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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Sat, 10 Apr 2004 18:12:07 +0200

At 00:35 10/04/04 -0400, Stephen Paul King wrote:

*> > BM: I agree with this. There is no embedding of QM in a Boolean
*

*>representation,
*

*> > if by embedding we mean a injective function which preserves the value of
*

*> > the observable. But ...
*

*>
*

*>
*

*>[SPK]
*

*>
*

*> Ok. Well please help me how does my argument not follow? I am trying to
*

*>understand how my claim fails. You seem to understand this, I need to
*

*>understand this, help me please.
*

BM: My feeling is that we just have different fundamental hypotheses. More

in the sequel.

*>BM:
*

*> > >it follows
*

*> > >that it is impossible to fully simulate a QM system on a classical
*

*>computer
*

*> > >unless we allow for some rather exotic special conditions.
*

*> >
*

*> > I disagree. Unless "fully" means "in real time" ? Not only a classical
*

*> > computer can compute all "quantum computable functions", but if you
*

*> > allow the classical computer to simulates the system consisting of
*

*> > "you + a quantum computer", then the classical computer will, relatively
*

*> > to you, be able to simulate all quantum processes (and not only the
*

*>function).
*

*>
*

*>[SPK]
*

*>
*

*> I have one situation in mind where your conclusion follows but it seems
*

*>to be a Very Special case, the case where we have infinite resourses
*

*>available for the classical systems to simulate the QM systems, all of the
*

*>possible.
*

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.

*> 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 accouting for the appearence of
*

*>implementation.
*

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

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.

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.

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).

*> 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?
*

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. 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.

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

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).

*>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?
*

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?

Bruno

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

Received on Sat Apr 10 2004 - 12:12:05 PDT

Date: Sat, 10 Apr 2004 18:12:07 +0200

At 00:35 10/04/04 -0400, Stephen Paul King wrote:

BM: My feeling is that we just have different fundamental hypotheses. More

in the sequel.

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.

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

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.

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.

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).

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. 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.

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

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).

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?

Bruno

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

Received on Sat Apr 10 2004 - 12:12:05 PDT

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