On 13 Dec 2013, at 19:37, Stephen Paul King wrote:
Hi Bruno,
Why does an entire universe need to be simulated?
?
If "I" (third person self-reference) is Turing emulable, then the
"entire universe" is certainly not emulable, nor even well definable.
Could not just finite portions of some universe be simulated, that
which is perceived by the "observers" (however such might be defined).
Yes, that is what the UD does, all computations going through your
comp state, below (and above) your substitution level. The "physical
universe" is an epistemological relative (indexical) view from inside,
and the FPI makes it a priori not computable, below the substitution
level.
Keep in mind I only translate a problem in arithmetic. That is a
"miracle" made possible by the conjunction of the Church-Post-Turing
thesis and the "yes doctor" bet/assumption. (You know the details).
Why does it seem that a "god's eye view needs to be simulated?
Stephen, you make me anxious. I have never said such a ridiculous
thing. Even a first person point of view of a machine, cannot be
simulated or even defined by that machine, or other machines.
The "ONE" of comp is Arithmetical Truth (or the set of Gödel numbers
of true arithmetical sentences). That is not Turing emulable at all.
Arithmetical truth is the union of all sigma_i, all pi_i, sentences,
and that's the "God" of the machine (in a first approximation, in the
meta-theology of simple machines).
The simulable = the sigma_1 truth = the universal machine (a finite
being) = the "man" (Plotinus) = us (in our local terrestrial context
or relative universal machines (and that follows from the assumption).
BTW, David Albert's argument against the narratability of the
universe is a very strong case against any concept of a "god's eye
view", IMHO.
For a "physical universe appearance" that is an easy consequence of
computationalism. If Albert derives this from QM, that confirms the
type of thing a universe can be with computationalism.
Don't confuse arithmetical, and computable. The computable is the tiny
sigma_1 part of the arithmetical (which contains the pi_1, sigma_2,
etc. sentences.
Many machine's attribute are not computable, especially her relation
with "Truth", which are quite NOT computable, and physics inherit some
of those non computable parts. (a priori too many, reducing the mind
body problem in an arithmetical justification of physics problem).
Keep in mind:
sigma_1 truth = simulable = equivalent to proving a sigma_1 sentence
EnP(n) in RA or in any universal system.
Arithmetical-truth is the much vaster set union of all sigma_i and
pi_i. It contains very complex sentences, like a Pi_3 sentence
AxEyAzP(x, y, z).
The Riemann hypothesis is only Pi_1, that is a negation of a sigma_1
sentence, they have the shape AxP(x), with P decidable.
For any correct Löbian machine his consistency (or existence of a
model/reality), that is Dt, or <> t, is a true pi_1 sentence, yet
unprovable by the machine.
No worry, the "god" of the machine is not Turing emulable, God's eyes
is not Turing emulable, not computable.
And the complete "Noùs", the second hypostases (with the quantified
modal logic), qG*, is worse. Even God cannot emulate it.
At the propositional level, yet, by Solovay, those theories are
decidable, even about the undecidable. G cannot prove Dt reflects that
the correct machine cannot prove its consistency, and G* (decidable,
even nicely representable in G) proves Dt, and all similar unprovable
propositions. They are trivial for us because the little machine is
kept simple and rational. The result is "irreversible" or "essential",
in the sense it will remain true for any effective or mechanical
extension of the machine.
The arithmetical clothes of B can change and develop, but as long as
the machine keep self-referential correctness, its science will obey
G, and its theology will obey G*, and its soul obey S4Grz. (and the
three physics are qS4Grz1, qZ1*, qX1*"
where in Z: []p = Bp & Dt. In X, []p = Bp & Dt & p. And "1" means we
add "p -> Bp" to G, to restrict the atomic sentences to the computable".
Bruno
On Thursday, December 12, 2013 1:39:33 PM UTC-5, Bruno Marchal wrote:
On 12 Dec 2013, at 19:06, meekerdb wrote:
On 12/12/2013 9:21 AM, Bruno Marchal wrote:
2) the lower level: the description of the Heisenberg matrix state
of the entire (quantum observable) state of the entire local
cluster of galaxies, (including dark matter!) and all this at the
level of the "right" fields, or at the level of elementary strings
and branes, and this with 10^(10^10) decimals. Use the
Schroedinger picture if you prefer. No collapse!
But in this case the doctor doing the substitution is included in
the substitution. I think this produces a contradiction.
That happens all the time with universal machines. They can simulate
another machine simulating themselves, and the UD brought this in
the picture. With the phi_i and the W_i, many apparent
contradictions are resolved through the fact that we are confronted
with non stopping machines.
Of course, as I said, it would make the thought experience
difficult, for no reason, in the first six steps.
In this list, the first presentation of the UD was a presentation in
15 steps, where I made explicit the neuro-high level assumption used
in "step 1-6" and show explicitly at "step 7" how the UD* (the
complete running of the UD) discharge that assumption.
The mathematical reason why we escape the contradiction is related
to the closure of diagonalization, and to Kleene's second recursion
theorem, which allows machine to invoke machines invoking them. It
is standard in theoretical computer science.
Judson Webb explains well how Gödel's theorem protect Church thesis,
which protect mechanism. In fact Gödel's theorem and the whole of G*-
G, create the points of view (by the machine distinction between Bp
and Bp & p, etc.), and protect the whole machine's theology, by
splitting the communicable part from the non communicable one.
Mathematical logic distinguish also what is expressible by the
machine, and what is not expressible, yet "known" or produces as
"true" in many possible ways.
The UD even run dreams in dreams in dreams .... in a completely
circular way. We cannot impeach it to dig in the absurd, once it is
computable. That would be like trying to eliminate the number 13
from the integers.
Obviously, if the level is so low you need to simulate the entire
universal wave, in practice you will say NO to the doctor, but at
step seven, even if the level is that low, the main consequences
remain unchanged.
Bruno
Brent
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