by a physical theory, this theory will be ruled out, because
> only one mathematical structure will be allowed. At least, I guess. I'm not
> too sure about this, because I think that the argument in favor of this
> theory will always be dependant of the current physical theories : perhaps
> someday the word "physical constant" will no longer have any meaning.
>
> ---------------------------------------------------------------
> Fabien Besnard
>
> http://perso.wanadoo.fr/fabien.besnard
>
>
Regards
Received on Thu May 11 2000 - 19:34:25 PDT