– In your scientific research, you most often apply chaos theory. What fascinates you most about it?
– What fascinates me most about chaos theory is the internal paradox – the fact that a system with no randomness can behave completely unpredictably.
First, we should explain what we study in general. Chaos theory is part of a larger field – nonlinear dynamics. We study the dynamics of various systems, i.e., processes that constantly change over time. This can be anything from a swinging pendulum or the growth of an animal population in a forest to much more complex engineering processes. We describe this change with mathematical formulas and observe how the system evolves, where it eventually settles, and on what external factors its behavior depends.
It is very important to emphasize one aspect – in the systems we study, there is no randomness. For example, if we toss a coin or observe the fall of lottery balls, these are already random processes, for which probability theory is applied. This is not the case in the systems we study. If I run the same experiment on a computer ten times with the same initial settings, I will get an identical result all ten times. What could be complicated about that, one might ask? Everything is described by rules, there is no randomness, so predicting the future of such a system should be simple. But it turns out that this is not always the case.
This is where chaos theory becomes relevant. A system is chaotic if it is very sensitive to initial data. Imagine: we perform two experiments with the same system, only in one of them we slightly shift the initial reference point. Initially, the evolution of both systems will look almost identical. However, over time, that tiny difference will begin to grow like a snowball, and soon we will get two completely different results. This is what fascinates me: chaos is not randomness. It arises from the nature of the system, its extraordinary sensitivity, and its ability to turn even the slightest changes into enormous consequences.
– Chaos theory is applied in many fields – from engineering to medicine. How is it applied in sensitive areas such as cardiology or neuroscience?
– This indeed sounds like a paradox, as we are used to associating chaos with disorder or loss of control. However, applying this science to human biology reveals a completely opposite fact that shatters centuries of medical intuition: strict regularity in the human body is often a harbinger of serious illness, while unpredictable, chaotic behavior is a sign of good health.
Chaos theory has shown that an extremely uniform heart rhythm can be dangerous.
For example, in cardiology, for decades, the belief prevailed that a healthy human heart beats with the precision of an ideal metronome, and any significant deviations between beats were considered pathology. However, chaos theory turned this view upside down and showed that an extremely uniform heart rhythm can be dangerous.
Today, one of the most important applications of chaos theory in medicine is the ability to predict cardiac arrhythmia. Unlike traditional statistical methods, which fail to distinguish natural rhythm fluctuations caused by stress or physical exertion from signs of illness, chaos theory methods are able to filter out these changes and detect hidden patterns of pathology.
Chaos theory is also successfully applied in neurology. The human nervous system is perhaps the most complex dynamic system, where billions of neurons and synapses operate through intricate feedback loops and chaotic impulses. Scientists have even coined the term “dynamic diseases.” These arise not from a virus or a “broken” body part, but when the system suddenly transitions from a healthy, chaotic state to an unhealthy, overly orderly state.
A prime example of this is epilepsy. Healthy brain activity is extremely complex, desynchronized, and naturally chaotic – this is what allows us to think freely, form memories, and move. An epileptic seizure occurs when this chaos disappears: millions of neurons suddenly synchronize and begin to function in an unusually orderly manner. Looking at brain waves through the prism of chaos theory, this transition to pathological order can be observed much earlier than physical symptoms appear. This opens up the possibility of predicting a seizure and providing timely assistance.
Another interesting area of application is psychiatry. A healthy person’s mood is characterized by natural chaoticity, which allows for flexible and adequate responses to various situations. In the case of bipolar disorder, this flexibility is lost: the psyche seems to get stuck in regular extreme fluctuations of mania or depression. Therefore, the goal of treatment should not be to completely “flatten” the patient’s emotions to a static state, as this would dull the person, but rather to gently return the system to its inherent natural chaos.
These are just a few examples, but from them, we already see a very interesting and unexpected conclusion: contrary to what we are used to thinking, chaos in our body is not something harmful or destructive. On the contrary, it is an essential indicator of human vitality, adaptability, and health.
– The 21st century is often called the era of artificial intelligence (AI). Do you think chaos theory could become just as important as AI in the future?
– I view these two fields not as competing, but as an excellent tandem. AI here becomes a powerful tool, allowing for further expansion of chaos theory research and application. It operates on a completely different principle than traditional mathematical models, which require strict, predefined rules and equations. If a person, when creating a model, does not consider some variable or parameter, the model simply will not see that hidden interaction. Meanwhile, AI does not need such strict rules. It analyzes vast amounts of historical data, discovers hidden patterns unknown to us, and can automatically adapt to them.
Recently, so-called physics-informed neural networks have also been gaining popularity very rapidly. During training, such a neural network is mathematically “penalized” not only when its predictions deviate from historical data but also when they violate fundamental laws of physics.
This synthesis of chaos theory and AI already has practical applications, for example, in weather forecasting. Traditional models, running on the most powerful supercomputers, consume enormous resources and reach their limit of capability after 10–14 days, as they can no longer cope with chaotic noise. AI can fundamentally change this situation.
Instead of trying to ideally simulate the state of every air molecule, it recognizes patterns by analyzing centuries of meteorological data and uses significantly fewer computational resources. Already, meteorological agencies are actively exploring the possibilities of reliably forecasting weather up to 30 days in advance. Such an extension of the forecast period would be very important for agriculture, shipping logistics, and the prevention of natural disasters worldwide.
Thus, the tandem of AI and chaos theory opens up many new possibilities. AI allows us to understand and manage chaos to an extent that seemed impossible just a decade ago.
