Fundamentals of Cybernetics Fundalllentais of Cybernetics A. Ya. LERNER Translated from Russian by E. G R OS Translation edited by F. H. G E 0 R G E A PLENUM/ROSETTA EDITION Library of Congress Catalogingjn Publication Data Lerner, Aleksandr IAkovlevich. Fundamentals of cybernetics. Translation of Nachala kibernetiki. "A Plenum/Rosetta edition." Bibliography: p. Includes index. 1. Cybernetics. I. Title. Q31O.L3913 1975 001.53 75-30901 ISBN-13: 978-1-4684-1706-7 e-ISBN-13: 978-1-4684-1704-3 DOl: 10.1007/978-1-4684-1704-3 Reprinted by arrangement with Scientific Information Consultants Ltd. First paperback printing 1975 © 1972 Scientific Information Consultants Ltd. Softcover reprint of the hardcover 1st edition 1972 A Plenum/Rosetta Edition Published by Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011 United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Company, Ltd. Davis House (4th Floor), 8 Scrubs Lane, Harlesden, London, NWIO 6SE, England All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Contents Foreword page vii Preface to the English edition ix Preface to the Russian edition xi 1. Introduction 1 2. Movement 11 3. Models 23 4. Dynamic Systems 39 5. Signals 56 6. Control 75 7. Automatic Control 89 8. Optimal Control 112 9. Automata 128 10. The Computer 146 11. Adaptation 169 12. Games 183 13. Learning 195 14. Large Systems 209 15. Operational Control 224 16. The Brain 238 17. Organised Systems 255 18. Man and Machine 268 19. Outline of Future Prospects 278 Bibliography 287 Index 291 v ForeW'ord by the Editor of the English translation In editing this translation I have- tried to assure a clear English version of Professor Lerner's excellent Russian text, in rendering which the Translator deliberately used everyday English so far as practicable. The aim was to retain the fullness of the Author's meaning while preserving every technical detail. The book itself, which is called Fundamentals of Cybernetics, is a treatment which has the breadth it claims. In saying this one has to add that while it successfully covers the bulk of cybernetic material, it does so, inevitably, from a particular point of view. The point of view adopted is that of the engineer and the applied mathematician. The emphasis is very much on control theory, and although the book carefully eschews detailed rna thema tical analysis, a certain number of equations are included which amplify the descriptions given. These equations which are the mathematical descriptions of the control functions involved can generally be omitted without vitiating the reader's understanding of the text. One of the most interesting features of this book is the approach to theory of games, communication theory, behavioural and biological systems, all through the eyes of engineering cybernetics. This is a book whiCh provides a good insight into the contemporary Russian approach to cybernetics, and one that should prove of interest and value to all Western readers. F. H. GEORGE vii Preface to the English edition Is it possible to build a machine which will be cleverer than man? Do we live at the dawn of the 'era of robots'? Is the machine a danger to people who are fighting for their existence? Such and similar questions worry many people whose field of activity is far removed from cybernetics. These questions are hotly discussed, and many popular and semi-popular books and articles have been written about them. On the other hand, more topical although less sensational problems as, for instance, the use of computing techniques and data processing systems for controlling production, for commercial and banking uses, in medical diagnostics, etc., seem to attract less interest. In order to be able to examine knowledgeably vital contemporary and long-term problems which are associated with the emergence and development of cybernetics, it is only necessary to know the concrete contents of those ideas and methods which form the basis of this remarkable science. To impart this information to the reader was the task which the author of this book has set out to accomplish. The author is very glad that readers in English speaking countries will now be able to acquaint themselves with the contents of this book. If the book will give even a little help towards developing science and utilising its achievements in the interest of progress, the author will consider that his work has contributed to the efforts of other colleagues who devote their lives to this aim. A. Va. LERNER ix Preface to the Russian edition The need for a book which presents the fundamental concepts of cybernetics with a sufficiently strict scientific treatment, yet in a form which is acceptable to people who have no deep specialist knowledge of mathematics, has been obvious for a long time. However,most people have recognized the difficulty of writing