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From: Alastair Malcolm <amalcolm.domain.name.hidden>

Date: Tue, 6 Jul 1999 00:02:05 +0100

[Replies to Russell Standish, Bruno Marchal also below]

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

From: Jacques M Mallah <mailto:jqm1584.domain.name.hidden>

*> On Sat, 3 Jul 1999, Alastair Malcolm wrote:
*

*> > If our world can be equated to a mathematical structure which is
*

*> > related by the physical laws that are apparent to us, then it can also
*

be

*> > a far more complex mathematical structure which explicitly specifies the
*

*> > universe as it has evolved during our lifetimes (for example a phase
*

*> > space specification of all the particle positions/momenta for a universe
*

*> > coming into existence say in 1850, and happening to obey
*

*> > classical/quantum-mechanical laws as required to convince us that the
*

*> > universe does follow simple laws).
*

*>
*

*> Yes, but that structure would not implement any computations.
*

*> Many of us are computationalists.
*

*>
*

*> > Now there would seem to be far more different mathematical structures
*

*> > where this type of scenario occurs (but with sufficient deviation from
*

*> > 'normality' such that we would notice - the odd white rabbit scuttling
*

*> > across a ceiling, for instance, to reuse an earlier example), than there
*

*> > is of the relatively simple mathematical structure(s) that science
*

*> > implies underlies our phenomenal world. So statistically we should be in
*

*> > one of these 'contrived' universes.
*

*>
*

*> In the case of typical 'junk' data, yes, but there would be no
*

*> computations.
*

As a counter to the challenge to Tegmark's hypothesis, I am afraid I can't

see the relevance of this or the other statement above (a contrived

computation (or appearance of computation, if you prefer) can readily be

produced from a sufficiently complex mathematical structure, and it only has

to convince us that it looks like a computation), so I'll presume you are

responding from a different, computationally-generated-universe

(cgu)standpoint. Perhaps I could just clarify why, at my rather rudimentary

level of understanding, I don't find these (cgu) kind of ideas very

attractive (with one possible exception) - apologies if I am retreading old

ground:

Any cgu idea must fall into one of two exhaustive categories:

1. There is a required process of execution of programs which leads to the

existence of universes.

For this category, then clearly any program must be executed from a universe

other than the one (or more) that is produced by it. Where does this

'higher' universe come from? Schmidhuber implies a chain of universes, but

if there is an original universe somewhere, why can't it be this (our) one,

and forget the chain? Similarly, an infinite hierarchy of TM's solves

nothing, it just sweeps the problem under the carpet of infinity. [Note to

BM: this is where the turtles come in.]

2. There is no required process of execution of programs leading to the

existence of universes.

To retain any semblance of cgu, then it would seem that either

a) The program(s) still specify the universes, but do not need to be

formally executed . . . but this cannot be the case, since without a

computer/TM to run on, a program can be no more than a string of bits (or

however it is encoded) - another TM could well generate a totally different

universe from the same bit string; or

b) The bit strings specifying our, and other, universes in explicit detail

are in some sense already present - no execution of a program is necessary.

If the measure is applied on all these bit strings, then not only do we hit

the flying rabbit problem again, but we are also departing from a

computational scheme, since the input program and TM process become defunct.

But if the measure is on the input side (to obtain the advantages of simple

physics via non-functional code), how can the input be responsible for the

output if no execution of a program is to be posited?

This is why Tegmark's hypothesis seems to me to have more mileage in it than

a computational scheme, if a good response can be found to the challenge I

described in my previous post.

Russell Standish wrote:

<This issue was discussed in depth in the thread "Why physical

laws?". A possible solution relates to giving greater measure to items with

smaller description. see "unlikely universes" thread (Schmidhueber)

I think this is an important problem, and I suspect the answer comes

down to the same sort of reasoning as Occam's razor. I don't think it

has been adequately resolved yet, but also don't believe it is an

effective counter argument to Tegmark's thesis.>

As I have mentioned before, my DA challenge was specifically aimed at

Tegmark's hypothesis (though I have a horrible feeling I may have just got

myself embroiled in another one), and not Schmidhuber's - I wouldn't want to

quarrell with the solutions he mentioned to the flying rabbit problem as

applied to *his* hypothesis.

As regards Ockham's Razor, it is this principle itself that suggests the

ultimate ensemble theory, which in turn *results* in the flying rabbit

paradox, so it is difficult for me to see how Ockham's Razor or an

equivalent on their own could be used to circumvent it.

Bruno Marchal wrote:

<My answer was that I don't see how Tegmark can make this challenge

effective because the collection of mathematical structures is

not definable in mathematical terms.>

Don't we only need a rough idea of the relative measure of small samples of

these mathematical structures in order to pose the challenge? Surely it is

the case that any mathematical structure entirely confined to the

specification of a relatively simple interpretation of our universe (as

implied by current physical theories) must be of far smaller measure than

that of the myriad of 'flying rabbit' type universes? (The picture that I

have in mind here, though probably not really apposite, is of the relative

number of rotation states of a cube, and a dodecahedron.)

