- Steve.
At 11:19 PM 4/23/98 -0400, Brian Harper wrote:
>
>Here is a little test of design motivated by the SETI
>example in Bill Dembski's essay recently posted by
>Howard. I have two more that I hope to give later if
>I find time:
>
>
>Spiral Phyllotaxy
>====== ==========
>
>Suppose you are a botanist investigating possible
>geometrical growth laws in plants. In particular, you
>are studying a group of plants displaying a growth
>pattern which has come to be referred to as spiral
>phyllotaxy. But you don't know this obviously, since
>you are the lucky scientist who is going to make this
>discovery :). As you look down the stem of a plant
>from the top you note that successive leaves form a
>spiral pattern as you move up the stem with a constant
>angle of divergence. Careful measurements reveal this
>angle to be very nearly 137.5 degrees. As you study
>more and more plants with this spiral pattern you
>find this same constant divergence angle again and
>again.
>
>Well, this is not particularly surprising. Its not
>really surprising that the divergence angle should
>be a constant. This constant must be some number,
>why not 137.5? As to why the same angle in so many
>plants one imagines three possible explanations,
>all perfectly reasonable: (1) some type of developmental
>constraint, (2) historical contingency (frozen accident)
>or (3) natural selection (this particular angle confers
>some advantage and was thus selected for during evolution).
>
>OK, fine. Several weeks later you are reading your
>favorite "joy of math" book during one of your many
>"time-outs" imposed by the Emperor, err, I mean the
>Department Chair. You are fascinated to learn about
>the Golden Rectangle and the mystical and magical
>Golden Ratio. The ratio that Kepler referred to as
>the "Divine Proportion" and a "precious jewel", one
>of the two "great treasures" of geometry, the other
>being the theorem of Pythagoras.
>
>Now the thought occurs to you: What angle will
>divide a circle into the divine proportion?
>IOW, consider a circle of circumference A and
>some angle that divides the circumference into two
>parts B and C (A = B + C) in such a way that the
>ratio C/B = B/A = R, the Golden Ratio. This is
>a fairly simple problem and after a few moments
>you discover, to your great horror :), that the
>required angle is 137.5 degrees.
>
>And so you have discovered that the divergence
>angle during the growth of the plants you have
>been studying divides a circle into the Divine
>Proportion. Surely a more astounding result than
>a sequence of prime numbers.
>
>Brian Harper
>Associate Professor
>Applied Mechanics
>The Ohio State University
>
>"It is not certain that all is uncertain,
>to the glory of skepticism." -- Pascal
-- Steven H. Schimmrich Physical Sciences Department schimmri@kutztown.edu (office) Kutztown University schimmrich@earthlink.net (home) 217 Grim Science Building 610-683-4437, 610-683-1352 (fax) Kutztown, Pennsylvania 19530 http://home.earthlink.net/~schimmrich/