From: brian harper (harper.10@osu.edu)
Date: Mon Aug 04 2003 - 15:47:56 EDT
At 07:50 PM 8/3/2003 -0400, George Murphy wrote:
[...]
>Glenn -
> I'm not just out for pedantry either - though I've been known to
> do that - & was
>going to try to turn to a similar question.
> There are natural processes that generate some of well-defined
> sequences which
>can be generated by the type of formula that I've spoken of. E.g., a
>source of waves
>can be thought of as "generating" a sequence related to the zeroes of
>appropriate
>oscillatory functions (sines & cosines &c). For the primes, however, I
>just can't think
>of any plausible natural process that would carry out the sieve procedure.
>(I realize that this isn't a proof!)
> The Fibonacci numbers do show up in patterns of leaves,
> seashells, &c. Does
>anyone know why they do - i.e., the natural processes that produce those
>patterns? IF
>we knew that & IF part of a Fibonacci sequence could be considered a
>specifiable message
>then we would have a clear counterexample to the claim that such messages
>can be
>produced only by intelligent design (in the ID sense). But those are
>significant IFs.
Actually, I did propose this with the counterexample in mind :).
I looked at this several years ago and the main reference I had at the
time was the following:
Douady and Couder, "Phyllotaxis as a Dynamical Self Organizing
Process" (in three parts), J. Theoretical Biology (volume 178, 1996)
Of course, a lot could have happened since then. This is also
discussed in a less technical manner in Goodwin's
<How the Leopard Changed its Spots> and in Webster
and Goodwin's <Form and Transformation>.
Now let me try to give a hint at the physical explanation as to
why phyllotaxis corresponds to the pattern of a Fibonacci series.
Before starting we need to remind ourselves of the Fibonacci series.
0 1 1 2 3 5 8 13 21 34 55 ...
and now the ratios of successive numbers and their
approach to the Golden Ratio:
0/1=0 1/1=1 1/2 = 0.5 2/3 = 0.667 3/5 = 0.6 5/8 = 0.625
8/13 = 0.615 13/21 = 0.619
Basically, as a new shoot forms, its position is not
immediately set. It can and will move a little due to
interference with previous shoots. This can be modeled
by new shoots appearing in such a way as to minimize
the repulsive forces from previous shoots. It seems that
only the previous two shoots interfere significantly
with a new shoot, analogous to a particular number
in the Fibonacci sequence being determined by the
previous two numbers. Also, there would be more interference
from the closest neighbor just as 13 (for example) is a
larger fraction of 21 than is 8.
Again, this is just a hint at why a series growth might
be related to plant growth. Douady and Couder have
developed a nonlinear dynamical morhogenesis model which
describes the growth of real plants very well.
Now I want to go back to the quote of Dembski:
=======Dembski on specification============
Suppose now that we represent a photon passing through the filter with a
"1" and a photon not passing through the filter with a "0." Consider the
specification 11011101111101111111..., namely, the sequence of prime
numbers in unary notation (successive 1s separated by a 0 represent each
number in sequence). For definiteness let's consider the prime numbers
between 2 and 101. This representation of prime numbers is ontologically
subjective in the sense that it depend on human subjects who know about
arithmetic (and specifically about prime numbers and unary notation). It is
also epistemically objective inasmuch as arithmetic is a universal aspect
of rationality. Moreover, once this specification of primes is in place,
the precise probability of a sequence of photons passing through the filter
and matching it is ontologically objective. Indeed, that probability will
depend solely on the inherent physical properties of photons and polaroid
filters. Specified complexity therefore is at once epistemically objective
(on the specification side) and ontologically objective (on the complexity
side once a specification is in hand).
=====================================
I cannot see how the example suffers if we replace the sequence of
primes by a Fibonacci sequence.
Brian Harper
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