2016 Jan

Butterfly Effect and Chaos

January 5, 2016

Butterfly Effect and Chaos

The weather prediction that you see on your smartphone is a result of humongous amount of calculations crunched by modern supercomputers. Accurate weather prediction is such a challenge that it wasn’t a reality until recently, till the advent of supercomputers. Edward Lorenz coined the word ‘butterfly effect’ a metaphorical example used to describe the importance of the knowledge of initial conditions in making predictions. Butterfly effect loosely implies that a flap of butterfly wing can affect a hurricane. Does it really happen? What is this thing called as ‘initial conditions’ and how is it related to the butterfly flap? The answers to these questions lie in chaos theory.

According to Newton’s theories, if one knows the position, velocity and forces acting on an object at a given snapshot of time then the particle’s position and velocity at all time points in the future can be calculated. For example lets say there is a planet whose position and velocity needs to be calculated five years from now, then if one has information about the particle’s current velocity and position one can use Newton’s equations and get the work done. This is called determinism i.e., given the position and velocity of the particle, the path it takes for a given span of time and its velocity can be determined precisely. Just to note, this differs from what we have introduced during our Physics tuition classes on Quantum Physics – the un-deterministic world of Heisenberg and Schrodinger.

The preliminary information required to make the predictions mentioned above is called as ‘initial conditions’. So, as per the above stated principles one should be able to calculate the motion of every particle in the universe after any given amount of time. Newton’s laws can be used to predict phenomena solar and lunar eclipses hundreds of years into future. The triumph of Newtonian mechanics has hit a dead end when it was observed that two systems with same initial conditions showed different behavior in time. And it seemed that the laws of motion are violated. Henri Poincare deciphered this behavior of nature and the seemingly weird phenomena was due to the tiny, most of the time un-observable difference, in the initial conditions that has resulted in drastically different paths and velocity values. These systems where the future states of the particle are very sensitive to the initial states are called as chaotic systems. Chaotic systems do obey Newton’s laws its just that they are very sensitive to the
initial conditions.

So, coming back to butterfly effect; weather prediction calculations use complex form of Newtonian mechanics and the prediction of the future of such complex systems depends on the accuracy of the initial conditions. Hence a flap of butterfly affects initial conditions and consequently changes the future of the system under consideration drastically. And it also can, theoretically, change the course of a hurricane or initiate a hurricane. Remember the same flap of butterfly can, theoretically, stop it.

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