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From: Russell Standish <R.Standish.domain.name.hidden>

Date: Mon, 25 Oct 1999 10:17:52 +1000 (EST)

*>
*

*> ----- Original Message -----
*

*> From: Russell Standish <R.Standish.domain.name.hidden>
*

*> > Why it fails is that you assume that all universes are wffs. The
*

*> > underlying challenge of white rabbits and dragons is that the number
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*> > of non-wffs vastly outnumber the number of wffs. The assumption is
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*> > that that each non-wff corresponds to to a white rabbit universe. As
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*> > we discussed, and you have explained fairly clearly on your web page,
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*> > most non-wff universes are in fact indistinguishable from a wff
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*> > universe sufficiently close to it, so may be identified with it. In
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*> > that case, the number of non-wff universes corresponding to white
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*> > rabbits or dragons (ie actually recognisable paranormal phenomena) is
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*> > a vanishingly small proportion of the total.
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*>
*

*> No! I am very sorry, but I have to correct this - every sentence above is
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*> false!!! (Though stemming from one underlying misunderstanding, I think.)
*

*>
*

*> One of the main reasons to use the formal systems approach is that it solves
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*> the principal interpretation problem - some symbol strings build wff's, some
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*> wff's are axiom sets, some axiom sets build theories, some theories specify
*

*> universes. In my first post to this thread (my web pages don't mention
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*> wff's - yet), wff's rather than non-wff's are selected - wff's are a
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*> precondition for the specification of *any* universe (with or without
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*> dragons/white rabbits); a non-wff is like a nonsense bitstring - totally
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*> irrelevant (except conceivably for some measure purposes).
*

We're obviously running up against a misunderstanding here, which I

believe we should be able to resolve. Surely dragon universes are

nonsense bitstrings (the non wffs mentioned above), just ones that

happen to be close to a mathematical system, but not so close to be

indistinguishable. I thought the whole point of our argument was that

while most bitstrings are non-wff, the vast majority of them are

completely uninterpretable, and hence irrelevant. Of the ones that

are interpretable, the vast majority will be indistinguishable from a

mathematical system. (Sorry, I realise the last sentence of the above

paragraph that you objected to is a little misleading) This then

justifies the Tegmark position of adopting the "all mathematical

systems" plenitude from the more basic "all bitstrings" plenitude.

*>
*

*> The only way that a universe couldn't be specified by a wff is if it is not
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*> mathematically modellable (*and* certain other conditions pertain), since
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*> mathematics is grounded in formal systems (see fig 1 in Tegmark's paper) and
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*> formal systems are derivable from axiom sets (a subset of all wffs).
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*>
*

*> > I am currently writing a paper as I mentioned outlining this argument
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*> > (amongst others). Currently, it is in draft hand-writing form, so I
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*> > can't send it to you yet. I hope to type it up in the next week or
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*> > so. It would be useful getting feedback - maybe we could even
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*> > co-author it.
*

*>
*

*> I think it would be a good idea if some people on the list look over
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*> drafts/pre-drafts of papers (I don't mind volunteering in this case, though
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*> I'm afraid I've too much on my plate to co-author at the moment - thanks for
*

*> the offer anyway), but potential commenters should stick to making factual
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*> points (otherwise interminable discussions could ensue), and authors should
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*> try to be fair to alternative all-universe hypotheses.
*

*>
*

*> May be one day we'll all agree on one theory?
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*>
*

*> Alastair
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*>
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*>
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*>
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*>
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*>
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*>
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*>
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*>
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*>
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*>
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*>
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----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit,

University of NSW Phone 9385 6967

Sydney 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Sun Oct 24 1999 - 17:17:07 PDT

Date: Mon, 25 Oct 1999 10:17:52 +1000 (EST)

We're obviously running up against a misunderstanding here, which I

believe we should be able to resolve. Surely dragon universes are

nonsense bitstrings (the non wffs mentioned above), just ones that

happen to be close to a mathematical system, but not so close to be

indistinguishable. I thought the whole point of our argument was that

while most bitstrings are non-wff, the vast majority of them are

completely uninterpretable, and hence irrelevant. Of the ones that

are interpretable, the vast majority will be indistinguishable from a

mathematical system. (Sorry, I realise the last sentence of the above

paragraph that you objected to is a little misleading) This then

justifies the Tegmark position of adopting the "all mathematical

systems" plenitude from the more basic "all bitstrings" plenitude.

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit,

University of NSW Phone 9385 6967

Sydney 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Sun Oct 24 1999 - 17:17:07 PDT

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