<<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,
Leaves have many shapes and sizes. Does 137.5 degrees provide maximum
exposure to all? Probably not. Would not one predict that natural selection
would select the angle best suited for each population of plants? Therefore
should we not expect to find a variety of angles for maximum exposure keyed to
the varied morphology of leaves?
The Golden Spiral, the Golden Rectangle, and the Magic Ratio are all
designations of some elusive phenomenon that is extremely widespread in nature
and in human life. The phenomenon appears in astronomy, oceanography,
biology, archi-
tecture, art, and music. It is found in the curving arms of spiral galaxies;
the curling lip of a wave, the shoreline of Cape Cod; in the arrangements of
florets of a sunflower, seeds in pine cones, the arrangements of leaves on a
plant's stalk, and the number of petals in a daisy; in the "exquisitely
beautiful molluscan
shells" (Thompson, 1942), the shape of a snail's shell and that of a chambered
nautilus; in a ram's horn, a parrot's beak, a lion's claw; in the Great
Pyramid of Egypt, the front elevation of the Parthenon, in Greek vases and
statues, in class-
ical art; in the proportions found in musical chords; in the proportions of
the human body. The phenomenon is too widespread in too many different
circumstances to be discounted as mere chance (Hoffer E., "A magic ratio
recurs throughout art and nature" _Smithsonian Magazine_1975, p. 120),
although none of the examples is exactly perfect in nature.
Has anyone found anywhere a general naturalistic explanation of the Magic
Ratio? I'd like a reference if anyone has one. Does it have a function in
nature, or is it just there? Does the Magic Ratio fit Dembski's "complex
specified information" criterion for intelligent design? Its generality and
ubiquity, it seems to me, argue for design.
Cheers,
Bob