From: RDehaan237@aol.com
Date: Wed Aug 06 2003 - 18:19:46 EDT
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.
Shalom,
George
George,
The best treatment of the topic that I know of is D’Arcy Thompson’s classic
treatise, On Growth and Form. He does not provide any “natural processes that
produce those patterns” of the kind that I think you are looking for.
Rather, he relates them to the process of growth and what he calls, “mathematical
reasons.” In Chapter XI, “The Equiangular Spiral,” he spends more than 100
pages on more aspects of this spiral than I thought possible, but primarily
mathematical ones. Chapter XII is entitled, “The Spiral Shell of the Foraminifera;”
Chapter XIII is, “The Shapes of Horns, and of Teeth or Tusks with a Note on
Torsion;” Chapter XIV, “On Leaf Arrangement, or Phyllotaxis.”
In Ch. XIV he discusses the spirals in the fir cone and the sun flower head,
spiral leaf order, and the Fibonacci series (giving an interesting footnote on
how Fibonacci got his name. His real name was Leonardo of Pisa [1170-1250].
His nickname, Fi Bonacci [filius bonassi] appeared in one of his major works,
and stuck).
Thompson is not sympathetic to an explanation of the botanical spirals that
invokes natural selection. “We come then without more ado to the conclusion
that while the Fibonacci series stares us in the face for the fir-cone, it does
so for mathematical reasons; and its supposed usefulness, and the hypothesis
of its introduction into plant-structure through natural selection, are
matters which deserve no place in the plain study of botanical phenomena” (p. 933).
Hope this helps,
Bob
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