Chaos

After the response to my last pseudo-scientific post, Incomplete, I've decided to try my hand at another one. This one though, covers not a theorem, but a whole science in itself. Again I'd ask anyone reading this to hold on and read through the whole thing. You'll never think the same way about the world again...

The story begins in the year 1961 at MIT, Massachusetts, USA. Meteorologist Edward Lorentz was simulating global weather on his primitive computer. He had boiled weather down to the barest skeleton, to a set of few equations. The output was in the form of a string of numbers, merrily spewing out from a printer. If you knew how to read the printouts you could see westerly winds changing course, cyclones erupting and dying down, temperatures and pressures playing see-saw in
the atmosphere. One day Lorentz, wanting to examine a particular sequence in greater detail, decided to start his simulation midway through. He bootstrapped his simulation using numbers from one of his earlier printouts. He had expected the simulation to start and proceed from the point, from where he had taken the numbers he input and take the already pre-determined course. But on returning from his coffee break he found what was to be the birth of a new science.

His current simulation did not resemble the older one in any way. It had diverged at some point, and gone on diverging more and more after that. Even though he had initialized it with the same input values. Soon he realized that while his program maintained numbers up to six places of decimal (for e.g., 1.264067), the printout showed them rounded off to three place (i.e., 1.264). The only difference had been that he had used that rounded off value to initialize his toy weather. The result - where it was snowing earlier, it was now a scorching summer.

This came to be known as the Butterfly Effect which implies something like "If a butterfly flaps its wings in New York, the air currents change such that it will rain next Tuesday in Beijing."

And from this emerged the fascinating science of Chaos.

Risking a little bit scientific imprecision, let me try explain what is it all about. Determinism is the philosophical belief that every event or action is the inevitable result of preceding events and actions. Thus, in principle at least, every event or action can be completely predicted in advance, or in retrospect. Translated into laws governing the physical world it means, that given accurate measurements of the world around us, we can predict the state of the world at any point in the future. Now let us throw the monkey wrench into the machinery - No real measurement can be infinitely precise. All physical systems need measurements to start with. And hence long-term predictions about the state of these systems are nothing but mere guesses. This science of the unpredictable is called Chaos Theory.

So what? Why should you care with some arcane set of physical laws not doing something they were supposed to do? Chaos permeates our universe. Some examples: It has been found in systems describing wildlife and human population patterns, stock prices, shapes of clouds, paths of lightning bolts, intertwining of blood vessels, physiological models of the human heart, galactic clustering of stars, evolution. And it means you will never get an accurate weather prediction beyond 3 or 4 days.

But Nature is not chaotic - everywhere in Nature we see order and patterns. Where does this order come from, when there is chaos everywhere? But Chaos does not rule out patterns: Since our world is classified as a dynamical, complex system, our lives, our weather, and our experiences will never repeat; however, they should form patterns. They do and in precise terms it is called the concept of self similartiy and self similar patterns are called fractals. It is like this: never in history have two events been exactly the same, but as everyone knows history repeats itself.

For a most wonderful introduction to this subject I would suggest: "Chaos: The Amazing Science of the Unpredictable" by James Gleick.

I have an uncanny feeling that it has some metaphysical implications as well, like understanding the human mind and thought. Just think in terms of the assumptions we make daily about ourselves and others and our world, and the actions we take, and consequently the future we build for ourselves and others. But I'll not venture there. I'll leave you with this quote from William Blake:


"To see a world in a grain of sand and heaven in a wild flower
Hold infinity in the palms of your hand and eternity in an hour"



References:

• Chaos: The Amazing Science of the Unpredictable by James Gleick.
• An Introduction to Chaos Theory and Fractal Geometry
• What is Chaos?