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
>>> Pedro Marijuan <marijuan@unizar.es> 11/17/06 12:22 PM
>>>
Dear FISers,
I was recently asked some short views summarizing the field of
biological
computation. After several weeks delay, I finally penned a few lines.
Maybe
someone in the list can find some interest in the very rough reflections
below.
-----------------------
In my view, there is some trouble in biological computation or
bioinformation or whatever name one chooses for the field. One of the
main
inputs has traditionally come from theoretical biology, even in the 60's
(e.g., Waddington, Dancoff & Quastler, von Bertalanffy), but mostly in
late
80's and early 90's, with leading figures such as Michael Conrad and
Robert
Rosen. They both were very critical on any easy-going marriage between
computers and biology. Michael produced a very fine contraposition of
computational differences, between living cells and classical computers,
from the point of view of adaptability. On the other side, the
influences
from computer fields did crystallize into Artificial Intelligence, and
more
recently into Artificial Life (Holland, Brooks, Langton, etc.) and
perhaps
complexity theorists (Kauffman); notwithstanding important differences
among these fields , as a whole they never saw any terrible difficulty
in
the cross-fertilization, or better hybridization, between computers and
biology.
In actuality I think that around "biological computing" there is a very
tough problem --that means I am unable to produce any really convincing
argument! But the whole point may be that biological microscopic
functional
elements (say the enzyme, or the nucleic acid stretch) are not amenable
to
"sufficient" logical description in similar terms to functional
components
of computers. Structure, functionality, estrategy, etc. are in every
respect (and every "level") non-comparable, and in general
non-compatible.
The basic functionalist point of separability between hard and software
DOES NOT RULE biologically. Of course, in science one can always drop
embarrassing elements of distinction... by "disciplinary" fiat. And
then
produce flamboyant names "artif. intel.", "artif. life",
"biocomputing",
etc.
In the fis discussion list I produced several further arguments
( http://fis.icts.sbg.ac.at/mailings/ ), in the 2005 discussion on
molecular bionetworks.
Anyhow, thanks for the stimulus to pen these late reflections.
Pedro
--------------------------------------------
PS. Jumping from biological complexity to "social complexity", as we
will
start discussing in a few weeks (hopefully!), one would expect a
serious
scientific-foundational problem too. It is the fate of those
informational
entities, so poorly amenable to formal treatments.
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Received on Fri Nov 17 20:11:59 2006
