Order is invariably associated with the organization and structure of the institution. “Order” is a word that is often heard, as a rule, in the mouth of the director or head of the organization. This is a term that has essentially become a symbol of the strength of management; we associate it with good organization.
However, “too much organization is just as bad as not having any,” argues Alan Lakein in his acclaimed book, The Art of Getting Things Done.
The opposite of order is chaos. Chaos in an organization is probably a bad thing?
The great F. Nietzsche (1844-1900) was a master of philosophical aphorisms. One of them says: “You still need to carry chaos within yourself in order to be able to give birth to a dancing star.” He meant that without the chaotic movement of the elements that make up the system, it will not acquire a new quality, will not achieve success, and will not be able to invent an unprecedented new thing - the “dancing star.” This means that everyday understanding is not quite enough to determine “order in the house”, in the organization.
“What do we mean when we talk about order? What do we mean when we talk about clutter? - Ilya Prigozhin and Isabella Stengers ask questions. “Our definitions of order and disorder,” they answer, “include both cultural judgments and science...”
This needs to be looked into.
5.1. Traditional view.
“Order is a place for everything, where everything is in its place,” says Henri Fayol in “The Principles of Management.” It is clear that this is a metaphor that simplifies the essence of the matter. Simplicity is good for initial understanding. But simplicity elevated to an absolute is dangerous, because the world is extraordinarily complex. For example, “fascism has non-economic reasons,” notes Peter Aven, “the desire to embody some simple and understandable model of social existence; I call fascism a “revolt of simplicity” against the incomprehensible and unnecessary complexity of democratic life,” sums up Aven.
“Mental order is pathological,” say scientists.
Evaluations of order are thus ambiguous and lead to the question: is it synonymous with strict simplicity, or is it a “relative” of elegant complexity?
If everything is in full swing in the office, the desks are littered with business papers, among which you cannot immediately make out where and what is located, and what they are intended for; if employees and endless visitors endlessly enter and exit the office; if faxes are crackling, telexes are working, computers are humming, telephones are ringing incessantly; If you happen to be here and hear snatches of the most incomprehensible conversations and phrases, you involuntarily ask yourself whether there is order in this institution?
If the office is shiny, decorated with fashionable materials, employees are dressed decorously and strictly in accordance with the instructions of the director: jacket, tie, fresh shirt, no sweaters or frivolous blouses; if people talk in low voices, afraid to disturb each other in a raised tone, special days and hours are reserved for visitors; If all the papers are neatly placed in special cabinets, and on the table there is only a stack of the most necessary things for work today, is there order in this institution?
5.2. New understanding.
Synergetics states that chaos is internally structured and contains its own internal order. In addition, it is chaos that can and does generate order at a fundamentally new level in any structure, in any organization!
For example, turbulent fluid flows have long been thought to be a prototype of disorder. On the other hand, the crystal was considered to be the embodiment of order. Now scientists are forced to abandon such a straightforward point of view. A turbulent system turns out to be internally ordered, since in the seemingly completely unorganized movement of liquid molecules, forming vortex flows, there is a subtle structure that is indistinguishable to the naked human eye. The atoms that form a crystal, as physical studies show, oscillate around equilibrium positions, and do so in an inconsistent manner, that is, from the point of view of thermal motion, the crystal is disordered.
One can try to extrapolate such an understanding of the relativity of chaos and order, the internal structure of chaos to social objects. For example, our cities are the personification of chaos and order at the same time. On the one hand, they disrupt the natural stability of human life, tearing us out of our natural environment. It seems that the city is the personification of chaos. But at the same time, the city is a source of social, cultural, technical, and intellectual innovations. Life in cities is vibrant, new technologies are being created here that will ultimately make human existence easier, make human life more comfortable, and fill it with creative meaning. From this point of view, cities are the very embodiment of order.
Any chaos is at least somewhat orderly, and any order has its own degree of chaos. Chaos in complex systems of very different nature, studied by synergetics, is always relative. It contains a certain measure of chaos and a measure of order. Chaos is organized in a certain way. This is deterministic, or dynamic, chaos. Chaos can have a fine structure, as in the case of turbulence, or chaos can be organized into a beautiful fractal structure that has the property of self-similarity, or scale invariance.
Order and disorder in the world are closely interconnected, interdependent and give rise to each other. It has long been believed that the devil is a kind of measure of disorder in the world. The devil upsets plans, brings chaos and confusion (as they say, the devil got lost), multiplies disorder, in general, is the entropy principle. The devil, as it were, probes for possibilities, and the person realizes one of them. The devil enters into a game with the world, gains access to a treasury of potentialities (the yawning abyss of chaos), and, perhaps, ominous and disastrous potentialities of the course of events, and man reins him in, pacifies him. But the fact is that a particle of the devil, of monstrous demonic forces, lives in each of us, and it can break through, manifest itself, striking with fireworks of brilliant creative or dark destabilizing forces.
Chaos, as a complex relationship between order and disorder in real systems, performs many different functions in the processes of self-organization in nature, the human psyche and society:
■ chaos as a way to achieve the trend of self-structuralization of an open nonlinear environment;
■ chaos as a way to synchronize the pace of evolution of subsystems within a complex system and thereby as a way to preserve its integrity;
■ balancing on the edge of chaos as a way to maintain a complex organization (self-organized criticality);
■ chaos as a factor of adaptation to changing environmental conditions;
■ transition from order to chaos, from symmetry to asymmetry, and back, as a way of giving birth to beauty;
■ chaos, or more precisely the share of internal chaos, as a necessary addition to external management, control, planning as a way of self-government of a complex system;
■ chaos, dispersion, diversity of elements as the basis for achieving their unity, organization (unity through diversity as a principle of systems theory, order through chaos /I. Prigogine/, order through noise /H. von Foerster/, organizing randomness /A. Atlan/) ;
■ falling into chaos as a way out of an evolutionary dead end;
■ chaos as a stimulus, a push for evolution, spontaneity as a vital impulse;
■ and, finally, it is precisely at the stage of decline in activity and increase in dissipative, scattering, chaotic processes that new connections can be established, new structures arise, processes of morphogenesis can be initiated, in a word, chaos is a factor in the renewal of a complex organization.
The limitlessness of the knowledge of chaos is associated with the discovery and study of the most diverse functions of chaos, both promoting self-organization and evolution and inhibiting them, both constructive and creative, and destructive and destructive.
In connection with the development of the theory of self-organized criticality (P. Buck, S. Kauffman), a beautiful metaphor has now appeared “ self-organization on the edge of chaos". Complex adaptive systems not only allow chaos, which makes them quite flexible and pliable, allowing them to adapt well to changing environmental conditions, but also balance on the edge of chaos, existing as if on a razor’s edge. Complex adaptive systems, especially living beings, are extremely fragile, so that even the best step towards improving their organization can lead to rapid spontaneous decay and death. S. Kauffman notes that life is an emergent phenomenon, which is based on “order for freedom”, or self-organization, and the latter is characteristic of the mode of evolution of a system “on the edge of chaos” 40.
Is there a “unit of measurement” for chaos? This is entropy. This term comes from thermodynamics, and the word itself is of Greek origin [ εν means in, inside + τροπη , translated as turn, change, transformation]. Entropy is a measure of internal disorder in a system.
So, the measure of chaos (disorganization) of a system is a quantity called entropy, and the measure of order (organization) is negative entropy, called negentropy, or "information".
Term "information" put here in quotation marks to emphasize the inappropriateness of simply identifying information with negentropy. Although they coincide quantitatively, there is a significant difference between them qualitatively: information appears only where and when one ordered system is “reflected” in another, i.e. where there is a relation of one order to another order. It is not entirely correct to identify order in itself as an objective property of a material system with information.
As noted above, in closed systems, which are, generally speaking, an idealization of reality, entropy increases (the second law of thermodynamics), that is, heat moves from a hot body to a cold one, and the reverse process is impossible. Synergetics showed the limits of the second law of classical (equilibrium) thermodynamics. In open systems, far from the state of thermodynamic equilibrium, ordered structures can arise not due to a decrease in chaos, but due to dissipation, chaotic processes. Complex dissipative structures arise and develop on the basis of intense “burning out” of the medium, i.e. precisely due to the production of entropy, the growth of chaos at the micro level, manifested in the form of macroscopic dissipative processes.
Thus, without chaos nothing new is born. Without the chaos of transformation, it is impossible to create a new structural order in the organization. Scientists have come to the conclusion that at certain stages of development in open systems from their chaotic state all of a sudden, as if by magic, appears new order, a new structure of these systems, a new organization. This is a sudden and unpredictable occurrence all of a sudden called emergence– a special property of open systems.
By revealing the patterns of the emergence of order from chaos, synergetics gives us greater confidence in our future, in the possibility of effective social management and predicting what awaits us tomorrow, building scenarios for future development.
