In one of his pamphlets, Robert mentioned Godels theorem. More
siginificant is ,I think, the algorithmic info-theory equivalent
of Godels theorem. Actually, there are several of these, all due
to Chaitin (I believe). I won't go into why this is the equivalent
of Godels theorem, but just roughly paraphrase the result as:
"You can't get a 200 lb baby from a pregnant woman that
weighs 100 lbs."
or
"a twenty pound theorem could not have been derived from
10 lbs of axioms"
or
"an algorithm cannot compute a result more complicated
than itself"
Let's first use these ideas to test the reductionistic viewpoint
of Dawkins or Dennett, i.e. let's test the following premises:
a) living things are just machines, mechanisms
b) life came to be by a mechanistic (algorithmic)
process
c) life is reducible to physics, i.e. the algorithm for producing
life is comprised of the laws of physics.
I believe this claim to be already falsified by Chaitin's results.
Chaitin has determined the algorithmic complexity of the laws of
physics and found it to be very small (not surprising). The algorithmic
complexity of DNA is very very large (Yockey). In other words, the
laws of physics are the 100 lb. pregnant woman whereas DNA is the
200 lb. baby.
Now, what does this mean? Let me argue it two ways, i.e. provide
two possible answers to the question "where does the complexity
of DNA come from?". The safest answer is, I think, Yockey's answer,
i.e. the question is undecidable (here we see the tie in with
Godels theorem). Based upon the laws of physics, life is undecidable.
Or, in other words, life is consistent with but not reducible to
the laws of physics.
Now for a more daring approach. If the complexity does not come from
the laws of physics themselves then it must come from some other
input to the "algorithm" responsible for evolution (whether it be
chemical or biological). The only possibility I can think of,
limiting ourselves to the rules of the game :-), is through
specificity in initial or boundary conditions. But this magnitude
of specificity leads one to Anthropic Principle type of arguments
with their inherant implications regarding design.
So, that's where I'm at with it now, undecidable or design via the
Anthropic Principle. What I kind of like about the second approach
is that it is a design viewpoint which incorporates evolution.
There is also at least one other possible viewpoint here that I
don't yet know how to think about properly. I have mentioned
several times here recently the infamous self-organizationalists.
I think some of them would respond to this by saying that living
things are not mechanisms, nor is evolution a mechanistic (algorithmic)
process. For example, I found a proceedings volume awhile back
entitled <Complexity, Chaos, and Biological Evolution>, Plenum, 1991.
On the cover page for the section "Evolutionary Dynamics and Artificial
Life" there is the following slogan:
"The mechanical world view will be swept away and replaced
by the picture of a self-creating world."
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Brian Harper |
Associate Professor | "It is not certain that all is uncertain,
Applied Mechanics | to the glory of skepticism" -- Pascal
Ohio State University |
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