Imagine that you are walking down the street and all of a sudden you bend down to tie the loose lace of your shoe.
Behind you comes a gentleman walking carefully, with a very hot coffee in his hands, but he doesn’t notice you’re crouched there. He trips over you, spills his coffee, and burns himself—and ends up having to go to the ER for treatment.
The man who took the coffee is a plane pilot and, due to the accident, he is unable to arrive on time for the flight he had scheduled. With that, the flight is delayed.
One of the passengers on the flight was traveling for a job interview. As she didn’t arrive in time, she lost her seat. Another was a man who was traveling to get married and left the bride waiting alone at the altar.
And there were also two brothers who wanted to say goodbye to their grandmother who was suffering from a terminal illness and were unable to say their last goodbye.
Did you see the chaos you caused?
This seemingly insignificant detail of tying the shoelaces right then and there caused a series of events very different from what was expected by many people.
But do not worry. If this ever happens in real life, you won’t need to feel remorse. What happened was just the action of chaos theory and the butterfly effect.
These two concepts are present in our daily life, help to understand how the universe works and serve as a basic principle for the development of new technologies with application in different areas of knowledge. But what are they about?
BUTTERFLY EFFECT
Let’s start with the butterfly effect, which inspired artists, filmmakers, writers and scientists.
In 1952, American science fiction writer Ray Bradbury published the short story “The Sound of Thunder”. In this tale, a character steps on a butterfly, and that small detail has serious consequences — including the rise of a fascist leader to power.
In 1961, what was fiction became scientific reality. That year, meteorologist Edward Lorenz, also an American, was working on a mathematical model for forecasting the weather.
To do this, he entered data such as temperature, humidity, pressure and wind direction into his computer and observed the results. Then he re-entered the same data to check the results obtained the first time.
And behold, unexpectedly, starting from the same data on both occasions, the second weather forecast was completely different from the first.
At first, the two predictions were similar, but as the model progressed in time, the differences between the two results became larger and larger.
WHAT HAPPENED?
Such a radical difference between the two predictions was simply because, the second time around, Lorenz’s computer had rounded the data, that is, it counted a few decimal places less.
Thus, it was realized that a few seemingly insignificant decimal places, over time, can cause monumental changes. For Lorenz, this was equivalent to saying that the wind that causes a butterfly to flap its wings in Brazil can cause a tornado in Texas, in the United States.
Thus was born chaos theory with its butterfly effect, indicating that very small variations may seem insignificant, but will generate huge changes over time, causing a feeling of chaos.
CHAOS THEORY
Chaos theory posed a major challenge to classical physics, which is governed by Newton’s laws.
According to these laws, once the initial conditions of an object are known, it will be possible, with relative ease, to predict its behavior in the future.
That is, Newton’s laws are deterministic. Thanks to Newton, it is possible, for example, to predict the movement of planets or the trajectory of a bullet.
But chaos theory warns that initial variations, however tiny, will make predictions impossible over time.
In principle, Newton’s laws state that, given the perfect data, it is possible to make predictions. But, in practice, chaos theory teaches us that, as it is impossible to have perfect data, after a certain point predictions become unfeasible.
“Chaos theory is revolutionary because it claims that, even for Newtonian physics, there may be cases where, in principle, determinism is right, but in practice the system seems to behave as unpredictably as rolling dice. “, as told to BBC News Mundo (the BBC’s Spanish service) Paul Halpern, professor of physics at the University of Sciences in Philadelphia, in the United States.
CHAOS BUT NOT DISORDER
Chaos theory is a principle applied to what mathematicians call “dynamic systems”.
A dynamic system is any set of successive facts that change or evolve over time, such as weather conditions or the population of a city. When this system is very sensitive to variations in initial conditions, it is called a chaotic system.
But while chaos makes it seem like everything moves randomly, haphazardly, or unpredictably, the chaos itself actually creates patterns over time.
As chaotic as it may seem, a system follows a trajectory to certain points. These system destination points are known as “attractors”.
In the case of Lorenz, for example, the calculations used for his model created, over time, a pattern that, coincidentally, resembled the wings of a butterfly. The set of attractors in a system form the so-called “fractals”.
FRACTALS
“A fractal is something that is ‘self-similar'”, according to Halpern. It is a mathematical object in which any section, when observed closely, looks similar to the complete object.
“The perfect fractal is the one that, when the image is approached, has the same appearance that is observed when moving away”, according to the specialist. “Some of the attractors are seen as fractals.”
REACHING THE LIMIT
For Halpern, in daily life, chaos theory “serves for us to know the limits of our knowledge”.
In the meteorological field, for example, it is useful to know at what point the weather forecast starts to lose accuracy.
Halpern also mentions that the concept of patterns that create attractors underpins medical research that seeks to predict what might happen to people’s health, based on data collected over time.
On the other hand, fractals are widely used in the development of digital technology, telecommunications, production of high definition images and even in the development of cosmological models.
If we go any further, chaos theory will lead us to existential questions. “It demonstrates that, even if our determinism is perfect, there are gaps in our knowledge – when it comes to predicting the future,” according to Halpern.
And the professor claims that for some people this is an argument that proves the existence of free will, but this would be an even more chaotic discussion.
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