Re: My claim on Omega's defn
From: |-|erc (H_at_r.c)
Date: 01/31/05
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Date: Mon, 31 Jan 2005 18:50:48 +1000
"r.e.s." <r.s@ZZmindspring.com> wrote in
> >> But it doesn't matter; if one calculates
> >>
> >> K_U = sum(all halting P) (2^(-identifyingnumber(P)))
> >>
> >> instead of
> >>
> >> omega_U = sum(all halting P) (2^(-numbits(P)))
> >>
> >> then K_U will always converge, and both are uncomputable by a UTM.
> >
> > It does matter if you define OMEGA as the reason reals are uncountable
> > and then you say nobody can use it.
>
> Still haven't read this, eh? ...
>
> C. S. Calude, et al, "Computing a Glimpse of Randomness"
> http://www.expmath.org/expmath/volumes/11/11.3/Calude361_370.pdf
>
> Get a clue about UTMs with prefix-free domain.
>
> --r.e.s.
no. but somebody explained its just a 3 tape TM and if it halts on <a,b,c> it also halts on <a,b,c,d>
This is not a mechanism to reduce the branching to ensure convergence.
The formula is WAY OUT. It only converges if the number of programs that halt
for any given size is constant.
I've gone into lots of detail to illustrate this, why don't you EXAMINE EXACTLY why
it converges or not, instead of shooting from the hip and relying on Chaitan.
Herc
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