Resistance to chaos is extremely common in our society, as in any society. People constantly resist chaos, investing a lot of emotions, thoughts and strength into it. It is a total and powerful tendency to struggle with uncertainty and the unknown, trying to take control of your life.
Most religions - especially Buddhism, Hinduism, Christianity, Sufism, Neo-Sufism, esoteric traditions and the religion of psychology - try, with more or less success, to create belief systems that contribute to the orderliness of chaos - that game of chance that we find intolerable and which we resist with all our might.
However, to become free, we must voluntarily ride the swift and uncontrollable horse of chaos. Only then will we be able to immerse ourselves in a unified field that connects us with the world and the Universe. In other words, by refusing to resist chaos, we incomprehensibly and paradoxically create order that leads beyond chaos. This is the context of psychology choosing chaos as the organizing principle and means to achieve a more universal and integrated state - what I call the state beyond the state. This state without state is the true and highest degree of order. In other words, the very chaos we resist helps us create a deeper order.
Perhaps chaos is actually just natural order, and in this chaos there are possible islands of order. But chaos is order.
Resistance to chaos maintains chaos, often making life unbearable . Moreover, it deprives us of the opportunity to achieve higher order, unity and the deepest connection with the universe and the Universe.
In reality, order is born from chaos, not chaos from order.
For example, imagine that you are floating along a stormy and fast-moving river. If you try to swim against the current, you will experience chaos to the fullest. You will feel the pressure of the water on your chest and stomach; The current can knock you over and hit you against rocks. But if you become like water and flow with it, suddenly a new order will arise out of chaos. One Zen master said that he achieved enlightenment after he went on a journey and saw that all the cars were going in the same direction. Then he decided that he should go in the other direction - to where the cars had already been.
So we're going to explore the concept that within chaos lies natural order. This chaos, which we so strenuously resist, truly has inner meaning and beauty. When we perceive it as a flow of energy, chaos allows us, as one might say, David Bohm, "find a deeper connection with your own universe" .
We have to admit the fact that the Universe appears to us as chaotic, incomprehensible, uncontrollable and mysterious. The philosophical systems to which we turn in the hope of gaining understanding or at least “calm” are in reality attempts to resist the fact that chaos is the rule rather than the exception. Various systems are trying to bring order to chaos, while we need the TAO OF CHAOS - the path of non-resistance and acceptance of chaos, the path on which we allow chaos to engage in its own self-organization and manifest its true nature.
Parallel universes and inner reality
Just as the stars and planets in the sky are separated by space, so are our inner universes separated from each other. From the point of view of personality, we can say that we consist of parallel universes, or - in the language of psychology - parts of the personality. We call these worlds roles, parts, subpersonalities, false egos or schemas. Different schools of psychology call these parallel universes differently.
The only thing we will add to this is the idea of emptiness. Each part of our “personality” is endowed with different feelings, thoughts, memories, etc. For example, while working, you are in a world of independence and decision-making. You act and react in ways that best solve the problems you face and implement solutions. In the world of family, you may feel vulnerable, dependent and indecisive. Both of these parallel universes live inside you, and at different times you merge with one of these worlds. And both of these universes are limited and surrounded by emptiness.
Fractals and chaos
How can we discover the deep order (Bohm's second implicit order)? To answer this question, consider fractals. Typically, most of us think of expansion as moving from the inside out. For example, if you look at an object and expand your area of attention, you see other objects. However, fractals can help us direct our attention from the outside in and thereby move closer to infinite order.
What are fractals? You can think of them as fractional units of measurement. Let's think of fractals in terms of measuring some quantity - for example, the volume of a room. The smaller the volume we take as a unit of measurement, the larger the room will seem. And not only does the room grow larger - a specific pattern or deep order emerges, increasing as the scale is fragmented into smaller and smaller segments.
This process is called iteration. Mandelbrot discovered that as we multiply a fractal by itself, the universe becomes larger and larger.
In other words, when objects decrease, the universe with its marvelous order increases.
Therefore, we can answer the question something like this: to achieve the second implicit order, one must go inside and diminish so much as to discover the emptiness, which, condensing, contains everything.
For example, if we start with one fraction and continually multiply it by itself, we get a self-creating order.
In the case of fractals, development continues through the constant application of the same procedure, but on a decreasing scale.
Excerpt from Stephen Wolinsky's book "The Tao of Chaos"
Doctor of Physical and Mathematical Sciences A. DMITRIEV, leading researcher at the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences (Moscow).
Dynamic (deterministic) chaos and fractals are concepts that entered the scientific picture of the world relatively recently, only in the last quarter of the twentieth century. Since then, interest in them has not faded not only among specialists - physicists, mathematicians, biologists, etc., but also among people far from science. Research related to fractals and deterministic chaos is changing many of the usual ideas about the world around us. And not about the world of micro-objects, where the human eye is powerless without special equipment, and not about phenomena on a cosmic scale, but about the most ordinary objects: clouds, rivers, trees, mountains, grass. Fractals force us to reconsider our views on the geometric properties of natural and artificial objects, and dynamic chaos introduces radical changes in the understanding of how these objects can behave over time. The theories developed on the basis of these concepts open up new opportunities in various fields of knowledge, including information and communication technologies.
Science and life // Illustrations
Trees, like many other objects in nature, have a fractal structure.
Science and life // Illustrations
Crimean pine (left) and artificial fractal structure (right) are surprisingly similar.
Response of an oscillatory circuit to an external periodic signal: a - periodic response of a linear circuit, b - chaotic response of a nonlinear circuit. The role of nonlinear capacitance is performed by the p-n junction of the semiconductor diode.
The motion of a dynamic system can be visually represented by a trajectory on the phase plane, where the X and Y axes are the generalized coordinate and momentum of the particle. a - oscillations of a damped pendulum.
Examples of systems with chaos.
Science and life // Illustrations
The main ways of synchronizing chaotic systems: a - through global connections: each system influences each other; b - with the help of a pacemaker, or “pacemaker”: one of the systems sets the rhythm for all other elements.
Science and life // Illustrations
An example of recording information using deterministic chaos.
Employees of the InformChaos laboratory of the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences A. I. Panas and S. O. Starkov conduct an experiment on high-speed direct chaotic data transmission in the microwave range (above).
This is what chaotic microwave oscillations look like, making it possible to increase the speed of information transfer tens of times compared to traditional systems.
What is a fractal?
Fractals are everywhere around us, both in the outlines of mountains and in the winding line of the seashore. Some of the fractals are constantly changing, like moving clouds or flickering flames, while others, like trees or our vascular systems, maintain a structure acquired through the process of evolution.
H. O. Peigen and P. H. Richter.
The geometry we studied in school and use in everyday life goes back to Euclid (about 300 BC). Triangles, squares, circles, parallelograms, parallelepipeds, pyramids, spheres, prisms are typical objects considered by classical geometry. Man-made objects usually include these figures or fragments of them. However, in nature they are not found very often. Indeed, are, for example, the forest beauties of spruce similar to any of the listed items or their combination? It is easy to notice that, unlike Euclid’s forms, natural objects are not smooth, their edges are broken, jagged, their surfaces are rough, corroded by cracks, passages and holes. "Why is geometry often called cold and dry? One reason is its inability to describe the shape of a cloud, a mountain, a tree, or a seashore. Clouds are not spheres, mountains are not cones, shorelines are not circles, and the crust is not smooth." , and lightning does not travel in a straight line. Nature shows us not just a higher degree, but a completely different level of complexity,” these words begin “The Fractal Geometry of Nature,” written by Benoit Mandelbrot. It was he who first introduced the concept of fractal in 1975 - from the Latin word fractus, broken stone, split and irregular. It turns out that almost all natural formations have a fractal structure. What does it mean? If you look at a fractal object as a whole, then at a part of it on an enlarged scale, then at a part of this part, etc., then it’s easy to see that they look the same. Fractals are self-similar - their shape is reproduced on different scales.
The discovery of fractals revolutionized not only geometry, but also physics, chemistry, and biology. Fractal algorithms have also found application in information technologies, for example, for the synthesis of three-dimensional computer images of natural landscapes, for compression (compression) of data (see “Science and Life” No. 4, 1994; No. 8, 12, 1995; No. 7, 1998). Next, we will make sure that the concept of a fractal is closely related to another no less interesting phenomenon - chaos in dynamic systems.
Determinism and chaos
CHAOS (Greek caos) - in Greek mythology, an unlimited primitive mass,
from which it was subsequently formed
everything that exists. In a figurative sense - disorder, confusion.
