Okay before I get to the main theory let me just talk about the motivation of this theory. Today in chemistry lab we were supposed to identify certain compounds which were numbered. As it turns out most of the students had already figured out a pattern as to which compound is assigned which number and thus the identification was just a piece of cake. But, out teacher was constantly pointing out that the numbers are rather randomly distributed and hence we shall not jump to any conclusions. This provoked a friend to say, “No finite set is random.”
At first thought this statement seem pretty correct. But when you think about it, how often do we deal with events/things which happen infinite number of times? And yet, countless number of times we talk about event being random or chaotic. So what is this chaos anyways!?
Okay, so talk to a kid who has just learnt counting. And show him this sequence:
Trivially, this is an arithmetic progression with a difference of 3. But to that kid this is just a sequence of random numbers separated by ‘periods’.
Now just forget about the kid and have a nice look at this:
Glare at this stream of numbers till you find a pattern or your mind terms it as chaotic or random.
Just to let you know this is known as Hofstadter’s Q Sequence, and it follows a well defined pattern details of which you can find at: http://en.wikipedia.org/wiki/Hofstadter_sequence
The whole point of this exercise was to show that the randomness of a phenomenon is not just the function of that phenomenon but also the observer. The first sequence I mentioned must not have been random for you but the second sequence, I must admit seemed pretty chaotic for me as well for quite some time. So, the idea is that each and every moment that we live through is a result of a pre-defined mechanism. It’s only a matter of observation and perception. We tend to call anything for which we are not able to find an explanation or mechanism as chaotic. For instance, consider butterfly effect, also known as chaotic effect. Now, butterfly effect put into simple words is amplification of small changes by a series of events. But, to most of us it is highly unlikely that how not greeting someone morning in India can result in getting an FedEx employee in USA fired, and thus we term this effect as chaos.
Chaos is relative. Every moment of our lives we are observing, perceiving and learning. When I see a chaos all I feel is the zeal to learn. Pattern is beautiful but chaos is inspirational.