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Alan Turing and the mathematics of pattern formation in nature (nytimes.com)
137 points by YeGoblynQueenne on Dec 26, 2018 | hide | past | favorite | 10 comments



I typed in the preface to Morphogenesis, and scanned the drawing inside the front cover by Alan Turing's mother of her son watching the daisies grow.

https://donhopkins.com/home/archive/Turing/Morphogenesis.txt

Hockey or Watching the Daisies Grow: https://i.imgur.com/AX6Bg9q.jpg

Turing, Alan Mathison, 1912-1954. Morphogenesis / edited by P. T. Saunders. p. cm. -- (Collected works of A. M. Turing, Volume 3). Includes bibliographical references and index. ISBN 0 444 88486 6. 1. Plant morphogenesis. 2. Plant morphogenesis -- Mathematical models. 3. Phyllotaxis. 4. Phyllotaxis -- Mathematical models. (C) 1992 Elsevier Science Publishers B. V. All Rights Reserved.

https://books.google.nl/books?id=GX7NCgAAQBAJ&pg=PR8&lpg=PR8

Watching the daisies grow: Turing and Biology

http://tokillamachine.co.uk/alan-turing/watching-the-daisies...


Thank you for this. What a wonderful find.


Thank You for typing this up.

> Not all biologists, however, have accepted this view. One of the strongest dissenters was D'Arcy Thompson (1917), who insisted that biological form is to be explained chiefly in the same way as inorganic form, i.e., as the result of physical and chemical processes. The primary task of the biologist is to discover the set of forms that are likely to appear. Only then is it worth asking which of them will be selected. Turing, who had been very much influenced by D'Arcy Thompson, set out to put the program into practice. Instead of asking why a certain arrangement of leaves is especially advantageous to a plant, he tried to show that it was a natural consequence of the process by which the leaves are produced. He did not in fact achieve his immediate aim, and indeed more than thirty-five years later the problem of phyllotaxis has still not been solved. On the other hand, the reaction-diffusion model has been applied to many other problems of pattern and form and Turing structures (as they are now called) have been observed experimentally (Castets at al. 1990), so Turing's idea had been vindicated.

Reading most of this introduction, especially this last paragraph, I couldn't but help think about Stephen Wolfram's A New Kind of Science. Wolfram's book is very empirically philosophical, or maybe I should say just purely explorational, and he goes into the problems described above almost word for word. He uses programs to demonstrate that, for example, the variation in patterns on shellfish is due to minimal changes in genetic programs.


D'Arcy Thompson's 'On Growth and Form' is worth a read.

As a lapsed biologist, I would say he's right that in biology, shape results from the interaction of physical forces and the properties of materials. But he misses the point that the properties of materials are governed by genes. There's no gene that makes a sea urchin spherical, but there are genes such make its skin flexible but inelastic (or whatever), and it's spherical because of that. Evolution is perfectly happy to form the shape indirectly by selecting alleles of those genes. But a notional anti-Thompson who thinks genes are everything would be missing the point that lots of shapes are impossible, because there's no plausible combination of force and material which would produce them.


Your fingers are patterned by a system just as proposed by Turing:

http://science.sciencemag.org/content/345/6196/566



Anyone have a mirror?


It seems the article was saved to archive.is a few months ago [0] but you can also read it by using NoScript or uBlock.

[0] http://archive.is/VuXE7



The NYT paywall is bypassable using Pocket: save the article and read it.




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