such a book. How can one single subject encompass such problems as modelling cybernetics on one hand and coding signals on the other? How should the theory be presented without the use of differential equations or other mathematical methods? Is it possible to select examples that reveal sufficiently clearly internal similarity of the 'behavioural' features of the different economic, biological and engineering systems? These systems apparently have nothing in common, but must be shown to be similar to each other, as they in fact are. The problem of presenting the main ideas and methods of cybernetics to a wide circle of readers is considered sufficiently important to justify this attempt. Obviously the author has tried not to omit important or interesting sections of cybernetics. But this was not the main task. The most important consideration was to find methods of presentation to make the book suitable for teachers and engineers, doctors, students and managers. The author wished particularly to assist people with inadequate mathematical knowledge and without the necessary time to study the works of Wiener, Shannon, Andronov, Kolmogorov and others, but who, in spite of this, wanted to study the methods of solving cybernetic problems. These problems were to be studied more deeply than can be done, for instance, from reading the excellent work of Stanislaus Lem. Another secret aim of the au thor should also be mentioned: he wanted to dampen enthusiasts who see cybernetics as a new magic or a panacea. On the other hand, he wished to reduce the pessimism of sceptics who do not anticipa te xi xii: PREF ACE anything useful from cybernetics. Extreme views about the evolution of cybernetics are usually due to ignorance of the real content of this science. Of course, the contents of the book and the method of presentation of the material may become the subject of sharp criticism and may give many pleasant minutes to friends and colleagues of the author, who will find in it a sufficient cause for discussion. Thanks to the participation of the many people involved in the production, the book has been completed fairly quickly. Some of the people helped to collect examples and problems (L. Mikulich, L. Dronfort, V. Epshteyn, V. Burkov, et af.), others have read the text and made critical comments (Ya. Khurgin, A. Butkovskiy, B. Biryukov, B. Kogan), while others helped with shaping the text (E. Mezenov and I. Doronkin). The reviewer, A. Kobrinskiy, and the editor, L. Levitin, also worked very hard on the manuscript. L. Levitin and Yu. Shmukler not only improved considerably the presentation of the material, but also filled a number of gaps in the contents, especially in Chapters 18 and 19. To all these friends the author is deeply grateful and takes full responsibility for all the inadequacies of the book and errors which apparently occur, in spite of all the help he received from so many quarters. A. Ya. LERNER 1 Introduction The development of science consists not only of deepening and widening the already established scientific disciplines but also depends on the emergence of new ones. The emergence and development of new sciences is influenced primarily by two factors: isolation and generalisation. Isolation of scientific disciplines is due to the discovery of new objects of investigation and the emergence of specific scientific trends. This leads to the study of a relatively narrow class of objects which are characterised by their specific approach to both the formulation and the solution of problems. Examples of this type of specific scientific diSciplines include, for instance, chemistry of high molecular compounds and the theory of electrical machines, which are both devoted to the study of a relatively narrow field. In addition there are the more general scientific disciplines, whose characteristics are that they are created for the purpose of studying such natural phenomena as occur in a very wide class of objects. Disciplines of this type are, for instance, the theory of dimensions and the theory of similarity, the theory of dynamic systems and thermodynamics. The very general, as opposed to the very specific, sciences tend by their nature to be more theoretical and depend much more on the language, mathematical or otherwise, used to describe them. Cybernetics belongs to this same category of generalising disciplines. The founder of cybernetics, Norbert Wiener, defined it as a science of control and communication in mechanisms, organisms and society. At present cybernetics represents the general theory of control which can be applied to any system. Here, by 'system' we mean a group of elements of whatever kind, considered as an interconnected whole. Strictly speaking, the elements unified in the world around us form interconnected wholes and should be considered as systems.