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But what about at the other end of complexity, at the tip of the ray of Thermodynamics? In a completely different way, but clarity and unambiguity also disappear. The foundation of physics – the measurability of the properties of objects, disappears with increasing complexity. The trouble is that if more and more complex systems are included in the consideration, the concepts of temperature, entropy, and energy for them lose their rigor. It is impossible to measure or mathematically describe such parameters for society or for an organization. The basic concepts of thermodynamics – energy, entropy, temperature – turn out to be only metaphors in the world of people. Physics, as you move up the scale of complexity, disappears as an exact science. It seems that the tips of both divergent beams blur in a haze of fundamental uncertainty.
And in this haze, our hopes for help from physics in the world of business problems dissolve?
And that’s not all – washes his hands and the instrument of physical knowledge – Her Majesty Mathematics!
Even where equations for the behavior of complex systems are still being written, they turn out to be nonlinear. In such complex systems and their models, everything depends on everything! Dependencies are sometimes contradictory: it is good for predators in the forest if there are many small animals around – their food supply. Predators multiply, and… and destroy their food supply. The population of predators begins to decline sharply.
Solutions of non-linear equations lose their stability at certain points, which means that they become ambiguous. Such points on the mathematical trajectories of mathematics are called bifurcations.
«The bifurcation point is a critical state of the system, at which the system becomes unstable and uncertainty arises: whether the state of the system will become chaotic or whether it will move to a new, more differentiated and high level of order. A term from the theory of self-organization.»
The number of both predators and their prey can fluctuate, and under certain conditions one or both populations can end their existence catastrophically.
How to «feel» this very bifurcation? Play with it, look at this strange self-organization. This, it turns out, is not difficult – there are a lot of bifurcations with us and around us!
Fig. 3. Expected behavior of an elastic object
It is unlikely that in today’s computer world someone uses an eraser – an elastic band to erase what is written with a pencil or pen. Maybe you remember this subject from school? Such a small brick of gum, which was fun to play with, squeezing it with your fingers. And now, let’s extract science from such an» anti-stress» of our childhood.
Squeezing the elastic between the fingers, we make it shorter. We compress even more – we deform the elastic bar even more.
But at some point, the elastic band suddenly refuses to compress further and bends to the side. Squeezing and unclenching our fingers, we repeatedly reach this point, when the behavior of a simple elastic object changes qualitatively. And each time in a different way: once the deflection will be in one direction, and once in the other.
Fig. 4. Buckling – the real behavior of an elastic object
We will not write the equation, as we promised, but we will only say that it has a unique solution only up to a certain compression. And at this critical point, the solution loses stability. If we imagine that we have an absolutely perfect bar of gum inside and out, and we press our fingers strictly along its longitudinal axis, the gum will continue to shrink without bulging. But this will already be an unstable segment of solutions. Just as a ball can, in principle, stick to the top of a convex surface, but only in an absolutely ideal case.
If you «move» your finger at least a little bit – physically, or the homogeneity parameter of our rubber band – mathematically, the solution of the equilibrium equation will immediately rush to another, stable state. But! Now there are two possible stable states in the solution – the deflection is either «to the right» or «to the left», and which one our object will fall into depends on those very random, literally microscopic «movements».
That is, the point is not that we do not know how to count, but that mathematics fundamentally cannot give an unambiguous solution. On the contrary, mathematics proves that now there can be no uniqueness! Moreover, if we took not a rubber block, but a rubber cylinder, we would get not two possible positions after the deflection, but an infinite number – any direction in a circle.
Fig. 5. The condition of the gum under pressure. Pitchfork bifurcation
To sum up, in what state the system will pass, hitting the critical point, mathematicians cannot unambiguously calculate – the solutions become unstable with respect to fluctuations. This means that there are solutions to the equations, but there can be many of them. And even infinitely many. What solution is implemented in practice depends on infinitesimal deviations in parameters that occur only in the real world, more precisely, in the microcosm, and which a person and, therefore, mathematics can never know. These are such small movements, such small inhomogeneities of the gum material, that it is impossible to measure, plan, or take into account in advance. Such small deviations are fluctuations. To calculate the exact state of a complex system in the future, it is necessary to know a huge number of initial conditions onshore, which will never be known to anyone. And someone who, and business is definitely a system with an infinite amount of uncertainty.