Encyclopedia
Cyril and Methodius
When they talk about the determinism of a certain system, they mean that its behavior is characterized by an unambiguous cause-and-effect relationship. That is, knowing the initial conditions and the law of motion of the system, you can accurately predict its future. It is this idea of motion in the Universe that is characteristic of classical, Newtonian dynamics. Chaos, on the contrary, implies a disorderly, random process, when the course of events can neither be predicted nor reproduced. What is deterministic chaos - the seemingly impossible unification of two opposing concepts?
Let's start with a simple experience. A ball suspended on a thread is deflected from the vertical and released. Hesitation occurs. If the ball is slightly deflected, then its motion is described by linear equations. If the deviation is made large enough, the equations will no longer be linear. What will change? In the first case, the oscillation frequency (and, accordingly, the period) does not depend on the degree of initial deviation. In the second, such a dependence takes place. A complete analogue of a mechanical pendulum as an oscillatory system is an oscillatory circuit, or “electric pendulum”. In the simplest case, it consists of an inductor, a capacitor (capacitance) and a resistor (resistance). If all three of these elements are linear, then the oscillations in the circuit are equivalent to the oscillations of a linear pendulum. But if, for example, the capacitance is nonlinear, the period of oscillations will depend on their amplitude.
The dynamics of an oscillatory circuit is determined by two variables, for example, the current in the circuit and the voltage across the capacitor. If we plot these quantities along the X and Y axes, then each state of the system will correspond to a specific point on the resulting coordinate plane. This plane is called phase. (Accordingly, if the dynamic system is defined n variables, then instead of a two-dimensional phase plane it can be associated n- dimensional phase space.)
Now let's start influencing our pendulums with an external periodic signal. The response of linear and nonlinear systems will be different. In the first case, regular periodic oscillations with the same frequency as the frequency of the forcing signal will gradually be established. On the phase plane, such movement corresponds to a closed curve called attractor(from the English verb to attract - attract), - a set of trajectories characterizing a steady-state process. In the case of a nonlinear pendulum, complex, non-periodic oscillations can occur when the trajectory on the phase plane does not close for an arbitrarily long time. In this case, the behavior of a deterministic system will outwardly resemble a completely random process - this is the phenomenon dynamic, or deterministic, chaos. The image of chaos in phase space - chaotic attractor- has a very complex structure: it is a fractal. Due to its unusual properties it is also called strange attractor .
Why does a system that develops according to well-defined laws behave chaotically? The influence of extraneous noise sources, as well as quantum probability, has nothing to do with it in this case. Chaos is generated by the own dynamics of a nonlinear system - its ability to exponentially quickly separate arbitrarily close trajectories. As a result, the shape of the trajectories depends very much on the initial conditions. Let us explain what this means using the example of a nonlinear oscillatory circuit under the influence of an external periodic signal. Let's introduce a small disturbance into our system - slightly change the initial charge of the capacitor. Then the oscillations in the disturbed and undisturbed circuits, initially practically synchronous, will very soon become completely different. Since in a real physical experiment it is possible to set the initial conditions only with finite accuracy, it is impossible to predict the behavior of chaotic systems for a long time.
Predicting the future
- Because of such a small thing! Because of a butterfly! - Eckels shouted.
She fell to the floor - a graceful little creature capable of breaking the balance, small dominoes fell... big dominoes... huge dominoes, connected by a chain of countless years that make up Time.
R. Bradbury. A Sound of Thunder
How organized is our life? Are certain events predetermined in it? What is predictable for many years in advance, and what is not subject to any reliable forecasting even for short time intervals?
A person constantly has to deal with both ordered and disordered processes generated by various dynamic systems. We know that the Sun rises and sets every 24 hours, and this will continue throughout our lives. After winter, spring always comes, and it is unlikely that it will ever be the other way around. Utilities that supply us with light and heat, institutions and shops, as well as transport systems (buses, trolleybuses, subways, planes, trains) function more or less regularly. Disturbances in the rhythmic operation of these systems cause legitimate indignation and indignation among citizens. If failures occur repeatedly, they talk about chaos, expressing a negative attitude towards such phenomena.
But at the same time, there are processes that are well known for their unpredictability. For example, when tossing a coin, we never know exactly what will come up - heads or tails. Such unpredictability does not cause alarm. It can lead to much more dramatic consequences when playing roulette, but those who like to tempt fate consciously take this risk.
Why are some processes predictable in their results, while others are not? Maybe we just don’t have enough initial data for a good forecast? You need to improve your knowledge of the initial conditions - and everything will be fine, both with the coin and with weather prediction. Laplace said: give me the initial conditions for the entire Universe, and I will calculate its future. Laplace was wrong: he and his contemporaries were not aware of examples of deterministic dynamic systems, the behavior of which cannot be predicted for a long time. It was only at the end of the 19th century that the French mathematician Henri Poincaré first felt that this was possible. However, another three-quarters of a century passed before the era of vigorous study of deterministic chaos began.
Dynamic systems can be divided into two types. For the former, the motion trajectories are stable and cannot be significantly changed by small disturbances. Such systems are predictable - that is why we know that the Sun will rise tomorrow, in a year and in a hundred years. To determine the future in this case, it is enough to know the equations of motion and set the initial conditions. Small changes in the values of the latter will only lead to an insignificant error in the forecast.
Another type includes dynamic systems whose behavior is unstable, so that any disturbances, however small, quickly (on a time scale characteristic of this system) lead to a radical change in the trajectory. As Poincaré noted in his work “Science and Method” (1908), in unstable systems “a completely insignificant cause, eluding us due to its smallness, causes a significant effect that we cannot foresee. (...) Prediction becomes impossible, We have before us a random phenomenon." Thus, forecasting for long periods of time loses all meaning.
The nonlinear oscillatory circuit example discussed above shows that chaotic behavior with an unpredictable future can occur even in very simple systems.
Reconstruction of the past
So, predicting the future is not always possible. What about the past? Is it always possible to reconstruct (“predict”, unambiguously interpret) the past? It would seem that there should be no problems here. Since the trajectories move away from each other when moving forward, they must approach each other when moving backward. The way it is. However, there is not one, but several directions along which convergence or divergence of trajectories in phase space can occur. When moving both forward and backward, trajectories can converge along one part of the directions, but diverge along the other.
Is the past "unpredictable"? Nonsense! After all, something has already happened. Everything is known... But let's think. If everything was so simple with the reconstruction of the past, how could it happen that for some Nicholas II is still bloody, but for others he is a saint? And who is Stalin: a genius or a villain? Let us ignore for now the problem of how free they were to make certain decisions, to what extent these decisions were predetermined by circumstances, and what could be the consequences of alternative decisions. Let us consider the historical process as the dynamics of some hypothetical chaotic system. Then, when trying to reconstruct the past, we will be faced with a rapidly increasing number of options (trajectories) that correspond to the current state of the system. Only one of them corresponds to the real course of events. If you choose not him, but some other one, you will get a distorted “version” of history. On what basis is the correct trajectory (“version”) selected? The information we can rely on is the totality of available specific facts. Trajectories that are incompatible with them are discarded. As a result, given enough reliable facts, there will be one trajectory that defines a single version of history. However, even for the recent past there may be significantly more trajectories than reliable information - then an unambiguous interpretation of the historical process can no longer be made. And all this with a conscientious and respectful attitude towards history and facts. Now add here the biases of primary sources, the loss of some information over time, manipulation of facts at the stage of interpretation (silencing some, protruding others, falsification, etc.) - and replacing black with white will not be such a difficult task. And what is most interesting is that, if necessary, the same interpreters after some time can easily assert the opposite. Is this a familiar picture?
So, the dynamic nature of the “unpredictability” of the past is similar to the nature of the unpredictability of the future: instability of the trajectories of a dynamic system and a rapid increase in the number of possible options as one moves away from the starting point. To reconstruct the past, in addition to the dynamic system itself, information from this past, sufficient in quantity and reliable in quality, is needed. It should be noted that in different parts of the historical process the degree of its chaos is different and can even drop to zero (a situation where everything essential is predetermined). Naturally, the less chaotic the system, the easier it is to reconstruct its past.
Can we control chaos?
Chaos often gives birth to life.
G. Adams
At first glance, the nature of chaos excludes the possibility of controlling it. In fact, the opposite is true: the instability of the trajectories of chaotic systems makes them extremely sensitive to control.
Let, for example, it is required to transfer a system from one state to another (to move a trajectory from one point of phase space to another). The required result can be obtained within a given time by one or a series of subtle, insignificant disturbances of the system parameters. Each of them will only slightly change the trajectory, but after some time the accumulation and exponential amplification of small disturbances will lead to a significant correction of movement. In this case, the trajectory will remain on the same chaotic attractor. Thus, systems with chaos demonstrate both good controllability and amazing plasticity: sensitively reacting to external influences, they maintain the type of movement.
