I don't think anyone said they don't exist. Its the measure of the
worlds that contain that is interesting. There are two possibilities:
a) The dragon universe is the outcome of a mathematical
description. In the sense we use dragon here of being non-lawlike, we
may suppose that they are the outcome of a very complex mathematical
description. As we well know, the measure of such universes is much
smaller than the very lawlike universe we inhabit.
b) The dragon universe corresponds to one of the "nonsense
bitstrings", which we know to vastly outnumber the lawlike ones. In
this case, we must apply the argument I worked out with Alistair
Malcolm to show that indeed these dragon universes are of small
measure compared with lawlike universes, and that the remaining
"nonsense" universes are like noise - unobservable.
Cheers
>
> Why on earth should dragons not exist? Why should that be a 'nonsense
> bitstring'? Why should it not be describable mathematically? I am convinced
> that such universes do exist, about as convinced as I am that you exist. If
> they don't, MWI is false.
>
> > -----Original Message-----
> > From: Russell Standish [SMTP:R.Standish.domain.name.hidden]
> > Sent: Monday, October 25, 1999 1:18 AM
> > To: amalcolm.domain.name.hidden
> > Cc: R.Standish.domain.name.hidden; everything-list.domain.name.hidden.com
> > Subject: Re: Flying rabbits and dragons
> >
> > >
> > > ----- 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
> > > > of non-wffs vastly outnumber the number of wffs. The assumption is
> > > > that that each non-wff corresponds to to a white rabbit universe. As
> > > > we discussed, and you have explained fairly clearly on your web page,
> > > > most non-wff universes are in fact indistinguishable from a wff
> > > > universe sufficiently close to it, so may be identified with it. In
> > > > that case, the number of non-wff universes corresponding to white
> > > > rabbits or dragons (ie actually recognisable paranormal phenomena) is
> > > > a vanishingly small proportion of the total.
> > >
> > > No! I am very sorry, but I have to correct this - every sentence above
> > is
> > > false!!! (Though stemming from one underlying misunderstanding, I
> > think.)
> > >
> > > One of the main reasons to use the formal systems approach is that it
> > solves
> > > the principal interpretation problem - some symbol strings build wff's,
> > some
> > > 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
> > > wff's - yet), wff's rather than non-wff's are selected - wff's are a
> > > precondition for the specification of *any* universe (with or without
> > > dragons/white rabbits); a non-wff is like a nonsense bitstring - totally
> > > 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
> > > mathematically modellable (*and* certain other conditions pertain),
> > since
> > > mathematics is grounded in formal systems (see fig 1 in Tegmark's paper)
> > and
> > > formal systems are derivable from axiom sets (a subset of all wffs).
> > >
> > > > I am currently writing a paper as I mentioned outlining this argument
> > > > (amongst others). Currently, it is in draft hand-writing form, so I
> > > > can't send it to you yet. I hope to type it up in the next week or
> > > > so. It would be useful getting feedback - maybe we could even
> > > > co-author it.
> > >
> > > I think it would be a good idea if some people on the list look over
> > > drafts/pre-drafts of papers (I don't mind volunteering in this case,
> > though
> > > 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
> > > points (otherwise interminable discussions could ensue), and authors
> > should
> > > try to be fair to alternative all-universe hypotheses.
> > >
> > > May be one day we'll all agree on one theory?
> > >
> > > Alastair
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> >
> >
> >
> > --------------------------------------------------------------------------
> > --
> > 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
> > --------------------------------------------------------------------------
> > --
>
>
----------------------------------------------------------------------------
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 Mon Oct 25 1999 - 17:24:39 PDT