Introduction to ashby cybernetics for economics. Ashby W.R

Preface to the Russian edition
Author's Preface
Chapter 1.	New
	Features of cybernetics
	Applications of cybernetics
	A complex system
Part I. Mechanism
Chapter 2	Changes
	Transformations
	repeated changes
Chapter 3	Deterministic machines
	Vectors
Chapter 4	Cars with entrance
	Connecting systems
	Feedback
	Independence within the whole
	Very large system
Chapter 5	Sustainability
	perturbations
	Balance in part and in whole
Chapter 6	Black box
	Isomorphic machines
	Homomorphic machines
	Very large box
	Incompletely observable "box"
Part II. Diversity
Chapter 7	The amount of variety
	Diversity
	Diversity restrictions
	Importance of Diversity Restrictions
	Variety in cars
Chapter 8	Diversity Transfer
	Encoded Message Reversal
	Transfer from system to system
Chapter 9	Continuous transmission
	Markov chain
	Entropy
	Noises
Part III. Regulation and management
Chapter 10	Regulation in biological systems
	Survival
	Table of contents
Chapter 11	Necessary Variety
	Law of Necessary Variety
	Control
	Some variation on the theme
Chapter 12	Error-driven regulator
	Markov machine
	Markov regulation
	Deterministic regulation
	Amplifier
	Games and strategies
Chapter 13	Regulation of a very large system
	Recurring perturbations
	Regulator design
	Choice quantity
	Choice and machines
Chapter 14	Increased regulation
	What is an amplifier?
	Regulation and choice
	Strengthening in the brain
	Strengthening mental abilities
Annex I
Appendix II
Literature
Literature added during translation
Answers to the exercises
Alphabetical index

Analogies between:

a) conscious expedient human activity;

b) the work of man-made machines;

c) the most diverse activities of living organisms, which are perceived as expedient, despite the absence of consciousness that controls them.

Human thought has been searching for centuries for an explanation of these analogies, both on the paths of positive knowledge and on the paths of religious and philosophical speculation. A solid foundation for their scientific study and rational philosophical understanding was created when:

1) Darwin proposed a consistently developed theory of the natural origin of the expedient structure of living organisms and, in particular, the origin of a complex apparatus that allows living organisms to transmit their expedient device by inheritance to their descendants;

2) Pavlov established the possibility of an objective study of the behavior of animals and humans and the brain processes regulating this behavior without any subjective hypotheses expressed in psychological terms.

Over the past decades, the rapid development of communication technology (radio, television), automation and computer technology has led to a significant expansion of the factual material itself for comparing the operation of machines with the activity of living organisms and with the conscious activity of man. At the same time, the use of analogies between the work of the machines they create and the work of human consciousness began to penetrate into the thinking of engineers more and more. For example, communication means perceive "information" and transmit it accurately or with "errors"; automata are tasked with following one or another "strategy" or "tactic" and even "learning" from the enemy the tactics he has mastered in order to work out expedient response tactics; computers have "memory devices" ("memory"); programming machines themselves "develop the program" of complex calculations, using more or less perfect "logic", and so on. It is difficult to see any philosophical intentionality in this practice of engineers: it is just that these analogies are too natural and obviously help engineers think and invent.

It is quite clear that the "purposeful" operation of machines has no independence and is only a technical appendage to the purposeful activity of man. However, the rich experience accumulated in the design of automata and computers is now of great interest as a reserve of models that help to imagine possible natural control and regulation mechanisms. The processes of formation of conditioned reflexes are successfully studied with the help of machines simulating these processes. Modern works that analyze the activity of the brain are essentially based on analogies with complex electronic machines. In modern works on the theory of heredity, ideas about the methods of "coding" information developed in the technical theory of communication find considerable application.

To understand the causes of the emergence of a new science - cybernetics - another consequence of the latest development of the above sections of technology is more essential. Their development not only provides new material for the philosophical analysis of the concepts of "control", "regulation", "expediency" as applied to machines and living organisms, but, in addition, led to the emergence of some auxiliary special disciplines of a non-philosophical nature.

These disciplines arose directly from practical needs under the names "information theory", "algorithm theory", "automata theory". Concrete results obtained within their limits are now quite numerous. For example, they allow: 1) to estimate the "amount of information" that can be reliably transmitted by a given transmission device or stored by a given storage device; 2) estimate the smallest number of simple links with a given action scheme, which is necessary so that a control device that performs certain specified functions can be composed of them. In both examples, the results are expressed by certain mathematical formulas, but these results are applicable in exactly the same way both in the design of machines and in the analysis of the activity of living organisms.

