What is chaos theory?

It is one of the most important laws of the Universe, present in the essence of almost everything that surrounds us. The central idea of ​​chaos theory is that a small change at the beginning of any event can bring huge and absolutely unknown consequences in the future. Therefore, such events would be practically unpredictable – chaotic, therefore. It sounds scary, but it only takes a look at the more casual phenomena of life to see that this idea makes sense. Imagine that, in the past, you missed the entrance exam at the college of your dreams because a nail punctured the bus tire. Disappointed, you enter another university. So, the people you will live with will be different, your friends will change, your loves will be different, your children and grandchildren may be different…

In the end, his life was completely changed, and all because of that nail at the beginning of this sequence of events! This type of unpredictability was never a secret, but the thing gained the air of serious scientific study in the early 1960s, when the American meteorologist Edward Lorenz discovered that apparently simple phenomena behave as chaotic as life itself. He arrived at this conclusion by testing a computer program that simulated the movement of air masses. One day, Lorenz typed in one of the numbers that fed the machine’s calculations with a few decimal places less, hoping that the result would change little. But the insignificant change, equivalent to the nail in our example, completely transformed the pattern of air masses. For Lorenz, it was as if “the flapping of a butterfly’s wings in Brazil would later cause a tornado in Texas”. Based on these observations, he formulated equations that showed the so-called “butterfly effect”.

Chaos theory was founded. Over time, scientists concluded that the same unpredictability appeared in almost everything, from the rhythm of the heartbeat to the quotations of the Stock Exchange. In the 1970s, the Polish mathematician Benoit Mandelbrot gave a new impetus to the theory when he noticed that Lorenz’s equations matched those he himself had made when he developed fractals, figures generated from formulas that mathematically portray the geometry of nature, like the relief of the ground or the ramifications of our veins and arteries. The combination of Lorenz’s experiment with Mandelbrot’s mathematics indicates that chaos seems to be in the essence of everything, shaping the Universe. “Lorenz and I were looking for the same truth, hidden in the middle of a great mountain.

The difference is that we dig from different places”, says Mandelbrot, now at Yale University, in the United States. And recent research has shown something even more surprising: identical equations appear in chaotic phenomena that have nothing to do with each other. “The Lorenz equations for the chaos of air masses also appear in experiments with laser beams, and the same formulas that govern certain chemical solutions are repeated when we study the disordered rhythm of drops from a faucet”, says mathematician Steven Strogatz, from the Cornell University in the United States. This means that there may be a strange order behind all the unpredictability. Only the continuation of the “excavations” can solve the mystery.

DECISIVE INCIDENTS
The central idea of ​​the thesis is that small changes in a situation bring incalculable effects.

1. The essence of chaos theory is that a very small change in the initial conditions of a situation leads to unpredictable effects. This is what happens in this hypothetical example, where a girl is carefree playing with her ball. It seems like a no-brainer situation, but…

2. … a butterfly surprises the little girl! That’s it: the so-called “small change in the initial conditions” appeared. Frightened, she drops the ball.

3. The ball rolls towards the road and the girl runs after it to retrieve it. Meanwhile, a truck loaded with salt is passing by.

4. In order not to run over the girl, the driver suddenly turns the wheel. But the truck can’t handle the maneuver and overturns. The vehicle starts to catch fire.

5. All salt supply begins to roast. The smoke from the fire is laden with tiny particles of sodium chloride, which rise into the clouds.

6. In clouds, sodium chloride particles attract tiny droplets of water vapor and begin to form raindrops, which grow until they are heavy enough to fall

7. With the heavy clouds, it starts to rain after some time. That is, the girl’s innocent prank, in the end, produced an unpredictable change in weather conditions!