Chaos Theory … Basic UnderstandingPosted: January 13, 2010
There are certain aspects of nature which arent as well undertood or appreciated as others. This may be because we dont understand them too well. Whatever the reason, science is not as well appreciated as one would think it to be. One of the aspects is something i am reading about, Chaos Theory.
The subject is something i dont understand much about either, my knowledge about it coming from the book i am reading by James Gleick. There is i am sure lot more to the subject than what i understand today, so you will have to excuse my only too apparent lack of depth on the subject, something that would require delving into the Mathematics behind the science which i have yet to do. What i have managed to understand is this:
Dynamic systems cannot be described completely by means of mathematics because these arent exactly linear in nature, while there is a certain amount of chaos or uncertainty which is inherent in these. This uncertainty is stable which means that this is not a parameter of system variables, while on the other hand this means that the stability of the system is also uncertain because of the inherent non-deterministic nature of these systems.
Phew! Because i believe that if you cant describe a thing in ten words or less, then you havent understood it, i should summarize. Basically, chaos in stability and stability in chaos. What this means is that what may be stable at macro level still has instability or chaos built into it while while this chaos is stable which means that it isnt impacted by changes to system variables.
Lets take the coast of England conundrum. The question here is exactly how long is the coastline of England. Or India? Or any country? Or how does one calculate the exact length of the border of a country? Looked at from a satellite one may get an answer which wouldnt quite match with the answer someone walking on the ground may arrive at, and this isnt only about approximations. The same concept can be applied to when looking at the surface finish of an object. While the surface may seem smooth to the eye or to the touch, it doesnt seem so under the microscope.
This brings us to the idea of fractals. A topic much written about so i am not going to bore you with a layman’s definition. What is interesting about fractals is that they are the same at the microscopic level as they are at the macroscopic level. In other words one could say that while the macroscopic contains the microscopic, the microscopic contains the macroscopic, too. And this, to me, is a profound concept. Try to associate this idea with what the philosophies of the world tell us about our true relationship with God.