OTHER TITLES IN THE ZOOLOGY DIVISION General Editor : G. A. KERKUT Vol. 1. RAVEN — An Outline of Developmental Physiology Vol. 2. RAVEN — Morphogenesis: The Analysis of Molluscan Development Vol. 3. SAVORY — Instinctive Living Vol. 4. KERKUT — Implications of Evolution Vol. 5 TARTAR — The Biology of Stentor Vol. 6. JENKINS — Animal Hormones—A Comparative Survey Vol. 7. CORLISS— The Ciliated Protozoa Vol. 8. GEORGE— The Brain as a Computer Vol. 9. ARTHUR — Ticks and Disease Vol. 10. RAVEN — Oogenesis Vol. 11. MANN — Leeches (Hirudinea) Vol. 12. SLEIGH— The Biology of Cilia and Flagella Vol. 13. PITELKA — Electron-Microscopic Structure of Protozoa Vol. 14. FINGERMAN—The Control of Chromatophores Vol. 15. LAVERACK— The Physiology of Earthworms Vol. 16. HADZI— The Evolution of the Metazoa Vol. 17. CLEMENTS— The Physiology of Mosquitoes Vol. 18. RAYMONT — Plankton and Productivity in the Oceans Vol. 19. POTTS and PARRY — Osmotic and Ionic Regulation in Animals Vol. 20. GLASGOW— The Distribution and Abundance of Tsetse Vol. 21. PANTELOURIS— The Common Liver Fluke Vol. 22. VANDEL — Biospeleology—The Biology of Cavernicolous Animals Vol. 23. MUND AY — Studies in Comparative Biochemistry Vol. 24. ROBINSON — Genetics of the Norway Rat Vol. 25. NEEDHAM— The Uniqueness of Biological Materials Vol. 26. BACCI — Sex Determination Vol. 27. JORGENSEN — Biology of Suspension Feeding Vol. 28. GABE — Neurosecretion OTHER DIVISIONS IN THE SERIES IN PURE AND APPLIED BIOLOGY BIOCHEMISTRY BOTANY MODERN TRENDS IN PHYSIOLOGICAL SCIENCES PLANT PHYSIOLOGY CYBERNETICS AND DEVELOPMENT BY MICHAEL J. APTER, Ph.D. PERGAMON PRESS OXFORD · LONDON ' EDINBURGH · NEW YORK TORONTO * PARIS * FRANKFURT Pergamon Press Ltd., Headington Hill Hall, Oxford 4 & 5 Fitzroy Square, London W.l Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1 Pergamon Press Inc., 44-01 21st Street, Long Island City, New York 11101 Pergamon of Canada, Ltd., 6 Adelaide Street East, Toronto, Ontario Pergamon Press S.A.R.L., 24 rue des Écoles, Paris 5e Pergamon Press G.m.b.H., Kaiserstrasse 75, Frankfurt-am-Main Copyright © 1966 Pergamon Press Ltd. First Edition 1966 Library of Congress Catalog Card No. 64-66353 Printed in Great Britain by Cheltenham Press Ltd., Cheltenham and London 2442/66 TO MY PARENTS PREFACE THIS book is about the ways in which growing and developing biological systems control themselves during development, and it consists of a preliminary attempt to apply some of the insights and techniques of cybernetics to the problem of understanding such development and its control. Enough background material is provided to make the book understandable both to the biologist with little knowledge of cybernetics and the cybernetician with no great knowledge of developmental biology. The first chapter is devoted to a discussion of the nature of cybernetics and an attempt is made to justify its methods. In par- ticular it is argued that the cybernetician is doing more than merely drawing analogies between animals and machines, but is concerned with the development of conceptual systems at a level of generality which subsumes both animals and machines but which can be related to them by means of models. The field of biological development is looked at in the second chapter, and it is noted that cybernetics might be of particular use here in the future since developing systems are complex ones which are difficult to understand without reference to principles of organ- isation. By development is meant the process by which a single cell transforms itself into a large and complicated animal of a pre- determined form. Some basic axioms of development are postulated and several fundamental questions are asked. In the third chapter a critical survey is made of previous relevant work in that part of cybernetics particularly related to automata theory, and it has been remarked that there is not a very great deal of direct relevance to developmental biology in existence at present. In the next chapter, attempts which have been made to apply information theory to development are critically assessed, and the conclusion is reached that any such attempt using information theory alone is not likely to constitute a very helpful approach to the problem of understanding development. In the following chapters some models of development are pre- sented. ix PREFACE Chapter 5 contains some computer programmes which con- tinually replicate themselves and in the course of this also control the resulting development. A general growth subroutine is also presented which will allow any programme which specifies itself appropriately to be self-reproducing, so that a general way is introduced by means of which programmes of any complexity can be used to simulate development. Chapter 6 examines