On Sunday, May 18, 2014 9:34:40 PM UTC-4, Russell Standish wrote: > > On Sun, May 18, 2014 at 08:43:23AM -0700, Craig Weinberg wrote: > > Free Will Universe Model: Non-computability and its relationship to the > > ‘hardware’ of our Universe > > > > I saw his poster presentation at the TSC conference in Tucson and > thought > > it was pretty impressive. I'm not qualified to comment on the math, but > I > > don't see any obvious problems with his general approach: > > > > http://jamestagg.com/2014/04/26/free-will-universe-paper-text-pdf/ > > > > Some highlights: > > > > > > Some Diophantine equations are easily solved > > > automatically, for example: > > > ∃𝑥, ∃𝑦 𝑥² = 𝑦² , 𝑥 & 𝑦 ∈ ℤ > > > Any pair of integers will do, and a computer programmed > > > to step through all the possible solutions will find one > > > immediately at ‘1,1’. An analytical tool such as Mathematica, > > > Mathcad or Maple would also immediately give symbolic > > > solutions to this problem therefore these can be solved > > > mechanically. But, Hilbert did not ask if ‘some’ equations > > > could be solved, he asked if there was a general way to solve > > > any Diophantine equation. > > > > > > ... > > > *Consequence* > > > In 1995 Andrew Wiles – who had been secretly working on > > > Fermat’s ‘arbitrary equation’ since age eight – announced he > > > had found a proof. We now had the answers to both of our > > > questions: Fermat’s last theorem is provable (therefore > > > obviously decidable) and no algorithm could have found this > > > proof. This leads to a question; If no algorithm can have > > > found the proof what thought process did Wiles use to answer > > > the question: Put another way, Andrew Wiles can not be a > > > computer. > > > > > > > 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. > > 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. Thanks > > Cheers > > -- > > ---------------------------------------------------------------------------- > > Prof Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders > Visiting Professor of Mathematics [email protected]<javascript:> > University of New South Wales http://www.hpcoders.com.au > > Latest project: The Amoeba's Secret > (http://www.hpcoders.com.au/AmoebasSecret.html) > ---------------------------------------------------------------------------- > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
