Guys,
I'm getting great enjoyment out of the titanic battle between
Juergen and Bruno over the meaning of the UD. I'm learning a lot from
the exchange, however, I must admit I do see Bruno's point of
view. His UD does seem to generate the reals (or equivalently the set
of all infinite binary strings) in countable time. However, I know
that infinity (like probability) is a nasty concept, that can easily
trip you up.
There other ways of approaching this - for instance a finite set of
axioms, when enumerated into theorems will tell us all that can be
known about the real numbers.
I have sympathy for one point of Juergen's though - in the space of
descriptions (which we should agree by extension of logical positivism
is all that can be discussed), computable descriptions must have
higher measure than noncomputable ones. However, it seems to me that a
random oracle is an essential component of consciousness and free will
- why this is so I can only guess - and so the anthropic principle
constrains the interesting universe to having these. It could be that
this random oracle is simply a consequence of 1st person indeterminism
that arises through the duplicability assumption, as Bruno points out,
but then why should duplicability be necessary?
Cheers
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Dr. Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967
UNSW SYDNEY 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Thu Feb 08 2001 - 15:02:58 PST