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
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Received on Tue Dec 02 2008 - 14:07:07 PST