On 24 Aug 2011, at 21:34, meekerdb wrote:

On 8/24/2011 11:57 AM, Bruno Marchal wrote:


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


Thanks to Jones, Matiyasevitch. Some number Nu verifying that system of diophantine equations (the variables are integers) are "Löbian stories", on which the machine's first person indeterminacy will be distributed. We don't even need to go farer than the polynomial equations to describe the ROE.

I'm reminded of the apocryphal story of Euler being asked by Catherine the Great to counter Diederot who was trying to convert the Russian court to atheism. Euler wrote "e^(i*pi) + 1 = 0 therefore God exists."

Well, it looks like, but you should quote the dialog: here I was asked *explicitly* to use only addition and multiplication. So I did. What I give was a *specific* universal system written using only addition and multiplication. The difference with, say, this:

0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x

is that here we usee more symbols and, furthermore, assume classical logic. The purpose was illustrative only.

Note that Benjayk could have asked me a universal number. We have that X belongs to W_Nu (with W_i = domain of the phi_i) if and only if X and Nu satisfy the the polynomial equation above. So a universal "Nu" is a number such that W_Nu which is a Sigma_1 complete set. That exists, but it would be very tedious to isolate it.

Bruno

http://iridia.ulb.ac.be/~marchal/



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