Qualitative Considerations
So it looks like we’re left with nothing?
However, let’s listen to the greats. It seems that not everything is so hopeless!
The mathematics of describing nonlinear effects is highly non-trivial. But, as Academician V. I. Arnold (1937—2010), one of the greatest mathematicians of the 20th century, said:
«These objective laws of the functioning of nonlinear systems cannot be ignored. Only the simplest qualitative conclusions have been formulated above. The theory also provides quantitative models, but qualitative conclusions seem to be more important and at the same time more reliable: they depend little on the details of the functioning of the system, the structure of which and the numerical parameters may not be well known.»
Henri Poincaré (1854—1912), «the last of the great universal mathematicians,» also said that only a limited amount of qualitative information is needed to understand qualitative changes in the behavior of systems.
So there are no formulas. They are useless. But there is good news! It turns out that it is important not to calculate the exact trajectory of changes, but to be ready for the phenomenon – for the critical point and for the qualitative transition that will follow. Actually, this is what we do in the morning when we boil water for tea. We do not calculate or measure anything, we just wait for the moment of a qualitative transition – we wait for the water to boil. And this is enough for us to understand that the moment has come, you can make tea.
Let’s return to our elastic band, to our manual bifurcation. When we squeezed it and got a deflection, we can play with it further, for example, try to put pressure on the bulge.
Fig. 6. Longitudinal and transverse action on an elastic object
Our «antistress» with a certain effort will begin to flip in the opposite direction. If we draw a set of solutions to the equation in the parameter space: Deflection / Longitudinal pressure / Transverse pressure, then we will find a funny surface in it, similar to the assembly of a fabric. This surface is in a section of mathematics called Catastrophe Theory and is called Cusp catastrophe.
On this decision surface, we will see the buckling path under longitudinal pressure, which we have already seen in Fig. 5. To do this, it is enough to cut our Assembly with a vertical plane, for which the transverse pressure is equal to zero.
Fig. 7. Surface of the state of an elastic object. Buckling under longitudinal compression
The area of instability is represented by a triangular «tongue», indicated by a dotted line in the middle of the Cusp, where the system can get and stay in this state for some time, until any infinitely small impact throws it into one of the stability zones – a deflection in one direction or another.
We can also trace the trajectory of the state of the object under the influence of transverse pressure.
Fig. 8. Transverse route on the state surface. Memory effect
By itself, the understanding of a mathematical catastrophe, as a kind of map, a qualitative picture of the space of possible states, already allows us to understand a lot about the behavior of an object, to be prepared for surprises, and moreover, to use these properties. Despite the fact that our pictures of catastrophic behavior do not promise any quantitative accuracy, the operating point of the system, having fallen into the zone of instability, for example, does not know when and where it will leave it.
The transverse route – the transfer of such systems from one state to the opposite (the so-called hysteresis phenomenon) is used in many places, for example, in binary memory cells. And in order to use this memory, it turns out that it is necessary to control only one control parameter, which switches the cell.
Is a high-quality picture enough to expect and manage high-quality transitions in our systems, including business ones? We will see this below.
Beyond the boundaries
Beyond the boundaries of physics as an exact science, there are attempts to generalize the formation and self-organization of structures in open systems that are far from thermodynamic equilibrium. As conceived by its creator, Professor Hermann Haken, synergetics is an interdisciplinary direction that is called upon to play the role of a kind of metascience, noticing and studying the general nature of those patterns and dependencies that private sciences considered «their own».
«Synergetics (from other Greek prefixes «syn» with the meaning of compatibility and «ergon» – activity) – «together action».
«It should be emphasized that synergetics is by no means one of the frontier sciences such as physical chemistry or mathematical biology, emerging at the intersection of the two sciences.»
This is a fairly new area of science – there are still no clear boundaries, or even clear definitions of areas. The area of research in synergetics is not clearly defined and can hardly be limited, since its interests extend to all branches of natural science. A common feature is the consideration of the dynamics of any irreversible processes and the emergence of fundamental innovations.