growing automata nets as models of develop- ment, and the Turing conceptualisation of an automaton is used to describe such automata. It is shown that it is possible for predeter- mined spatial patterns to emerge on the basis of no more than the instructions to the original automaton, and a number of such patterns are demonstrated to be algorithmic. An efficient method by means of which a system can control the relative sizes of its parts during development and afterwards during regeneration is demonstrated in model form in Chapter 7. This is shown to be consistent with some recent work in genetics. Some general conclusions are drawn and some possibilities for further research are noted in the last chapter which also includes a discussion of self-reference in development and a discussion of the problem of increasing complexity during development. I would like to express my sincere gratitude to Dr. F. H. George of the Department of Psychology, the University of Bristol, both for his constant personal encouragement of the work described here and for his practical help and advice. As far as the biological side of this research is concerned, I owe a great deal to experience gained during my work with Dr. Lewis Wolpert, Reader in the Department of Zoology, University of London King's College, and to Dr. G. Webster of the same depart- ment; on the computer side I am indebted to Mr. Ο. B. Chedzoy, Head of the computer section of the Department of Mathematics, the Bristol College of Advanced Technology, for his time and advice. My thanks are further due to Professor J. L. Kennedy of the Department of Psychology, Princeton University, for initiating my interest in the study of developing systems, and to Dr. W. Grey Walter, Head of the Physiology Department of the Burden Neuro- logical Institute, Bristol, and Professor George A. Miller of the Department of Psychology at Harvard University, for their en- couragement. I would also like to thank Mr. Peter Alexander of the χ PREFACE Department of Philosophy at the University of Bristol, for his critical reading of the first chapter. Chapter 4 is based on a paper written in collaboration with Dr. Lewis Wolpert, and any deficiencies in this version are entirely my own, as are, of course, any other shortcomings in the body of this work as a whole. I would like to thank Dr. Penrose for allowing me to reproduce the drawing on page 63. Finally, I am grateful to the Department of Scientific and In- dustrial Research and to International Computers and Tabulators Ltd. for grants which enabled me to carry out some of the research described in this book. CHAPTER 1 THE CYBERNETIC APPROACH Introduction Since 1948, when Norbert Wiener's classic book* 1* was published, cybernetics has rapidly become established as a subject in its own rights, at the very least in the pragmatic sense that it now incurs an ever increasing round of conferences, such as the regular Namur conference,*2) and a number of journals ;< 3_6) also several university departments devoted wholly or partly to cybernetics now exist in this country. Nevertheless, it has to be admitted that considerable currents of antipathy towards it still exist, especially among many of the more empirical scientists, and some of these would still go as far as to deny both its validity and its viability as an independent discipline. This is inconvenient to anyone working within the field because it means that before reporting on the results of his work the cybernetician often feels compelled at least to attempt to justify his methods. In the first part of this chapter an explanation of the nature of cybernetics will be given, and then in terms of this, some of the arguments opposed to it will be examined and it will be asked whether cybernetics really is a meaningful and useful subject or not. But before this, some of the background of the subject should be mentioned. Fortunately, there is no longer any need to go into detail here since this ground has at last been well covered. Of course, the early history of the subject was well summarised by Wiener himself(7) from some embryonic ideas held by him and Arturo Rosenblueth early in the Second World War, through work carried out in collaboration with Julian Bigelow on a computer to control anti-aircraft gun tracking, resulting in their historic paper on "Behaviour, purpose, and teleology" <8> and the work described in the early Josiah Macy Jr. Foundation meetings, < 9> up to the publica- tion of his book in 1948. But the progress of cybernetics since then has now been described and explained in numerous books of varying 1 2 CYBERNETICS AND DEVELOPMENT degrees of popularity, and some of the better of these are listed in the Appendix. <1 °-15) A collection of some of the most important papers during this period is presented by Automata Studies^ and a bibliography complete up to 1959 has been compiled by D. J. Stewart.