On Monday, May 19, 2014 2:40:54 AM UTC-4, Bruno Marchal wrote: > > > On 18 May 2014, at 21:37, Craig Weinberg wrote: > > > > 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, > > > Only digital machines. >
But how do you know the difference between what a digital machine happens to do because of the way that it is implemented (machine + sense + physics) rather than what follows from mechanism alone? > > > > or does computationalism have to be grounded, by definition, in elementary > means? > > > It does not, but always can, by Church Thesis. > Why doesn't it? Why isn't the same loose grounding afforded to consciousness? I'm not really sure what would even constitute being always allowed to be grounded in the elementary but not having to be. > > > > > >> You did not provide evidence that they cannot do that. >> > > His evidence was the negative answer to Hilbert's 10th problem. > > > > By using Church thesis. The proof consists in showing that the 10th > problem of Hilbert is Turing complete. Diophantine polynomials are Turing > universal. See below for an example of UD written as a system of > Diophantine equations (exponent are abbreviation here(*) > >From what I've gathered so far, it seems like the proof shows that the halting problem has a Diophantine representation, so that because Church-Turing proves the halting problem is not computable, then Hilbert's 10th problem of whether Diophantine equations can be computed generally must be a no. The fact that Wiles did prove a solution to FLT but could not have done so using a general algorithm shows, according to Tagg, that Wiles is not a Turing machine. > > > > > >> 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? > > > Mathematical logic, theoretical computer science. > Does it explain where the emergence comes from, or just demonstrates that it appears to emerge from an unknown property? > > > > Maybe there is something about the implementation of those machines which > is introducing it rather than computational factors? > > > ? > The non-elementary part may be from the inference of the mathematician's consciousnesses, or physics of implementation rather than the math. Craig > Bruno > > > (*) > Nu = ((ZUY)^2 + U)^2 + Y > > ELG^2 + Al = (B - XY)Q^2 > > Qu = B^(5^60) > > La + Qu^4 = 1 + LaB^5 > > Th + 2Z = B^5 > > L = U + TTh > > E = Y + MTh > > N = Q^16 > > R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + + > LaB^5Q^4)Q^4](N^2 -N) > + [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1) > > P = 2W(S^2)(R^2)N^2 > > (P^2)K^2 - K^2 + 1 = Ta^2 > > 4(c - KSN^2)^2 + Et = K^2 > > K = R + 1 + HP - H > > A = (WN^2 + 1)RSN^2 > > C = 2R + 1 Ph > > D = BW + CA -2C + 4AGa -5Ga > > D^2 = (A^2 - 1)C^2 + 1 > > F^2 = (A^2 - 1)(I^2)C^4 + 1 > > (D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1 > > (unknowns range on the non negative integers (= 0 included) > 31 unknowns: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, > W, Z, U, Y, Al, Ga, Et, Th, La, Ta, Ph, and two parameters: Nu and X. The > polynomial emulates the universal question "X is in w_Nu", or "phi_Nu(X) > stops". > > > 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 [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. >> >> >> 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 [email protected] <javascript:>. > To post to this group, send email to [email protected]<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 [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.
