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From: Stephen Paul King <stephenk1.domain.name.hidden>

Date: Wed, 21 Jan 2004 11:46:17 -0500

Dear CMR,

Interleaving.

----- Original Message -----

From: "CMR" <jackogreen.domain.name.hidden>

To: <everything-list.domain.name.hidden>

Sent: Wednesday, January 21, 2004 1:07 AM

Subject: Re: Is the universe computable?

*>
*

*> > Think of it this way, what is the cardinality of the equivalence
*

class

*> > of representations R of, say, a 1972 Jaguar XKE, varying over *all
*

*> > possible languages* and *symbol systems*?
*

*> > I think it is at least equal to the Reals.
*

*> > Is this correct? If R has more than one member, how can we coherently
*

*> > argue that "information is physical" in the material monist sense?
*

*> >
*

*> [CMR]
*

*> Assuming you mean R is countably infinite(?), then a solution would be a
*

*> finite universe of underlying discrete structure, ala Fredkin, I imagine.
*

*>
*

[SPK]

If Fredkin is proposing a Cellular Automata based model that would be

the case, but CA based models have a problem of their own: how to show that

the global synchrony of the shift function can obtain. It is puzzleling to

me why it is hard to find a discussion of this in the literature.

*> >[SPK]
*

*> > What if the "informing" and "constraining" (?) is done, inter alia,
*

*> > by the systems that "use up" the universal resources?
*

*> >
*

*> > What if, instead of thinking in terms of a priori existing
*

solutions,

*> > ala Platonia, if we entertain the idea that the *solutions are being
*

*> > computation in an ongoing way* and that what we experience is just one
*

(of

*> > many)stream(s) of this computation. Such a computation would require
*

*> > potentially infinite "physical resources"...
*

*> > Would it be to much to assume that all we need to assume is that the
*

*> > "resources" (for Qcomputations, these are Hilbert space dimensions) are
*

*> > all that we have to assume exists a priori?
*

*> > Does not Quantum Mechanics already have such build in?
*

*> [CMR]
*

*> Yes, this would indeed follow. But what of a view of QM itself emerging
*

form

*> qubits?
*

*> as, for instance, expressed in the so-called Bekenstein bound: the entropy
*

*> of any region
*

*> of space cannot exceed a fixed constant times the surface area of the
*

*> region.
*

[SPK]

Maybe I am mistaken but does not QM enter into the very definition of a

qubit?

As the to idea of Bekenstein's bound, that is, IMHO, more of a problem

than a solution and leads in the wrong direction. It has been shown

(http://tph.tuwien.ac.at/~svozil/publ/embed.htm) that it is impossible to

completely "embed" the logical equivalent of a QM system (with Hilbert space

dimensions greater than 2) into the logical equivalent of a classical

system.

I take this to explicitly rule out considerations that space-time can be

treated as just a Minkowskian (or, more generally, one would consider the

Poincare' group) space and expect to be able to treat it as the background

or "support" for the necessary machinery of a QM system.

*>[CMR]
*

*> This suggests
*

*> that the complete state space of any spatially finite quantum system is
*

*> finite, so
*

*> that it would contain only a finite number of independent qubits.
*

*>
*

[SPK]

Again, that does not work because we can not take space-time (ala GR) to

be "big enough" to allow us to fit QM into it. On the other hand, it has

been shown that a QM system, considered as a quantum computational system,

can simulate, with arbitrary accurasy, any classical system, given

sufficient "Hilbert space" dimensions - which play the role of "physical

resources" for QM systems.

See: http://arxiv.org/abs/quant-ph/0204157

This leads me to the idea that maybe space-time itself is something that

is secondary. It and all of its contents (including our physical bodies)

might just be a simulation being generated in some sufficiently large

Hilbert space. This idea, of course, requires us to give Hilbert space (and

L^2 spaces in general?) the same ontological status that we usually only

confer to space-time. ;-)

Kindest regards,

Stephen

Received on Wed Jan 21 2004 - 12:01:31 PST

Date: Wed, 21 Jan 2004 11:46:17 -0500

Dear CMR,

Interleaving.

----- Original Message -----

From: "CMR" <jackogreen.domain.name.hidden>

To: <everything-list.domain.name.hidden>

Sent: Wednesday, January 21, 2004 1:07 AM

Subject: Re: Is the universe computable?

class

[SPK]

If Fredkin is proposing a Cellular Automata based model that would be

the case, but CA based models have a problem of their own: how to show that

the global synchrony of the shift function can obtain. It is puzzleling to

me why it is hard to find a discussion of this in the literature.

solutions,

(of

form

[SPK]

Maybe I am mistaken but does not QM enter into the very definition of a

qubit?

As the to idea of Bekenstein's bound, that is, IMHO, more of a problem

than a solution and leads in the wrong direction. It has been shown

(http://tph.tuwien.ac.at/~svozil/publ/embed.htm) that it is impossible to

completely "embed" the logical equivalent of a QM system (with Hilbert space

dimensions greater than 2) into the logical equivalent of a classical

system.

I take this to explicitly rule out considerations that space-time can be

treated as just a Minkowskian (or, more generally, one would consider the

Poincare' group) space and expect to be able to treat it as the background

or "support" for the necessary machinery of a QM system.

[SPK]

Again, that does not work because we can not take space-time (ala GR) to

be "big enough" to allow us to fit QM into it. On the other hand, it has

been shown that a QM system, considered as a quantum computational system,

can simulate, with arbitrary accurasy, any classical system, given

sufficient "Hilbert space" dimensions - which play the role of "physical

resources" for QM systems.

See: http://arxiv.org/abs/quant-ph/0204157

This leads me to the idea that maybe space-time itself is something that

is secondary. It and all of its contents (including our physical bodies)

might just be a simulation being generated in some sufficiently large

Hilbert space. This idea, of course, requires us to give Hilbert space (and

L^2 spaces in general?) the same ontological status that we usually only

confer to space-time. ;-)

Kindest regards,

Stephen

Received on Wed Jan 21 2004 - 12:01:31 PST

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