My first conscious appreciation of emergent behaviour was during those evenings, when, after finishing homework and settling on the terrace, I'd spot those flocks of pigeons zigzagging through the sky, among other things. I used to wonder how all the pigeons took the same turn simultaneously, making the entire flock take a single turn, making it look as if it was guided by some invisible force. I was a deep believer in God then, with all the pujas in the house, the "coconut breaking" promises (always broken :p) made to the local deity before exams, those postal Bible courses and all, and so I used to think that it was the hand of almighty God at work. But as I grew up, I realized it isnt so.

It all started when I borrowed a book, Chaos: Making a New Science by James Gleick, from Naren Gorthy, my friend. That was four years back. I was only 18 then and to my mind, all of it was quite heavy. Anyway, it turned out to be one of the most wonderful ideas that I came across, the idea that everything that is seemingly chaotic only looks chaotic and that it is after all determined by simple laws (see Chaos theory).

My interest in all this, chaos, complexity etc. grew and I wanted to read more of similar stuff and one day, I caught sight of Three Roads to Quantum Gravity by Lee Smolin at a book shop. The book, the concepts it presented, it was surreal even though it was heavy stuff. Though not centrally concerned with complexity, the book allows Lee Smolin to give us an idea of how the universe emerged to be as complex as it is today.

Still, I knew little of the behaviour exhibited by the pigeon flock and Michael Crichton's Prey helped. The novel, apart from being one of the best I've ever read, introduced me to the world of emergent behaviour and swarm intelligence. It was through this book that I learned how the pigeon flock manages to exhibit seemingly intelligent behaviour.

It happens like this. You might've noticed that a flock, more or less, resembles a triangle, with one pigeon at the apex. Let us look at this pigeon in isolation. Let us call this the leader. The leader, of course, keeps close to its flock. This is herd behaviour. The leader is free to fly in any random direction except of course, from where it came :p So, let us assume it flew left. The two pigeons behind the pigeon will see that the leader flew left and so they also fly left. Likewise, this information is passed throughout the flock and the entire flock flies left.

Nothing very great happened at the individual pigeon level. All a pigeon would do is to notice the pigeon in front of it. Now on, its simple. If the front one flies left, it flies left and vice versa. Simple principle. But note that this simple behaviour at the local level gave rise to seemingly intelligent behaviour at the level of the flock. It is as if all the pigeons know that they have to  turn in the same direction at that particular instant. This is called emergent bevahiour and I love it!

So, naturally I'd be thirsty for more of this stuff, and last month, I picked up Complexity: Life at the Edge of Chaos by Roger Lewin. I finished reading it yesterday and midway itself, it found its way into my list of great books (or maybe it was the science that was great).

Roger Lewin is a science writer, like James Gleick, not a scientist himself, like Lee Smolin. So, the book is a narration of Lewin's encounters with all these complexity studies guys at the Santa Fe Institute, and others. Lewin reports on the new science, a hypothesis kind of thing rather, that is brewing up in their minds, becoming increasingly fitter to be called a theory of everything one day! That is the theory of Complexity.

Chaos theory and complexity theory are closely related. In fact, chaos theory is a part, or in the author's words, "a subset" of complexity theory. According to Chaos theory, chaotic systems are very sensitive to initial conditions, a property famously referred to as the Butterfly Effect. Small changes in the input to a dynamical system cause astonishingly large variations in the output. Example: Weather is a dynamical system. "A butterfly flaps its wings over the Amazon rain forest" (small input), "and sets in motion events that lead to a storm over Chicago." (large output) Bizarre? But not impossible eh?

This is the essence of chaos. In a state of chaos, this is what happens. What is chaos? Disorder, a state in which you cannot predict the output to a certain input. Outputs to the same input may show wild, random variations but this output doesnt come out of nowhere. It comes from interactions with the system, based on simple laws.

What is complexity then? Simply put, all complexity is "poised at the edge of chaos". What is the "edge of chaos"?

A system can be present in three states. 1.Orderly, 2. Chaotic or 3. Something in between: orderly but close to chaos. In this state, the system is said to be at the "edge of chaos" – an edge beyond which is chaos, like a transition phase between liquid and gas.

