Re: loose ends --(Fibonacci)

From: Terry M. Gray (grayt@lamar.colostate.edu)
Date: Sun Aug 10 2003 - 18:00:34 EDT

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    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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