Bruno, Since you mention Leibniz and since MWI is deterministic and if comp can derive a universal consciousness, that consciousness may know all possible futures, could not the consciousness following Leibniz select the best future of all the possible futures resulting in a single world rather than many worlds? Richard
On Wed, May 21, 2014 at 11:39 AM, Bruno Marchal <[email protected]> wrote: > > On 20 May 2014, at 22:03, Craig Weinberg wrote: > > > > 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? > > > I don't know that. > > I would know that, I would know that comp is true, which I don't know, nor > could I know. > > > > > > >> >> >> >> 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. > > > Computationalism assumes that the relevant part of our bodies (relevant > for making our consciousness related to our probable computations) is > grounded in computations, a notion which is elementary (definable in first > order arithmetic language, and existing provable in weak little segment of > the arithmetical truth). > > But our consciousness itself is not grounded on that tiny part of > arithmetic, nor is the behavior in general grounded in arithmetic, even the > whole of arithmetic. Even the machine's theology escapes arithmetic. > > For example, although G and G* are decidable, their first order extension > is as undecidable as they can be (qG is Pi_2, and qG* is Pi_1 ... *in* the > whole arithmetical truth as oracle. this means that even using God as an > oracle, you can't solve all general theological question on the machines). > > That is why the "ONE" of the machine (arithmetical truth) is already > overwhelmed by what emanates from it, the Noùs, which get bigger than the > ONE (which is rather natural given that is gives rise to the MANY, but this > is something that greeks could not seen (as they didn't discover the > universal languages and machines). Leibniz was close, though. > > When the complexity of machines grows, there is a threshold which makes > impossible for any machines or entities to confine the behavior of the > machine in any simple theories. That threshold is low, you get it with any > entities which is able to add and multiply. > > With classical computationalism, Gödel's theorem applies to us, and it > explains to us that the arithmetical truth, and the truth about machines in > general, can only be scratched by us. > > > > > > > > >> >> >> >> >> >>> 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. > > > OK. > > > > 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. > > > That is not correct. > > 1) As I said, it is an open question if Wiles proof can be made > elementary, in which case PA could fin it, given enough time. > > 2) But even if that was not the case, a machine can also use non > elementary means. No mathematicians would doubt that Wiles theorem can be > proved in or by ZF + kappa. > Another example: there are no algorithm to win a chess game in less than > one hour, but this does not mean that a machine cannot learn and use > excellent heuristics and become gifted in beating humans in less than one > hour. > > Machines can search the arithmetical reality, which is richer than > themselves, and so, they can find new things, and find new things, without > having been able to predict them. > > > > > > > > >> >> >> >> >> >>> 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? > > > I would say that it explains where the emergence comes from. It comes > > 1) from the self representation ability of the universal numbers > relatively to the arithmetical reality. > > 2) from the degrees of consistency and closeness to the arithmetical truth. > > > > > > > > >> >> >> >> 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. > > > Yes. Sure. That is exactly what I show to be precisely testable. If > non-comp is true, machine's theology, by including machine's physics, will > gives a tool to measure "our" degree of non (classical) computationalism. > But to be honest, we know already that it has to be a strong form of > non-computationalism, as G and G* applies also to large class of divine > (non Turing emulable) self-referentially correct entities. > > Bruno > > > > 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]. >> 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]. > 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]. > 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. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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