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

Date: Fri, 5 Jul 2002 20:25:31 +0200

Hal Finney wrote:

*>Yes, I meant a constant additive term. Any UTM can emulate any other
*

*>TM using a fixed size prefix in front of the other TM's input tape.
*

*>(This assumes that the two TMs use the same basic alphabet of characters
*

*>for their input tape.)
*

OK. That follows from Church Thesis.

*>
*

*>However I may have been too general in making this assertion about all
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*>universal computers (a larger set than UTMs). It's possible that some
*

*>UC's would need to scale the size of the program in order to emulate
*

*>others, so in those cases it is not just a fixed additive term. I would
*

*>have to look more closely at other models of universal computation to
*

*>get a better understanding of this point.
*

Church thesis is equivalent to assert that a UTM, or JAVA, lambda,

... including Deutsch Universal Quantum Turing Machine, ... can

emulate each other.

All those thesis are provably equivalent, giving an empirical evidence

that "computability" is sort of large invariant for combinatorial finite

digitilizable open manipulations. Open means *hopefully* capable of

getting more memory, (qu)bytes.

Quantum computing has demolished a weaker thesis saying that UTM can

simulate each other with slow-down/speed-up polynomial delay.

Church thesis is, imo, independent from what I would like to call

Deutsch thesis, which is that a QUTM (and thus a UTM) can simulate

all physical phenomena.

There is a paper by Freedman making seemingly possible some sort

of analogical universal machine which could beat UTM. But that "physical

phenomena" are capable of more than computing is almost "trivial"

for the computationalist which expect even white rabbits and

white noise a priori.

Perhaps I should recall that comp, as I have always presented, is

the hypothesis that "we" (whatever that means) are turing emulable.

It is not the more schmidhuberian hypothesis that

1) there is a physical universe (but what's that exactly?)

2) That universe is Turing emulable.

Quite the contrary if *we* are turing emulable then from our

inside view we have reasons for expecting trace of

non computationnal features with respect with our most probable

neighborhood. If we look below our "functionnal substitution

description" level, we should "see" (and share) trace of the

computationnal indeterminacy.

Now, a priori, this does not entail at all there exists a universal

analogical machine, and Freedman machine is intringuing. So I am

motivated for Chern Simons theory and topological field theories and

(not less fascinating fact!) how and why knots does help on the path.

You can guess that, for me, the question is: does such analogical

universal beast lives in some Z1* models?

M. Freedman. P/NP, and the quantum field computer.

Proc. Nat. Ac. Sci. USA, 95 (1998), 98--101.

You should find it on the net.

Received on Fri Jul 05 2002 - 11:22:38 PDT

Date: Fri, 5 Jul 2002 20:25:31 +0200

Hal Finney wrote:

OK. That follows from Church Thesis.

Church thesis is equivalent to assert that a UTM, or JAVA, lambda,

... including Deutsch Universal Quantum Turing Machine, ... can

emulate each other.

All those thesis are provably equivalent, giving an empirical evidence

that "computability" is sort of large invariant for combinatorial finite

digitilizable open manipulations. Open means *hopefully* capable of

getting more memory, (qu)bytes.

Quantum computing has demolished a weaker thesis saying that UTM can

simulate each other with slow-down/speed-up polynomial delay.

Church thesis is, imo, independent from what I would like to call

Deutsch thesis, which is that a QUTM (and thus a UTM) can simulate

all physical phenomena.

There is a paper by Freedman making seemingly possible some sort

of analogical universal machine which could beat UTM. But that "physical

phenomena" are capable of more than computing is almost "trivial"

for the computationalist which expect even white rabbits and

white noise a priori.

Perhaps I should recall that comp, as I have always presented, is

the hypothesis that "we" (whatever that means) are turing emulable.

It is not the more schmidhuberian hypothesis that

1) there is a physical universe (but what's that exactly?)

2) That universe is Turing emulable.

Quite the contrary if *we* are turing emulable then from our

inside view we have reasons for expecting trace of

non computationnal features with respect with our most probable

neighborhood. If we look below our "functionnal substitution

description" level, we should "see" (and share) trace of the

computationnal indeterminacy.

Now, a priori, this does not entail at all there exists a universal

analogical machine, and Freedman machine is intringuing. So I am

motivated for Chern Simons theory and topological field theories and

(not less fascinating fact!) how and why knots does help on the path.

You can guess that, for me, the question is: does such analogical

universal beast lives in some Z1* models?

M. Freedman. P/NP, and the quantum field computer.

Proc. Nat. Ac. Sci. USA, 95 (1998), 98--101.

You should find it on the net.

Received on Fri Jul 05 2002 - 11:22:38 PDT

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