Prigogine I., Stengers I. Order out of chaos. M.: Progress, 1986.

Haken G. Information and self-organization. M.: Mir. 1991.

Capra F. Web of Life. New scientific understanding of living systems. K.,: Sofia, M.: Publishing House Gelios, 2002.

Wiener N. Cybernetics, or Control and Communication in Animals and Machines. M. 1983.

1. Ashby W.R. Introduction to cybernetics. M., 2006.

Questions for self-control

What is management?

What dissipative structures do you know?

What is Brusselator?

What is the relationship between management and self-organization in social systems?

Lecture No. 6. The structure of the noosphere and the interaction of nature and society

The term “noosphere” is etymologically related to the Greek word “noos” - mind. The concept itself was first used by the French scientist E. Leroy, noting that he came to this idea together with another researcher P. Teilhard de Chardin. At the same time, they were based on the ideas of V.I. Vernadsky, voiced in 1922 - 1923 during lectures at the Sorbonne.

Later, Pierre Teilhard de Chardin developed a teleological concept of the noosphere, which was based on theosophical ideas (the Omega point as the final point of evolution, at which the union of man with God occurs). V.I. Vernadsky developed the idea of ​​the noosphere in a completely different way. This difference in the approach to the interpretation of the concept of the noosphere is called the Vernadsky-Chardin dilemma, as a contrast between objective and subjective factors in the formation of the noosphere 32 .

The doctrine of the noosphere was formed at the end of his life by V.I. Vernadsky. He first used this term in a letter to B.L. Lichkov on September 7, 1936 in Carlsbad, and said it publicly in 1937 in a report “On the importance of radiogeology for modern geology,” which he read at the 17th session of the International Geological Congress. In 1945, after Vernadsky’s death, his article “Biosphere and Noosphere” was published in the American Scientist magazine, which became widely known in scientific circles. But Vernadsky’s main ideas about the noosphere were outlined in two works, unfinished during his lifetime, on which he worked during the war years. V.I. Vernadsky’s ideas about the noosphere were most fully developed in the work “Scientific Thought as a Planetary Phenomenon”. It was first published in 1977, then, with amendments, was included in the book “Philosophical Thoughts of a Naturalist” (1988), and the 3rd edition as a separate book was published in 1991 33 .

V.I. Vernadsky identified the geological role of life, living matter in planetary processes, and in this living matter he identified man as a geological force that changes the natural biogeochemical processes of the planet. In his opinion, the noosphere is a material formation, as a result of the natural historical development of the biosphere and as a result of the systematic work of mankind. The formation of the noosphere is a natural phenomenon, sharply materially manifested in the human environment

The prerequisites for the formation of the noosphere are associated with the natural process of cephalization. This is a certain direction of evolution, expressed as a complication of the central nervous system and an increase in the volume of the brain.

The geological effect of humanity on the biosphere manifested itself a considerable time after its appearance in the biosphere, first with the mastery of fire, then with the development of agriculture.

The noosphere is not just “humanized nature”, it is a state of the natural environment consciously formed by man 34 .

Vernadsky’s works name a number of specific conditions necessary for the formation and existence of the noosphere:

human settlement of the entire planet,

a dramatic transformation in the means of communication and exchange between different countries,

strengthening ties, including political ones, between all states of the Earth,

the predominance of the geological role of man over other geological processes occurring in the biosphere,

expanding the boundaries of the biosphere and going into space,

discovery of new energy sources,

equality of people of all races and religions,

increasing the role of the broad masses in resolving issues of foreign and domestic policy,

freedom of scientific thought and scientific research from the pressure of political, religious and other theories; creating conditions favorable for free scientific thought,

improving people's well-being; creating a real opportunity to prevent malnutrition and hunger, poverty and reduce the impact of diseases,

intelligent transformation of the primary nature of the Earth in such a way that it is capable of satisfying the material, aesthetic and spiritual needs of a growing population,

exclusion of wars from the life of society 35 .

Vernadsky believed that the formation of the noosphere is associated with the period when people become able to organize their activities consciously. The current situation in this sense is assessed pessimistically - pollution of the natural environment, irrational use of resources, wars - one cannot talk about the advent of the era of the noosphere, but one can talk about formation, about the transition to the period of noogenesis (evolution controlled by human consciousness) 36 .

