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 + +
+ [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)
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.
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