According to complexity theory, the edge of chaos is the most optimal state in which a system can be present and that all complex adaptive systems (this term is quite simple. We are all complex adaptive systems. We are complex atleast because we are not simple like a virus and we are adaptive because… well, remember your first dog bite. If you had had one, you would've learnt that it's dangerous to screw around with a dog) travel from being in the state of "Orderly" to the edge of chaos as a natural consequence of adaptation. This is the best state to be in, it is a state of optimality, one in which maximum processing of information takes place,maximum computational ability is achieved. All this is heavy. I shall illustrate with an example, an analogy rather… my own

Human beings are complex adaptive systems (I explained why in the bracket above). Mr. X is a human being. X has a decent job, has a nice family and is quite content with what he is in life. He just goes to office and comes back, spends some time with his family and goes to bed and repeats the same everyday. His current state can be described as calm, satisfied etc. Let us call it Orderly.

X has an ego (this is an assumption). He wants to keep ahead of everyone. He wants to the best but slowly, X comes to realize that he's living a rather monotonous life as he sees other human beings performing more activities than he is. He fears that if he stays the same, in the future, he might lose out in this competitive world. So he decides to take up multifarious activities like swimming, pubbing, gardening, trekking, gymming, designing, social working etc. so that he can buttress his resume to increase his chances of getting a job… or more importantly, to decrease his chances of losing his job to more competent guys.

X feels good. He's doing a lot of things. He's no more the boring, "one dimensional" individual that he used to be but there's a problem: there are too many things, too many things to do in a day. He has to wake up at 4.30 in the morning and go for a jog, go to the gym at 5.30, come home to have breakfast at 7.30 and leave for office at 8.30 and work till 5.00 in the evening. Then, he has to do something or the other till 8.00 and then go to that party at 8.00 and then he comes back at 12.00 and collapses on the bed, much to the chagrin of his wife :p He has to wake up at 4.30 the next day and he's back at it again.

X likes it in the beginning. He's excited by all this but as days pass by, he becomes a stressed individual. One day, after too much stress has built up, he sits down at a corner and says "Fuck it!".

X's life has become disorderly. His family begins to complain, his performance levels at the office drop and basically, all hell breaks loose. He has travelled from an Orderly state to a Chaotic state.

Yearning for a little solitude and space, X goes to the nearby bar and orders a shot of Chivas on the rocks :p and gives strict instructions to the waiter not to disturb him. He begins thinking and reflects deeply "I cant be what I used to be and I cant continue to be what I am. Isnt there a middle ground?"

Yes! There is a middle ground between the Orderly state and the Chaotic state of X's life. It is called the Edge of Chaos.

X realizes, thanks to good ol' Chivas, that he can optimize his daily life between being monotonous and extremey busy. He cuts down a few tasks, so that all the daily tasks that he has fit inside 24 hours.

Both relieved and excited, he goes back and reorganizes his daily life. He adopts a life in which he can do as many tasks as possible and yet, be stable… or, orderly. This is an optimum state, the best state he can be in, in his given environment. Here, he processes maximum information, he attains maximum computational ability. Stab! Mr. X went from nothing to dude!
(Warning: Mine was just a loose analogy. It might not fit in the complexity theory picture exactly.)

"So what?", you might ask, "you've wasted all my time for this??" Well, this sequence, in which a complex adaptive system travels from a state of simplicity, increases in complexity and reaches the edge of chaos as a result of adaptation in its given environment, is seen in many natural processes. "Oh really?" Yes. The list might astonish you:

1. Evolution – complexity theory is a new challenge to Darwin's idea about evolution. It can explain both explosions and extinctions of species of life.

2. Ecosystems.

3. Businesses and at a larger level, economies.

4. Societal transitions.

5. Earth as a whole (you know, the Gaia concept)

6. Even the universe and many, many more.

"How??", you might ask. Well, go read the book.

Phew! I know… long post.

My next book on this subject: Emergence: From Chaos to Order by John Holland. If you have it, please, please be good enough to lend