N.N. Moiseev writes about the process of transition of the biosphere into a new, noospheric state, as a “painful and slow process of developing new principles for coordinating one’s actions and new behavior of people,” “new morality” 37.

The idea of ​​the noosphere underlies the noospheric strategy for the development of civilization, which is different from the extensive strategy of past centuries. Rationality in extraction, use, processing, disposal is the key to this strategy 38 .

Sometimes components of the noosphere are distinguished - the anthroposphere, the technosphere, living and inanimate nature modified by man, and the sociosphere, while the anthroposphere is understood as a set of people as organisms, the sociosphere as a set of social factors and institutions, and the technosphere as a part of the biosphere, radically transformed by man. in technical buildings and structures 39.

Literature

Vernadsky V.I. Biosphere and noosphere. M., 2002.

Moiseev N. Man and the noosphere. M., 1990.

Ursul A.D. The path to the noosphere: The concept of survival and sustainable development of civilization. M., 1993.

Questions for self-control:

What is the history of the formation of the concept of “noosphere”?

What does cephalization mean?

What are the conditions for the formation and existence of the noosphere?

What meaning did N.N. put into the concept of the noosphere? Moiseev?

Lecture No. 7. Anthropogenic-natural factors of instability in the biosphere.

Global and regional climate changes.

Meteorological data indicate an increase in the average temperature of the Earth's surface (for example, in Russia, the average annual surface air temperature has increased by 1 ºC over the past 100 years). However, in a number of regions (southern USA, Brazilian Amazon) some cooling is occurring. The frequency and intensity of extreme weather events (storms, floods, droughts, winter thaws, etc.) are increasing.

Many scientists correlate global climate change with an increase in the concentration of so-called greenhouse gases (carbon dioxide, methane, nitrous oxide, etc.) in the atmosphere.

The Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) concluded that there is a 90% probability of ongoing climate change being anthropogenic. A number of researchers note that the Earth has experienced global climate change before, experiencing cooling and warming, but the rate of change in average temperature in our time is really high. There is a point of view that denies anthropogenic influence on climate 40

Framework Convention and Kyoto Protocol.

At the World Summit on Sustainable Development in Rio de Janeiro, the United Nations Framework Convention on Climate Change (UNFCCC) was signed, which entered into force on March 21, 1994.

This is an important political document for the entire international community, focusing on the problem of global climate change. The UNFCCC has a framework character. It provides the rationale for the need for an international agreement regarding global climate change. The Convention uses the principle of “common but differentiated responsibilities”, which is reflected in softer requirements for countries with economies in transition.

All parties to the UNFCCC accepted certain obligations to inventory anthropogenic emissions from sources and removals by sinks of all greenhouse gases, develop national programs to limit climate change, scientific cooperation and information exchange and education of the general public on these issues.

In December 1997, the Kyoto Protocol was adopted. The Protocol is an international political and legal document adopted as part of the implementation of the UNFCCC. It came into force on February 19, 2005. Only 2 countries refused to participate in the Protocol until 2013 - the USA and Australia.

The Protocol established a list of greenhouse gases, the total emissions of which will be taken into account when assessing the achievement of target indicators. These are carbon dioxide (CO 2), methane (CH 4) and nitrous oxide (N 2 O), as well as three groups of long-lived industrial gases - hydrofluorocarbons (HFCs), perfluorocarbons (PFCs) and sulfur hexafluoride (SF 6). Industrialized countries must reduce their total emissions of these gases by at least 5.2% compared to 1990 levels, and do this by 2008-2012.

The EU countries have the highest commitments to reduce emissions (8%), Australia, Iceland and Norway can increase their emissions by 8%, 10% and 1% respectively. Russia and Ukraine can maintain emissions at 1990 levels. There are no emission reduction obligations for developing countries.

The significance of the Kyoto Protocol lies in the translation of the Convention's framework agreement into the language of clear, practical mechanisms. It is important that the obligations are legally binding for the participating countries.

Another significant point is the possibility of a flexible approach, which is provided by the system of trading quotas for greenhouse gas emissions. This approach will allow countries where the costs of emission reduction measures are high to reduce the economic burden by meeting part of their obligations by purchasing corresponding emission allowances in countries where such measures are, for various reasons, cheaper 41 .

