“Can a butterfly flapping its wings in Brazil trigger a tornado in Texas?” That was the brilliant question asked for more than five decades at a puzzled audience. Since then, the Butterfly Effect has been known as the possibility of generating an unpredictable and chaotic future, with actions as small as a butterfly flapping its wings. Although today it has gained popularity, especially in the philosophical area, the implications of this effect began in the study of meteorology.
From determinism to the unpredictable
If we travel to the past, up to about four centuries ago, we will find the emergence of the deterministic physics concept. In the seventeenth century, thanks to the contributions of Isaac Newton, the reality seemed to be subject to absolute determinism. That is, it was the period in which Newton developed his systems of integral and differential calculus, necessary to calculate the trajectories of comets and other cosmic objects. Furthermore, he solved the problem that for many years intrigued physicists, motion, for which he stipulated his laws of dynamics. Thus arose a kind of spirit where everything seemed predictable: the movements of the moons, planets, comets, and hundreds of other events could be predicted with accuracy. In that sense, if one wonders about the future, it could be said that it is already predicted, we just have to wait for it to manifest.
However, if a third object is introduced into the equation, then everything changes. Newton’s equations represented a whole revolution for the understanding of physics, there’s no doubt about that. But even the father of physics faced an unsolvable problem for him; the problem of the three bodies.
Newton and his equations were extremely important in calculating the trajectories of celestial bodies, including the interaction between two objects that depend on gravitational attraction. Yet, by introducing a third object with a certain mass, which also depended on the gravitational interaction, everything became complicated. This problem persisted without solution until, 200 years later, Henri Poincaré, a French mathematician and physicist, came to introduce a term. According to Poincaré, the three-body problem did not have a simple solution, for it depended on chaos.
The ‘birth’ of chaos
But humankind did not know the power of chaos until 1963, when Ed Lorenz, an American meteorologist, tried to do a basic computer simulation of the Earth’s atmosphere. A system of twelve equations intervened in this process, with twelve variables such as temperature, humidity, and other factors. And so far, everything seemed normal; he obtained the desired results until he decided to recalculate a section of them.
In this second calculation, the unimaginable happened. At first, the results were almost identical to the previous ones. But, as the calculation progressed and the computer printed the following figures, Lorenz realized that the results were diametrically different from what they were supposed to be. Then, he noticed that the computer had done a rounding in the numbers and, instead of entering the 6 decimals that the figures had, it only entered 3.
The Butterfly Effect
Thanks to this serendipity, he realized that a change in the initial conditions, no matter how insignificant, would cause a different future. He discovered what physicists call ‘initial-condition sensitive dependence,’ the ultimate brand of chaos. Here is where the deterministic view of dynamic systems is broken, which is now known that it can exhibit unpredictable behaviors.
For this reason, Lorenz launched in front of the 139th meeting of the American Association for the Advancement of Science, his question about the flapping of a butterfly that seems insignificant, but could completely change the future of a complex system. Thanks to Lorenz’s question, this condition is currently known as the Butterfly Effect. This is curious since it is not possible to predict how each individual that is part of the system will evolve, but its evolution as a whole can be predicted. This is called a chaotic attractor and if the attractor discovered by Lorenz is plotted, the shape of a butterfly is obtained. Curious, don’t you think?
Text and photos courtesy of Ecoosfera
Translated by Gaby Flores
