Algorithmic processes and logic

Peter Cariani 960315 1100:

Thanks Martin for the interesting reply. I think we're on much more
similar wavelengths on these issues than I had thought. I think we
have accomplished some clarification and mutual understanding of terms,
but I still maintain contra Dennett that evolution is not an
algorithmic process.

Martin Taylor excerpted from [Martin Taylor 960314 11:10]:

    As I, and I think Dennett, use the term, an "algorithmic process"
    it means a process that delivers consistent results if it starts
    from the same state and is given the same data over and over.

The difficulty with evolution and natural selection is that they involve
interactions of organisms with their material environments, and that
neither the organism nor its environment have well-defined "states", so
that it's specious to even talk in a manner that implies that one can
put organisms in environments in a particular starting state
and <always> get the same results. If only because cosmic rays cause
mutations and there are quantum mechanical undertainties built into
the mutation process, one doesn't have a process whereby consistent
results are delivered "if one starts from the same state and
is given the same data over and over". One doesn't
even need to go that far, since there are indefinite numbers of
factors that can potentially affect the outcome of an evolutionary
process that are not counted in any (well-specified) state description.

This is a basic problem that I have with realist (or "classical
physics") ways of describing material systems in general, and biological
systems in particular. When people talk as if there is an objective,
exhaustive description for a material system, I want them
to tell me what it is, or failing that, at least, what are
all the state varibles involved. If we can't have a list of those,
then a procedure for finding them, and so on. One goes through a
chain of these demands, one "in principle" postulation after another,
and the rubber never meets the road.

You, like Bill, deal with "algorithm"
only in the sense of a simulation of what is going on in the outer world.

I won't attempt to speak for Bill, but I use the term in the sense
of a formal procedure, a sequence of operations (like pencil-and-paper
arithmetical operations) for manipulating symbols in order to reach
a definitive result. I think this is very close to
the classical definition and meaning of the word, which came from
Arabic inventions of arithmetic operations and algebra. What concerns
me is the debasing of concepts like "computation" and "algorithm"
by their indiscriminate extension.

When you are dealing in representations, you have to be concerned with
fidelity, and obviously within the limits of any measuring system, there
can be a discrete system that is so faithful to the continuous "real?" system
that no difference can be measured or detected.

This is my point. One has to make a discrete measurement with some limits
on accuracy in order to compare quantities (outcomes), and in doing so,
one has operationally converted what was continuous and undifferentiated
into something that now is discrete. One needs to watch carefully what
mathematicians and modellers are doing with their hands, and not
to accept without critical reflection what they say they are doing.
(Much of what they say they are doing belongs in theology, as Brian
Rotman has playfully pointed out.)

Your discussion of dynamical systems and "logic-systems" is interesting, and
very similar to how we (Pattee's group at Binghamton over a decade ago)
were thinking of the material substrates of "symbolic" and
"computational" processes. And yes, one can make the energy
barriers higher and higher to increase reliability, but there is always
some chance of error. If the boundaries of the attractor basins can shift,
then one can create new stable macro-states that can be coupled to the
world in a new way. The kinds of devices I postulated adaptively modify
and construct their hardware so as to add new attractor basins to add
more accesible computational states, and to link those to other parts
of the external world, so as to create new sensors. And yes, I agree, this
is a "non-alorithmic process". In contrast to a digital computer,
whose dynamics are designed to ensure that basins of attraction are
stable over operationally-relevant time scales (stable states),
these kinds of devices would be designed to be conditionally
stable (i.e. "trainable").

Peter Cariani