Quick thought. Isn't 'designedness' directly proportional to a local
reduction in entropy (= a measure of disorder, etc.) ? There's lots of
math on entropy.
Robert C
Nicholas Thompson wrote:
All,
I confess I have not followed the mathematical side of this discussion into
the blue underlined stuff. Nor do I claim to understand all of the plain
text.
However, I am tempted by the idea of a mathematical formalization of
"natural design". Here is the argument: What EVERYBODY --from the most
dyed in the wool Natural Theologist to the most flaming Dawkinsian --
agrees on is that there is some property of natural objects which we might
roughly call their designedness. Tremendous confusion has been sewn by
biologists by confusing that property -- whatever it might be -- with the
CAUSES of that property, variously God or Natural selection, or
what-have-you. So much of what passes for causal explanation in biology
is actually description of the "adaptation relation" or what I call, just
to be a trouble-maker, "natural design".
It seems to me that you mathematicians could do a great deal for biology by
putting your minds to a formalization of "natural design". It would put
Darwin's theory -- "natural selection begets natural design" out of the
reach of tautology once and for all. What I am looking for here is a
mathematical formalization of the relations --hierarchy of relations, I
would suppose -- that leads to attributions of "designedness". Assuming
that one had put a computer on a British Survey Vessel and sent it round
the world for five years looking at the creatures and their surroundings,
what is the mathematical description of the relation that would have to be
obtained before the computer would come home saying that creatures were
designed (and rocks weren't). Then -- and only then -- are we in a
position to ask the question, "is natural selection the best explanation
for this property.
My supposition is that ALL current theories will not survive such an
analysis. Indeed, we may need a new metaphor altogether. Many of you will
be familiar with the notion of fitness landscape. For intuitive purposes,
let me turn the landscape upside down, so its peaks are chasms and its
valleys are peaks. Now, drop a ball at random into the upside down
landscape. Assuming that the landscape is rigid, the ball will roll around
until it finds a local minimum. If you put some jitter in the rolling, it
might, depending on the size of the jitter and the roughness of the
landscape, find the absolute minimum. But all of this assumes that the
ball has no effect on the landscape! If we turn the landscape into a
semi-rigid net so that the ball deforms the landscape as it rolls through
it, then we have a much better metaphor for the relation between an
organism's design and the environment in which it is operating. Some
organisms -- weedy species -- cause the environment to rise under their
feet, so to speak, so they are constantly driven out of whatever valley
they settle in; Other organisms modify the environment in their favor and
in effect, dig their way into a pit in the landscape. If the ball
representing such organisms has inadequate jitter or the landscape is not
sufficiently springy, such an organism can dig its way into a pit and then
go extinct.
In short we need a dynamical theory. But such a theory will never happen
until we have a sufficiently subtle (and verbalizable) mathematical
formalization of the momentary relation between organisms and their
environments that we are trying to explain. Get at it, you
mathematicians!!!!
Nick
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