Another global problem is the change in the ozone layer. There is a drop in ozone concentration in the Earth's ozone layer, which is associated with anthropogenic impact and the release of freons. (There are also hypotheses pointing to the natural nature of the formation of “ozone holes.”

The thinning of the ozone layer was first noticed over Antarctica in 1985, and was later also recorded in the northern hemisphere over parts of Europe and North America. It is believed that the destruction of the ozone layer leads to pollution by “hard” ultraviolet radiation, which is dangerous for animal and plant organisms.

The protection of the ozone layer is carried out on the basis of such international documents as the 1987 Montreal Protocol on Substances that Deplete the Ozone Layer and the Vienna Convention for the Protection of the Ozone Layer.

Problems of biodiversity decline

Biological diversity (or biodiversity) is understood as the diversity of life in all its manifestations, as a combination of three elements - genetic diversity (diversity of genes and alleles), species diversity and diversity of ecosystems (this understanding is enshrined in such an international document as the UN Convention on Biological Diversity).

Each species, regardless of the degree of its usefulness to humans, is valuable; each species has a unique set of genes formed during the process of evolution, therefore the entire gene pool of the biosphere is subject to protection.

The main causes of decline in biological diversity are habitat destruction or disturbance; fishing (hunting), introduction of alien species, direct destruction for the purpose of protecting agricultural products, accidental destruction (on roads, during military operations, on power lines, etc.), environmental pollution. In addition, the destruction of one species may lead to the disappearance of several more.

The nature of Russia has a significant level of biodiversity; on the territory of the country there are more than 12,500 species of vascular plants, 2,200 - bryophytes, about 3,000 - lichens, 320 - mammals, more than 732 - birds, 75 - reptiles, about 30 amphibians and almost 343 species of fresh water fish , 9 - cyclostomes and about 1,500 species of marine fish. Our country's contribution to global biodiversity is great (see table).

Main parameters of biodiversity of the Russian Federation 42

Taxonomic group	Estimation of the number of species in Russia	% in world fauna
Plants
Seaweed
Lichens
Bryophytes
Vascular plants
Animals
Protozoa
Coelenterates
Flatworms
Roundworms
Shellfish
Crustaceans
Arachnids
Insects	About 100,000
Freshwater fish
Marine fish	About 1500
Amphibians
Reptiles
Mammals

The protection of biodiversity in Russia is carried out, in particular, within the framework of a system of protected areas of various types. A special role is played by maintaining the “Red Books”, as well as the development of economic and political mechanisms for the protection of biodiversity, research and educational work.

Problems of using natural resources.

Natural resources are a set of natural objects and phenomena used in the present, past and future for direct and indirect consumption, contributing to the creation of material wealth, reproduction of labor resources, maintaining the conditions of human existence, and improving the quality of life 43 . These are soil cover, beneficial wild plants, animals, minerals, water (for water supply, irrigation, industry, energy, transport), favorable climatic conditions (mainly heat and moisture), wind energy, etc.

Natural resources are classified according to their source of origin (biological, mineral, energy), according to their belonging to certain components of nature (land, forest, water, energy and other resources), according to the degree of depletion (inexhaustible and exhaustible, divided into renewable and non-renewable) K Inexhaustible include space and climate resources - air, precipitation, solar radiation, wind energy, sea tides, etc.

Biological resources (animals and plants), as well as some mineral resources (salts deposited in lakes, for example), are considered renewable. The rate at which renewable resources are used must be consistent with the time required to regenerate them. Most mineral resources are classified as non-renewable. Relatively renewable resources are soil and forest resources. Some natural resources have the properties of replenishment and substitutability.

Renewal of natural resources - their natural restoration over time or cultivation. Some natural resources are renewable quantitatively, but non-renewable (non-renewable qualitatively) 44 .

To carry out a comprehensive assessment of the severity of the problems of depletion of natural resources, indicators of the intensity of use and potential reserves are correlated. For renewable resources, indicators such as the level of production and the potential for its annual growth are taken into account 45 .

The current state of renewable resources is associated with a number of problems - the disappearance of a number of animal and plant species (about 400), the annual reduction in forest area and the deterioration of the structure of the land fund, a simultaneous increase in water consumption and water pollution.