According to many researchers, it is the combination of these two properties that causes chaotic dynamics to characterize the behavior of many systems of living organisms. For example, the chaotic nature of the heart rhythm allows it to flexibly respond to changes in physical and emotional stress, adapting to them. It is known that regularization of heart rhythm leads to death after some time. One reason is that the heart may not have enough “mechanical strength” to compensate for external disturbances. In fact, the situation is more complex. The ordering of the heart’s work serves as an indicator of a decrease in chaos in other systems associated with it. Regularity indicates a decrease in the body’s resistance to random influences of the external environment, when it is no longer able to adequately track changes and respond flexibly to them.
It is obvious that any complex systems operating in a changing environment should have such plasticity and controllability. This is the key to their preservation and successful evolution.
From chaos to order
How is the integrity and stability of living organisms and other complex systems ensured if their individual parts behave chaotically?
It turns out that in addition to chaos in complex nonlinear systems, the opposite phenomenon is also possible, which could be called anti-chaos. If chaotic subsystems are connected to each other, their spontaneous ordering (“crystallization”) can occur, as a result of which they acquire the features of a single whole. The simplest version of this ordering is chaotic synchronization, when all subsystems connected to each other move, although chaotically, but equally, synchronously. Processes chaotic synchronization can occur not only in the body of animals and humans, but also in larger structures - biocenoses, public organizations, states, transport systems, etc.
What determines the possibility of synchronization? Firstly, the behavior of each individual subsystem: the more chaotic and “independent” it is, the more difficult it is to force it to “reckon” with other elements of the ensemble. Secondly, the total strength of the connection between subsystems: its increase suppresses the tendency towards “independence” and can, in principle, lead to ordering. At the same time, it is important that there are connections global, that is, they existed not only between neighboring, but also between elements that were far apart from each other.
In real systems, including a large number of subsystems, communication is carried out through material or information flows. The more intense they are, the greater the chance that the elements will behave in a consistent manner, and vice versa. For example, in a state, the role of connecting flows is played by transport, mail, telephone communications, etc. Therefore, an increase in tariffs for these services, in the case where it leads to a decrease in the corresponding flows, weakens the integrity of the state and contributes to its destruction.
From the theory of chaotic synchronization it follows that the coordinated operation of individual parts of a complex system can be ensured by one of its elements, called pacemaker rum, or "pacemaker". Being connected in a one-way way with all components of the system, it “guides” their movement, imposing its own rhythm. If we make it so that the individual subsystems are not connected to each other, but only to the pacemaker, we get the case of an extremely centralized system. In a state, for example, the role of “pacemaker” is performed by the central government and... the media operating throughout the entire or significant part of the country’s territory. Today this especially applies to electronic media, since they are significantly superior to others in terms of mobility and general information flow. Intuitively understanding this, the central government tries to keep the media under control and also limits the influence of each of them individually. Otherwise, she will no longer govern the state.
Here we touched on a very important issue. Since the average strength of connections is a summary parameter, which includes both material and informational connections, this means that the weakening of some of them can be compensated by the strengthening of others. The simplest example is the replacement of real goods with paper or even electronic money. In this case, the supplier, in fact, instead of a material product, receives information about a change in his account - and he is quite happy with such an exchange. In the same way, huge amounts of money are gained or lost every day through stock exchange transactions, which, ultimately, someone must compensate for in real products or services.
How can a synchronized state be destroyed?
We have already mentioned one possibility. This is a weakening of ties. Another reason is the inadequate influence of the “pacemaker” on the ensemble. Indeed, if the “rhythm” dictated by the pacemaker is too contrary to the natural behavior of the system components, then even with sufficient connection strength he will not be able to impose his line of behavior on the ensemble. However, the previous behavior will not remain the same. As a result, synchronization will be destroyed.
Fractality and stability
We have already seen that the theory of dynamic chaos can be applied to many systems, including the state and society as a whole. What role does the fractal structure of chaos play in this? After all, the image of chaos in phase space - a strange attractor - is geometrically a fractal. Despite the fact that each individual chaotic trajectory is extremely sensitive to the slightest disturbances, a strange attractor (the set of all possible trajectories) is a very stable structure. Thus, dynamic chaos is like a two-faced Janus: on the one hand, it manifests itself as a model of disorder, and on the other, as stability and order at different scales.
If you think about it, it’s easy to see that in society, as in nature, many systems are built on the principle of fractals: some complexes are formed from small elements, they in turn serve as elements for larger complexes, etc. How, for example, are they organized viable economic and production structures? Two extreme positions: large transnational companies and “small businesses”. Each of them separately is unviable. Large companies, having enormous economic power, are inactive and cannot quickly respond to changes in the surrounding economic environment. “Small business” is not capable of solving large problems or ensuring infrastructure development. Where is the golden mean? In medium-sized enterprises? Not at all. A sustainable economic infrastructure is provided (with the necessary pumping of the necessary resources) by a set of different-scale (here is a fractal!) economic objects that form a pyramid. At the base there are many small companies and firms, higher up the pyramid the size of enterprises gradually increases, and their number, accordingly, decreases, and, finally, at the top there are the largest companies. This structure is typical, for example, of the US economy. At the same time, small businesses are the most mobile: they are often born and die, being the main suppliers of new ideas and technologies. Innovations that have received sufficient development allow a number of enterprises to grow to the next level or transfer (sell) accumulated innovations to larger companies. If the environment is sufficiently receptive, such a mechanism can create new industries and economies in a few years. It is not without reason that in the so-called “new economy” the bulk of even large enterprises are companies that 15-20 years ago either did not exist at all or were classified as small.
Another example. During perestroika, a lot was written and said about the “wrong” structure of the USSR, in which the state had a complex hierarchical structure, organized according to the matryoshka principle. What was offered in return? Each nation has its own native army, its own language, its own “elite,” its own tribal leaders. Sounds good. Now look at how this idea turned out for many peoples of the former USSR and Yugoslavia... From the point of view of stability theory, the idea of a homogeneous structure of the Russian state is a loser’s idea. Why? The matryoshka principle is, in fact, a fractal principle, thanks to which a chaotic system acquires structure and stability. The USSR and the Russian Empire were built on the principle of fractal systems, and this ensured their stability as states. At different levels, natural state, ethnic, territorial and other entities with well-functioning mechanisms of internal functioning, with their own rights and responsibilities, were interspersed into the overall system.
Chaos gives rise to information
We have already established that the behavior of chaotic systems cannot be predicted over large time intervals. As you move away from the initial conditions, the position of the trajectory becomes more and more uncertain. From the point of view of information theory, this means that the system itself generates information, and the speed of this process is higher, the greater the degree of chaos. From here, according to the theory of chaotic synchronization discussed earlier, an interesting conclusion follows: the more intensely the system generates information, the more difficult it is to synchronize it, to force it to behave somehow differently.
This rule seems to be true for any information-producing systems. For example, if a certain creative team generates a sufficient number of ideas and A actively working on ways to implement them, it is more difficult for him to impose from the outside some line of behavior that is inadequate to his own views. And vice versa, if, in the presence of the same material flows and resources, the team behaves passively in the information sense, does not create ideas or does not implement them - in other words, follows the principle “...warm and damp” - then it is very easy to subjugate it .
Chaotic computers
What do we miss in modern computers? If a living organism, in order to exist in a changing environment, must have elements of chaotic behavior, then it can be assumed that artificial systems capable of adequately interacting with a changing environment must be chaotic to one degree or another. Modern computers are not like that. They are closed systems with a very large but finite number of states. Perhaps in the future, on the basis of dynamic chaos, a new type of computer will be created - systems that are open from a thermodynamic point of view, capable of adapting to environmental conditions.
However, today chaotic algorithms can be successfully used in computer technologies for storing, searching and protecting information. When solving some problems, they turn out to be more effective than traditional methods. This applies in particular to working with multimedia data. Unlike texts and programs, multimedia information requires a different way of organizing memory. The ultimate dream of users is the ability to search for a melody, video or necessary photographs not by their attributes (directory and file name, creation date, etc.), but by content or association, so that, for example, using a fragment of a melody one can find and play a musical work. It turns out that such associative search can be accomplished using technologies based on deterministic chaos. How?
We have already discussed the generation of information by chaotic systems. Now let’s ask ourselves the question: is it possible to match the trajectory with specific data written in the form of a certain sequence of symbols? Then some of the trajectories of the system would be in one-to-one correspondence with our information sequences. And since each trajectory is a solution to the equations of motion of the system under certain initial conditions, then any sequence of symbols could be restored by solving these equations, setting a small fragment of it as the initial conditions. This would make it possible to search for information associatively, that is, search by content.
