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. 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). Cheers -- ---------------------------------------------------------------------------- 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) ---------------------------------------------------------------------------- -- 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.
