Butterflies, tornadoes and a world chaotic

Muhammad Rakibul Islam | Published: January 18, 2019 20:25:18

Let me tell you a story of a certain butterfly in Brazil which flapped its wings causing a tornado in a distant land in Texas. This tale might sound familiar to you because it is the highly popularised concept called the Butterfly Effect. Now, of course, this is an overly-exaggerated analogy. If a single butterfly flapping its wings could cause a tornado elsewhere, given the possibly millions of butterflies around the world flapping their wings at a given moment, the earth would be home to constant storms and chaos.

Notice how I used the word chaos in the last sentence of the last paragraph, because what I am going to talk about in this article is none other than chaos theory. What if I told you that this so-called world of order and meaning actually harnesses more chaos in the most trivial of systems than what you'd believe? You might have heard of Einstein famously writing "God does not play dice". As a mathematician, I do not obsess over the question of whether God plays dice or not, but studying the rules of this complex game of dice. But I would further elaborate on this point in the next paragraph.

The ideal Newtonian world, while it holds true in a clockwork universe, where if you know the basic rules of the universe you would know everything about it, breaks down in reality. Mathematician Pierre-Simon Laplace introduced the concept of Laplace's demon, an articulation of the idea of scientific determinism, where if someone (the demon) is able to acquire knowledge of the location and momentum of each and every atom in the universe, they can predict and know the future and know the past. This idea of determinism began to be followed as a form of bible for a generation of physicists to come afterwards. The belief in determinism is one of the reasons for Einstein to mention that God does not play dice. However, with advancements in quantum mechanics, specifically Heisenberg's Uncertainty Principle, this view changed. An implication of the principle, in easy words, is that one cannot possibly determine accurate measures of both speed and position of a given particle. If you cannot simply measure the speed and position of a single particle, one cannot possibly know about the location and momentum of each and every atom in the universe and hence Laplace's idea of determinism fails to uphold. The future hence does hold mysterious out of the realm of human cognition.

Moreover, in addition, there exists a whole world of complex systems, other than the quantum realm, where even the slightest of changes in the initial conditions could bring dramatic changes in that of the future. As summarised by Edward Lorenz, father of the theory, chaos is "when the present determines the future, but the approximate present does not approximately determine the future."

A way to understand chaos theory better is to know the story of how exactly Edward Lorenz came to discover it. Lorenz was using a computer to calculate weather patterns and while running simulations decided to run it twice. The first time he inputted the data correct to six decimal places and used three decimal places the second time. Now using the idea of conventional understanding of the world, a trivial change like this will only cause a trivial change in the results of the experiment. However, changing just three seemingly insignificant decimal places from a value completely changed the simulation results. The world of chaos is born.

Now here is the thing. I do not want to mislead my reader, getting them depressed in the sense that all hope of an orderly world is gone. While chaos theory has given rise to witnessing the chaotic events of certain systems, what we study is not just the disorder itself but to find order in it. Strangely enough, chaos also gives rise to order and patterns and as mathematicians, we study that, painting and colouring a rather distraught world, void of colour and form - in a way taming the shrew! The world is in a constant balance - an eternal dance of chaos and order in rhythm.

By understanding the existence of chaos and utilising the mathematical tools born to tame it, we can make pretty accurate predictions of certain occurrences. We can now, by running simulations using different parameters and repeating our calculations, predict weather patterns to a higher accuracy. Whether it is the irregularities of our heartbeat, growth of an insect or bacterial population, uncertainty in the world of quantum mechanics - knowing the ideas of chaos can give order to a rather disordered and unstable world and we can be better predictors! Notice my emphasis on the word prediction, however. While we can build better models of analysis using chaos theory, we cannot completely eliminate the factor of unpredictability. In a way the dice is still being rolled but we can be better gamblers making the most gain out of the game.

Muhammad Rakibul Islam writes from Clark University, Worcester, Massachusetts USA

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