«17 > The Nature of Cybernetics It is difficult to say what cybernetics is, and the difficulty exists for a number of different reasons, among which we may list the follow- ing: 1. Cybernetics, as it has developed, has no one central part, but consists rather of a number of strands which overlap each other in different ways. These include computer and communication engineer- ing, the mathematics of decision procedures, logic, biology, and psychology, and secondarily a list of numerous relevant areas including semantics, linguistics, psychology, psychiatry, medicine, education, industry, management, economics, physiology, and so on. While it is this very broadness which lends to cybernetics its peculiar excitement, it also contributes an aura of differing emphases which at times seem irreconcilable. 2. There appear to be genuine differences of opinion among cyberneticians themselves as to what cybernetics is and what it should be. As Gordon Pask points out in his exposition of cyber- netics : At one extreme, there is the original definition, "the science of control and communication in the animal and the machine," advanced by Norbert Wiener. At the other extreme is Louis Couffignars proposal, put forward as an expansion in 1956, "La Cybernétique est l'art d'assurer l'efficacité de l'action." The gap between science and art is filled by a continuum of interpretations. Thus, Stafford Beer looks upon cybernetics as the science of proper control within any assembly that is treated as an organic whole ... Ashby, on the other hand, gives emphasis to abstracting a controllable system from the flux of the real world.^18) He goes on to claim that both Ashby's and Beer's definitions are included by Weiner's global dictum, but he does not explain exactly how. 3. Little guidance has, as yet, come from philosophers of science. This is no doubt due to the newness of the subject, but when one considers both the apparently unusual methodology of cybernetics THE CYBERNETIC APPROACH 3 and its potential importance in the future of science, the deficiency remains surprising. How, therefore, can one begin to describe cybernetics? Until now, facile comparisons between cybernetics and statistics have often been considered adequate and, indeed, they have usefully emphasised the wide applicability of cybernetics. But if cybernetics is not simply a technique like statistics, neither is it simply a subject-matter in the sense that geology is primarily a subject-matter; in fact it would seem to be a unique combination of both subject-matter and tech- nique. In the writer's opinion it is possible to some extent both to disentangle the overlapping strands and to reconcile to some degree the conflicting opinions by bringing them together into a coherent and meaningful structure, and it is this which is attempted in what follows. It should be emphasised, of course, that this is no more than a preliminary attempt to provide a possible structure or framework. Although physics and chemistry differ from biology in their subject-matter, it can also be argued, as, for example, H. J. Jordan has done,<19> that there is another more subtle but equally important and far-reaching difference between them: a methodological dif- ference. According to this argument, while both attempt to arrive at general laws, the generality of the laws of physics and chemistry is wide enough to embrace both the actual and the possible, whereas the laws of biology are strongly bounded by the actual. This gener- ality in physics and chemistry is achieved in two ways : firstly by the experimental isolation of factors operating on each other, and secondly by means of useful simplifying theoretical assumptions. For this reason it is not important to the physicist or chemist that, for example, perfect gases do not exist, that a falling object will rarely fall in a vacuum, or that two substances may never meet in a pure form outside the laboratory, although they can use their knowledge of the possible to explain an actual specific event, if required to do so. The biologist, on the other hand, is concerned with the way that things actually do happen in living creatures. He is concerned with real organisms in a concrete spatio-temporal environment, and because of this he is largely restricted to descrip- tion and the generality inherent in classification. There are important exceptions to this; at one end of the scale we have the Theory of Evolution, and at the other end we have Genetic Theory. But in between these two regions, especially in the area of growth and development, which is the particular concern of this work, there is