It certainly has been a while since I last wrote about chaos. Perhaps you could say I’ve been a little… unpredictable? Maybe the seemingly inconsequential decision of a certain someone on one side of the world, having read the post and enjoyed it, to not give the post a like (yes, I’m looking at you) somehow had the net effect of delaying me writing this one on the opposite side of the world. Or maybe I’m just incredibly unorganised… nah, it can’t possibly be the latter.
When I mention the word ‘chaos’, people generally think of the butterfly effect. This involves the metaphorical example that the flap of a butterfly’s wing in Brazil could set off a hurricane in Texas a few weeks later. The idea behind this seemingly simple concept is that very small causes, which one might expect to have no tangible impact, can have very significant effects in the long term, due to the successive buildup of minute interactions that flourish out of control when repeated over and over. Edward Lorenz, a pioneer of chaos theory, first popularized the use of this term in his talk at the American Association for the Advancement of Science, which he aptly titled ‘Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?’. I know, how creative.
Before pursuing the field of chaos, Lorenz worked in meteorology, looking at the properties of the atmosphere and using this understanding to predict the weather. In 1961, he had programmed a very primitive computer model to print out lines of numbers which represented specific characteristics of the weather, such as amount of rainfall. On one particular day he decided to repeat some of the computations from a previous run so that he could examine in greater detail what was happening. In order to save time, Lorenz input data from the middle of that previous run, and let it run while he headed down the hall for a cup of coffee. Upon returning to his simulation an hour later, however, he noticed that the weather model had developed a completely different scenario from what he had obtained before. After some testing, it seemed that the problem arose from the fact that he had entered the initial condition 0.506 from the printout instead of entering the full precision of 0.506127. This initial rounding error had slowly amplified itself in his simulation until it completely changed the course of the model.
This idea nicely demonstrates the idea that chaotic systems have very high sensitivity to their initial conditions, which results in our inability to predict what the system will do in the long term, even though interactions fully obey the laws of classical physics. It is often believed that the terms chaotic and random can be used interchangeably, but this is not the case. If a system is random, that means we can only determine what will happen to it based on probabilistic analysis. We can predict what general direction the system will move in, but we don’t know what will be happening within the system at any specific point in time. This is because every action and event is completely random, not predetermined by its past or present conditions. Chaos, on the other hand, applies to a system that is completely deterministic. Every action should in theory be able to be predicted based on its initial conditions. The problem that arises, however, is that we can never have perfect knowledge of a system’s conditions. As they build up, the smallest of discrepancies can throw the system completely out of control over a long period of time.
One of the reasons these two get mixed up so readily is due to the similarity of results they can often produce. As a result, chaotic results are often used to demonstrate random systems. For example, modern day computers are unable to generate truly random numbers simply due to the way they were programmed, so chaotic iteration is often used to produce a similar effect.
My friend recently told me about a certain scene in Jurassic Park and which I just cannot get over. It’s so ridiculous that I’ve come to love it. I must say, it sure does explain chaos much better than I could ever do…