~ butterfly and its wing ~

One of the topic that always intrigue me in branch of maths, is a chaos theory. The first quote given by my favorite lecturer on his undergrad class is this - if the butterfly flip its wing in Brazil, will there be tornado in Japan? - and as naive as I am as typical undergrads, at that moment of time, I know that I'm hooked for life, and the classes seems to awed me more and more each time (only after finishing the class, do I know that the quote is easily accessible anywhere, but still, my thanks go to Dr Salmi for making the class as interesting as that).

Chaos theory is kind of new in math. It is unlike the study of geometry, which originated as early as Euclid (when the Greek is well known for their wise scholars), or the algebra (thanks to al-Khawarizmi and the era where people believe that, to be close to God, is to get as close as you can to the knowledge apprehended as a gift from God). Chaos theory is the science in our time. A science develop by our intellectual scholar, and that might probably the reason why it became quite dear to me personally. However, in all branches of knowledge, there are of course, elements from different branches that help this theory to develop. As the saying goes: The reason that I can see further, is because I'm standing on the shoulders of giants (you can relate this to the saying of Newton, and also being familiarize by google scholar, and an alternative music band named oasis for one of their album).

It is Mr Edward Lorenz who pioneering this theory. He is a meteorologist, and studying mathematics during his youth. He came with this finding by surprise. He let his machine do the calculation of weather system (if I'm not mistake, this is a problem with a differential equation for weather prediction, the one with few variables and some initial points involved). When he considered different initial point, that is very small different, what comes to his surprise it that the end value diverge significantly as oppose to his first iteration (the different in initial point is just a probably mere 0.000001). This is the gist in chaos theory. What define this problem, is its sensitivity to the initial condition. Some even quote this as a 'butterfly effect' - strangely enough, this is also the name of a movie lead by Aston Kutcher. All this started in early 1960's, and the study is actively undertaken by many until now. He (Lorenz, not Kutcher) died of cancer at 2008.

Some regard that the development of a computer what makes all this easier and that make this area has big potential to go further. This might probably has a sense. The earlier work might already there, the works by Poincare, Hadamard, to name a few, but since it is hard to express the abstract idea, the works mostly underdevelop. The use of machine in recent years helps make sense of many things, as well as give color to this field and probably make it less people (wishful thinking?) to judge maths as a dry subject (and what more abusive, to those who regard mathematician a dreamer, and that the study of maths in particular the theoretical part is a waste?). But in the end, the butterfly will always flip its wing; and the wind, will always blow.

tagline: chaos theory, strage attractor, butterfly effect