(excerpts from the book)

Cybernetics deals with all forms behavior insofar as they are regular, or deterministic, or reproducible.
Information theory plays a big role in the problems of cybernetics, since information theory characterized essentially by the fact that it always deals with a certain set of possibilities; both its initial data and its final conclusions always refer to many as such, and not to any individual element within it.
Often, even the closedness or openness of the system in terms of energy does not matter - only the degree to which the system is subject to determining and controlling factors is important. No information, or signal, or determining factor can pass from one part of the system to another without being marked as significant event.
That which experiences the action is called operand. The active factor is called operator. What the operand has become is called way. The change that occurs is called transition. A transition is defined by two states. The set of transitions for a certain set of operands is transformation. Transformation refers to what happens, not why it happens. Conversion definitely, if it turns each operand into only one image.
Deterministic machine is defined as a machine that behaves in the same way as a closed one-to-one transformation. Deterministic systems follow regular and repeatable paths in their change.
Under condition system is understood as a precisely defined condition or property that can be recognized if it occurs again. Every system naturally has many possible states. The fact that a deterministic machine cannot go from one state to two other states at once corresponds to the requirement that the transformation be unique.
Every machine or dynamic system has many distinguishable states. If this is a deterministic machine, then fixing the conditions influencing it and the states in which it is located will determine, i.e. will make the only one the next state into which it will go. These state transitions correspond to operand transitions during conversion.
The transformation representing the machine must be closed. If a closed single-valued transformation is given, as well as some initial state, then the trajectory starting from this state is completely definite (i.e., single-valued) and can be calculated.
Every material object contains no less than an infinite number of variables and therefore no less than an infinite number of possible systems. We need to select and study only the facts that are of interest to us from the point of view of a certain, pre-specified goal. The truth is that in the world around us, only some sets of facts can give closed, unambiguous transformations. Finding such sets is sometimes easy, sometimes difficult. Usually the detection of such sets is associated with another method system definitions- with method listing the variables that must be taken into account.
System does not mean a thing, but a list of variables that ensure unambiguous transformation.
A real machine, the behavior of which can be represented by some set of closed single-valued transformations, is called converter or machine with entrance. Its input is mutable parameter. Changing the parameters (or input) affects the behavior of the machine (converter).
Transition process is defined as a sequence of states that a converter goes through under constant conditions before it begins to repeat itself.
Two or more machines can be combined into one new machine. If machines must retain their individual nature after being combined into a single whole, then only the inputs and outputs can be connected to each other without affecting the other parts.
If the action between the parts of a dynamic system is circular, then it has feedback. Where there are only two parts connected so that each affects the other, the feedback properties provide important and useful information about the properties of the whole. But if the number of parts increases to at least four and each part affects the other three parts, then twenty closed loops can be drawn through them, but knowledge of the properties of all these twenty loops does not yet provide complete information about the system. Such complex systems cannot be viewed as an intertwined set of more or less independent feedback loops - they can only be viewed as a whole.
Through all the meanings of the word " sustainability"the main idea passes" invariance". It consists in the fact that although the system as a whole undergoes consistent changes, some of its properties ( invariants) remain unchanged.
State equilibrium- a state that is not changed by the transformation. Cycle A sequence of states is called such that repeated applications of the transformation cause the states to reverse this sequence. Typically, a dynamic system that changes continuously is subject to small disturbances almost all the time. Equilibrium states can be stable, indifferent and unstable. It may be necessary to eliminate many of them in order to reduce the system to a set of states that have a realistic chance of persisting. Often the system is considered sustainable on the assumption that indignation lie within a certain area.
Stability is usually considered desirable, because its presence allows you to combine some flexibility and activity with some constancy. However, sustainability is not always good because the system may persist in returning to a state that is otherwise considered undesirable.
Two cars connected" homomorphism", when a transformation that is unique in only one direction, applied to a more complex machine, can reduce it to a form that will be isomorphic to a simpler machine. Thus, two machines homomorphic, if they become identical (isomorphic) when one of them is simplified, i.e. when observing it with incomplete discrimination of states.
There is no such thing as a (single) behavior of a very large system, taken by itself, independent of a given observer. For as many observers, as many sub-machines and as many patterns of behavior, which can vary to the point of incompatibility in one system. Science is not directly concerned with discovering what a system “really” is, but with reconciling the discoveries of various observers, each of whom is only a part or aspect of the whole truth.
