Bruno Marchal wrote: ... > ------------- technical footnote to be seen by technically inclined > reader ------------------------------------- > (*) I think that not so much people here realize that the Universal > Machine and the Universal Dovetailing are things very specific and non > trivial. You can see an explicit Universal Dovetailer described in the > language LISP by clicking on GEN et DU for a pdf here > http://iridia.ulb.ac.be/~marchal/bxlthesis/consciencemecanisme.html > Or better, thanks to the crazily formidable work of H. Putnam, M. > Davis, J. Robinson, Y, Matiyasevitch, and with the help of J. Jones: > here is a purely equational presentation of a universal machine in the > integers: > > There are 31 unknowns ranging on the non negative integers (= 0 > included): > 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 there are two parameters: Nu and X. > > The solution of the following system of diophantine equations define, > taking together, one view, very precise here, of the mathematical > object that I am talking about. I think the Mandelbrot set is another, > one, and of course a dovetailer in Lisp, another one. Robinson > Arithmetic gives yet another short one, expressible in first order > logic with the symbol 0,S, +, *, and very few axioms, and it is the > one needed to begin the interview of a lobian machine (which can > "known" they are universal). Without allowing any other symbols than > "=" and an implicit "E" quantifier, we can get a purely equational > definition of such universal system: for those who remember the W_i, > we have that X is in W_Nu (a universal relation) iff there exists > numbers A, B, C, ... such that > > > 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 > > This is an explicit "theory of everything" acceptable for a > computationalist. Assuming QM correct, Schroedinger equation (and the > phenomenological quantum collapse) have to be derived from that, by > those who believes in comp, or those who want to test comp. > Such equations determine a "consciousness flux", and matter emerges in > a precise way from observational invariance. > No need, to understand this (at this stage). It can help to have > images later to understand the difference between a computation, and a > description of a computation, and how computations can emerge from > number relation, and why this is non trivial. And things like that.
I don't remember the W_i, but without doing the math I can accept that for a given value of Nu=j the above equations pick out some values of X which allow them to be satisfied by integer values of A...Ph, and you express this as X has property W_j. But what does it mean to say W_Nu is a "universal relation"? Has any explicit solution to this set of equations been found? Brent --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---