*>Could you tell us if you agree that Schmidhuber "great programmer"
*

*>approach
*

*>should also met the flying rabbit challenge ?
*

Yes, I agree that it should, and moreover on the face of it appears to do

so.

*>
*

*>And could you explain more precisely the 'turtles all the way down'
*

*>accusation against Schmidhuber Great programmer?
*

Please see my reply to Jacques Mallah above (Point 1.).

Thanks for all your replies, but despite rereading the threads you have

suggested, I am still looking for a clear solution to the flying rabbit

paradox challenge to Tegmark's hypothesis!

Received on Mon Jul 05 1999 - 16:22:30 PDT

Date: Tue, 6 Jul 1999 00:02:05 +0100

[Replies to Russell Standish, Bruno Marchal also below]

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

From: Jacques M Mallah <mailto:jqm1584.domain.name.hidden>

be

As a counter to the challenge to Tegmark's hypothesis, I am afraid I can't

see the relevance of this or the other statement above (a contrived

computation (or appearance of computation, if you prefer) can readily be

produced from a sufficiently complex mathematical structure, and it only has

to convince us that it looks like a computation), so I'll presume you are

responding from a different, computationally-generated-universe

(cgu)standpoint. Perhaps I could just clarify why, at my rather rudimentary

level of understanding, I don't find these (cgu) kind of ideas very

attractive (with one possible exception) - apologies if I am retreading old

ground:

Any cgu idea must fall into one of two exhaustive categories:

1. There is a required process of execution of programs which leads to the

existence of universes.

For this category, then clearly any program must be executed from a universe

other than the one (or more) that is produced by it. Where does this

'higher' universe come from? Schmidhuber implies a chain of universes, but

if there is an original universe somewhere, why can't it be this (our) one,

and forget the chain? Similarly, an infinite hierarchy of TM's solves

nothing, it just sweeps the problem under the carpet of infinity. [Note to

BM: this is where the turtles come in.]

2. There is no required process of execution of programs leading to the

existence of universes.

To retain any semblance of cgu, then it would seem that either

a) The program(s) still specify the universes, but do not need to be

formally executed . . . but this cannot be the case, since without a

computer/TM to run on, a program can be no more than a string of bits (or

however it is encoded) - another TM could well generate a totally different

universe from the same bit string; or

b) The bit strings specifying our, and other, universes in explicit detail

are in some sense already present - no execution of a program is necessary.

If the measure is applied on all these bit strings, then not only do we hit

the flying rabbit problem again, but we are also departing from a

computational scheme, since the input program and TM process become defunct.

But if the measure is on the input side (to obtain the advantages of simple

physics via non-functional code), how can the input be responsible for the

output if no execution of a program is to be posited?

This is why Tegmark's hypothesis seems to me to have more mileage in it than

a computational scheme, if a good response can be found to the challenge I

described in my previous post.

Russell Standish wrote:

<This issue was discussed in depth in the thread "Why physical

laws?". A possible solution relates to giving greater measure to items with

smaller description. see "unlikely universes" thread (Schmidhueber)

I think this is an important problem, and I suspect the answer comes

down to the same sort of reasoning as Occam's razor. I don't think it

has been adequately resolved yet, but also don't believe it is an

effective counter argument to Tegmark's thesis.>

As I have mentioned before, my DA challenge was specifically aimed at

Tegmark's hypothesis (though I have a horrible feeling I may have just got

myself embroiled in another one), and not Schmidhuber's - I wouldn't want to

quarrell with the solutions he mentioned to the flying rabbit problem as

applied to *his* hypothesis.

As regards Ockham's Razor, it is this principle itself that suggests the

ultimate ensemble theory, which in turn *results* in the flying rabbit

paradox, so it is difficult for me to see how Ockham's Razor or an

equivalent on their own could be used to circumvent it.

Bruno Marchal wrote:

<My answer was that I don't see how Tegmark can make this challenge

effective because the collection of mathematical structures is

not definable in mathematical terms.>

Don't we only need a rough idea of the relative measure of small samples of

these mathematical structures in order to pose the challenge? Surely it is

the case that any mathematical structure entirely confined to the

specification of a relatively simple interpretation of our universe (as

implied by current physical theories) must be of far smaller measure than

that of the myriad of 'flying rabbit' type universes? (The picture that I

have in mind here, though probably not really apposite, is of the relative

number of rotation states of a cube, and a dodecahedron.)

Yes, I agree that it should, and moreover on the face of it appears to do

so.

Please see my reply to Jacques Mallah above (Point 1.).

Thanks for all your replies, but despite rereading the threads you have

suggested, I am still looking for a clear solution to the flying rabbit

paradox challenge to Tegmark's hypothesis!

Received on Mon Jul 05 1999 - 16:22:30 PDT

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