Tuesday, November 22, 2005

Re-Organization, Self-Organization, Complexity, Chaos and God: Part 2

One of the main arguments employed by the propagandists of the Intelligent Design (ID) theory is that there is a remarkable amount of order in the universe. This is in spite of the Second Law of Thermodynamics (approximately stated thus): "The Entropy, or degree of disorder, of a closed system can only increase". If there is nobody out there controlling things, how does order persist?

The answer lies partly in the Theory of Chaos; partly in the Theory of Self-organization; and partly in the Fundamental Laws of Nature. Before I dive into these topics, I want you to imagine the following conversation between a Priest and a Scientist:
Priest: The four seasons drive the rhythm of life. There is beauty, purpose and order to it. How can you deny that it is the work of God?
Scientist: The four seasons occur because of the tilt of the Earth and the manner in which it revolves about the Sun. I don't see what God has to do with it.
Priest: Ah, but who caused the Earth to tilt and rotate in that manner?
Scientist: The Laws of Gravity and Motion are more than sufficient to explain it.
Priest: And who defined those laws and brought them into our reality?

Here the Scientist is stuck. For all the proofs and explanations that Science derives, it is still based on certain axioms and fundamental laws, which can't be proved; they just are. Chew on this for a while... but for now, some geeky stuff...

One of the Fundamental precepts of the Theory of Chaos is that there is Order in Chaos. If something is entirely unpredictable, then it is random: which is very different from saying that it is chaotic. A chaotic system is merely one that cannot be simplified by studying on a smaller scale, eg. calculus, or a larger scale, eg. statistics. And a basic characteristic of many, perhaps all, chaotic systems is the presence of an "Attractor".

An Attractor is a stable state of a system. If the system is mildly disturbed, it still returns, for no apparent reason, to the same state; give it a large enough disturbance and it equally inexplicably goes into a fluctuating, disorderly state that we call chaos. The ecological balance is a good example of this. The presence of the attractor gives these systems a self-organizing nature, that can be mathematically predicted. Nothing mysterious or magical about them, once you've run the Matlab simulation and seen for yourself!!

However, in general, when you talk about a self-organizing system, you are usually talking about the existence of an "intelligence". We are so used to the way humans run things that we can only think of intelligence as a centralized entity; hence a lot of things that are controlled by no visible central mind get attributed to God. However, it is often noticed that distributed dumbness can behave like centralized intelligence!

I know I said I'll explain distributed systems in this post, but it looks like it'll have to wait for the next one...

Cheers,
Prashanth.

11 comments:

Vc said...

eh ???

Anonymous said...

That was a really interesting and fascinating post. At some point of the argument, science has to give up. I don't know how convincing it may sound, but here's another theory to the way we set our beliefs and thought processes. Think of our logical world of science and technology as a box the dimensions of which are well defined by laws and axioms. As long as we accept those laws and axioms everything seems orderly. Anything that doesn't fit the box becomes illogical simply because the our brain is a part of that box now! We never questioned those axioms and laws yet we accepted them only because we saw them transalated into day to day phenomena.
Similarly the religious school of thought believes that every phenomenon is initiated by a superhuman power about which we do not know and so every situation surprisingly fits that rule without exception.

Prashanth said...

Perhaps I should have given a caveat at the beginning: Heavy Geek Content! Tread with Caution!

Anonymous said...

hehehe cu....
i mean.. nice..:)
-divster

Prashanth said...

This Divster is going to be the death of me... I'm going to die of indignation one day...

Anonymous said...

Death always brings with it a new beginning..
Better luck in the new one! LOL

-devilster

Artful Badger said...

So, the famous post on non-linear dynamics. I need to read this :D..

Artful Badger said...

How does calculus come under chaos?? This I need to know. Calculus is just a fancy way to find the sum and difference.
Well, the basic idea here is that you have a very large number of units, each whose behaviour is simple and predictable but whose behaviour as a whole cannot be predicted. For example, it might be possible to predict how a person might act under a given situation, but you cannot predict human history.
Many of these systems have fractal like behaviour. The stock market. The one year graph looks identical to the 1 month graph to the 1 day graph, just that the magnitudes are different. The re is something called the Zipfs law, you might want to take a look at it.

Artful Badger said...

Intern's idea of God I agree with. Something that is responsible for the world as it is.

Prashanth said...

Actually, I said that Chaotic systems CANNOT be analyzed using calculus or statistics. Their behaviour does not become any easier to predict or analyzed over smaller or larger scales.

Artful Badger said...

Ok ok.
Such systems are related to fractals. There is a new approach to studying the apparantely random stock market index called Fractal Finance. This can also be extended to other Chaotic Systems.