Re: Detecting Design

Steven Schimmrich (schimmrich@earthlink.net)
Thu, 23 Apr 1998 23:50:31 -0400

I have read (but am not sure I could rigorously prove) that this
angle of 137.5 degrees is the angle between leaves that insures that
the maximum area of each leaf is exposed to sunlight. Surely such an
angle could arise through the process of natural selection and so what
if the constant phi (the symbol usually used to denote the golden ratio)
shows up - other constants like pi and e also pop up in surprising places.

- 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)
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