The merit of N. Wiener is the establishment of the fact that the totality of these disciplines (Wiener took a significant part in the creation of some of them) naturally combines into a new science with a fairly specific subject of study of its own. It is now too late to argue about the extent of Wiener's luck when, in his famous book in 1948, he chose the name "cybernetics" for the new science. This name is quite established and is perceived as a new term, little connected with its Greek etymology. Cybernetics is the study of systems of any nature capable of receiving, storing and processing information and using it for control and regulation. At the same time, cybernetics makes extensive use of the mathematical method and strives to obtain specific special results that make it possible to both analyze such systems (restore their structure based on experience in handling them) and synthesize them (calculate schemes of systems capable of performing specified actions). In its concrete character, cybernetics is in no way reduced to a philosophical discussion of the nature of "expediency" in machines and living organisms, without also replacing the general philosophical analysis of the range of phenomena it studies.

The position of the author of the book - W.R. Ashby - as a biologist who has thoroughly studied the abstract, mathematical side of the matter, is very advantageous for popularizing the general ideas of cybernetics among people for whom the mathematical apparatus presents great difficulties, and an overly detailed entry into the issues of technical cybernetics It would also be difficult. At the same time, W.R. Ashby is quite cautious in his conclusions and is far from the often encountered advertising style of glorifying cybernetics. However, the reader should be critical of the author's statements of a methodological and philosophical nature. It should also be borne in mind that some of the author's conclusions are debatable.

A.Kolmogorov

Many workers in the biological sciences - physiologists, psychologists, sociologists - are interested in cybernetics and would like to apply its methods and apparatus in their own specialty. However, many of them are hampered by the conviction that this must be preceded by a long study of electronics and the higher branches of pure mathematics; they had the impression that cybernetics was inseparable from these subjects.

The author, however, is convinced that this impression is false. The basic ideas of cybernetics are essentially simple and require no reference to electronics. More complex applications may require more sophisticated apparatus, but much can be done, especially in the biological sciences, with a very simple apparatus; it is only necessary to apply it with a clear and deep understanding of the principles involved. If one substantiates the subject with generally accepted, easily accessible propositions and then expounds it gradually, step by step, then, in the opinion of the author, there is no reason to expect that even a worker with elementary mathematical knowledge will not be able to achieve a complete understanding of the basic principles of the subject. And such an understanding will allow him to decide exactly what apparatus he still needs to master for further work and - which is especially important - which apparatus he can safely ignore as having nothing to do with his tasks.

This book should serve as such an introduction. She starts with general, easily accessible concepts and shows step by step how these concepts can be refined and developed until they lead to such questions in cybernetics as feedback, stability, regulation, ultra-stability, information, coding, noise, etc. .d. Nowhere in the book is knowledge of mathematics beyond elementary algebra required. In particular, the proofs are nowhere based on the infinitesimal calculus (the few references to it can be safely neglected; they are given only to show how the infinitesimal calculus can be applied to the issues under consideration). Illustrations and examples are taken mainly from the biological, less often from the physical sciences. There is little overlap with The Brain, so that the two books are almost independent of each other. However, they are closely related to each other, and it is best to consider them as complementary: one helps to understand the other.

The book is divided into three parts.

Part I discusses the main features of the mechanisms; it discusses issues such as the representation of mechanisms through transformations, the concept of "stability", the concept of "feedback", various forms of independence that can exist within mechanisms, and the connection of mechanisms with each other. This part sets out the principles to be followed when a system is so large and complex (such as the brain or society) that it can only be considered statistically. It also discusses the case of a system that is not fully accessible to direct observation, the so-called "black box theory".

In Part II, the methods developed in Part I are applied to the study of the concept of "information" and to the study of the coding of information as it passes through mechanisms. In this part, the application of these methods to various problems of biology is considered and an attempt is made to show at least part of the entire abundance of their possible applications. This leads to Shannon's theory, so that, after reading this part, the reader can proceed without difficulty to a study of Shannon's own work.

