The mathematics, like the nautilus shell, is just an effect of linear growth site(s) rotating about a central axis at constant angular velocity. Interesting, but not amazing. The Fibonacci sequence and golden mean are related concepts through additive sequences.
jl: Quantum physics displays counter-intuitive behavior exactly along these lines. Look at the diagram of the lifeguard and the swimmer here, to see how light seems to "know" the quickest path to its destination before it starts.
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jleader
01-22-2003
01:51 PM ET (US)
Asking "do plants know math" remind's me of Djikstra's "Asking whether a computer can think is like asking whether a submarine can swim."
I guess I would answer your question by responding that plants, like the rest of the Universe, "do" math. Does a falling rock "know" math when it follows a parabolic path?
Perhaps it would be more accurate to say that math knows plants.
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aha
01-22-2003
11:17 AM ET (US)
These patterns may relate to what physicists call least action--the principle that says when anything changes it does so in a way to minimize the effort required. But its never that simple, because theres interaction with animals, light, climate, and the conflicting need to optimize reproduction. I wonder if the colorful hexagonal pattern inside many flowers is especially attractive to bees, which evolved hexagonal cells through the efficiency of shared walls.
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JohnR
01-22-2003
06:57 AM ET (US)
It seems to me that your title is a 'Chicken or Egg' question.
Math and molecules are one.
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severian
01-22-2003
01:46 AM ET (US)
Cool stuff. And if you go shopping at Rainbow Groceries in SF, they often carry romanesque broccoli (the top image on the linked page). It's so fractal it blows my mind.
But my favorite math-in-nature thing are the Sierpinksi seashells that have the cellular automaton image following the leading edge of the shell. Looks just like a program I wrote in high school!