Such laws do exist to explain evolutionary diversity even under contingent
circumstances, such as the laws of genetics. The problem, unlike a regular
system such as one body orbiting another, is that much evolutionary change
is clearly in response to changing environments. And such patterns are more
likely to be governed by chaos theory than by more regular laws. Having
said that, however, one thing that chaos theory has taught us is that even
chaotic events are governed by specific patterns that do not vary, so the
idea that contingency may in fact be "predictable" may not be so far
fetched.
>
>This example is good only because it is so short. A better,
>but lengthier example (also from Goodwin) is spiral phyllotaxis.
>I wrote something on this about a year ago and so I'm going
>to just copy it here with slight modifications. It is written
>in a narrative form because of original context which might
>seem strange here, but I'm taking the easy way out (an obvious
>example of historical contingency :).
>
>
>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 two possible explanations:
>(1) historical contingency (frozen accident) or
>(2) natural selection (this particular angle confers
>some advantage and was thus selected for during evolution).
>
A third possibility: the growth pattern could be the result of some
chemical system similar to the one that causes stems to grow against gravity
and roots to grow with gravity (see more about this below).
>
>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. So you have to add a 3rd possibility
>to the list of explanations above: (3) magic :)
>
>Just kidding. The actual explanation (more correctly,
>the explanation I find more appealing :) is that
>there are fundamental laws at play, the operation of which
>give rise to a restricted set of possible divergence
>angles. Learning how this works (beautiful mechanics :)
>is very satisfying.
>
But those fundamental laws need not be all that unusual. For instance, why
do all large bodies like planets, moons and stars take on the shape of the
sphere? Is there some mystical law like the Golden Ratio at work, something
that ties pi into the very structure of the universe? Carl Sagan suggested
as much in the final chapters of his book _Contact_. However, in this case
the reason is more mundane. It's because under the influence of a
gravitational field, any sufficiently large mass tries to maximize its
volume to surface area ratio, and the sphere has the largest possible volume
to surface area ratio of any of the perfect solids.
Spiral phyllotaxy (which by the way does seem to be a real phenomenon) may
have more to do with the fact that this allows a plant to maximize the
exposure of all leaves to the sun than to some fundamental law, contingent
event or natural selection scenario. Though there is certainly some genetic
control over the shape, since plants are able to move their body parts a
plant may simply develop that way just as all plants develop in such a way
that roots grow down and stems grow up. (Speaking of which, plants raised
on a spinning disk can develop so that the stems grow towards the axis of
the disk while the roots grow away; obviously this growth pattern is based
on the ability of the plant to sense and respond to gravity -- even false
gravity -- and not some fundamental law.)
Kevin L. O'Brien