Since there are no clear boundaries and definitions, there is an inevitable dispute in scientific and pseudo-scientific circles. Anyone is ready to declare himself a zealot of true metaknowledge, and to call everyone else pseudo-scientists, scholastics and charlatans.
I must say that this is a completely normal phenomenon for science. True Science differs from faith or ideology in that it itself calls into question all its achievements. Especially on the frontier of knowledge, that is, exactly where new knowledge about the self-organization of matter is being formed today.
Maybe our approach will be accused of being pseudo-scientific. Real academics are simply obliged to do this.
Truth, scientists say, is just the most appropriate concept to explain facts. I think this principle is good for business as well. Let’s test our theory with practice.
So, what do we get from the sciences at the start of the path? No strict laws, no numerical mathematical apparatus. The more complex and larger the system, the less numerical accuracy, the more qualitative considerations. Is this enough to put such knowledge into practice and apply it successfully?
Here we’ll see. What difference does it make whether it is physics or something else, as long as the conclusions work! That is, they would help us in business.
Chaos that creates
Progress
The evolution of matter today is already widely considered as part of a global synergetic process. And the emergence of life on the planet, and the origin of the mind, the evolution of conscious life – as part of the epic self-organization of matter.
The origin of life itself is still a big mystery. And we’re not going to solve it. But, since we live in this world, now we are concerned about another question – how to live? For us, it is only important that with the transition from inanimate nature to living nature, the essential feature of systems changes. Inanimate systems are passive systems. And self-organization arises only when the system is pumped with energy from outside. The water in the kettle starts to move (convection), and then boils just because we turned on the stove. Whirlwinds in the atmosphere – cyclones and tornadoes – are the result of its heating by the energy of the sun. If the energy supply is cut off, the systems will rush to an equilibrium state, any heterogeneity will sooner or later be resolved.
But living matter is a completely different matter, these are active systems. Which have their own behavior. And the behavior of living organisms is aimed at reaching the sources of energy necessary for life. Energies in a broad sense are both the heat of the sun for plants, and a nutrient medium, and other living beings that serve as food for a predator, and all kinds of resources necessary for a person to live.
With the transition of passive-to-active systems, the driving force of self-organization changes by 180 degrees. If for the passive it is an excess of energy, then for the active, the main reason is its lack, or, in other words, resource hunger. Indeed, living nature has the ability to reproduce, to produce its own kind. And, in combination with a purposeful movement towards the most favorable living conditions, this inevitably leads to the fact that living organisms, populations and societies always create redundancy. Which, in turn, causes intra- and interspecies struggle and, finally, competition. As a result, there is a resource hunger, which is characteristic of wildlife in all its manifestations. As the poet noted: «Sweet gingerbread is always not enough for everyone.»
This pressure of hunger forces any systems to undergo stages of self-organization, qualitative rebirth, it is hunger that constantly drives them to more and more complex levels of organization, increases disequilibrium. Both the development of life and the emergence of its intelligent form, followed by the evolution of social and economic forms, are precisely the most ambitious stages in the growth of complexity. And within these global stages, many subsystems are just as precisely involved in their struggle for survival and evolution: the origin and disappearance of species, populations, peoples, states… And of course, businesses!
Progress, therefore, is not at all an optimistic process of endless and unrestrained improvement of everything and everything. But only a chain of stages necessary for the survival of any active systems in the face of ever- increasing resource hunger. A chain of alternating stages of adaptation – adaptation, and bifurcation – rebirth.
The principle of minimum dissipation (scattering) of energy, as Academician of the Academy of Sciences of the USSR Nikita Nikolayevich Moiseev (1917—2000) suggested calling it the compass of global development in the world of active systems. In the chaos of competition and selection, the structures that make the most efficient use of fading resources win.
«Dissipation of energy is the transition of part of the energy of ordered processes into the energy of disordered processes, and ultimately into heat.»
