Collected Works of A.M. Turing Morphogenesis P.T. Saunders, Editor Preface It is not in dispute that A.M. Turing was one of the leading figures in twentieth-century science. The fact would have been known to the general public sooner but for the Official Secrets Act, which prevented discussion of his wartime work. At all events it is now widely known that he was, to the extent that any single person can claim to have been so, the inventor of the "computer". Indeed, with the aid of Andrew Hodges's excellent biography, A.M. Turing: the Enigma, even non-mathematicians like myself have some idea of how his idea of a "universal machine": arose - as a sort of byproduct of a paper answering Hilbert's "Entscheidungsproblem". However, his work in pure mathematics and mathematical logic extended considerably further; and the work of his last years, on morphogenesis in plants, is, so one understands, also of the greatest originality and of permanent importance. I was a friend of his and found him an extraordinarily attractive companion, and I was bitterly distressed, as all his friends were, by his tragic death - also angry at the judicial system which helped to lead to it. However, this is not the place for me to write about him personally. I am, though, also his legal executor, and in fulfillment of my duty I have organized the present edition of his works, which is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. The edition will comprise four volumes, i.e.: "Pure Mathematics," edited by Professor J.L. Britton; "Mathematical Logic", edited by Professor R.O. Gandy and Professor C.E.M. Yates; "Mechanical Intelligence", edited by Professor D.C. Ince; and "Morphogenesis", edited by Professor P.T. Saunders. My warmest thanks are due to the editors of the volumes, to the modern archivist at King's College, Cambridge, to Dr. Arjen Sevenster and Mr. Jan Kastelein at Elsevier (North-Holland), and to Dr. Einar H. Fredriksson, who did a great deal to make this edition possible. P.N. Furbank Alan Mathison Turing - Chronology 1912 Born 23 June in London, son of Julius Mathison Turing of the Indian Civil Service and Ethel Sara nee Stoney 1926 Enters Sherborne School. 1931 Enters King's College, Cambridge as mathematical scholar 1934 Graduates with distinction 1935 Is elected Fellow of King's College for dissertation on the Central Limit Theorem of Probability 1936 Goes to Princeton University where he works with Alonzo Church 1937 (January) His article "On Computable Numbers, with an Application to the Entscheidungsproblem" is published in "Proceedings of the London Mathematical Society" Wins Procter Fellowship at Princeton 1938 Back in U.K. attends course at the Government Code and Cypher School (G.C. & C.S.) 1939 Delivers undergraduate lecture-course in Cambridge and attends Wittgenstein's class on Foundations of Mathematics 4 September reports to G.C. & C.S. at Bletchley Park, in Buckinghamshire, where he heads work on German naval "Enigma" encoding machine 1942 Moves out of naval Enigma to become chief research consultant to C.G. & C.S. In November sails to USA to establish liaison with American code-breakers 1943 January-March at Bell Laboratories in New York, working on speech-encypherment 1944 Seconded to the Special Communications Unit at Hanslope Park in north Buckinghamshire, where he works on his own speech-encypherment project "Delilah" 1945 With end of war is determined to design a prototype "universal machine" or "computer". In June is offered a post with National Physical Laboratory at Teddington and begins work on ACE computer 1947 Severs relations with ACE project and returns to Cambridge 1948 Moves to Manchester University to work on prototype computer 1950 Published "Computing Machinery and Intelligence" in "Mind" 1951 Is elected FRS. Has become interested in problem of morphogenesis 1952 His article "The Chemical Basis of Morphogenesis" is published in "Philosophical Transactions of the Royal Society" 1954 Dies by his own hand in Wimslow (Cheshire) (7 June) Preface to This Volume It may seem surprising that this collection of Alan Turing's work includes a whole volume devoted to biology, a subject in which he published only one paper. Biology was, however, far more important to Turing than is generally recognized. He has been interested in the subject right from his school days, and he has read, and been much impressed by, the book that has had such a strong influence on many theoretical biologists over the years, D'Arcy Thompson's (1917) classic "On Growth and Form". He was also, like so many who work in biology, attracted by the sheer beauty of organisms. He wrote his (1952) paper not as a mathematical exercise, but because he saw the origin of biological form as one of the fundamental problems in science. And at the time of his death he was still working in biology, applying the theory he had derived to particular examples. I found reading the archive material a fascinating experience. For while at first glance Turing's work on biology appears quite different from his other writings, it actually exhibits the features typical of all his work: his ability to identify a crucial problem in a field, his comparative lack of interest in what others were doing, his selection of an appropriate mathematical approach, and the great skill and evident ease with which he handled a wide range of mathematical techniques. The biological work thus complements and completes the picture of Turing that the other volumes reveal: it shows the same style applied to a different problem. On the other hand, the nature of the material means that this volume differs from the others in two significant ways. Most of what the other three contain has appeared before; for the most part there seemed no reason to disagree with Turing's own judgment about what was worth publishing. The biological manuscripts, however, remained unpublished not by his choice but on account of his sudden death. I have therefore included a large amount of previously unpublished material. Much of it is from manuscripts prepared by N. Hoskin and B. Richards from a manuscript by Turing and from notes of his lectures, but some is by Turing himself. There is also a paper prepared by Richards from the work he did for his MSc. Thesis under Turing's supervision but also not published. I have, however, omitted a number of fragments. The manuscripts were never edited into a form ready for publication