A team of employees at our institute created mathematical models for recording, storing and retrieving information using the trajectories of dynamic systems with chaos. Although the algorithms seemed very simple, their potential information capacity significantly exceeded the amount of all information available on the Internet. The development of the idea led to the creation of a technology that allows processing any type of data: images, text, digital music, speech, signals, etc. (RF Patent 2050072, US Patent 5774587, Canadian Patent 2164417).
An example of the use of technology is the Forget-Me-Not software package, designed for working with archives of unstructured information both on personal computers and on information servers. Forget-me-not is implemented as a search engine that runs under standard Internet browsers such as Netscape and Explorer. All information in the archive is recorded and stored in the form of trajectories of a chaotic system. To search for the necessary documents, the user composes a request by typing in free form several lines of text related to the content of the required document. In response, the system will provide the required document if the input information is sufficient for its unambiguous search, or will offer a set of options. If necessary, you can also receive a facsimile copy of the found document. The presence of errors in the query does not significantly affect the quality of the search.
Additional information on the Forget-Me-Not complex, as well as a demo version of the program, can be obtained at http://www.cplire.ru.
Communication through chaos
Most modern communication systems use harmonic oscillations as an information carrier. The information signal in the transmitter modulates these oscillations in amplitude, frequency or phase, and in the receiver the information is separated using the inverse operation - demodulation. The imposition of information on the medium is carried out either by modulating already formed harmonic oscillations, or by controlling the parameters of the generator during its operation.
In a similar way, you can modulate a chaotic signal. However, the possibilities here are much wider. Harmonic signals have only three controllable characteristics (amplitude, phase and frequency). In the case of chaotic oscillations, even small variations in the parameter value of one of the elements of the chaos source lead to changes in the nature of the oscillations, which can be reliably recorded by instruments. This means that chaos sources with variable element parameters potentially have a large set of schemes for inputting an information signal into a chaotic medium (modulation schemes). In addition, chaos fundamentally has a wide spectrum of frequencies, that is, it refers to broadband signals, the interest in which in radio engineering is traditionally associated with their greater information capacity compared to narrowband oscillations. A wide carrier frequency band allows you to increase the speed of information transmission, as well as increase the system's resistance to disturbing factors. Wideband and ultra-wideband communication systems based on chaos have potential advantages over traditional wide-spectrum systems in such defining parameters as simplicity of hardware implementation, energy efficiency and information transfer speed. Chaotic signals can also serve to mask information transmitted through a communication system without using spectrum extension, that is, when the frequency band of the information and transmitted signals coincides.
The combination of these factors stimulated active research into chaotic communication systems. At present, several approaches have already been proposed to expand the range of information signals and to construct transmitters and receivers that are simple in architecture.
One of the latest ideas in this direction is the so-called directly chaotic communication schemes. In a direct chaotic communication scheme, information is introduced into a chaotic signal generated directly in the radio or microwave wavelength range. Information is introduced either by modulating the parameters of the transmitter, or by superimposing it on a chaotic medium after it has been generated. Accordingly, the extraction of an information signal from a chaotic one is also carried out in the region of high or ultra-high frequencies. Estimates show that broadband and ultra-wideband direct-chaotic communication systems are capable of providing information transfer rates from tens of megabits per second to several gigabits per second. The Institute of Radio Engineering and Electronics of the Russian Academy of Sciences has already conducted experiments on direct chaotic transmission of information at speeds of up to 70 Mbit/sec.
Chaos and computer networks
In communication schemes, chaos can be used as a carrier of information, as a dynamic process that ensures the transformation of information into a new form, and, finally, as a combination of both. A device that converts a signal in a transmitter from one type to another using chaos is called chaotic coder. With its help, you can change information in such a way that it will be inaccessible to an outside observer, but at the same time it will be easily returned to its original form by a special dynamic system - chaotic decoder, located on the receiving side of the communication system.
In what processes can chaotic coding be used?
Firstly, with its help it is possible to organize the common information space in a fundamentally new way, creating large open groups of users in it - subspaces. Within each group, its own “language” of communication is introduced - rules, protocols and other features of this “information subculture” that are common to all participants. For those wishing to master this “language” and become a member of the community, there are relatively simple means of access. At the same time, it will be difficult for outside observers to participate in such an exchange. Thus, chaotic coding can serve as a means of structuring the “population” of the common information space.
Secondly, multi-user access to information can be organized in a similar way. The presence of the global Internet network and main information flows (Highways) presupposes the existence of common protocols that ensure the passage of information through common channels. However, within certain groups of participants (for example, within corporate networks) there is an urgent need to deliver information to specific consumers, without allowing access to “foreign” participants. Chaotic coding methods are a convenient means of organizing such virtual corporate networks. In addition, they can be used directly to ensure a certain level of information confidentiality, moving into the field of traditional cryptography.
Finally, another function of chaotic coding is very relevant in connection with the development of e-commerce and the aggravation of the problem of copyright on the Internet. This especially applies to online sales of multimedia products (music, video, digital photography, etc.). Based on deterministic chaos, it is possible to provide such a way to protect copyrights and intellectual property rights as reducing the quality of an information product when publicly available. For example, music tracks encoded using chaos will be distributed on the network without any restrictions, so that every user can use them. However, when listening without a dedicated decoder, the sound quality will be poor. What is the point of this approach? The disseminated information remains open and is not subject to restrictions imposed by the use of cryptographic protection methods. In addition, the potential buyer has the opportunity to familiarize himself with the product, and only then decide whether to purchase its high-quality version.
It should be noted that the above functions of chaotic coding do not exhaust the potential possibilities of its application in modern information technologies. In the course of further study and development of this issue, apparently, new facets and promising areas of use may open up.
Thus, the use of dynamic chaos and fractals in information technology is not exotic, as it might have seemed just a few years ago, but a natural way to develop new approaches to creating systems that operate effectively in a changing environment.
Since society is a super-complex self-organizing dissipative system, the general laws of the evolution of such systems operate in its history - but act in a specific form.
In any dissipative system, two oppositely directed processes occur: one (entropic) leads to the destruction of its structure, disorder and chaos, and the other (anti-entropic) leads to the structuring of the system, an increase in its order. Thus, order arises and exists in conjunction with chaos (both in the external environment and within the system). The relationship between chaos and order is a necessary condition for the existence of dissipative systems.
Self-organization is the result of the synthesis of chaos and order. In a self-organizing system they do not exclude, but, on the contrary, generate and complement each other. Chaos arises from order, and order from chaos. In this case, the birth of order from chaos and chaos from order is determined not by the external environment, but by the internal nature of the dissipative system and the mechanisms operating in it.
The chaos that arises as a result of the destruction of order is “deterministic chaos.” It is caused by those processes that destroy order. It turns out that chaos can be different - depending on how it is formed. Order emerging from chaos also bears the mark of its origin. Chaos, no matter how strange it may seem, is constructive in its very destructiveness: it “burns out” all unnecessary structural formations - non-viable, unstable, not integrated into the overall structure of the system. Chaos, therefore, has the ability to give birth to order. He is not an absolute evil, but an important aspect of the processes of self-organization.
“Order is inseparable from chaos. And chaos sometimes appears as super-complex orderliness.”
Order and chaos in a dissipative system constantly accompany each other, but their ratio changes during the evolution of the dissipative system. At some stages order prevails, at others - chaos. Extreme cases are a state of maximum stability, when a stable order reigns in the system, and disorder is reduced to a minimum, and a state of instability, instability, in which chaos quickly increases, and order decreases and can collapse under the influence of the slightest chance. Various modes of system transitions from one state to another are possible.
Considering society as a highly complex dissipative system, social synergetics aims to explore the specifics of its self-organization and the peculiarities of the relationship between social order and social chaos.
A society in which there is no order cannot exist. An unorganized, uncontrollable society in which chaos reigns is doomed to destruction if it does not come out of this state. Living in it is dangerous, and people almost instinctively fear such a life.
T. Hobbes believed that people, realizing the impossibility of living in conditions of complete chaos, when there is a “war of all against all” (omnia bella contra omnes), conclude a “social contract”, according to which they agree to recognize the power of the state over themselves, provided that it will establish law and order in society.
“Lawlessness,” the lack of norms and rules governing people’s behavior, is scary even for hardened criminals; rejecting the authority of the state and the social order established by it, they consider it necessary to have their own “thieves’ law” and their own “authorities.”
But there cannot be a society in which there would be “absolute order” that does not allow any “unauthorized” actions of people. Such a society would become a mechanical system in which individuals and groups would be deprived of all freedom of action. This means that their behavior would become completely algorithmic. In such a society, not only free will, but also reason, in essence, turns out to be redundant, unnecessary and even harmful from the point of view of protecting public order. This mechanical system, strictly speaking, would no longer be human society. In addition, it would be unable to respond to changes in the external environment and would “break down” either under their influence or due to the “failure” of some of its “cogs”.
