Advocate for Max Tegmark's hypothesis

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Tue, 13 Jul 1999 00:01:57 +0100

    
----- Original Message -----
From: Marchal <marchal.domain.name.hidden>
> I really think that it is not possible to solve the rabbit problem
> with Tegmark hypothesis (that all mathematical structures exist),
> because it makes the indeterminism domain to big. The more we
> make Tegmark's hypothesis precise, the more will it be likely that
> we should seen white rabbit flying ...

The general problem here seems to be that if one has a scheme that differs
in any way from Tegmark's hypothesis, then it is subject to Tegmark's category 1b
challenge: 'why are only *these* mathematical structures implemented?' or
'why should *this* mathematical structure be represented more than another?'
Without its own philosophical justification to compare in profundity to Tegmark's idea
that the bird view in some sense just *is* the mathematical structure, then
a putative universal hypothesis has no advantage over any of a number of
single universe TOE's - it will just be another category 1b casualty. I
suppose this has to be a personal opinion, but I just don't feel that the
category of mappings that are provided by the set of all TM's (or an individual
UTM) can seriously be considered in its own right as providing the deep
intuitive or philosophical ground for an everything theory. (Neither can I
see how it can coincide with Tegmark's hypothesis, except perhaps
fortuitously, though I agree in general terms with Hal that a formal system
approach might be able to make progress.)

If this is the case, then the flying rabbit problem still haunts, and no one has provided
me with a substantive answer to it so far. So, partly for this reason, I shall make a
try at a solution to the flying rabbit challenge to Tegmark's
hypothesis. (I should just like to say that my own ideas don't quite coincide with
those of Tegmark - I don't assume a direct ontological equivalence between some
mathematical structures and universes - but there is I think a sufficient overlap for
the solution to work for both, if it is going to work.) I would be happy for anyone to
supply rationally-based criticism, or even shoot it down in flames if it deserves it.
(Sorry if it's been discussed before, but I *have* asked for solutions to
this problem earlier.)

The basic idea is that the significant source of measure (for say a
particular type of universe, or conscious instant) is contained *within* the
mathematical specification/structure. (Perhaps this idea is obvious to some,
controversial to others, I am not sure). This internal source of measure
already occurs with Everett many-worlds - there is an implicit specification
of multiplication of subjective ('common sense') universes (or conscious
instants, if one prefers) with unfolding time contained within its overall
mathematical structure. In general, it does not seem unreasonable to suppose
that there is some maximal fecundity of universes per information unit that
is possible within any mathematical structure; that is, for any given length
of bit string then the highest measure of universes will be associated with those
specifications (bit string combinations) which have the highest proportion devoted
to specifying maximal copies/variations of universes. It follows from this
that for any countable bit string length, and considering all possible bit
combinations within that length, we are most likely to be in one of those
universes that are part of one of these specifications, subject to having just
enough bits 'left over' to generate/specify sufficient complexity for
intelligent life to be present - in other words, a universe with the simplest possible
physical laws conducive to sentience ... and so no flying rabbits. (This solution does
also happen to tend to favour Everett many-worlds over several other
hypotheses (for us), because the multiplicity/splitting serves the dual purpose of
fecundity, and variation necessary for life, but the splitting could well be
the tip of the fecundity iceburg.)

Alastair
Received on Mon Jul 12 1999 - 16:18:52 PDT