The Biological Tradition of D=Arcy Thompson and Alan Turing

Broadly speaking, the Thompson/Turing biological tradition goes back to the early Greek naturalists such as Empedocles and Democritus, and their followers such as Lucretius, who rebuked intentional, functional, and teleological biological explanations. Growth and biological form, insofar as they can be scientifically characterized, arise through physical and structural necessity and chance, leaving talk of proper function, purpose, goal, and design aside. Thompson/Turing regard teleology, evolutionary phylogeny, natural selection, and history to be irrelevant distractions from fundamental biological explanation. As Turing put his general project, his new ideas were intended to Adefeat the argument from design@ (Hodges 1983, p. 431). Turing was not referring to William Paley=s watchmaker argument for the existence of God, an argument long before displaced by Lamarck and Darwin. (Darwin endorsed Aristotle=s biological work, writing that his Aidols,@ Covier and Linnaeus, seemed Amere school boys@ compared to Aold Aristotle.@ Darwin had cut his biological teeth in rapt fascination with Paley=s detailed teleology, whose designed-ness Darwin in no way wished to dispel from biological descriptions but sought to derive it through mother nature=s rather than God=s selections).

Turing, rather, endorses D=Arcy Wentworth Thompson=s view that the teleological Aevolutionary explanations@ endemic to Darwinian Aadaptationist@ biology are non-fundamental, fragile, misdirected, and at best mildly heuristic (Thompson 1917). One of Thompson=s favorite examples was Aheliotropism,@ an instinctive striving toward the sun attributed to the leaves of plants by adaptationist biologists. Once the simple stem growth mechanisms that incline leaves toward maximum sun exposure are known, Aheliotropism@ disappears from biological vocabulary. AThe primary task of the biologist is to discover the set of forms that are likely to appear [for] only then is it worth asking which of them will be selected@ (Saunders in Turing 1992, xii). And Turing meant not only to steer clear of forward-looking teleology but also backward-looking talk of efficient causality in Aristotle=s original sense that would distinguish two chemically identical molecules, or two chemically and structurally identical organisms, if one were produced Anaturally@ and the other in the laboratory. Nor would Turing allow that biological description of a particular organism is crucially incomplete or indeterminate if several selective descent pathways might have led to it, with which one possibly simply an historical accident but nonetheless supposedly part of its biological description. Similarly, to draw on Chomsky=s example, the H20 that comes from my tap is Awater@ even though it may have more tea in it than the week Atea@ I brew for myself. As Turing wrote,

Unless we adopt a vitalistic and teleological conception of living organisms, or make extensive use of the plea that there are important physical laws as yet undiscovered relating to the activities of organic molecules, we must envisage a living organism as a special kind of system to which the general laws of physics and chemistry apply. And because of the prevalence of homologies of organization, we may well suppose, as D=Arcy Thompson has done, that certain physical processes are of very general occurrence [these are the general properties of organic systems to which Chomsky refers; Turing follows with a specific instance]... What is novel in the theory is the demonstration that, under suitable conditions, many diffusion reaction systems will eventually give rise to stationary waves; in fact to a patterned distribution of metabolites. (Turing and Wardlaw, C. W. (1953/1992, p. 45)

The anti-teleological, morphological tradition that Thompson and Turing articulate, and exemplify, proximally goes back to Etienne Geoffroy Saint-Hilaire, who, in a month long debate before the Academie des Sciences in 1830, maintained the unity of type thesis that all structured multicellular animals have the same ground plan (bauplane) against the selectionist demands of existence of Georges Cuvier, Darwin=s idol. Poet naturalist Johan Wolfgang Goethe also felt party to the debate since he maintained that plant appendages C carpels, stamens, petals, sepals, and leaves C are all metamorphoses of a kind of urleaf. Work by embryological and molecular geneticists in the last decade extravagantly confirm the claims of Geoffroy and Goethe. With one trifling exception C Bryozoa C all 20 odd animal phyla appeared within a few score million years in the great Cambrian Aexplosion,@ as if nature were quick to run through all the basic possibilities of the animal type in less than 5% of the time there have been animals on earth. More substantially, it appears more and more likely that all animal phyla are variations of the same structural plan and use virtually the same homeobox Amaster genes@ and proteins to determine segmentation and segmental identity.

