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: collierj@ukzn.ac.za
>http://ukzn.ac.za/undphil/collier
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Received on Wed Nov 22 14:02:20 2006
