I've just finished reading Tegmark's "The Mathematical Universe",
which I commend for being well written, and also containing enough new
ideas on the subject to be worth reading for the old timers.
I only found one obvious mistake. On page 19, he states that
"Schmidhuber has hypothesized that all halting programs correspond to
physical realities". This is not true, as Schmidhuber is explicitly
agnostic in Schmidhuber97 about whether our universe is a halting
program, and in Schmidhuber00 explictly deals with the nonhalting
case.
There is an interesting classification in section VII.D of levels of
mathematical realities (there was a spelling error here).
I would say that Bruno's COMP, or Schmidhuber's ensemble are basically
level 4 mathematical universes (all structures defined by computations
not guaranteed to halt). My own "all strings" ensemble lies somewhere
between level 4 & 5, in that it has uncountably many elements, but
does not cover all mathematical structures.
But I would still say the UDA entails the existence of my ensemble
(the UD*) as the internal experience of a conscious observer, even if
not assumed as a fundamental ontology.
However, if what Max calls the Computable Universe Hypothesis is true,
then that would rule out the existence of the all strings ensemble.
Cheers
--
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A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpcoder.domain.name.hidden
Australia http://www.hpcoders.com.au
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Received on Tue Sep 25 2007 - 22:13:09 PDT