Real societies always lie somewhere between these extreme states of “absolute order” and “absolute chaos.” The “historical pendulum” oscillates within the interval separating these states, never reaching its extreme points. But, moving in one direction, it “asymptotically brings” society closer to states of total order, and in the other - to states of monstrous disorder, lawlessness and general chaos. These fluctuations are accompanied by a pulsation of processes of various types: differentiation - integration, hierarchization - dehierarchization, divergence (increasing diversity) - convergence (decreasing it), weakening - strengthening, etc.
It is known from history that there were (and still exist) societies with a harsh despotic regime and severe suppression of all dissent and liberties. Such societies are characterized by the dominance of order over chaos. Societies of this type are called “closed” (A. Bergson, K. Popper), as well as “traditional”, “totalitarian”, “collectivistic” (K. Popper), “mega-tires” (L. Mumford). They are characterized by strict adherence to established traditions, “excessive normativity” of culture, petty regulation of all forms of human life, disapproval of all kinds of creative innovations, hostility to everything foreign, and the desire for self-isolation from neighboring societies. The consequence of all this is their stagnant nature.
Bergson defines a closed society with a succinct formula: “authority, hierarchy, immobility.” According to Popper, closed societies are dominated by a magical worldview, taboos, authority and tradition.
Such features were typical of a primitive community, where strict discipline was maintained mainly by the force of tradition and belief. These features were also inherent in ancient states formed in the post-primitive era, with the difference that strict adherence by citizens to the social order established by the state was ensured by the power of totalitarian power, capable of dealing with the disobedient by force. Such were the states in Ancient Egypt and China, Ancient Babylon and Assyria, the Inca and Aztec empires, etc.
A social order based on an oppressive totalitarian regime has been the ideal of the “powers that be” throughout history. And they sought to establish it in various forms. In the 20th century it was embodied in fascist states and in states of the Soviet-socialist type. Now he continues to live in countries such as Iraq, Iran, and Taliban Afghanistan.
At the same time, history knows states of society close to complete social chaos. These are “eras of storms and upheavals” associated with mass movements, riots, uprisings, and revolutions. Such conditions are characterized by social unrest, the collapse of political structures, economic ruin, impoverishment, hunger, civil strife, violence and mass bloodshed. Chaos sometimes reaches such a degree that society falls apart and disappears.
The described opposite states of society - the state of “closedness”, in which despotic power dominates, and the state of social chaos - are asymmetrical in relation to time. The first contains a tendency towards stable existence and is capable of persisting over a long historical time. This becomes possible thanks to the formation in society of a hierarchy of fractal structures that repeat the same “pattern” of power at all levels. Fractality makes such a society stable (if it is not fractal, that is, it does not include self-similar structures, then it is unstable and does not exist historically for long - as was the case, for example, with the empire of Alexander the Great). The second state cannot exist for long, because in it the hierarchy of social structures is broken and fractality is destroyed. Society strives to get out of this state by restoring social order.
But both of these states are interconnected and give rise to each other. A stagnant totalitarian regime holds back the emerging social changes as long as it is able to do so. Only the fire of social cataclysms can “burn out” its frozen and incapable of improvement social structures. The new is forced to be born in this fire - otherwise it cannot be born in a closed society. But chaos in society is a difficult test for people. It is not for nothing that in China one of the most terrible curses is considered to be: “May you live in an era of change!” The time of change is an intermediate time that ends with the establishment of a new order (even if, as it most often turns out, it is far from what it was seen by the people who started the troubles, and again becomes totalitarian).
In the historical past of mankind, there were many closed societies that existed for more or less a long time, which from time to time exploded with brief outbreaks of social cataclysms and chaos, after which a stable order characteristic of a closed society was re-established.
However, along with this, in the past there were also relatively rare cases of the emergence of more harmonious social systems, in which flexible forms of social order were formed, associated with democracy and allowing relative freedom of thinking and behavior of people. These are, for example, ancient Greek city-states such as Athens or medieval city-republics. The Renaissance era undermines the foundations on which the closed type of society is based. Utopian socialists challenge the state, which guards social inequality and injustice. The Age of Enlightenment (18th century) introduced the ideals of “freedom, equality, fraternity” into public consciousness. In the 19th century in Western Europe, harsh regimes of despotic power are increasingly giving way to republican-democratic forms of state. And in the 20th century. The most prosperous countries are those that develop a society built on democratic principles and civil liberties. Such a society, as opposed to a closed one, is called an “open” society.
In an open society, the hierarchy of power structures is placed (to a greater or lesser extent) under the control of the population. The legal system ensures peaceful competition among various political forces in the struggle for power. The election and rotation of government representatives makes power structures more mobile and accessible to renewal. This allows us to improve social order, avoiding destructive social cataclysms and without plunging society into complete chaos. In other words, an open society synthesizes order and chaos, discipline and freedom. And, moreover, in such a way that they seem to mutually prevent the achievement of extreme degrees of both. In society there is a “constantly operating” chaos (freedom), but maintained in certain forms, the local strengthening of which leads to the destruction of individual non-viable social structures while maintaining social order as a whole.
In modern open societies, there are many different voluntary organizations of citizens (communities, foundations, clubs, etc.), which they create on their own initiative, and not on orders from above. The free, unregulated and uncoordinated activity of many such organizations, it would seem, should lead to the disorganization of society. However, in fact, on the contrary, it contributes to the preservation of social order: these organizations are heterogeneous and different in scale fractal structures that harmonize and stabilize society.
An open society is characterized by social mobility, the possibility of moving through levels of the social hierarchy depending on personal achievements and merits, the absence of strict regulation of people’s behavior “from above”, pluralism of opinions, and recognition of the individual’s right to free development. All this stimulates activity, personal initiative and the search for original innovations that can provide more successful solutions to problems of interest to individual social groups and society as a whole. This results in a high rate of its development.
An open society is “a society in which individuals are forced to make decisions.” Expanding opportunities for individual freedom of action increases the chaos of society at the micro level (at the level of individuals) while maintaining the stability of its orderliness at the macro level (at the level of large social structures). Finally, an important feature of an open society is that, in contrast to a closed one, it is open to external contacts and interaction with neighboring societies. If a closed society is “introverted,” then an open society is “extroverted.” Moreover, it cannot develop without exchanging resources with the outside world, without involving other societies in the orbit of its interests and in the process of solving its problems.
This explains the fact that the emergence and development of open societies is accompanied by active - and often aggressive - economic, political and cultural expansion into other countries. The history of the British Empire is a vivid example of such expansion. The experience of history shows that closed societies cannot withstand the onslaught of open ones. Their resistance to this onslaught continues, but perhaps the 20th century. was the last century in which major closed world powers emerged and lasted for several decades - Nazi Germany and the Soviet Union. It can be noted that after their fall, Western-style civilization began to more intelligently implement the principles of an open society, and public opinion in Western countries began to more resolutely defend the need for peaceful development. Along with the spread of the economic, political and cultural influence of open societies, the desire to assimilate the experience accumulated in other societies has intensified.
The creation of open societies necessarily generates a tendency towards globalization of the historical development of mankind. In the second half of the 20th century. this trend led to general cultural exchange, the formation of a global economic market, and the emergence of a single political field for interaction between all states of the Earth.
In the light of what has been said, it is obvious that the development of an open society is not just a fact of the internal history of an individual people, but a turning point in the history of all mankind.
“The transition from a closed society to an open one can be described as one of the most profound revolutions that humanity has gone through.”
Of course, closed and open societies are not separated from each other by a Chinese wall. History knows many intermediate options that carry the features of both types of society. We are talking only about a long historical era, during which, through various intermediate forms, the transformation of open society into the main type of social systems occurs.
With the establishment and spread of open societies, the “amplitude” of oscillations of the “historical pendulum” decreases. Humanity shows a desire - and finds means of its implementation - not to bring these fluctuations to the extreme states of a closed society and social chaos.
However, the “pendulum-like” course of historical processes continues, leading to a cyclical alternation of periods of a relatively stable, ordered state and “times of change,” disturbance, and instability. These “waves of history” in an open society become less stormy, but it “sways” in them, experiencing alternating periods of evolution and periods of crisis in some particular sphere of social life or society as a whole. During periods of evolution, a regime of more or less smooth, orderly, “laminar” flow of events is established, and during periods of crisis, a “turbulent,” unstable, more or less chaotic flow of unpredictable changes arises.
Order and chaos
Today we will talk about chaos and order. All over the world, in all ancient religions and views, there was an explanation for such a thing as chaos.
For example, in Hesiod’s “Theogony” we see that chaos gave birth to all the gods, that is, all the Greek deities known to us come from chaos - from the thunderer Zeus to Hecatoncheires, who have many forms.
