Unreal optimism regarding certain so-called obvious and explainable phenomenon has been the hallmark of all of humankind’s scientific history. However, after countless counter-intuitive theories and deliberations, it is high time when we speculate on what is possible and what is not. Take Von Neumann, for example, who built his first computer with an intention of predicting and controlling the weather, among other intentions. However, we know today, that we cannot forecast the weather. It is true, however, that we might make probabilistic predictions for one or two days ahead, without making significant errors, but no meteorological office can dare predict even a week ahead. Beyond two to three days, the world’s best forecasts are speculative, and beyond six or seven, they are worthless. The solution to this problem does not concern building faster and more efficient computers. For we are dealing with systems that are complex, non-linear in nature – we are dealing with systems which have a sensitive dependence on initial conditions – we are dealing with chaos.
Chaos is a phenomenon seen in our everyday lives. Whether it is the turbulent flow of water from a faucet, or the pillars of smoke that rise from chimneys in industrial towns, or a boiling kettle, chaos is everywhere. Classical methods can never calculate where a piece of paper might end up when a certain period has passed after it has been thrown over a waterfall, can it?
Butterfly effect is a term coined specifically indicating the futility of weather forecast attempts. In the 1950’s and 60’s, the philosophical heart of science was stated somehow like this – ‘Given an approximate knowledge of a system’s initial conditions, and an approximate understanding of natural law, one can calculate the approximate behavior of the system’. This would be true for linear systems where a small error in fixing the position of the Halley’s Comet would lead to a tiny error in the prediction of the next appearance. However, in non-linear systems, approximation of the initial conditions (like ignoring the effect of a butterfly fluttering its wings) leads to rapid divergence from the desired path and could lead to a tornado in South America, even if clear weather had been predicted for that day. Since with current technology, we can never measure the state of the universe at a snapshot instant, and even if we had the technology, the measurements would not be correct, since by Heisenberg, we change whatever we observe, we have to declare the future of weather forecasting as ‘doomed’.
Addressing the same issue somewhat differently, can physics approximately predict the final position of a billiard ball after it has been struck across the table? The answer is yes, for a few collisions, the equations governing motion and friction can be useful. But let us find out whether such a prediction is possible for a large number of collisions. For starters, let us assume we have a very powerful computer and sensors located all over the earth. All the initial data is correctly recorded. However, we ignore the effect caused by a falling leaf in some distant planet some light years away. Let us assume that the ball deviates by 10^(-140) degrees due to the leaf. For linear collisions, this error would lead to a minor deviation from where we predicted the ball to end up at. But when a billiard ball strikes another, the collision is non-linear. Let us consider that the deviation from prediction is amplified 10 times for each non-linear collision. So, after one collision, the error is 10^(-139) degrees, after two, it is 10^(-138) degrees, and so on. After the 140th collision, it is 1 degree, after the 141st, it is 10 degree, until at the 143rd collision the error in prediction has amplified to 1000 degrees. It is like a fractal where minor changes can lead to a radically different patterning altogether. We even do not know in which direction the ball is moving, let alone, predict the final approximate position of the ball.
Chaos exploits the disorder in such systems and finds out the underlying order in the apparently disorderly systems. Had chaos merely pointed out the disorder, it would have been of little use as a science. Scientists believe that Chaos holds the key to the understanding of the universe. Population biologists, mathematicians, physicists, all recognize chaos as a potent tool for the understanding of complex systems – systems whose behavior cannot be predicted classically.
I hope that this discussion has led to the reader being in a position to appreciate the importance that chaos plays in our everyday lives. I have purposefully refrained from discussing what chaos theory is all about and concentrated only on the background information. The interested reader might find it very “fulfilling”, if I may say so, to go through a good book on the theory of chaos to find out more on what this science has to offer. Happy hunting readers!
No comments:
Post a Comment