Re: Computational irreducibility and the simulability of worlds

From: Bruno Marchal <>
Date: Wed, 14 Apr 2004 16:04:18 +0200

Dear Stephen,

> > [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.
> 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 Mendeelev discovered new atoms by that method. I am not sure what you

>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.

It necessitates the experienciable truth, and "worlds" emerge from that.

> 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 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
>( and
> than from hypostatization.

"arithmetical truth" is not (by Godel, Tarski, ...) formally definable in
any formal arithmetic.

> 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.?

I know you dislike arithmetical realism, but it is hard for me to believe that
the primality of 317 is contingent, or even remotely linked to us.

> 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

I don't understand. You should put your cart on the table. What are your

> > >[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.

But I do. See the ref to the everything-list in my url.

> >
> >[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).
> A priori existing UDA, Platonia, whatever, how is this more than mere

Because those are well defined arithmetical object. UD is a well defined

>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.

Yes, but our first person experiences rely on that infinity just because
we cannot be aware of any delay in the UD processing, so that we must take
into account the infinite union of all initial segment of the whole processing
of the UD.

>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?

Not exactly. It is less false to consider it as a "partial view" on an
infinity of traces, giving that we cannot distinguish the infinity of
version of
that trace.

> > [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.
> 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.

That is true for any "block universe". In general relativity time is also
a view from an observer.The timeless existence of "everything" is not
completely apprehensible from inside. The computational steps are indexed by
natural numbers. Plausibly the continuum is a projection from inside.

>How do you propose
>that we recover our experience of time from this? Perhaps I need to learn

You should better learn modal logic, especially the S4Grz system. It makes it
possible to associate (at least) a form of Bergsonian/Brouwerian sort
of Duration/Consciousness to any sound (and enough rich) machine.

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

 From an inside view derived from self-reference.

> > [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).
> 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. :_(

Computational complexity could play a role for a justification on some
cosmological aspect like the feeling we are embedded in a long and deep
story. May be Schmidhuber or Tegmark could say more. But for the logic
of the verifiable physical proposition I need only the infinite-complexity
(unprovability, unsolubility, etc.). This comes from the fact that we arrive
at a measure on "all path/computations". To solve Feynman integral you don't
need to evaluate the complexity of any particular path. With comp
something similar happens.

> > > [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.
> 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... ;-)

Actually you are correct here. The S4Grz time logic is a sort of solipsistic
logic, but then consciousness and duration (a la Bergson) are *first* person
predicate. And there is no third person time, except if you consider the
natural numbers as a sort of time (just a matter of defintion).

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

Not at all. If we are machine we will never know for sure exactly which
machine we are, that is, if we are machine we just cannot be any
prespecified machine. To belief that machine implies "pre-specifiablity"
can only be based on the pre-godelian (pre-turingian, pre-churchian,
pre-postian) conception of machine. This is important, and I am afraid
that confusion will be a roots of many troubles for the next millenium :(

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

It was just Plato's definition. And I was just pointing to the fact that
thesis has been made 25 centuries ago. No question of limiting all this
to Plato.

> > >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?
> 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.

But it is, Stephen, it surely is. Don't tell me you are hypostatizing *me*
now ;-)

Received on Wed Apr 14 2004 - 10:07:15 PDT

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