Homo sapiens (reasonable man) as a biological species, unlike others, ceased to develop immediately upon its appearance. What’s the matter? Everything, the end of development? No, just with the emergence of consciousness, development was transferred to the area of the technosphere – to the area of creating a protective shell around itself, a «fur coat», the so-called «second nature». Machines, mechanisms, technologies – these are all tools that allow a reasonable person to exist more and more efficiently. And the very existence in terms of the creation and use of technology gives rise to the economy, special ways of managing the economy, trade,.. business, finally.
Thus, the global synergetic process is a series of continuous complication of currently existing systems:
• living beings have come a long way from the simplest organisms to very complex ones, to mammals, to «reasonable man» as a result;
• technologies born by a thinking being – man, are continuously becoming more complex from the simplest stone tools – to information technologies, space ships and biotechnologies;
• and the very ways of doing business, business models, are constantly becoming more complicated: a shop in the market – a small store – a supermarket – a trading network – e-commerce – a marketplace.
Evolution, revolution, turbulence
Let’s take a closer look at this continuous progress in all areas. What will we notice? We have already used the combination «sequence of complications». This implies the phenomenon of some transitions – rapid, in historical terms, almost instantaneous changes. The emergence of new qualities.
Indeed, progress is moving in leaps and bounds. Periods of calm change of some forms are replaced by moments of the emergence of others, new ones. Which can remove the former from the historical stage. How capitalist relations and states replaced feudal ones, leaving in some places the monarchs a purely decorative role. How internal combustion engines replaced steam engines. Airplanes have removed balloons and airships from the scene of serious transport. Mobile communications have taken landlines out of widespread use. The old taxi services in major cities have been largely superseded by services like Uber.
So, periods of evolution and periods of revolutions. Prolonged calm stages, and quick qualitative upheavals.
We are particularly interested in technological progress, as it always goes hand in hand with changes in business life. Progress is a constant process. And the technological revolution is a sharp leap in development.
«The scientific and technological revolution is a fundamental qualitative transformation of the productive forces, a qualitative leap in the structure and dynamics of the development of the productive forces.»
There are various ways to describe the history of leaps and bounds in technological change. Some speak of six technological revolutions in human history. Others are about the development chain: Industry 1.0, Industry 2.0, Industry 3.0, Industry 4.0.
Still others begin the history of high-quality technological transitions from the end of the Stone Age – from the Neolithic.
«The Neolithic revolution or neolithization is the transition of mankind from an appropriating economy
to a manufacturing economy, which includes agricultural sub-sectors (agriculture and animal husbandry), as well as handicrafts that stand out as a separate industry.
In any description of the chains, it is important for us to note the fact of a clear acceleration of the scientific and technological spiral of development. It turns out that each stage of calm evolution following the technological leap was about 2 times shorter than the previous one.
You can ask questions about the dates in Table 1 – most likely, they are simply adjusted to the doubling pace model, you can argue about the significance of certain scientific discoveries or inventions in history, but hardly anyone will dispute the very fact of accelerating scientific and technological progress.
Table 1. Acceleration of scientific and technological progress
And today we exist in an era of technological turbulence – it is no longer possible to talk about years or months between jumps – now they happen all the time: high-speed Internet in mobile communications, cloud computing, GPS, Internet of Things, artificial intelligence and drones, generative neural networks – these transitions fundamentally change capabilities of modern technologies and products based on them, and do it continuously.
The business sector has become just as turbulent. New technologies are continuously bringing new service delivery models to the fore. Free online trading to replace brokerage houses. Ordering through the application and delivery is a replacement for going to the store. Affordable taxi at the touch of a smartphone to change the search for a car on the street or order by phone. Traditional businesses are rapidly being replaced by new, more innovative, and usually more global ones. And often these new ones, not having time to earn the title of «traditional», give way to even newer and more modern ones.
The pace picks up sharply. Futurologists warn that over the next 10 years, humanity will have to go through as much change as it has experienced in a thousand past ones.
So what happens? What does this mean for us?
First. Progress was not at all an optimistic triumph of pure knowledge. But just a way to survive. A means of struggle, in particular, the struggle for markets, if we look at the economy.