In Part III, the concepts of mechanism and information are applied to biological systems of regulation and control, both innate, studied by physiology, and acquired, studied by psychology. It shows how hierarchies of such regulation and control systems can be built and how, through this, increased regulation becomes possible. It gives a new and generally simpler exposition of the principle of ultrastability. This part lays the foundations for a general theory of complex control systems, developing further the ideas of the book "The Design of the Brain". Thus it provides, on the one hand, an explanation for the extraordinary power of regulation inherent in the brain, and, on the other hand, the principles on the basis of which the designer can build machines with such a power.

Although the book is intended as an easy introduction, it is not just a chatter about cybernetics - it is written for those who want to enter this field by self-study, for those who want to actually, practically master the subject. Therefore, it contains many easy exercises, carefully chosen for difficulty, with directions and detailed answers, so that the reader can test his understanding of what he has read and exercise his new intellectual muscles as he progresses. A few exercises that require a special apparatus are marked with an asterisk: "* Exercise." Skipping them will not hinder the reader's progress.

For ease of reference, the material is divided into paragraphs; all links are given paragraph numbers, and since these numbers are on the top of each page, finding a paragraph is as easy and simple as finding a page. Paragraphs are designated as follows: "§9/14", which indicates §14 ch.9. Figures, tables and exercises are numbered within each paragraph; so, fig.9/14/2 is the second drawing in §9/14. Simple references, such as "Ex. 4", indicate a link to material within this paragraph. Where a word is formally defined, it is printed in bold.

I would like to express my gratitude to Michael B. Sporn for checking all the answers to the exercises. I would also like to take this opportunity to express my deep gratitude to the administrators of the Barnwood House Hospital and to Dr. J.W.T.H. Fleming for the extensive support that made this research possible. Although the book touches on many issues, they serve only as a means; the purpose of the whole book was to find out what principles should be followed in an attempt to restore the normal functioning of a diseased organism, amazingly complex when it comes to a person. I believe that a new understanding can lead to new and effective methods, for there is a great need for them.

W.Ross Ashby

"Barnwood House" door Gloucester

A MACHINE IS SMARTER THAN ITS CREATOR

Norbert Wiener

This study by Wiener is a response to a book by the English scientist W.R. Ashby “Design of the Brain”, published in 1952 and which constituted an important stage in the formation of cybernetics (Ashby W.R. Design for a Braian. - New York: John Wiley & Sons, 1952; Russian translation from the 2nd English ed.: Ashby W .R. Design of the brain. - M .: IL, 1962). Subsequently, Ashby wrote “Introduction to Cybernetics” (Ashby W.R. An Introduction to Cybernetics. - London: Chapman & Hall, 1956; Russian translation: Ashby W.R. Introduction to Cybernetics. - M .: IL, 1958)

The last ten years have witnessed the emergence of a new view of communication technology and of automata as communication devices. The work done here can already be divided into two stages. The first of these was the one that featured my own work and on which Claude Shannon, one of the most original researchers in this field, directed his efforts to clarifying the very concept of communication, to the theory and practice of measuring communication, to the analysis of management as a phenomenon in essence one nature with connection, and in general on the grammar of a new science, which I called cybernetics

Dr. Ashby's work represents a branch of cybernetics that dates back to the dawn of science and is devoted not so much to elementary questions of definition and vocabulary as to those questions of the philosophy of the subject that affect the specific properties of cybernetic systems and which, although related to definitions, are questions of facts and logic. and go far beyond definitions.

Among the questions explored by Dr. Ashby are, in particular, the following: What is learning? must the ability to learn be embedded in the machine by means of some very specific organization, or can the learning phenomena be discovered by a machine with a largely random organization? Can a machine be smarter than its creator?

All these questions can be put in two different plans. On a purely biological plane, such reasoning has occupied biologists ever since biology emerged from the stage of purely theological foundations; they touch on the very essence of the problems of evolution, especially Darwinian evolution through natural selection. On a mechanical plane, these problems arise over the much more limited machines that man creates and the conditions that he must obey, consciously assuming the functions of the demiurge.

