Dear John and colleagues,
As usual I am having too short a time (will attempt to answer properly next
week, also to James and Jerry), but your reflections connecting with
mechanics and computability have initially reminded me a rather obscure
paper by Michel Conrad and Efim Liberman, where they discuss in a
philosophical annex the nature of physical law in connection with the
Church-Turing principle of computability. I could never make complete sense
of their speculations (quite deep ones)... it is the same type of reasoning
you are making: peripherally relevant as you say. I will try to quote from
Michael and Efim next week
Thanks for the stuff.
Pedro
At 20:10 17/11/2006, you wrote:
Dear colleagues,
Pedro has pointed out a real problem, I think. I have a few words to say
on it that may be of some help in sorting out the issues. They derive
partly from my trying to make sense of Atlan's use of computational
language along with his claim that some biological (biochemical really)
stuctures have "inifinite sophistication". A structure with infinite
sophistication cannot be computed from the properties of its
components. Sophistication, as far as I can tell, is a measure of
computational depth, which depends on the minimal number of
computational steps to produce the surface structure from the maximally
compressed form (Charles Bennett). Atlan has made the connection, but
also noted it is not fully clear as yet, since Bennett's measure is
purely in terms of computational steps, and is relative to maximal
compression, not components. Cliff Hooker and I noted these problems
(before we knew of Atlan's work -- well, I did, but it was presented
poorly by one of his students -- see Complexly Organized Dynamical
Systems, Open Systems and Information Dynamics, 6 (1999): 241-302. You
can find it at
http://www.newcastle.edu.au/centre/casrg/publications/Cods.pdf). The
question relevant to Pedro's post is why is computation relevant if
common biological systems have infinite sophistication, and thus are not
effectively computable, even if they have finite complexity?
Here is my stab at an answer: the notion of mechanical since Goedel and
Turing (I would say since Lowenheim-Skolem, since Turing's and Goedel's
results are implicit in their theorems) breaks up into to notions,
stepwise mechanical and globally mechanical. A globally mechanical
system can be represented by an algorithm that halts on all relevant
inputs (Knuth algorithm); these are computable globally. The stepwise
ones have no global solution that is effectively computable, but are
computable locally (to an arbitrarily high degree of accuracy). The
difference is similar to that between a Turing machine that halts on all
relevant inputs and one that does not. Both are machines, but only the
latter corresponds to Rosen's restricted notion of mechanical. So
computation theory can help us to understand the difference between
things that are stepwise mechanical, and things that are not. Things of
infinite sophistication are not globally mechanical. I will say without
proving that they correspond to Rosen's systems that have analytical
models but no synthetic models. They may still be mechanical in the
weaker sense. In fact I have not been able to see how they cannot be
mechanical in this way.
Consequently, there are Turing machines that are mathematically
equivalent to systems of infinite sophistication, but they do not halt.
So you are probably wondering how processes of this sort can occur in
finite time. The answer is dissipation. I'll not give the solution here,
as my coauthor on another paper just came into the room and asked me how
it was going, and I said I was writing something else that was
peripherally relevant :-) A case in point is given in my commentary on
Ross and Spurrett in Behavioral and Brain Sciences titled Reduction,
Supervenience, and Physical Emergence, BBS, 27:5, pp 629-630. It is
available at
http://www.nu.ac.za/undphil/collier/papers/Commentary%20on%20Don%20Ross.htm
as well as the BBS site.
All spontaneously self-organizing systems (see the Collier and Hooker
CODS piece) are only locally mechanical. I won't prove that here, but
there is a clue in the BBS commentary.
Cheers,
John
Professor John Collier
Philosophy, University of KwaZulu-Natal
Durban 4041 South Africa
T: +27 (31) 260 3248 / 260 2292
F: +27 (31) 260 3031
email: [EMAIL PROTECTED]
Http://ukzn.ac.za/undphil/collier
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