and so I have had to undertake this task myself. I have made some obvious minor corrections and filled in a few gaps where it was clear what was missing, but there are no significant alterations. My aim has been to produce nearly as possible the papers that would have appeared had Turing lived. To avoid cluttering the text with indications of trivial deviations from the manuscript, I have not marked the corrections. Readers whose primary interest is historical are therefore warned that not only does the archive contain more material than is in this volume, but not everything that is here is word for word as it appears in the manuscripts. In preparing this volume I have not felt the need to provide the sort of editorial notes that are found in the others. The mathematics is comparatively straightforward, and Turing was obviously trying to be as clear as he could for what he expected would be a mixed audience, very few of whom would know both mathematics and biology. Consequently, it is seldom necessary to explain what he is doing at any particular point. Instead, I have written introductions to the papers to put the work into context and to assist the reader with some points which are no longer as well known as they were when Turing was writing. Acknowledgements The Turing manuscripts are preserved in the library of King's College, Cambridge, and I am grateful to the College and the archivists for their cooperation. I am also grateful to the Royal Society of London, the Society for Experimental Biology, Bernard Richards and Alastair Wardlaw for agreeing to the publication of material in which they have interests. Finally, I wish to thank Robin Gandy, Mae-Wan Ho, Bernard Richards and Alastair Wardlaw for helpful information and comments, and especially Nick Furbank, who organized the whole project and contributed so much to its success. Introduction Turing's work in biology illustrated just as clearly as his other work his ability to identify a fundamental problem and to approach it in a highly original way, drawing remarkably little from what others had done. He chose to work on the problem of form at a time when the majority of biologists were primarily interested in other questions. There are very few references in these papers, and most of them are for confirmation of details rather than for ideas which he was following up. In biology, as in almost everything else he did within science -- or out of it -- Turing was not content to accept a framework set up by others. Even the fact that the mathematics in these papers is different from what he used in his other work is significant. For while it is not uncommon for a newcomer to make an important contribution to a subject, this is usually because he brings to it techniques and ideas which he has been using in his previous field but which are not known in the new one. Now much of Turing's career up to this point had been concerned with computers, from the hypothetical Turing machine to the real life Colossus, and this might have been expected to have led him to see the development of an organism from egg to adult as being programmed in the genes and to set out to study the structure of the programs. This would also have been in the spirit of the times, because the combining of Darwinian natural selection and Mendelian genetics into the synthetic theory of evolution had only been completed about ten years earlier, and it was in the very next year that Crick and Watson discovered the structure of DNA. Alternatively, Turing's experience in computing might have suggested to him something like what are now called cellular automata, models in which the fate of a cell is determined by the states of its neighbours through some simple algorithm, in a way that is very reminiscent of the Turing machine. For Turing, however, the fundamental problem of biology had always been to account for pattern and form, and the dramatic progress that was being made at that time in genetics did not alter his view. And because he believed that the solution was to be found in physics and chemistry it was to these subjects and the sort of mathematics that could be applied to them that he turned. In my view, he was right, but even someone who disagrees must be impressed by the way in which he went directly to what he saw as the most important problem and set out to attack it with the tools that he judged appropriate to the task, rather than those which were easiest to hand or which others were already using. What is more, he understood the full significance of the problem in a way that many biologists did not and still do not. We can see this in the joint manuscript with Wardlaw which is included in this volume, but it is clear just from the comment he made to Robin Gandy (Hodges 1983, p. 431) that his new ideas were "intended to defeat the argument from design". This single remark sums up one of the most crucial issues in contemporary biology. The argument from design was originally put forward as a scientific proof of the existence of God. The best known statement of it is William Paley's (1802) famous metaphor of a watchmaker. If we see a stone on some waste ground we do not wonder about it. If, on the other hand, we were to find a watch, with all its many parts combining so beautifully to achieve its purpose of keeping accurate time, we would be bound to infer that it had been designed and constructed by an intelligent being. Similarly, so the argument runs, when we look at an organism, and above all at a human being, how can we not believe that there must be an intelligent Creator? Turing was not, of course, trying to refute Paley; that has been done almost a century earlier by Charles Darwin. But the argument from design had survived, and was, and indeed remains, still a potent force in biology. For the essence of Darwin's theory is that organisms are created by natural selection out of random variations. Almost any small variation can occur; whether it persists and so features in evolution depends on whether it is selected. Consequently we explain how a certain feature has evolved by saying what advantage it gives to the organism, i.e. what purpose it serves, just as if we were explaining why the Creator has designed the organism in that way. Natural selection thus takes over the role of the Creator, and becomes "The Blind Watchmaker" (Dawkins 1986). 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.