----- Original Message -----
From: Russell Standish <R.Standish.domain.name.hidden>
[JM:]
> > > Again, this is clearly the same argument that I made, and that Wei
> > > Dai made for a different reason, that the set of all Turing programs
> > > should lead to the appearance of simple physical laws. It helps to
have,
> > > as in the Turing case, an 'end of program' symbol; the rest of the
string
> > > after this is functionless.
> >[AM:]
> > The scheme I have described is different in that it does not necessitate
> > TM's - all the computational-based
> > explanations for simple physical laws that I have seen have tended to
rely
> > on the specific mechanism of a sequential TM processor ('program stop'
> > codes, loop-backs and so on). As you stated in our last discussion
(11/7),
> > only *some* mathematical structures are TM's, and one would need first
to
> > show that TM's were the most prolific way of generating universes out of
all
> > possible such structures before any of these ideas could be given good
> > credance. (From what you have said before it doesn't seem to me that you
> > hold that *only* TM's are suited to generating consciousnesses - but no
> > doubt you will tell me if I am wrong in this surmisal.) All this however
is
> > not to say that TM's may not provide a useful analytical tool in this
area.
>
> All axiomatical mathematical systems can be encoded as bit strings,
> with the rules of symbol manipulation encoded as the rules of the
> Turing machine, and the all the output strings are theorems.
I think it is important to clarify here the difference between the two
potential applications of TM's (there are others of course).
Case 1) In my interpretation of Jacques Mallah's ideas from some of his
posts, TM's form a subset of all possible mathematical structures. Assuming
that TM's could somehow generate universes, then program loops and so on
might be able to explain the simple physical laws in most of these kinds of
universes. However it would have to be shown that the measure of these
universes was higher than those from any other possible subset of
mathematical structures.
Case 2) A TM generates theorems from axioms, as you describe above. Note we
are talking about one particular TM here (or perhaps a subset of possible
ones, dependent on the precise definition of the TM) - an inference engine.
This is possibly useful as an analytical tool, but to play any (and the
only) actual role
in the production of universes it would have to counter the challenge of
'why that particular TM with that particular set of machine instructions
(Modus Ponens/substitutivity or whatever) and no other generative entity?'
(I come back to the case of all possible TM's below). Note also that 'loop
back' arguments will not apply to a program with fixed (inference)
instructions.
> However,
> not all valid TM and initial bitstrings can be represented by a consistent
> mathematical system (a computer scientist might like to comment on
> this assertion?)
This seems clearly wrong to me (any tape sequence is in principle physically
(and so mathematically) realisable - unless you are asserting the
mathematical un-modellability of our universe, which takes us into a whole
new ball game) - I am guessing that what you really mean here is that in
general TM's can do more than just generate theorems (and so mathematical
structures) from axioms, and so (to continue to what you say below) are more
'basic'.
> Therefore, the all TM bitstring model is more general than the all
> mathematical structure model.
(If my guess above is correct, then this conclusion hardly follows,
otherwise brains, analogue computers and pre-programmed micro-chips
(which could also churn out theorems from axioms given simple inference
rules, as well as outputting other things) would also be more 'basic'.)
We are back here with what I think you are advocating - a *basic*
all-possible TM scheme. An incidental point to be made here is that the
scheme I have introduced can also be deemed to be more basic than
mathematical structures - it starts with symbol strings (which could be bit
strings), only some of which are wff's suitable for formal systems. But a
more important point is that any set of sequential TM processes (necessary
to invoke the advantages of loops etc) is itself a logical structure
(definable by a formal system), and for it to be considered to have any (and
the only) ontological/platonic role in the generation of universes (as
opposed to specific TM subsets being used as modelling tools), it must
be able to counter the charge 'why is the (wider) universe endowed with
that particular logical structure (and no other)?'
> Your argument would appear to work if
> you asserted the essential mathematical nature of the universe, but
> fails miserably in the TM bitstring case.
If you are referring to the argument I gave in response to Jacques Mallah, I
hope I have responded sufficiently, but if you are referring to the argument
in my original post in this thread, please say why you think it fails.
> However, we have already
> worked out the solution to the TM bitstring case (see the conversation
> between myself and Chris Maloney earlier in the archives).
What thread/date is this? If by chance you are mistaking me for Chris
(heaven forbid :), the scheme we worked on a few months back necessitated
neither TM's nor loops; however a more careful explication of it (see my web
pages) turned out to be rather long-winded, hence the new (conciser) scheme,
certainly bearing similarities to our one, but not dependent upon bits or
K-specifications.
Alastair
Many worlds discussions begin at:
http://www.physica.freeserve.co.uk/p105.htm
Received on Wed Oct 20 1999 - 14:22:55 PDT