In China, chaos was depicted in the form of a circle or an egg, from which everything arises - it arises from the emptiness of this circle, from a circle, or rather, even from a jade ring, which you have seen many times in museums.
Ancient India speaks of great cycles of chaos - Pralayas or Maha-Pralayas. During Maha-Pralaya, life sleeps, everything sleeps, and, according to ancient books, there is no sea, no earth, no starry sky. More ancient Tibetan texts, such as the Book of Dzyan, created before Buddha, say the same thing. In the beginning nothing existed, everything was in a state of waiting; two primary causes, as a kind of first couple, conceive everything: Prakriti, or Mulaprakriti (primary matter), and Purusha (spirit).
We also encounter chaos in Jewish Kabbalah, where it speaks of Adam Kadmon - not about Adam and Eve, but about the first Adam, Adam Kadmon, the first who arises from Chaos; in Sefer Yetzirah, Kether, the Crown, is also born first, as the initiator, the cause of everything manifested - Malkuth and Shekinah.
In the minds of the inhabitants of ancient Sumer, Babylon and all the peoples who inhabited the eastern mountains and the region between the Tigris and Euphrates, chaos is some huge object or large diorite stone that arose from black, unknown waters, and these waters cannot be defined.
You also know that in the biblical Old Testament, which Christians borrowed from the Jews, it is said that in the beginning there was nothing, and God created the earth and the heavens.
Even the peoples of pre-Columbian America, a little exotic and little-known to us, both the Popol Vuh and the Chilam Balam also mention chaos as the source of all things; in all the books and codes that have reached us, chaos is described as the opposite of the cosmos, that is, the order that must arise.
You also know that, according to Plato, chaos precedes every manifestation. Following him come pure, abstract and absolute archetypes, they gradually, step by step, descend into matter until they create the Universe and man. This idea will be repeated by Plotinus and Marcion in the Neoplatonic doctrine of Macrocosm and microcosm: Macrocosm, the Universe, arises from chaos and gives rise to microcosm - small life, or man, the image and reflection of the Universe.
Similar views existed even among the North American Algonquins: Manitou, the god of lightning and the sky, appeared from a dark starless night or from the mouth of a wolf.
The concept of chaos is also found among the peoples of Northern Europe. In Germanic mythology and the Scandinavians, chaos is the beginning of all things. They tried to give it some kind of image, but it is difficult to give an image to something that is unimaginable, to describe something that cannot be described, and therefore they call it Gimnungagap. It is something like a vast frozen abyss where everything exists in potential and not in reality; it is a bottomless abyss full of frozen dust with a block of ice in the very center. This lump is licked by a creature resembling a cow, licked until it gives shape to the primary elements that must be embodied.
Even today in English villages they talk about Humpty Dumpty - a character whose head, colliding with a wall, breaks into a thousand pieces, and from these pieces gnomes and many other fairy-tale creatures are then born. The same thing happens with the Hindu deity Padma Pani, whose white head scatters into many colors and shades that balance the universe.
So, we see that all peoples at all times and all over the Earth asked themselves the most important question that worries us today: what is chaos, what is order, what can we learn about them, how important is this for us? how to apply this in life?
We, ladies and gentlemen, live in special times. Why? The point is not only in the crisis of our system, but also in the fact that cosmically, that is, according to astrology, in 1950 we entered the Age of Aquarius. Aquarius, water, the alkahest of alchemists, the universal solvent - this is what brings chaos with it. I would like to clarify that these astrological connections have nothing to do with the articles in the newspapers where they write: “Libras better not leave the house today - something bad might happen. Virgo is in for a pleasant surprise or good luck in love.” No, absolutely nothing in common. I'm talking about ancient astrology, I'm talking completely seriously and from a scientific point of view. It’s not news to you that the human body, for example, mostly consists of water - liquids, fluid substances; in a sense, physically we are an “unstable colloid,” and all unstable colloids are affected by magnetic fields. Since celestial bodies are huge polarized magnetic masses, it is obvious that the position of celestial bodies can affect us both physically and mentally. It is also obvious that the cosmic rays penetrating into us at the moment - not all of them, because some are absorbed when colliding with different objects - reach not only each individual, but all of us together. And we are seeing a kind of gradual change in individual consciousness, and therefore in the collective consciousness of humanity.
They are not that easy to detect. This happens sometimes in life. Let's say, while shaving in front of the mirror, I suddenly peer into the reflection and exclaim: “Who is this fifty-year-old fat man?” And it turns out that this old fat man is me! What happened? It’s just that time has passed, and the one who considered himself a young guy suddenly realizes that he is no longer a young man. A child whom we have not seen for three or four years appears before us already dressed like an adult, and we exclaim: “How you have grown! You are already quite big, a real man!” But he grew up simply because time passed. The thing is that time flows so slowly that we hardly notice it. Time flows so slowly that we can catch its movement only with the help of the science that is so necessary for us all - History. After all, if we look at our photographs from twenty years ago, we will see that now we are completely different. And in the same way, if we, calling on history for help, return in our thoughts and consciousness through time and see what happened in Greece, Rome, during the Middle Ages, etc., then we will understand how humanity has changed over time . We are talking not only about physical change, but also about psychological and spiritual ones.
So, the era of Aquarius is in full swing, an era in which chaos rules. In other words, today everything is more or less in a state of chaos. But before I rush to talk about this, I would like to give a precise definition of some words, otherwise we will not understand each other. One of the features of this more or less chaotic stage is that words can be used in different meanings, including completely opposite to the original ones. This is the crisis of our language, the crisis of our speech: we very often cannot understand each other correctly; Even different generations, speaking the same language, use different expressions and do not come to mutual understanding.
Firstly, it should be noted that people usually associate the concept of chaos with freedom and say: “No, we don’t want order! Give us such freedom that everyone can do what they want!” But if “everyone does what he wants,” this is not freedom. Since none of us are Buddhas and are not absolutely free, since we are not able to do what we want, we have to do what we can and what our instincts, fears and limitations allow us. And this is the truth. A truth that we sometimes refuse to accept, but which I must convey to you, because as a philosopher I am obliged to tell the truth. Like you and I, we are not free, because we have not freed ourselves from a huge number of restrictions, which, I think, are not necessary to list, but with which we cannot be free. We are ready to take seriously the one who said: “Stop the Earth, I want to get off!” But this is pointless: we can hit the Earth a thousand times, but it will not stop and we will not be able to “get off.” And we not only cannot go beyond the boundaries of planet Earth, sometimes we cannot go beyond family problems, political traditions, the economic situation, we cannot, for example, change our gender and age. Each of us has our own limitations - some understand something better, some worse, some perceive it one way, others another. Someone will take pity on a stray dog and take it in their arms, and someone, perhaps, will give it a kick. It depends on our internal reaction, on the kindness of our hearts, or on what we associate with the image of a dog.
Then the first thing we must do is stop identifying chaos with freedom. Freedom is not in chaos, freedom is in order. Of course, you know how graphite - the lead of a pencil - differs from diamond. Both are made of carbon, both are exactly the same, but in graphite the molecules are arranged absolutely chaotically, in other words, they have no rhythm, and therefore do not transmit light. Thanks to this, you can write with graphite: graphite breaks easily, and if you run it over paper, particles of it will remain on it. However, run a diamond across the paper and you will see that it will cut it. Because diamond has order, a system, its molecules are built in such a way that light and force pass through them, its molecules are assembled together very tightly, and as much as order reigns in the structure of diamond, chaos reigns in the structure of graphite.
On the other hand, everything related to order is today identified exclusively with transnational companies or military structures. But let's ask ourselves: why are they so collected? There may be business executives or military men among you, but for the rest of you, I declare that businessmen and military men love order so much because they want to enter the market with their products or win a battle. They know that a disorganized person will not sell his goods and will not win the war. And one more thing: who is called to help during a major disaster, a large forest fire, if climbers are lost in the mountains or when a ship is wrecked? Military. The names are not hippies, but military ones. Why? Because they are trained and can really help. So, we must understand that in this sense, order allows us to create a whole theory of life: by maintaining order, a person does not lose his freedom, but, on the contrary, gains it.
Nowadays, many praise disorder, anarchy - everything that destroys and divides. But if we really decided to return to nature, if we are aware of the crisis of our system, let us, dear friends, ask ourselves the simplest questions. Let's assume that we all recognize the human right to strike. Wonderful. I know that the right to strike is a very controversial issue, so we will not discuss it today. Of course, a strike has certain reasons: social injustice, rising prices, pressure from different sectors of society, etc., but let us now calmly ask ourselves: would we allow our hearts to go on strike at this moment? No. Why? Because a heart strike is called cardiac arrest and means death. Would we give our lungs the right to refuse to perform their functions? No, because it means you stop breathing. Would young people like a long-term sex strike? Of course not.