Machines made by man and machines made by nature

While fully recognizing the greater efficiency and adaptability of the structure and action of natural machines in comparison with man-made machines, it must be noted at the same time that these latter have introduced new weapons into the arsenal of science, both for natural experiment and for mental experiment. Their role is similar to the role of the fruit fly - Drosophila. The latter seems to have been deliberately created in order to transform genetics from a science of centuries of observation, which it would inevitably be if limited to observations of humans and large domestic animals, into a science compatible with the spatial and temporal limitations of a small biological laboratory. In the same way, man-made machines promise to reduce our study of the biological processes of learning and adaptation, individual development and evolution to such a scale that we can deal with these shaky concepts with confidence and accuracy comparable to what we have in physical and technical sciences. laboratories. Among scientists who not only talk about these things, but actually do something, Dr. Ashby occupies one of the leading places.

The main idea of ​​natural selection, applied by Darenne to the theory of evolution, is that the terrestrial flora and fauna are composed of forms that have come down to us simply as residual forms, and not by virtue of any direct process of striving for perfection. This is not a piece of marble that turns into a perfect sculpture under the hands of an artist-creator, but rather one of those wind-sculpted sandstone pillars that adorn the canyons of Utah. Random processes of erosion combined to form these stone pillars, which look like castles and monuments, and even figures of people and animals. But their beauty and imagery are not the same as the beauty and imagery of a painting, but such as those of Rorschach spots - in other words, not for the eye of the artist, but for the eye of the viewer. Likewise, the seeming theodicy hinted at by the splendor and intelligence of the infinitely complex realm of nature is, according to Darwinism, only what is left after a random process of growth and change, when softer and less durable manifestations collapsed under the influence of the sand of time and under the burden of own weakness.

Sustainability is a characteristic of the world

Nature has yet another way of demonstrating residual forms, akin to natural selection, but with a different emphasis. Since the discoveries of the Curies, we have known that the atoms of certain elements undergo progressive metamorphosis. If we take an atom of radium, then sooner or later a metamorphosis will definitely occur with it, during which it begins to emit radium emanations. We cannot say when this transformation will take place, for, apparently, it occurs by chance. But we can say that after some time, called the half-life of radium, the probability that the transformation has taken place will be one-half.

But radioactive elements undergo not a single transformation, but a whole series of successive transformations into other elements, and each of them has its own half-life. Elements with a long half-life can be said to be stable, while elements with a short half-life can be said to be unstable. If we now trace any element in its transformations, then, as a rule, it will exist for a long time in the form of elements with a long half-life and for a short time in the form of elements with a short half-life.

As a result, by observing the process for a very long time, we will find that elements with a long half-life are more common than elements with a short half-life. This means that a study based on the frequency of observed elements and not tracing the fate of a single atom easily misses highly radioactive materials with a short half-life. From this we see that stability is characteristic of most of the world. Thus, the absence of unstable forms, which we find in biological series due to their inability to survive in the struggle for existence, is observed in the evolution of radioactive elements, because unstable forms pass so quickly that we do not notice them to the same extent as we notice forms more sustainable.

One consequence of this statistical predominance of stability in the universe is that we know very little about what happens during critical periods of instability. Take, for example, the well-known effect discovered by Arthur Compton: when a photon collides with an electron, both bounce off in directions that can only be determined statistically. There is at least a suspicion that, in fact, the electron and photon, initially uncombined, enter into conjunction here for too short a period of time for us to determine the actual course of events, and that they then leave this conjunction through increasingly weaker conjunctions, each of which proceeds in its own way. Some physicists, such as Wohm, have suggested that the actual course of events is not so indeterminate, but that during that tiny interval of time when the particles are together, a very complex sequence of events takes place that determines their future behavior. If this is true, then a significant part of the most important physical phenomena is not known to us, because we pass through them too quickly and do not know how to register them.

Of these two kinds of natural selection: through the destruction of the unusable, and through too hasty passage through the unstable, the latter is the only possible one in the case of conservation phenomena that prevent the simple elimination of the unstable. Ashby considers very complex machines in which elements are connected to each other in a more or less random way, so that we know something about the statistics of connections and very little about the details of them. These machines, generally speaking, are destroyed very quickly if safety elements are not introduced into them, like amplitude limiters in electrical circuits. The action of such limiters gives the system some conservatism. Therefore, Ashby machines tend to spend most of their existence in relatively stable states, and their unstable states, although they exist, are so limited in time that they show up very little in the statistical study of the system.