Second. This requires the attention of any entrepreneur – progress in business, in business has become so rapid that no one can dream of building a quiet, solid family business. Pass it on to your children, who will pass it on to their grandchildren. On the contrary, you have to be prepared for the fact that any business you start will not be durable. That in your life you will have to do many different things, master different professions or start different business projects, develop different products. Only change is permanent.
Third. Progress, the process of global self-organization is not only the birth of new structures, but also the disappearance, death of the old ones. Any structure of human society, be it an ethnic group, a state, a technological order or a separate company, has its own moment of birth. But the moment of death is the same. No system is permanent. Companies, businesses are exactly the systems in which we are honored to work, or even these are our projects that we ourselves have created and are developing. Why are they mortal? How are they dead? Can I, with my business, get out of this «wheel of samsara» – an endless chain of deaths and births? (Spoiler – you won’t be able to get out, but you need to be able to transform, reinvent your affairs. Then rebirth will not be a mortal enemy, but your ally.)
Life cycle
The person lives. He is born, grows, grows old and dies. No one can escape the inexorable law of being. But that’s not all sadness. A person lives in a society of other people, works in a team, coexists with the state, belongs to some ethnic group. So, each system (family, firm, country, etc.) like an individual is also born, develops, withers and dies. Not only is our own age of life a burden that we can’t do anything about. Quite independently of our desire, we are born in a country with a thousand-year history, or vice versa, which appeared quite recently, we find ourselves in a company that, perhaps, is experiencing the age of youthful folly, or is an example of a wise old man. Although nothing can be done about it, it probably won’t hurt anyone to understand life in general and social systems in particular.
Let’s start from the description of ethnogenesis – the theory of L. N. Gumilyov, which he created while in prison in Stalin’s Norillag.
Gumilev Lev Nikolaevich (1912 – 1992) – the son of Nikolai Gumilev and Anna Akhmatova, poets of the «Silver Age», the author of the term «Silver Age of Russian Poetry», historian and geographer, author of the theory (more precisely, teaching) of ethnogenesis – that is, the origin and development large supranational communities.
Reading Gumilev, the chaos of historical events appears as a clear picture of the complex, but natural interaction of emerging and disappearing systems. Before the genius of Gumilev, a picture of a pattern opened up, which he tried to explain. To do this, he had, for example, to introduce the concept of «passionarity» – a sexually transmitted genetic trait that determines the active behavior of people, thanks to which large social systems are created and developed.
«Passionarity is a sign that arises as a result of a mutation (passionary impulse) and forms within a population a certain number of people with an increased craving for action. We will call such people passionaries.»
(L. N. Gumilev)
However, following this, we would have to admit that molecules with atoms in vortices of cyclones or in layers of boiling water should also be supplied with a similar genetic factor. When summarizing the theory under the global historical picture that opened up to him, L. N. Gumilev rearranged cause and effect. Quite the contrary: this social system objectively implements strict rules for selecting a certain behavior of individuals, its components – at different stages, different, and not «innate» qualities of the elements determine the state of the system. The fact is that social systems are the same open dissipative structures as, for example, atmospheric anti- and simple cyclones, whirlwinds of boiling water in a kettle, or vibration modes of atoms inside a laser.
Let us state Gumilev’s theory, shifting it to the modern synergetic representation, as we understand it:
Every system (including human) arises, exists and disappears. The entire course of the life of the system can be divided into six stages: rise, growth, fracture, blooming (aka inertial), convolution and memorial.
1) Let us imagine some human system, a structure that is in a stable state balanced with the external world (this is the Memorial Phase). Let’s make a reservation right away – in fact, any human structure, be it a people, and even more so a company, the external environment gives too few chances to live to equilibrium. Let us assume, however, that adversity has not yet touched this part of society. In this system, people live (for example, in some hidden corners – in the mountains, on the islands) according to custom, according to the covenant of the fathers, according to the order established by someone once and for all. They do not claim anything beyond what their familiar environment gives them.