We all value what we have from nature, and we don’t want to spoil it. We want our eyebrows to be above our eyes, not below them, our teeth to be in our mouths, and our fingers to be on our hands. What can I do with the fingers growing on the back of my head? Just scratch your head. That is, we need everything to be in its place. My whole body, the body of each of you, the body of any person is the best example of the embodiment of order and a harmonious system. The one who created the body is very intelligent (although some say that it arose by itself - a brilliant statement!). We don't just have arteries, veins, and nerves—our arterial, venous, and nervous systems are so intricately intertwined that sometimes they use the same hole in the bone tissue to pass through bone. A good surgeon does the same. Do you think a good surgeon comes to a patient and says: “Well, fat man, where should we start the operation?” No, a good surgeon knows—that’s why he performs the operation—where to make the first incision in order to get to the sore spot, to the tumor, to the damaged organ. After the operation, he will sew up the incision and “fix” it to return the patient to its original state.
If we applied these simple principles that we apply in everyday life and that the doctor uses in medical practice (after all, the question of life worries everyone), we would understand how important it is to overcome our stage of chaos and achieve order. My friends, order is not something harsh, rigid, frozen. Often, when talking about order, we immediately imagine a man with a whip, usually in uniform, and the unfortunate people who obediently wander next to him. No, this is not order. Have you seen birds flying? How do bustards, geese, and other large birds fly - randomly or in an organized manner? Definitely organized. And if the small particles of snow did not gather together, they would not be able to fall to the ground. There is order in both mountains and rivers. In nature, everything is balanced, which once again proves to us the importance of this system of order, a deep, fundamental order, and not from scary stories about people in uniform. No, the order is not wearing boots or wearing shoes. This is something much deeper. Man is essentially physically ordered, psychologically he has yet to become so, and spiritually he is an archetype, a spark of the order that reigns in nature.
Now, in the Age of Aquarius, when the forces of water, dissolving and dispersing, prevail, it is worth thinking about how to be organized. How to achieve order? How to apply what we just talked about? Whether you like these ideas or not, can they be put into practice? Yes, you can. The simple fact is that the current disunity, alienation and general chaos make their use very difficult.
We are generally very disorganized, we prefer chaos, and even the connection between our mind and body is not strong enough. Sometimes we do something physical, like frying eggs, and at the same time we think about the article we have to write, about poetry, about whatever. And later, when we sit down to write an article, we are haunted by the image of fried eggs. We must overcome this internal division. I'm talking to you now, but I could, for example, sit down and start playing chess. Of course, this would be simply stupid on my part, and it would be disrespectful to everyone who took the time to come listen to me today. Firstly, I would lose the game, because I can’t play and talk at the same time, and secondly, you wouldn’t understand anything either, because I would constantly be calculating moves and thinking about whether to move with a bishop or a pawn. In other words, you cannot do several things at the same time. More than a thousand years ago, Muhammad said: “It is impossible to mount two camels at once.”
There is also no order in the way we eat: most often we do not sit down at the table, but have a snack on the go so as not to waste precious time. The “fast food” system in the form of a division into everyday and holiday menus has become firmly established in our everyday life: we usually eat almost standing, and when guests come to us, we cook only to sit at the table together. It seems to us that sitting at the table is the privilege of Etruscan princes. We don’t even notice how we are gradually limiting ourselves in everything. Have you heard about music salons in 19th century houses? Yes, at that time a music salon with a piano was a very common occurrence. What about today? Alas, today we listen to the radio, tape recorder, recordings performed by others, but have forgotten how to do anything ourselves. We can't sit down at the piano and play or sing for our friends. We can only listen to songs sung by someone else, and in our chaos this turns into real slavery. The same applies not only to nutrition, but also to many other things.
Agree, a completely absurd form of “social pressure” is a strike by railway workers. Tell me, please, who suffers from them? Millionaires who can rent a plane, wealthy people who have a car, or poor people who can only travel by train? The answer is obvious. Of course, many things have gone out of fashion today, many things have become a thing of the past, many things we do not know at all, and in conditions of chaos we put up with such methods, and sometimes even support them, instead of overcoming them.
How to overcome? Individually - starting with getting to know myself, learning to distinguish where my physical, mental, emotional and mental part begins and ends. Where am I, who am I? What I can? Which abilities have already been developed and which ones have not yet been demonstrated? Can I play the piano, can I paint pictures, sculpt statues, or can I simply read, walk, play football - what am I good for? What are you mentally capable of? Can I carry on the conversation? Can I not respond with animal rudeness to insults? Am I capable of real, sincere feelings, can I not be a hypocrite? Can I comprehend pure and sublime ideas with my mind, since my mind does not always resort to all sorts of tricks for its own benefit? This self-knowledge allows us to be truly free. And if we know ourselves, together we will create a more just society, where there will be less war and violence. Many times from this small philosophical platform in the “New Acropolis” it was said: humanity will be saved from troubles not by abstruse formulas and theories, not by models of a probable future; it will overcome all difficulties and move on only thanks to its own strength and real actions. And only so. We won't make the world a better place with slogans on walls. First, we must become better ourselves and try to infect our relatives, friends, co-workers, classmates with our example, and therefore make a real discovery, meeting our Self again, rediscovering the inner, spiritual power of a person, because this power cannot be shackled.
You can bind a person’s hands and feet, but not his soul, not his spirit. The soul, spirit, imagination, fantasy are higher than any prison, any chains, restrictions, illnesses, higher than age and distances. We must develop inner strength that will allow us to live again in harmony with nature, because we need to return to nature, but not by the methods of modern environmental organizations - banning hikes and tearing down flags; no, this does not mean returning to nature, this means returning to the stone age.
To return to nature means to start living naturally again, to dare to live naturally. If you paint a picture, paint what you feel in your heart, don’t ask yourself whether it will come out in the style of cubism or pointillism - let what really is in you or what you see around appear. If you need to express an opinion about politics, do not limit yourself to what you have already heard from others, try to understand what “politics” is (from the word “polis”, “city”, that is, population management) and what a politician should receive for salary - not because he talks nonsense, but because he serves the people. Let's decide how we should raise our children, because, if I'm not mistaken, there is still a debate about whether education is compulsory, whether children can be exposed to pornography, allowed to be capricious and rude to parents or teachers. And this is what we are arguing about? Have we really fallen so low that we still doubt whether it is worth getting an education, whether it is possible to be rude to our elders or those who teach us?
We should in no way allow this to happen, we are categorically against it, our spirit rebels, flares up like a torch, and calls out to us: “No, it shouldn’t be like this, even in the era of Aquarius, even if all the waters of the world surround us!” They say that once there was a flood, and Noah’s Ark was created, on which animals and birds were saved. Don’t we ourselves want to be saved from these waters, will we give up our opinion based on a higher power, on a higher order - natural, natural, and not imposed by someone? According to this order, amoebas live in water, a person stands on his feet, not on his head, and the stars rotate in the sky in a tiny spiral - tiny to us, but actually huge. Thanks to this force, trees grow, day turns into night, summer into winter; this is the magical force that created women and men - this is how love was born, this is how children are born, this is how houses and new things appear, this is how everything that we love is created and what we must carry through the era of decay, through the era of Aquarius.
And we, as philosophers, declare that it is necessary to defeat this chaos with a new order, an order that will create a new person - this is what we need, and this is not a symbol or an abstraction. Symbols alone are not enough, symbols only capture ideas, but a person is needed to revive them, proclaim them, write them down, embody them in stone and live them day after day. In other words, we must live in harmony with nature, and not resist it; we must be a continuation of our ancestors and a model of the man of the future. And let those who give lectures have students, and not just students who are capable of throwing tomatoes at the teacher on occasion. Let young people remember that someday they will grow old and will need young listeners; Let the old people remember: youth is a matter not only of epithelial cells, but of the inner world, the heart. This is the Golden Aphrodite of the Greeks, personifying the strength of spirit, youth, the strength that we talk about in this room and freely choose: the strength of man and faith in God. Why, dear friends, are we today ashamed to say that we believe in God, but we are not ashamed to say all sorts of nonsense? Today people are embarrassed to write on the wall: “I believe in God,” but without a twinge of conscience they write on the doors of institutions: “You are a fool!” The world has gone a little crazy, and it is clear that the insane cannot be punished or feared - they must be treated.
Therefore, we should all become like Asclepius - the god of medicine, healer of souls (this is what a philosopher is!). Everyone in his place, among friends or among strangers, among men, women, children or old people, can become a beacon, an unshakable support in the midst of storms and waters. I would like you to remember these words, full of hope and inner strength. I urge everyone: overcome yourself, withstand all possible and impossible tests, maintain the harmony of your pure soul in order to defeat the dark forces of chaos.
Jorge Angel Livraga, founder of the New Acropolis school of philosophy
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