"...all spirals in this world except whirlpools, galaxies, and spiral winds are, indeed made by living things. There is an extensive literature on this subject, which some readers may be interested in looking up (the key words are Fibonacci series and golden section).
What comes out of all this is that a spiral is a figure that retains its shape (i.e., its proportions) as it grows in one dimension by addition at the open end. You see, there are no truly static spirals.
But the class had difficulty. They looked for all the beautiful formal characteristics that they had joyfully found in the crab. They had the idea that formal symmetry, repetition of parts, modulated repetition, and so on were what teacher wanted. But the spiral was not bilaterally symmetrical; it was not segmented.
They had to discover (a) that all symmetry and segmentation were somehow a result, a payoff from, the fact of growth; and (b) that growth makes its formal demands; and (c) that one of these is satisfied (in a mathematical, an ideal, sense) by spiral form.
So the conch shell carries the snail’s prochronism – its record of how, in its own past, it successively solved a formal problem in pattern formation (see Glossary). It, too, proclaims its affiliation under that pattern of patterns which connects."
Mind and Nature
What comes out of all this is that a spiral is a figure that retains its shape (i.e., its proportions) as it grows in one dimension by addition at the open end. You see, there are no truly static spirals.
But the class had difficulty. They looked for all the beautiful formal characteristics that they had joyfully found in the crab. They had the idea that formal symmetry, repetition of parts, modulated repetition, and so on were what teacher wanted. But the spiral was not bilaterally symmetrical; it was not segmented.
They had to discover (a) that all symmetry and segmentation were somehow a result, a payoff from, the fact of growth; and (b) that growth makes its formal demands; and (c) that one of these is satisfied (in a mathematical, an ideal, sense) by spiral form.
So the conch shell carries the snail’s prochronism – its record of how, in its own past, it successively solved a formal problem in pattern formation (see Glossary). It, too, proclaims its affiliation under that pattern of patterns which connects."
Mind and Nature
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