Modern non-fiction and simply popular literature often uses the terms synergetics, chaos theory, and bifurcation point. This new trend of populist use of the theory of complex systems often replaces the conceptual and contextual meaning of definitions. Let us try not abstrusely, but nevertheless close to the scientific to explain to the interested reader the meaning and essence of these concepts.
Science and self-organizing systems
Interdisciplinary doctrine exploring patterns in complex systems of any nature is synergetics. The bifurcation point as a turning point or a moment of choice is a key concept in the theory of the behavior of complex systems. The synergetic concept of complex systems implies their openness (exchange of matter, energy, information with the environment), nonlinearity of development (the presence of many development paths), dissipativity (dumping of excess entropy) and the possibility of a bifurcation state (choice or crisis point). The synergetic theory is applicable to all systems where there is a sequence and spasmodic changes that develop over time - biological, social, economic, physical.
Buridan's Donkey
A common trick is to explain the complex with simple examples. A classic illustration illustrating the state of a system approaching a bifurcation point is an example of the famous 14th century logician Jean Buridan with a donkey, its master and philosopher. The initial tasks are as follows. There is a choice - two armfuls of hay. There is an open system - a donkey located at the same distance from both haystacks. Observers are the master of the donkey and the philosopher. The question is - what arm of hay does the donkey choose? In Buridan, in a parable for three days, people watched a donkey who could not make a choice until the owner connected the heaps. And no one died of hunger.
The concept of bifurcation interprets the situation as follows. We omit the end of the parable, focus on the situation of choice between equilibrium objects. At this point, any change can lead to a shift in the direction of one of the objects (for example, a donkey fell asleep, woke up, was closer to one of the heaps of hay). In synergetics, a donkey is a complex open system. The bifurcation point is the state of the donkey before equilibrium selection. A change in position is a perturbation (fluctuation) of the system. And two haystacks are attractors, the state that the system will come to after passing through the bifurcation point and reaching a new equilibrium state.
Three fundamental points of bifurcation
The state of the system, approaching the bifurcation point, is characterized by three fundamental components: fracture, selection, and ordering. Before the bifurcation point, the system resides in the attractor (a property that characterizes the stability of the system). At the bifurcation point, the system is characterized by fluctuations (disturbances, fluctuations in the indicators) that cause a qualitative and quantitative jump-like change in the system with the choice of a new attractor or transition to a new stable state. The multiplicity of possible attractors and the enormous role of chance open up the multivariance of the organization of the system.
Mathematics describes the points of bifurcation and the stages of its passage through the system in complex differential equations with a multitude of all parameters and fluctuations.
Unpredictable bifurcation point
This is the state of the system before a choice, at a crossroads, at the point of discrepancy between multiple choice and development options. In the intervals between bifurcations, the linear behavior of the system is predictable, it is determined by both random and regular factors. But at the bifurcation point, the role of chance comes first, and the insignificant fluctuation at the “entrance” becomes huge at the “exit”. At the points of the bifurcation, the behavior of the system is unpredictable, and any chance will shift it to a new attractor. This is similar to a move in a chess game - after it there are many options for the development of events.
If you go to the right, you will lose your horse ...
The crossroads of roads in Russian fairy tales is a very vivid image with the choice and uncertainty of the subsequent state of the system. When approaching the bifurcation point, the system seems to oscillate, and the smallest fluctuation can lead to a completely new organization, to order through fluctuation. And at this point in the fracture, it is impossible to predict the choice of system. That is how in synergetics, completely small causes give rise to huge consequences, opening up an unstable world of development of all systems - from the Universe to the choice of Buridan's donkey.
Butterfly Effect
The system’s coming to order through fluctuation, the formation of an unstable world, dependent on the slightest random changes, is reflected in the “butterfly effect” metaphor. Meteorologist, mathematician and synergetic Edward Lorenz (1917-2008) described the sensitivity of the system to the smallest changes. It belongs to him that one wave of the butterfly wing in Iowa can cause an avalanche of various processes that will end in Indonesia with the rainy season. A vivid image was immediately picked up by writers, writing more than one novel on the subject of the multiplicity of events. The popularization of knowledge in this area is largely the merit of Hollywood director Eric Bress with his box office film Butterfly Effect.
Bifurcations and disasters
Bifurcations can be soft and hard. A feature of soft bifurcations is the small differences in the system after passing through the bifurcation point. When an attractor has significant differences in the existence of a system, they say that this bifurcation point is a disaster. The French scientist Rene Federic Tom (1923-2002) first introduced this concept. He is the author of catastrophe theory, like bifurcation systems. Its seven elementary catastrophes bear very interesting names: fold, assembly, swallow tail, butterfly, hyperbolic, elliptical and parabolic umbilica.
Applied Synergetics
Synergetics and bifurcation theory are not as far from everyday life as they might seem. In everyday life, a person passes the bifurcation point hundreds of times during the day. The pendulum of our choice - conscious or only seeming conscious - sways constantly. And maybe understanding the processes of synergistic organization of the world will help us make more informed choices, not reaching catastrophes, but getting around with small bifurcations.
Today, all our knowledge of basic sciences has reached the point of bifurcation. The discovery of dark matter and the ability to save it has put humanity at a point where an accidental change or discovery can lead us to a state that is difficult to predict. Modern study and exploration of outer space, the theory of "rabbit holes" and the tube of space-time expand the possibilities of knowledge to unimaginable boundaries. It remains only to believe that, having approached the next point of bifurcation, random fluctuation will not push humanity into the abyss of nothingness.