[W]e have accumulated more and more evidence that the same homeobox genes are used in both vertebrates and invertebrates to specify the body plan and that the mechanisms of the genetic control of development are much more universal than anticipated. (Gehring 1998, p. 53).

Parallel results have appeared in the study of plants. Goethe=s fondest hopes have been realized: carpels, stamens, petals, sepals, and leaves are variations on the ur-leaf tripped off by homeobox structural genes and their protein employers (Coen 1999). Unity of type has received an extraordinary, and to evolutionary biologists a most unexpected and devastating confirmation. In the 1970s, Stephen J. Gould gently tried to reintroduce morphology and the bauplane into English-speaking evolutionary biology, most controversially in AThe Spanrels of San Marco@ (Gould & Lewontin 1979). Anglo-American evolutionary biologists greeted Gould=s proposals, and his skepticism about selectionist explanations, with even greater skepticism and scorn for wooly-headed, anti-empirical morphologizing, a willful blindness which some thought motivated by left wing disdain for the hereditarian and selectionist views of E. O. Wilson=s Sociobiology. The shoe is now on the other foot. Similarly, and more specifically, recent embryological and morphological research on mammalian brains suggest that the human brain is simply a scaled up version of the primate brain; its specific capacities perhaps more spandrels, or accidental byproducts, of general growth, rather than specifically winnowed through the protracted chiseling of natural selection.

Among biologists, Turing is famous for his ground breaking 1952 Royal Society paper, AOn the Chemical Basis of Morphogenesis.@ Indeed, this paper, which introduced what biologists inevitably now call ATuring structures,@ has received more citations than all the rest of Turing=s works altogether (Saunders 1992, p. xvi). Here Turing tackles a major aspect of what he sees as the central problem of biology, viz., how the zygotic cell of conception manages to grow into the immensely larger and enormously complicated structures of the fetus, the baby, and the mature organism, creating all along new information and structure. The exemplary chaotic reaction-diffusion models that Turing proposed now have an important role in theoretical biology and recently have been observed experimentally (Castets, V., Duclos, E., Boissonade, J., Kepper, P. 1990). They show how patterns or structures can burst forth in homogeneous mediums, the most specific example of ATuring structures.@

Turing=s general theoretical stance demands specification of some physical and chemical situation which defines Athe state of the system.@

One then describes how that state is to be determined from the state at a moment very shortly before ... In determining the changes of state one should take into account (i) The changes of position and velocity, as given by Newton=s laws of motion. (ii) The stresses as given by the elasticities and motions, also taking into account the osmotic pressures as given from the theoretical data. (iii) The chemical reactions. (iv) The diffusion of the chemical substances. The region in which this diffusion is possible is given from the mechanical data. (Turing 1952, p. 37-38)

Recent news stories give pictures of an adult cat and her clone, a kitten genetically identical to her mother. But the kitten does not have the same color pattern in its fur as the mother: this is precisely the result that Turing=s work predicted in 1952.

Castets, V., Duclos, E., Boissonade, J., Kepper, P. (1990). Experimental evidence of a sustained standing Turing type non-equilibrium chemical pattern. Physical Review Letters, 64, 2953-2956.

Coen, E. (1999). The art of genes: How organisms make themselves. Oxford: The University Press.

Gehring, W. J. (1998). Master control genes in developmental evolution. New Haven and London: Yale University Press.

Gould, S. J., Lewontin, R. C. (1979). The spandrels of San Marco and the Panglossian paradigm C a critique of the adaptationist program. Proceedings of the Royal Society of London B, 205, 581-598.

Hodges, A. (1983). Alan Turing: The enigma. New York: Simon and Schuster.

Thompson, D= A. W. 1917. On growth and form. Cambridge University Press.

Turing, A. (1952/1992). On the Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society of London, Series B, 237, 37-72. I am quoting from Alan Turing, P. T. Saunders, ed., collected works of A. M. Turing: Morphogenesis. Amsterdam: North-Holland.

_______ and Wardlaw, C. W. (1953/1992). >A diffusion reaction theory of morphogenesis,= The collected works of Alan Turing: Morphogenesis. Amsterdam: North-Holland.