Dear Bruno,

    Thank you for your wise and patient reply. Interleaving.

----- Original Message ----- 
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: "Bruno Marchal" <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Saturday, April 10, 2004 12:12 PM
Subject: Re: Computational irreducibility and the simulability of worlds


snip
> [BM]
> Giving that I *assume* that arithmetical truth is independent
> of me, you and the whole physical reality (if that exists), "I" do have
> infinite resources in that Platonia. Remember that from the first person
> point of view it does not matter where and how, in Platonia, my
> computational states are represented. Brett Hall just states that
> the proposition "we are living in a massive computer" is undecidable
> (and he adds wrongly (I think) that it makes it uninteresting), but
> actually with my hypotheses physics is a sum of all those
> undecidable propositions ...(Look again my UDA proof if you are not
> yet convinced, but keep in mind that I assume the whole
> (un-axiomatizable by Godel) arithmetical truth, which I think you
> don't.

[SPK]

    This is very unsettling for me as it seems to claim that we can merely
postulate into existence whatever we need to make up for deficiencies in our
theories. This can not be any kind of science. But I can put that complaint
aside. It is what is missing in this "Platonia" that bothers me: how does it
necessitate an experienciable world.
    The fact that I experience a world must be explained, even if it is
merely an illusion. It must be necessitated by our theories of Everything.

    I am reminded of an idea by Jaakko Hintikka where he criticizes the
notion in game theory that every player has complete knowledge of the
possible moves of the other players. He goes on to explain how "imperfect
information" games are more realistic.

http://www.maths.qmw.ac.uk/~wilfrid/kingsfeb00.pdf

    I tend to think of the "truth" in Arithmetic Truth (and any other formal
system) to be more of a notion that is derived from game theoretics
(http://www.csc.liv.ac.uk/~pauly/Submissions/mcburney.ps  and
http://staff.science.uva.nl/%7Ejohan/H-H.pdf) than from hypostatization.

    This, of course, degenerates the notion of "objective truth", but I have
come to the belief that this notion is, at best self-stultifying. What sense
does it make to claim that some statement X is True or that some Y "exists"
independent of me, you and the whole of physical reality when X and Y are
only meaningful to me, you, etc.?

    We can claim that anything at all is True, so long as it is not
detectable. This entire argument of "independence" teeters on the edge of
indetectability.



> >[SPK]
> >     I agree with most of your premises and conclusions but I do not
> >understand how it is that we can coherently get to the case where a
> >classical computer can generate the simulation of a finite world that
> >implies QM aspects (or an ensemble of such), for more than one observer
> >including you and I, without at least accounting for the appearance of
> >implementation.
>
>[BM]
> A non genuine answer would be the following: because the solutions
> of Schroedinger equations (or Dirac's one, ...) are Turing-emulable.
> This does not help because a priori we must take into account all
> computation (once we accept we are turing-emulable), not only
> the quantum one (cf UDA).

[SPK]

    A priori existing UDA, Platonia, whatever, how is this more than mere
hypostatization? Again I am reminded of Julian Barbour's notion of best
matching. He himself discussed the difficulty of running the computations
to find best matchings among a small (finite!) number of possibilities, and
yet, when faced with an infinity of possibilities the complexity is hand
waved away by an appeal to "Platonia"!
    Even if we assume that Platonia has "infinite Resources", the kind of
computation that you must run takes an Eternity to solve. It is like a
Perfectly Fair game: it takes forever to verify its fairness and, once that
infinity has passed, it is a game that never ends.

    Is our 1 person experience a trace of this game?

> [BM]
> A priori
> comp entails piece of non-computable "stuff" in the neighborhood,
> but no more than what can be produced by an (abstract) computer
> duplicating or differentiating all computational histories.

[SPK]

    Surely, but "all computational histories" requires at least one step to
be produced. In Platonia, there is not Time, there is not any way to "take
that one step". There is merely a Timeless Existence. How do you propose
that we recover our experience of time from this? Perhaps I need to learn
French...

> [BM]
> Remember that if we are machine then we should expect our
> "physical reality" NOT to be a machine. Indeed at first sight we
> should expect all "nearly-inconsistent" histories (white rabbits).
> But the godelian constraints add enough informations for defining a
> notion of normality, that is a beginning of an explanation of why coherent
> and sharable realities evolves from the point of view of the observers
> embedded in Platonia.

[SPK]

    I agree with this aspect but I still do not see how we get Becoming from
Being in your thesis.

> [BM]
> Most of Alan and David critics of comp works fine for Schmidhuber
> form of comp (where physics comes from a special program) or
> Tegmark where physical reality is a mathematical structure among
> all mathematical structures. I provide arguments showing that if we belong
> to a mathematical computation then our future/past (that is our physics)
> depends on an infinity of (relative) computations (all those going
> through our relative states).

[SPK]

     I would like to better understand how your argument deals with the
computational complexity of these relative computations. There is more to
this but my words fail me. :_(

> > [SPK]
> >     How is it that we necessarily experience an asymmetrical flow of
> >  time
> > given the assumption that all 1st person experiences are assumed to be
> > merely algorithms that exist a priori in Platonia?
> [BM]
> Your phrasing is a little bit misleading here I'm afraid. The first person
> experiences are knowledge states. If you agree with the usual axioms
> for knowledge (that is : I know A implies A, I know A implies that I know
> that I know A, I know (A -> B) entails that if I know A then I know B,
> plus the traditional modal inference rules, then with comp that
> knowledge states are completely captured by the S4Grz modal logic
> which has nice semantics in term of antisymmetrical knowledge states
> evolution.

[SPK]

    I do not agree that these axioms are sufficient. They might work for a
solipsist that does not have any experience inferring the existence of
another mind nor insanity. More on this reasoning later... ;-)


> [BM]
> What is absolutely nice is that from the machine point of view
> that knowledge cannot ever be defined. Only meta-reasoning based
> on comp makes it possible to handle it.

[SPK]

    The main problem that I have is that "machine" implies
pre-specifiability. I follow Peter Wegner's arguments against such.

> [BM]
> You can read the appendice (in english!) in "Conscience et Mecanisme"
> by the Russian logician Sergei Artemov which provides an argument
> for identifying the notion of informal (and even un-formalizable)
> provability
> by the conjonction of formal provability and truth. By Godel, that *is*
> different from just formal provability:
>
http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume4CC/6%20La%20these%20d'Artemov.pdf


[SPK]

    Thank you for pointing me to this.

> [BM]
> Note that this idea has been explicitly proposed by Plato in his
> Thaetetus (just replace "formal proof" by "justification" or "definition"
> (The historian of greek philosophy disagree on the meaning of the
> word we should use, but here I interpret it as "rigorous third person
> justification" or formalizable proof).

[SPK]

    That is fine, but limiting ourselves to Plato's imagination is hardly a
means to make an unassailable argument.


> >How is the issue of the
> >NP-Completeness problem of the computation of our experience a world
> > where
> >we interact successively with each other solved by the mere existence of
< < a solution to that problem?
> >     How does the a priori possibility of a solution imply that the
> > solution needs not be searched for and found?
>[BM]
> Because the physical appearances comes from a sum on *all* solutions
> existing in Platonia (a modal "inside" view of that sum, to be sure).
> You didn't have to prove the existence of "Stephen Paul King" to be born,
> isn't it?

[SPK]

    No, I do not need to prove my existence to myself other than the fact
that I can ask the question, but I do require some kind of justification
that Bruno Marchal (and his mind) is not just a figment of my imagination.
;-)

Kindest regards,

Stephen


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


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