Analyzing Chaos


 
Author: Vanshika Shukla
 
The field of study I’m in deals with data science jargons like machine learning, deep learning, big data, neural network, etc. Although the mathematics or statistics involved in the algorithm of these terms are not new, the advancement in the computational power of the computers in recent years has made its application feasible in practical life without one being a statistician and has opened up a new horizon in every discipline. The intermix of domains of data science with medicine, science, business, and entertainment could have a profound effect on our way of thinking. In recent days I could not resist the thought of its implications on the Chaos theory or colloquially known as “The Butterfly Effect”.
 
The Chaos theory is a branch of mathematics that deals with the study of chaos or randomness. It implies that in the seeming sea of disorderliness there are underlying patterns, repetitions, and fractals (fractals are repetitive geometric figures that exist in snowflakes, trees, and galaxy formations). These random states are subject to the deterministic laws and can, in principle, be predicted.
 
Edward Lorenz a meteorologist and mathematician accidentally discovered the effect in the 1960s when he entered some number into a computer program to simulate weather pattern – but he had rounded some number from 0.506127 to 0.506. This tiny alteration transformed the whole pattern produced by the computer program. Lorenz coined the term “the butterfly effect” as a metaphorical example to show how an insignificant event like the flapping of a butterfly wing could turn into a tornado in a distant place.
 
The thought that our future is deterministic is enthralling and has been the source of various fictional movies, books, and tv series. We humans love the idea of generating order out of chaos, it gives a sense of control and some predictability to our lives. But is it really possible?
 
Tiny insignificant choices that we make can have huge consequences later in our lives. It’s like a domino effect where one decision leads to others and creates a ripple effect in the long run which our brain could not even comprehend. Any particular event is a confluence of a lot of variables. Ripple effects created by every individual in the timeline create interference of these ripples, which subsequently creates other ripples and the process goes on. We are not the first to explore this idea, Pierre-Simon Laplace in 1814 published the idea of casual or scientific determinism. Determinism is a philosophical belief that physicists call Cause-and-Effect.
 
Laplace explored the idea that if someone(Laplace’s demon) knows the current position and velocity of each and every particle in the universe, then we can determine the past and present adhering to the laws of classical mechanics.
 
“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.”

— Pierre Simon Laplace, A Philosophical Essay on Probabilities.

 
It seems that after 200 years we are gradually getting closer to the Laplace’s demon. With our advancement in collecting a huge pile of data, called Big Data. Machine Learning algorithms which don’t have set parameters like a mathematical equation but learn from the fed data, weighing each input and deducing how they work together. These algorithms look to the observed data to provide information on likely parameters. By any chance if we miss a single parameter(feature variable), the resultant model formed will be flawed and we can suffer huge consequences. Thus reiterating the Butterfly effect. Hence, the more examples we feed them, the more accurate the output result.
 
Machine Learning is already being used in the field of weather forecasting and is able to predict weather accurately a week ahead. To conceptualize the movement of any chaotic system is an intractable task for a human brain, there are just too many variables to consider, but so is not the case for today’s supercomputers. Big data when it is not filtered by any algorithms or definitions is seemingly chaos. Data, which grows exponentially day by day, is at its very core, a chaotic system. The resources that are available to us are capable of collecting data at its granular level, for a given system, and if we subject those data to the known machine learning algorithms, then we could, in theory, predict the past and the future of a chaotic system.
 
We could agree upon, that some systems are more chaotic to predict than others, like predicting the stock market. The fluctuations in the stock market are dependent upon human behavior – which are to some degree, an uncharted territory. Most of the time we are unaware of the variables involved or might not know how to quantify a given variable. How does one quantify the unpredictability involved in human behavior?
 
But for a chaotic system like a game of Billiards, if we do know the parameters like velocity, momentum, and direction of the force applied, then we can, theoretically, predict the outcome of the game. Today’s AI is capable of predicting the outcome of a coin toss by measuring the parameters involved.
 
Things like artificial neural networks or deep learning are all subset of machine learning, where models are trained using large sets of labeled data. They only differ in the way feature variables are extracted and the number of hidden layers involved. Deep learning algorithms extract the feature variables from the dataset without any human involvement. Larger the data, better the accuracy.
 
With the current advancement in the field of data science, the day is not so far when the “Laplace’s Demon” would be able to predict human behavior – most chaotic of all systems.