On Sunday, May 18, 2014 1:56:48 PM UTC-4, Bruno Marchal wrote: > > > On 18 May 2014, at 17:43, 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. >> > > Also, he is the inventor of the LCD touchscreen, so that gives him some > credibility as well. > > > http://www.trustedreviews.com/news/i-never-expected-them-to-take-off-says-inventor-of-the-touchscreen-display > > > > You will not convince Andrew Wiles or anyone with argument like that. > > 1) it is an open question if the use of non elementary means can be > eliminated from Wiles proof. Usually non elementary means are eliminated > after some time in Number theory, and there are conjectures that this could > be a case of general law. > 2) machine can use non elementary means in searching proofs too. >
Does computationalism necessarily include all that is done by what we consider machines, or does computationalism have to be grounded, by definition, in elementary means? > You did not provide evidence that they cannot do that. > His evidence was the negative answer to Hilbert's 10th problem. > And you could'nt as a machine like ZF, or ZF + kappa, can prove things > with quite non elementary means. > What theory addresses the emergence of non elementary means? Maybe there is something about the implementation of those machines which is introducing it rather than computational factors? Craig > > Bruno > > > > > > -- > 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 everything-li...@googlegroups.com <javascript:>. > To post to this group, send email to everyth...@googlegroups.com<javascript:> > . > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
