On Fri, Oct 13, 2000 at 10:57:57PM +0200, Saibal Mitra wrote:
> Yes, this is inherent in the construction of the CSO. s(t) has to be
> smaller than 1 for any finite t. But what about transfinite values for t?
> Since transfinite numbers can be described in a mathematical consistent way,
> it is possible to define a mathematical model of the CSO surviving beyond
> s(t) = 1 . Following Tegmark one should thus believe that the CSO will
> experience this moment.

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But from Tegmark it's not possible to derive a measure for such an
observer moment. If you follow my suggestion that the measure of an
observer moment is equal to its universal a priori probability (which is
defined as the probability that a universal Turing machine with a
uniformly random input tape will produce that output), then the measure
of the CSO at subjective time 1 is zero (unless you count observers
having hallucinations that they are the CSO at subjective time 1). If
the measure is defined in terms of an automata with access to an
oracle for the halting problem, then the measure of the CSO would
presumably be much larger. I don't really know how to justify using the
universal Turing machine instead of any other automata.
Suppose someone said he had access to a RAC. How could he prove it to
you? The most he could do is show that he could solve any problem that
you can verify the solution of, but unless you already had access to a
RAC, all such problems can be solved in finite time on a regular Turing
machine. For an observer that starts out with finite computing resources,
there is no way to verify that anything purported to be a RAC actually is
one, so there is no possible empirical reason for him not to believe that
RACs don't exist.