Date: Fri, 24 May 1996 23:48:44 -0500
Subject: Re: Pigs could flya - Reply


Paul G:

>Raup's article astonished me - again I wish I had the citation with me.
>Molluscan and other shells are described by simple differential
>equations.  There are only certain forms thay can take.  Some of the
>bizarre forms shells have taken were explained as adaptations, but it
>turns out that they have to be that way according to the equations.
>This sounds a little mystical - that's why the article astonished me.
>But if I remember correctly, it's because shells develop incrementally.
>They can only keep adding to their edges.

Why mystical? As long as the most important mechanisms of shell formation
are fairly simple, there's no reason why one shouldn't be able to quantify
the process in a straightforward manner. If all that was done was to
recognize the mathematical relationship without finding the underlying
physical reasons, that's not mystical either, it's merely an attempt at a
partial understanding. If you find that on examining more shells the
relationship doesn't hold up, you toss out your hypothesis. Biologists need
not oppose the use of mathematics on principle, as people like Delbruck
have come close to doing.

Certain regularities can even be created by natural selection, I would
imagine. The opposition of described by differential equations against
adaptive consequences of natural selection has no intrinsic justification

Rahul




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