Butterfly Effect: Can the flapping of a butterfly in Sri Lanka cause a hurricane in the US?

"The flutter of a butterfly's wings can be felt on the other side of the world." This Chinese proverb is the origin, together with the research of the mathematician and meteorologist Edward Lorenz, of one of the most cinematographic physical theories: the butterfly effect. According to this concept linked to chaos theory, the flapping of an insect in Hong Kong can unleash a storm in New York. But is it possible that the fluttering of a butterfly in Sri-Lanka could cause a hurricane in the US?

In a non-deterministic system, small changes can lead to totally divergent consequences. A small initial disturbance, through an amplification process, can generate a considerable effect in the medium and short term. The disordered movement of the stars, the movement of plankton in the seas, the delay of airplanes, the synchronization of neurons; they are all chaotic or "nonlinear dynamic" systems.

"Nature is full of chaotic systems, such as the weather. Some other chaotic systems are animal populations, epidemics or the stock market (Econophysics). These systems are called 'non-linear', which means that they follow relationships that are not strictly proportional", says the Institute for Interdisciplinary Physics and Complex Systems (IFISC) on its website.

The theory of chaos and the butterfly effect comes to explain that something as complex as the universe  (a flexible chaotic system) is unpredictable . Chaos theory explains systems such as the atmosphere or weather conditions that prevent reliable weather forecasts beyond three days and is particularly useful for studying social phenomena that are difficult to resolve in terms of linear cause-effect relationships.

The seed idea of ​​the butterfly effect is that the endless sequence of events, seemingly triggered by each other, end up having completely unpredictable consequences . If we imagine a universe divided in two and in one of them we introduce a variable (for example, the subtle flutter of a butterfly or a variation of figures in decimals), each of the parts of that universe will react differently to the changes and it will evolve differently and unpredictably.

Rather than the fluttering of a butterfly, some researchers prefer to refer to the double pendulum experiment . This is two coupled pendulums, that is, a pendulum attached to the end of another pendulum. When it comes to just one, the movement is quite simple, but when there are two oscillating, it becomes unpredictable and chaotic.

Lorenz and a variation of three decimal places

Edward Lorenz, the father of chaos theory, considered the weather as a case of this type, to the extent that the initial conditions can never be known exactly. In fact, in 1963, Lorenz was conducting research on weather forecasts using computer equations and decided to review some of the data he had obtained. While a coffee was made (this is literal), the computer simulated the results of two months that were nothing like what he already had. Where did the error come from? From a simple rounding.

To simplify the operations and because the printer did not accept more than three decimal places, Lorenz decided to reduce the decimal places of one of the parameters with which he calculated the predictions from six to three (for example: from 53.453765 kilometers per hour, he started to use 53,453 kilometers per hour). The paradigm was clear: a minimal initial variation can produce changes in the short and medium term . Lorenz published the conclusions of his discovery in the Journal of the Atmospheric Sciences under the title "Nonperiodic Deterministic Flow" in 1963.

Lorenz was the leap from Newton 's deterministic laws and the application of equations to today's simulations. Astrophysics uses powerful computers to understand the evolution of the universe through simulations that take into account different elements and patterns, but there is always uncertainty in all experiments .  The practical consequence of the butterfly effect is that in complex systems such as the weather or the stock market it is very difficult to predict with certainty , which is why we speak of probabilities.

Chaotic systems: from the human body to artificial intelligence

The human body is a chaotic, flexible and unpredictable system. Medicine cannot predict the evolution of the body of a certain individual. However, the human body is resistant to changes, it maintains a more or less similar shape for more than 70 years , despite the fact that no atom of those that make up our body today was the same 7 years ago, and it resists diseases. and external conditions.

The explanation why a system as unpredictable as the human body is so stable is that the system is always attracted to a certain pattern of behavior; if we change something in the system, it returns as soon as possible towards the strange attractor. The behavior is unpredictable but we know where it will tend. Chaos allows the heart a range of behaviors that allow it to return to its normal rhythm after a change .

Let's take the self-organization of ant colonies as a reference to understand the flexibility of chaos. If we count the number of active individuals, we will verify that the number fluctuates with a periodicity of about 25 minutes . From time to time no element is active. That cycle of activity could only be a reflection of synchronization, however individual activity is completely aperiodic, chaotic. As the number of individuals increases, a collective behavior appears until, for a certain density of ants, regular oscillations begin to appear.

The example of ants can be compared to a fluid neural network in Artificial Intelligence (AI) . Fluidity in a chaotic system is manifested when the connections between elements change over time as a result of random movement or other causes.

The ingredients of chaos theory

There are several universal examples that have been taken to explain the theory of chaos: the beating of the wings of a butterfly, the double pendulum experiment or a ball bouncing in the doorway that will repeat different patterns. The American mathematician John Bush, from the Massachusetts Institute of Technology (MIT), added one more answer to the question: what are the minimum ingredients for chaos? A drop of water is placed on a soapy film. The way in which the drop of water bounces depends on the amplitude – the maximum variation of the displacement – ​​and the frequency – the number of repetitions – of the vibration. And these elements accurately describe the trajectory of the drop until it succumbs to chaos.

The theory of chaos and the butterfly effect explain everything from the behavior of nature and the human body to the trajectory of a drop of water. But the big question remains: could the fluttering of a butterfly cause a hurricane in a chaotic and unpredictable system? All our actions and decisions are connected and the possibilities of interrelationship are unpredictable.