Modern popular science and popular literature often uses the terms "synergy", "chaos theory" and "bifurcation point". This new trend of populist use of complex systems theory often replaces the conceptual and contextual meaning of definitions. Let's try not abstrusely, but still close to scientific, to explain to the interested reader the meaning and essence of these concepts.
Science and self-organizing systems
An interdisciplinary doctrine that explores patterns in complex systems of any nature is synergetics. The bifurcation point as a turning point or 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), non-linearity of development (the presence of many development paths), dissipativity (discharge of excess entropy) andthe possibility of a bifurcation state (choice or crisis point). 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 technique is to explain complex things with simple examples. A classic illustration describing the state of a system approaching a bifurcation point is the example of the famous 14th-century logician Jean Buridan with a donkey, his master, and a philosopher. These are the starting tasks. There is a subject of choice - two armfuls of hay. There is an open system - a donkey, located at the same distance from both haystacks. The observers are the master of the donkey and the philosopher. The question is, which handful of hay will the donkey choose? In Buridan's parable, for three days people watched the donkey, which could not make a choice until the owner connected the heaps. And no one starved to death.
The concept of bifurcation interprets the situation as follows. We omit the end of the parable and focus on the situation of choice between equilibrium objects. At this moment, any change can lead to a shift in the situation towards one of the objects (for example, a donkey fell asleep, waking up, was closer to one of the piles of hay). In synergetics, the donkey is a complex open system. The bifurcation point is the state of the donkey before the equilibrium choice. A change in position is a perturbation (fluctuation) of the system. And two haystacks are attractors, the state into which the system will come after passing the bifurcation point and reaching a new equilibrium state.
Three fundamental bifurcation points
The state of the system, approaching the bifurcation point, is characterized by three fundamental components: fracture, choice and ordering. Before the bifurcation point, the system is in an attractor (a property that characterizes the stability of the system). At the bifurcation point, the system is characterized by fluctuations (disturbances, fluctuations in indicators), which cause a qualitative and quantitative abrupt 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 huge role of randomness reveal the multivariability of the organization of the system.
Mathematics describes the bifurcation points and the stages of its passage by 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 the choice, at the crossroads, at the point of divergence of 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 an insignificant fluctuation at the “input” becomes huge at the “output”. At bifurcation points, the behavior of the system is unpredictable, and any chance will shift it to a new attractor. It's like 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 in Russian fairy tales is a very vivid image with a choice and the uncertainty of the subsequent state of the system. As the bifurcation point approaches, the system seems to oscillate, and the smallest fluctuation can lead to a completely new organization, to order through fluctuation. And at this moment of the turning point, it is impossible to predict the choice of the system. This is how, in synergetics, absolutely 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 by the butterfly effect metaphor. The meteorologist, mathematician and synergeticist Edward Lorenz (1917-2008) described the system's sensitivity to the slightest change. It is his idea that one stroke of a butterfly's wing in Iowa can set off an avalanche of various processes that will end in the rainy season in Indonesia. A vivid image was immediately picked up by writers, who wrote more than one novel on the theme 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 The Butterfly Effect.
Bifurcations and catastrophes
Bifurcations can be soft or hard. A feature of soft bifurcations is small differences in the system after passing through the bifurcation point. When the attractor hassignificant differences in the existence of the system, then they say that this bifurcation point is a catastrophe. This concept was first introduced by the French scientist René Federic Thom (1923-2002). He is also the author of the theory of catastrophes, as bifurcations of systems. His seven elemental catastrophes have very interesting names: the fold, the fold, the swallow's tail, the butterfly, the hyperbolic, elliptical, and parabolic umbilics.
Applied Synergetics
Synergetics and bifurcation theory are not as far from everyday life as it 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 seemingly conscious - swings constantly. And maybe understanding the processes of the synergetic organization of the world will help us make a more informed choice, avoiding catastrophes, but making do with small bifurcations.
Today, all our knowledge of fundamental sciences has hit a bifurcation point. The discovery of dark matter and the ability to conserve it has brought mankind to a point where a random change or discovery can lead us to a state that is difficult to predict. Modern exploration and exploration of outer space, theories of "rabbit holes" and the tubes of space-time expand the possibilities of knowledge to unimaginable boundaries. It remains only to believe that, having approached the next bifurcation point, a random fluctuation will not push humanity into the abyss of non-existence.
