Re: loose ends

From: brian harper (harper.10@osu.edu)
Date: Mon Aug 04 2003 - 15:47:56 EDT

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    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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