Chaos around us?
calendar_month March 26th, 2022 editBy: Thamir timer ~5 min read
When we think of everything around us, it seems very intuitive to say that “minor” tweaks in initial inputs or conditions usually lead to just tiny little changes in the output or macro-response we get. And this is not coming completely out of the blue, but rather this at first sight seems consistent because many times we don’t dig enough to see the consequences of things/inputs really precisely, so we deem it as insignificant because it wasn’t detected thoroughly in the first place. And the leap to generalize this observation is not a really big one if overlooking
detailed actualisation of say our behavior is common, to some extent. But all these assumptions were questioned head-on when chaos theory came to be around the 1960’s. So when we are talking about chaos theory (or chaotic systems) what we are saying essentially is that when a certain system just changes its initial conditions slightly, and when I say slightly I am talking one decimal number in a system, the whole system can completely change its behavior given some time (the decimal number is just an abstract representation of something real, a temperature in a certain place, for example). Chaos comes from the fundamental dependence on initial conditions of the system, and what I mean by that is if you imagine an infinite number that represents say the wobble of a hypothetical object (3.2539853…), no matter how much you walk through that infinite number, all infinite digits of this system are extremely relevant to its final behavior (or its wobble in this case).
Let’s take an example of a chair orientation in a university’s interview location. Imagine if the orientation of a waiting-room chair outside the interview room was situated in a way that faces other people/students who are being interviewed through a glass. Then at the end of the first interview, the first interviewer fist pumps the first interviewee (assume we live in a world where a fist pump is an extremely accepting gesture). It seems like this “initial condition” of say the chair orientation facing the glass won’t yield any big difference in students in the waiting rooms entering, quitting/leaving, or getting stressed for this competitive position of choosing one person, but we can infer from the behavior of chaotic systems/chaos theory that if we just change initial conditions i.e. chair orientation in this example, it might actually make a student enter, leave, be more competent for the interview, by extension alter the chance of the student entering the university, and one step further, change whole experiences that would shape this person in a certain way. Had we changed the orientation of this chair say opposite to the glass showing his peers being interviewed (or remove the glass), we would have had a completely different Ahmad, for example. This might be a slightly misrepresenting example, and not necessarily a clear-cut "chaotic system", but the analogy that might help here is thinking of the chair orientation as a very small decimal place, say the 8 in this number 1.9264257258 that represents Ahmad’s life, for example, and if we change that 8 to say a 1 (i.e the chair orientation) it might look trivial to the change it might yield in Ahmad’s “life”, but we have come to know through studying chaotic systems that it’s actually not that trivial to how these small “conditions” add up in the final output after all.
To touch base on the status quo, the weather is a very good example of chaotic systems (real ones, unlike the above example), specifically deterministic chaotic system. So if we choose to divide these words into two parts, what we mean by the deterministic part of it is that the system’s state is limited to a certain kind of behavior, in other words, we don’t seem to see rocks raining from the sky in the case of weather, but when we are talking about the chaotic part of the word, we mean that there is a fundamental limitation to tackle the system’s precision to its core, so we deem it as chaotic because of the inherent “unpredictability”. So to put the two words together again we can describe it as: the inherent unpredictability of a system within its limited bounds of behavior. So if we bring an alien species that look at the weather from the outside, and can calculate the digits of all the variables in the weather system to infinity (whatever that means), then the system wouldn’t be “chaotic” in our interpretation of the word. The way Ed Lorenz, a Meteorologist came across chaotic systems was indeed through trying to predict atmospheric patterns. So he ran a simulation on a computer with 12 different variables of the weather like the temperature and other related ones. After the first simulation was run, he wanted to run it again, but instead of entering all digits from the beginning of the first simulation again, he started from the middle of it to save time, and the digits in the second simulation were entered to 3 decimal places (0.345) rather than the six decimal places (0.345212) in the first simulation, and the final output of the second simulation was completely different from the first simulation due to this discrepancy.
“Sensitive dependence on initial conditions”, the words just seem like an intuitive and clear set of strings at first sight, like I can imagine myself saying to a person living prior to the explorations of chaos theory that certain systems are “sensitively dependent on their initial conditions” and a reaction that might be expected (maybe naively expected) is: “of course some things ‘sensitively depend’ on their first conditions, what are they dependent on other than that?” It’s almost like these words don’t really show the size of the conclusions, but to put it another way, let’s just say that after the explorations of chaos theory we came to know that some systems really really really sensitively depend on their initial conditions (we are talking infinitely sensitive here). To put all of this into perspective, different systems’ “chaos” differ from one system to another. Some are extremely chaotic systems, and others are less chaotic i.e. easily predictable. Each system seems to follow a certain kind of “attractor”, which is an abstract representation of states where a system seems to follow or emerge towards. These attractors can give us an indication of how chaotic a system is, and give us hints on it’s predictability as well.
(More on attractors and the mathematics behind chaos theory in this amazing video).