On 02 Apr 2011, at 13:52, Nick Prince wrote:



On Apr 1, 6:33 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
Hi Nick,

On 31 Mar 2011, at 23:41, Nick Prince wrote:

Bruno wrote
With both QTI and COMP-TI we cannot go from being very old to being a
baby. We can may be get slowly younger and younger in a more
continuous way, by little backtracking. We always survive in the most
normal world compatible with our states. But some kind of jumps are
not excluded.

Hi Bruno

Maybe what I am trying to say is that very old or dying brains might deterorate in a specific way that allows the transition from an old to a young mind i.e. the decaying brain becomes in some way homomorphic
to a young brain.

At the software level of the brain, I think that this is very
plausible. It already happens during sleep, and with some drugs. But
this can take many modalities. Darwinian selection might even have
selected "brain features" helping the recovering of shocks and
disease. And what is best than a little visit in Mother Platonia :)

That the dead brain does that, is more Harry Potter like, but then
dying consists in following the most normal world where we survive,
and this, very plausibly, is not a *very* normal world, despite it
obeys the same physical laws. Eventually, where you go, might even
depend on you and on what you identify yourself with.

Indeed this defines the consciousness I am
considering and is therefore subtrate dependent.

The UD reasoning shows that there is just no substrate at all. The
apparent 'substrate" is "made-of" (an internal sort of projection) an
infinity of (digital) computations, that is number relations.

 If all of physics
can be simulated on a computer then no problem.

Well, the substrate is not simulable on a computer. At least not a
priori. But your reasoning still go through, given that your mind is a
sort of truncation from that substrate, and that, by definition, you
survive on the (infinitely many) computations where you survive. But
this is indeterminate, if only because we cannot know our level of
substitution.



If you accept the classical theory of knowledge, it is easy. Computer
are already conscious. They have not the tools to manifest their
consciousness, and by programming them, we don't help them with that respect. Consciousness is not programmable. It exists "in Platonia", and a universal machine is only a sort of interface between different
levels of the Platonic reality (arithmetical truth).

This is an interesting comment!  Are you saying that everything
including consciousness  really emanates from platonia?

Yes.

Would you
agree that we exist eternally in platonia?

Yes. (but who "we"?)

Yes in a trivial sense. Comp makes arithmetical platonia enough, and
it contains our histories. It is the block ontological reality. It is
far greater than the computable (99,999...% of arithmetical truth is
not computable, decidable, etc.).

Yes, in less trivial senses:
- in the sense of the comp or quantum-like form of immortality, like
above.
- in the sense à-la 'salvia divinorum',  which is that we might be
able to remain conscious out of time, space, etc. It is like
remembering we really are one and live in Platonia. With comp, that
would be like remembering that we are nothing more than a universal
machine. I have not yet a clear opinion on this. Both practically and
theoretically. But there is something interesting in lurking there. It
is related to the personal identity question, and who are we?

If so then perhaps we need
only consider computationalism /QM as a means of comprehending the
steps to this understanding.

Sure.

This platonic realm is very useful but
hard to pin down as a concept.

With comp it is just the "well known" structure (N, +, *), often
called, by logicians, 'the standard model of Peano Arithmetic'. If you
accept that propositions like "24 is even" are true, or false,
independently of you and me, that almost enough. You can pin down the
arithmetical platonia by the set of true arithmetical sentences, or
even just the set of their Gödel numbers, so that it is only a
particular set of numbers. The arithmetical sentences are the
grammatically correct formula build from the logical symbol (A, E, x,
y, z, ..., &, V, ~, ->, (, ), = ) together with the symbol 0, s, +,
*.  For example:

- the arithmetical truth 1 < 2 can be written
Ex(s(0) + x = s(s(0))),
- the arithmetical truth saying that if a number is more little than
another number, then it is more little than the successor of that
another number is written: AxAy((x < y) -> (x < s(y))), where x < y
abbreviates Ez(x+s(z) = y),
- the proposition "24 is even" can be written
Ez(z * s(s(0)) =
s
(s
(s
(s (s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(0))))))))))))))))))))))))),
etc.

Best,

Bruno marchal
Hi Bruno

Okay so in some sense if everything logically possible can be formally
represented in arithmetic as a kind of algorithm, then it exists along
with the UD in platonia.  This "means" we are all in platonia
already.  Indeed could the platonic reality not be equivalent to the
"great simulation" or Schmidhubers algorithmic TOE?

What is the difference? The universal dovetailer is just an effective (and older) version of the 'great programmer', and it is equivalent, in provability terms, to sigma_1 completeness. It is thus equivalent to 'just' a tiny and effective part of arithmetical truth. Then Schmidhuber ignores the first person indeterminacy and exploits the "all computations" idea differently (more in the ASSA way, with priors). With the notion of digital physics he shows that he does not really exploit it at all. But if digital physics implies comp, comp refutes digital physics a priori (with the possibility to recover it or not: open problem, but there is few chances, I would say).

So the TOE does not need more, at the ontological level than Robinson Arithmetic, that is mainly the definition of addition and multiplication on the integers. The rest are beliefs by (universal numbers), and, from the point of view of the machines/numbers, the measure on the computations, or on the Sigma_1 proofs. That determines the entire consciousness flux, and its many-differentiation. But it is an internal epistemology that numbers develop from inside just due to addition and multiplication.

Now, it is fine, and very nice actually, to use combinators instead of numbers, for having a less coarse grain of the notion of computations, but in fine, any universal system do, and elementary arithmetic is the best known.

BTW, not every logically possible can be represented in arithmetic, but all the accessible "mental state" by a machine, can be, including thought on higher cardinals, or galaxies. Consciousness appears, or see all that, or part of that, only in the limit.



I know they're not
actually the same because the latter are essentially encompassed by
the former but it might be difficult to detect a difference.  It also
seems that this notion of platonic reality is anti materialistic like
saying all of reality is more of an idea than anything concrete.  I
think some ancient Indian philosophical traditions hold a similar idea
that everything we see and experience is illusionary and actually is a
representation in some kind of universal mindstuff. Are all these
ideas not informally equivalent?

I certainly think so. In the long text "conscience et mécanisme" I propose an arithmetical translation of the chinese TAO, on some hermeneutical thinkers, like I did later for Plotinus. Plotinus is often compared to some Indian or eastern traditions. It is only in Occident that monistic immaterial monism is so rare. But it "sleeps" in the Kaballah and in the Sufism. The problem is that most mystical researchers where just persecuted, so they developed ways to hide the doctrine which has lead to esoterism and, alas, to idolatry and supersitition. A traditional failure of theology which already appeared with Pythagorus. Greeks were really "rational". They didn't put the mystical insight under the rug. But all those who like to use authoritative arguments fears the mystical side, because it is a side allergic to authoritative arguments.

The math part exemplifies in a third person very transparent way that mystical dimension of the universal machine(s). It shows that the universal numbers are necessarily partially analytical and partially mystical. This is the main quasi-obvious consequences of the splitting between G (the self-referentially prouvable) and G* (the truth about the "self-referentialy provable", even when not provable, but still questionable). Consciousness is already a mystical state, just that most of us are blasé about it!

Gödel did not just prove the limitation of the machine/theories, he discovered also that machine/theories can discovered their own limitations, including their necessary and possible geometries/ topologies, and then transform themselves.


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



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