We actually operate with " black boxes", the theory of which is simply a theory of real objects or systems, in which special attention is paid to the question of the relationship between the object and the observer, the question of what information comes from the object and how it is received by the observer. Thus, black box theory is simply the study of the relationship between the experimenter and his environment, with special attention paid to the flow of information. Studying the real world comes down to studying transformers.
Emergent properties - properties that cannot be predicted based on knowledge of the parts and the way they are connected. When knowledge of the parts of the whole is complete, the prediction of the behavior of the whole can also be complete and no properties beyond those predicted can suddenly arise (emerge). Often, however, our knowledge is not complete for various reasons. Then the prediction must be made on the basis of incomplete knowledge and may turn out to be wrong. For example, it may happen that the only way to predict is by simple extrapolation - predicting that the whole will also have the same characteristic as the parts. Sometimes such extrapolation is justified. But often this method fails. And then we can, if we wish, call the new property "emergent." When a system becomes large and the difference in size between the part and the whole becomes significant, it often actually happens that the properties of the whole are very different from the properties of the parts.
An important part of the black box theory deals with the elucidation of those features that arise when the observer can observe only some components of the entire state. Once some of the variables become unobservable, the “system” represented by the remaining variables can exhibit remarkable and even miraculous properties. If a deterministic system is only partially observable and therefore becomes unpredictable, then the observer may be able to restore predictability by taking into account the past history of the system, i.e. allowing the existence of some kind of “memory” in it. Thus, the presence of “memory” is not a completely objective property of the system. This property is the relationship between the system and the observer and changes with the change in the communication channel between them. Appealing to "memory" in a system as an explanation for the system's behavior is tantamount to admitting the impossibility of observing the system completely. The properties of “memory” are properties not of a simple “thing”, but of a more subtle concept - “coding”.
A statement about something many can be either true or false when applied to elements multitudes. Act " communications"necessary presupposes the presence many possibilities, i.e. more than one possibility. Transfer and storage information are significantly related to the presence of some sets opportunities. The information conveyed by an individual message depends on the set from which it is selected. The information transmitted is not an internal property of the individual message.
Term diversity when applied to a set of distinguishable elements, it is used in two senses: 1) as the number of different elements; 2) as the logarithm of this number to base 2. In logarithmic form, the unit of diversity is called a "bit". Thus, gender diversity is equal to 1 bit. Variety of Sets vectors cannot exceed the sum of the varieties of their components (in logarithmic measure). Vector components independent, if the diversity of a given set of vectors is equal to the sum of the logarithmic diversity of the individual components. The diversity of a set is not an intrinsic property of it: it happens that in order to accurately determine diversity it is necessary to specify the observer and his ability to distinguish.
The existence of any invariant in a certain set of phenomena implies the presence diversity restrictions. Since any law of nature implies the presence of some invariant, then every law of nature is a limitation of diversity. A world without limits to diversity would be completely chaotic. The fact that something predictable, implies the presence of a diversity limitation. A common and very powerful constraint on diversity is continuity. A continuous function can only move to an adjacent value at each step. If the transformation results in two states merging into one, diversity decreases. When encoding through a one-to-one transformation, the diversity does not change, which makes it possible to unambiguously restore the original forms.
The amount of variety that a converter can transmit is proportional to its bit capacity multiplied by the number of steps taken. Operating long enough, any transducer can transmit any amount of diversity. The reason for this is that the output, taken step by step as a sequence, forms a vector, and the diversity of a vector can exceed the diversity of one of its components. Thus, the reduction in channel capacity can be compensated by increasing the sequence length.
Consider the case in which each operand, instead of being transformed into a specific new state, can go into one of a number of possible states, the choice of a particular state being carried out by some method or process giving each state constant probability become an image. It is the invariability of probability that provides the pattern or order on which precise statements can be based. Such a transformation, and especially the set of trajectories it can produce, is called stochastic, to distinguish it from a unique and deterministic transformation.
Such a sequence of states in which for different long intervals the probability of each transition is the same is called Markov chain. This means that the probability of each transition should depend only on the state in which the system is located, and not on the states in which it was previously. A set of vectors that does not exhibit diversity restrictions corresponds to a Markov chain in which at each stage all transitions are equally probable.