It should be remembered that in the phenomena of life and behavior we are interested in relatively stable, and not absolutely stable states. Absolute stability is achievable only at very high values ​​of entropy and is essentially equivalent to thermal death. If the system is protected from thermal death by the conditions to which it is subject, then it will spend most of its existence in states that are not states of complete equilibrium, but similar to equilibrium. In other words, the entropy here is not absolute, but a relative maximum or, at least, changes very slowly in the vicinity of these states. It is precisely such quasi-equilibrium - not truly equilibrium - states that are associated with life and thinking and with all other organic processes.

Machines with eyes and ears?

It seems to me that it would be quite in the spirit of Dr. Ashby to say that these quasi-equilibrium states, as a rule, are states in which there is a relatively weak exchange of energy between the system and the environment, but a relatively large information connection between them. The systems considered by Dr. Ashby have eyes and ears and in this way receive information to adapt to the external environment. They approach automata in their internal energy balance, but are very far from them in their external entropy or informational balance. Therefore, the equilibrium they strive for is one in which they are well adapted to changes in the external environment and to a certain extent insensitive to such changes. They are in a state of partial homeostasis.

Dr. Ashby constructs his homeostat as an instrument having just such a connection with the external environment and showing some randomness in the internal structure. Such a machine can learn to a certain extent; to adapt the forms of their behavior to a stable balance with the environment. However, the real homeostats developed so far by Dr. Ashby, although they are able to absorb information from the environment, contain in their internal structure an amount of information and decisions that obviously exceeds that which passes through their, so to speak, sense organs. In short, these machines can learn, but they are by no means smarter than their creators, or about as smart. Nevertheless, Dr. Ashby believes that it is possible to actually create machines that are smarter than their creators; and in this I completely agree with him. The amount of information that the device can perceive through its sense organs cannot be a priori limited to those values ​​at which no more decisions are required than have already been incorporated into the structure of the device. Usually, the ability of a system to absorb information grows rather slowly at first compared to the amount of information embedded in it. And only after the embedded information goes beyond a certain point, the ability of the machine to absorb further information will begin to catch up with the internal information of its structure. But with a certain degree of complexity, the acquired information can not only equal that which was originally put into the machine, but far exceed it, at this stage of complexity the machine acquires some of the essential characteristics of a living being.

Complexity needed

The situation under consideration allows for a curious comparison with an atomic bomb, with an atomic reactor, or with a fire in the hearth. If you try to build an atomic reactor or an atomic bomb too small, or light a big bast log with a single match, you will find that any atomic or chemical reaction you start will die out as soon as its causative agent is removed, and will never grow or stay at the same level. . Only when the igniter reaches a certain size, or a certain number of molecules are collected in an atomic reactor, or the mass of the uranium isotope reaches a certain explosive size, will the situation change, and we will see not only fleeting and incomplete processes. In the same way, the really essential and active phenomena of life and learning begin only after the organism has reached a certain critical level of complexity; and although this complexity is probably achievable by purely mechanical, not too difficult means, nevertheless, the utmost effort will be required.

From this analysis of only some of the ideas in Dr. Ashby's book, we can conclude that it opens up a broad view of new frontiers of thought. Dr. Eshban, though essentially a strong mathematical imagination, is not in the full sense of the word a professional mathematician, and it is up to professional mathematicians to put into practice many of the ideas he has sketched out. He does not consider himself a professional mathematician, but he undoubtedly possesses principles and talent, and his book should be read as one of the first fruits in a field that deserves diligent cultivation.

Wiener N. A Machine Wiser Than Its Maker.
// Electronics. - 1953. - Vol. 26. - No. 6. - R. 368-374.

This book, written by the famous English specialist in the field of cybernetics William Ross Ashby, outlines the basic concepts of cybernetics - "the science of control and communication in animals and machines." The author discusses the possibility of wide application of the ideas of cybernetics in various fields of human activity. The book begins with an explanation of general, easily accessible concepts, and step by step the author shows how these concepts can be refined and developed until they lead to such questions of cybernetics as feedback, stability, regulation, coding, etc. The presentation is accompanied by a large number of specially selected examples and exercises, without requiring the reader to know more than elementary algebra.

The book is intended both for specialists in the field of applied mathematics, informatics and cybernetics, and for representatives of other sciences who are interested in cybernetics and wish to apply its methods and apparatus in their specialty. Read online or download the book "Introduction to Cybernetics" in fb2, authored by William Ross Ashby. The book was published in 2015, belongs to the genre "Computer Literature" and is published by Lenand, Editorial URSS.

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