2) The family, as usual, is not without its black sheep – there is always a certain number of passionate individuals who cannot or do not want to be like everyone else. The main mass does not perceive them otherwise as eccentrics, renegades or, worse, degenerates; and crushes them in all possible ways – both moral and physical. Due to this, deviations from «normal» behavior, from the generally recognized standard, usually exist at the level of barely noticeable deviations – fluctuations. But as soon as the original community is weakened – natural disasters are to blame, the economic crisis, or the invasion of aliens – «renegades», passionaries get a chance: they first form small companies, communities, which are later joined by fragments of obsolete systems. This is the beginning of the Rise Phase. First of all, in the embryo of a new structure, a clear self-consciousness arises that we are We, they are not at all those who are near and around. Those are strangers, enemies! A spontaneous, unconscious unity arises – the psychology of the pack: «one for all, and all for one.» The ideological dominant has not yet been worked out. The vigorous activity of passionaries causes the growth of a new system. This structure is active, it seeks to annex new territories, markets, areas of activity. The stereotype of behavior of the old system «be like everyone else, do as usual» is replaced by the imperative of Duty:
«You must be just like that for the sake of the Common Cause, for the sake of our Community.» The general passionarity of the members of the system is growing. From quiet townsfolk, adapted to the old conditions, they turn into seekers of improvement, first without risk, and then at the risk of their lives. This marks the transition to the Growth Phase (according to Gumilev – «Akmatic).»
3) This is the phase of prophets, fanatics of the new cause, revolutionaries. This is the phase when «Striving for the ideal of success and victory» becomes the imperative of behavior. «The greatest rise in passionarity – the akmatic phase of ethnogenesis – causes people’s desire not to create integrity, but, on the contrary, «to be themselves» – not to obey general regulations, to reckon only with their own nature. In general, this is a very «boorish» stage. The right of force reigns here, whoever has time – he ate it, the end justifies the means, the competitive struggle for leadership is the most ruthless. During this period, the system spends a lot of energy both on external expansion and on internal civil strife.
4) So much energy is spent on fighting external enemies and leaders with each other that the Fracture Phase begins.
«Usually in history this phase is accompanied by such internal rivalry and slaughter that the course of ethnogenesis is temporarily hampered.»
Civil wars, conflicts at work, conspiracies begin. The passionary charge of the population is reduced: harmonious personalities become the leaders in the system, in which both activity and caution do not have excessive deviations. The imperative of this stage is: «We are tired of the Great Ones!» Away with the heroes! This period of the system’s life ends with the victory of one of the competing leaders.
5) The system enters the Inertial Phase. She is the Blooming Phase. The winner is proclaimed the slogan – «Be like me!» That is, a pattern of behavior is offered, an example to follow, sometimes from the heroes of a past heroic era. Extreme regulation of life and work, "Ordnung!», the establishment of a clear hierarchical organizational structure of the community. Differentiation of objects of activity, areas of responsibility, spheres of influence. living standards. Ordering everything and everyone: Laws and Rules. The accumulation of material culture, the creation and preservation of a huge number of cultural, scientific, technical and other monuments. In a word, the Inertial Phase is a flourishing, Civilization. It was the ethnic groups of this period of life that created everything that today we call Ancient Egypt, Hellas, Ancient Rome, the Mayan and Aztec civilizations, the Renaissance. It turns out, however, that the era of enlightenment and civilization is in fact not the heyday, the «spring», but the decline, the «autumn» of the system. All the numerous fruits of the Inertial Phase are only the gradual dissipation of the former passionary charge. Indeed, «golden mediocrity» is the social ideal of this era. The creations of artists, scientists, technicians, although numerous, are inferior in quality to the achievements of the restless era of «Sturm und Drang». Imitation prevails. Not creators, but artisans, not Artists, but Manufacturers. The social ideal is material gain. If the phases of rise, development and breakdown can be called the Age of Chivalry, then all subsequent stages are the Age of Trading: everything is just for money, altruism and heroism are ridiculous, personal income is the measure of everything. There is an erasure of features, outstanding personalities are persecuted, driven into the framework of the standard. (However, after their death, they are willingly canonized!) Zealots of traditions and law, conservatives – these are the favorites of the system at this stage.
