The number machine Nu must be defined by some specific encoding. The
polynomials depend on X and Nu. So what is an X and Nu for which they
have a solution and what enumeration is phi_mu?
Brent
P.S. I can believe statements are true without believing their referents
exist: "The Mad Hatter is insane and makes hats" is true.
On 1/20/2017 9:53 AM, Bruno Marchal wrote:
I think you miss the discovery of purely mathematical, even
arithmetical Turing universal relations. Just for the beauty of it, I
copy again below a system of diophantine relations which defines a
Turing universal system.
Bruno
Only bad faith fears reason.
Only bad reasons fear faith.
The Putnam-Davis-Robinson-Matiyasevich-Jones Polynomial equations:
We have that X is in W_Nu, that is phi_Nu(X) is defined, that is the
number/machine Nu stops on input data X, if and only if the following
system of polynomial equations ha a solution. It is short, and one
degree is very high (5^60), but we can diminish the degree to 4,
easily, by introducing a lot of other variables though. We can also
limit the syetm to one equation. From this you can conceive that once
you believe that 2+2=4 independently of you, then such a system
polynomial equation has or not solution, but this encoded the entire
universal dovetailing, including the non computable redundancy.
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
*you* emerges from the first person view on all solutions of that
equations.
The physical reality is given by the competition of infinitely many
universal numbers operating below your substitution level.
The bio-psychological reality the same, with finitely many universal
systems operating above your substitution level.
The goal is not doing a new physics. The goal is in applying reason in
metaphysics, and with the computationalist hypothesis, this is almost
... metamathematics (an "old" name of mathematical logic).
Bruno
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