On 20 May 2014, at 22:13, Craig Weinberg wrote:
On Sunday, May 18, 2014 10:53:57 PM UTC-4, Russell Standish wrote:
On Sun, May 18, 2014 at 07:01:01PM -0700, Craig Weinberg wrote:
>
>
> On Sunday, May 18, 2014 9:34:40 PM UTC-4, Russell Standish wrote:
> > This doesn't follow. An evolutionary algorithm with a real random
> > source, can potentially stumble upon any solution, not just ones
for
> > which no algorithm can find. There even remains some doubt that
"real
> > randomness" is required, so long as the entropy of the random
source
> > is sufficiently high.
> >
>
> The Wiles proof didn't have a random source though, it was developed
> intentionally.
The proof doesn't but Wiles probably did (in his brain, presumably,
although he
could have used a coin or something else).
>
>
> >
> > In COMP, the universal dovetailer provides plenty of real
randomness
> > from the subjective point of view, that can be harnessed. Perhaps
> > that's exactly what Andrew Wiles did. (In fact, I really rather
think
> > he did - my proofs, which are not so grand as Andrew's, usually
> > involve some "divine spark of inspiration", which is just
another term
> > for rolling a random number generator).
> >
>
> You're still the one intentionally doing the rolling.
>
That makes no sense. Rolling an RNG is a mechanical process, if ever
there was one. Intention to solve Fermat's last theorem is outside the
scope of the claim.
If you are intending to solve a problem, anything that you do in the
service of solving that problem is intentional, even if you employ
rolling a RNG as a step. Adding a RNG into a computer program does
not make it able to solve the Halting Problem. It probably doesn't
even make the solvability of the Halting Problem more or less
computable.
Besides, randomness is conceptual. As far as I know, there is no
proof of actual randomness, nor proof that such proof could exist.
There are no proof of actual <anything>.
Now, the notion of randomness can be handled in many ways, and
assuming some theories, can have a clear meaning, or can be
approximated by objects with clear meaning. probability theory,
algorithmic information theory, etc. I know it is math, those are
handy tools to reflect about randomness.
My favorite definition of randomness is what is it like, for most
survivors, to have been WM-duplicated (at the right level) iteratively.
In that sense, when you write the natural numbers in some base
(binary, decimal), most numbers have a random presentation. It is easy
to see that most numbers will not have simpler programs generating
them, for basic combinatorial reason.
It has been shown, by Kurtz(*), that some problem in arithmetic can be
solved by a machine using a random oracle only, and thus by no machine
using any pseudo-random subroutine.
Note that if comp is true, then self-multiplication makes office of
random oracle in the FPI on the sigma_1 complete set, or UD*, so comp
predicts locally some random oracle, as quantum physics suggest too
(with or without the MW). I guess it is part of the arithmetical
phasing out of the white rabbits.
Bruno
(*) KURTZ S. A., 1983, On the Random Oracle Hypothesis, Information
and Control, 57, pp.
40-47.
Craig
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Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [email protected]
University of New South Wales http://www.hpcoders.com.au
Latest project: The Amoeba's Secret
(http://www.hpcoders.com.au/AmoebasSecret.html)
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