Sustainable area a Markov machine has a set of states such that the representing point, having entered one of these states, will no longer be able to leave this set. State of balance there is simply a stable region reduced to a single state. Near the equilibrium state, the system behaves as if it were “striving toward a goal,” which is the equilibrium state. However, in the Markov case, the system does not move firmly and definitely towards the goal, but wanders, as it were, vaguely among various states, constantly moving into a new state, unless the old one was an equilibrium state, and just as constantly stopping if it happens to fall into an equilibrium state. The movement of a Markov machine to a state of equilibrium reveals the objective properties of the method of achieving success through trial and error. When two machines are connected, the whole can only be in a state of equilibrium when each part is itself in a state of equilibrium under the conditions determined by the other part.
Information cannot be transmitted in greater quantities than the amount of variety allows. Shannon introduced a measure of the amount of diversity found at each step by a Markov chain. This measure is called entropy many probabilities. It has a maximum value for a given set of probabilities that add up to 1 when all probabilities are equal. The entropy of a section of a Markov chain is proportional to its length. Information viewed as something that eliminates uncertainty, it is measured by the amount of uncertainty it eliminates.
Shannon's theorem on the transfer of information in the presence of noise: if, when transmitting messages over a certain channel, each message has a certain probability of random change, then excess channel capacity can reduce errors to any desired level.
Concepts survival" And " sustainability" are identical, they can be brought into exact correspondence. Some states corresponding to a living organism are those states in which certain essential variables remain within specified boundaries.
Essential function regulator is that it blocks the flow of diversity from disturbances to significant variables and thereby reduces the diversity transmitted. Only diversity in the controller can reduce diversity from disturbances.
A significant portion of some activities can be considered in two ways. On the one hand, the observer may notice that significant movement and change are in fact occurring; and on the other hand, that in all this activity, since it is coordinated and homeostatic, certain invariants are preserved, showing the degree of regulation being carried out.
Before any regulation can be implemented or even talked about, we must know What here it is essential (a set of essential variables) and What required (set of valid states). Regulation will be incomplete(imperfect) when the regulator, considered as a channel for transmitting diversity or information, has a capacity that, due to the law of necessary diversity, turns out to be insufficient to reduce the incoming (disturbing) diversity to the diversity of admissible states.
In many cases, preventative regulation is not possible, i.e. the regulator cannot complete its action before the outcome begins to be determined. Sometimes information entering the regulator must travel a longer path, so that the regulator is influenced only by the impact that has already occurred on the object of regulation. In this case, we obtain a simple tracking system, error-driven, or regulator with closed loop, With feedback. The main property of an error-controlled controller is that it cannot be perfect. In many cases, systems exhibit continuity such that the states of significant variables are distributed along some undesirability scale. A timely return on this scale from halfway can justifiably be called “adjustment”. Thus, the presence of continuity makes possible regulation, although incomplete, but of great practical importance. Small mistakes are made, and then by feeding their information to the regulator, they enable regulation to prevent larger mistakes.
Promotion of a separate Markovian of a machine to a state of equilibrium is much less orderly than the progression of a deterministic machine, and therefore the Markov type is little used in technical regulators. A Markov machine, like a deterministic one, can be used as a control tool, but it has the disadvantage that its trajectory is uncertain, but it has the advantage that it is easy to design.
Main source regulatory difficulties big system is variety of disturbances, against which regulation is directed. When the system is very large and the regulator is much smaller, the law of required diversity plays a major role. The significance of this law is that when the capacity of a regulator is fixed, it places an absolute limit on the amount of regulation (or control) that the regulator can perform, regardless of its internal design. R. Fisher showed that the information that can be extracted from available data has a maximum and that the task of every statistician is only to approach this maximum.
When the system is very large, the distinction between the source of influences and the system that determines the outcome may be somewhat vague in the sense that the boundary between them can be drawn in various equivalent ways. However, arbitrarily or not, but some kind of border must always be carried out, at least in practical scientific work, for otherwise no definite statement can be made.

This book, written by the famous English specialist in the field of cybernetics William Ross Ashby, sets out the basic concepts of cybernetics - “the science of control and communication in animals and machines.” The author discusses the possibility of widespread application of the ideas of cybernetics in various areas 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 cybernetics issues such 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 have knowledge beyond elementary algebra.

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