Saturday, May 2, 2009

Life - The stochastic model

I have often wondered about the meaning of life and the existential questions. I have always drawn a blank. Big surprise eh? For some reason, I just cannot come to terms with the notion that life just "is" and there is no logical reason or higher purpose behind it. If everything in nature stemmed from a few basics laws then it ought to be possible to bring about some semblance of order in the nature of things. I fully understand the problem of algorithmic compressibility and I am not looking for a way to figure out the future. I have always loved mathematics and all my initial attempts at understanding the universe were inherently mathematical.

I pondered over the fact that cause and effect are interrelated and a finite number of causes should always lead to a finite number of effects. Thus, if it is possible to limit the set of inputs, the output set should also be bounded. Under this hypothesis, if I could narrow down the number of factors that can effect a situation I could hypothetically have a very good chance of finding the outcome. Seemed simple enough but turns out that nature is far more complicated. This hypothesis kept me busy for a while and I attributed my failures to the fact that I was not accounting for all the variables.

Enter Chaos theory. It gave me nightmares. It went completely against my understanding of mathematics but here it was. I coded a computer program on one of the equations and nearly wrecked my machine but it was there and it was undeniable. It just stated that a given input can result in a wide range of outputs which seemed essentially random in nature. My initial hypothesis went out the window. Closely associated with Chaos was the concept of fractals and that puzzled me for a while. My initial consternation gave way to curiosity and I started to feel that a deeper understanding was needed to get to what Chaos was all about. It soon began to seem that Chaotic equations did settle down into a "pattern" after a while and though they do not stabilise, they do remain bounded. There was still hope. If the universe is based on Chaos then it has had enough time to settle into a pattern and we should be able to figure out the bounds.

Then came probability and gate crashed my concepts. The mathematical probability struck me as wondrous. It seemed to say that you can try doing something once and it may work, try twice and it may work but try it a zillion times and you will fail "x" percentage of the time. It was a surprising result but it was true because it is verifiable. Could life indeed be a stochastic process? Modern science does treat it as so and so you will see percentages like children in Somalia have 70% chance of survival etc etc. Statistics such as this are a clear indication that there is a probability lurking around the corner. Probability of survival, probability of success... what else? It seems we are on the verge of a scientific and philosophical breakthrough. A point in our history where we realize that there are just too many decisions to be made and each decision has a certain probability of success. The number of choices we see before us are in turn a result of the choices made earlier. So that's cause and effect. After all this, even in spite of good decisions and sound judgement it is still possible to screw up courtesy Chaos.

Which now makes me wonder about the probability of probability describing life... Hmmm... maybe another day.

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