There is an ongoing discussion of Chaitin's work on the FOM
(Foundations of Mathematics) list, archived at:
Skeptics here will be interested by these messages:
(JSL would be the Journal of Symbolic Logic)
and perhaps by this competition (deadline May 1):
For a mailing list, FOM is of amazingly high quality, but
the discussions are also extremely technical.
It would be interesting to see someone with a finitist philosophy
of mathematics ("there are no actual infinities") reinterpret
Chaitin's work. The halting probability Omega is doubly an
idealization in that it refers to asymptotic behavior (infinite
time) *and* input strings of arbitrary length (infinite space).
One could instead define halting probabilities for computers
with bounded resources that would be computable - "Omega's
noncomputability" would then be some sort of statement about
how these computable halting probabilities scale as one increases
memory size and time frame.
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