From: Terry M. Gray (grayt@lamar.colostate.edu)
Date: Sun Aug 10 2003 - 18:00:34 EDT
Brian et al.
As I read this thread, Brian Goodwin's book *How the Leopard Changed
Its Spots* came to my mind as well and I thought, "Haven't we done
this before?"
A quick Google search on "Goodwin Fibonacci ASA" brought up this
Brian Harper post from 1998
http://www.asa3.org/archive/asa/199804/0387.html
Sounds pretty similar to what's below.
I'm beginning to wonder if we actually make any progress here!
TG
>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
-- _________________ Terry M. Gray, Ph.D., Computer Support Scientist Chemistry Department, Colorado State University Fort Collins, Colorado 80523 grayt@lamar.colostate.edu http://www.chm.colostate.edu/~grayt/ phone: 970-491-7003 fax: 970-491-1801
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