I almost felt obligated to do this follow-up, considering how badly I lambasted the book that purported to explain the concept, because it seems that it was, at least to a degree, more the author’s dismal attempt to explain it than the concept itself.
We’re talking about chaos theory, and it does not bode well that I sought out multiple sources to try and get a grip on it and failed; however, this recent article did more for my understanding than all of those sources combined, and did so in a way that it fit well into the other disciplines of science. That article is The Forces of Chance by Brian Klaas who is, of all things, an associate professor in global politics at University College London – not (by vocation) a mathematician, though how far removed this is I cannot say. But all credit to him for pinning the idea down so well, with perhaps some caveats in there, which we’ll get to.
Basic definition: chaos theory is the manner in which large systems may depart from expected results in a non-linear manner. Well, that’s about worthless without exposition, but to add the necessary element, in some cases very small variations can lead to quite broad effects, and we’ll use the old standby of the weather to help explain it. Weather is hard to predict, even though we understand the mechanics of it just fine: air warms and expands, picks up moisture that can make clouds, and so on. But predicting it is hard and fraught with wide error margins, because a little extra warmth here, a bit of smoke there, and other such factors, can cause a storm to become raging or peter out entirely.
A quick note: physics is deterministic, meaning that if we know the energy that goes in, we know the effect that comes out. Full stop. The only place where this falls apart is on the subatomic level, and countless experiments at this level shows that it rarely ever can rise above it to have the slightest effect at all; there’s more than a suspicion that there’s at least another law of physics governing this subatomic ‘randomness’ to make that deterministic too. What this all means is, given enough information about conditions of any given system (for instance a cold front,) we can predict what it will do. The key factor in there is given enough information, which is many cases is far more than we have any way of gathering or collating. How much of that smoke from a volcano will reflect sunlight and drop regional temperatures, versus how high is the humidity where the smoke particles themselves form nuclei for raindrops and gets quickly carried back down to the ground?
Now, the ‘law’ of averages (we really should stop using that term,) indicates that small variations tend to balance out: a little bit this way, a little bit in the opposite way, and the effect largely cancels. What chaos theory addresses are the circumstances where that averaging fails, and a small variation leads the physical effects down a different path (this is where non-linear is a bit misleading, because it remains linear, just departing from average or even expectations.) My example is following a complicated set of driving directions, only inverting right and left in just one step – you might still get fairly close to your destination, or you might go incredibly far out of your way.
Klaas provides another example that highlights a difference in factors, by recounting a personal, emotional bond that affected the choice of targets for the atomic bombs dropped on Japan during World War II – and at the same time, a chance weather event. Both of these – human emotions and weather – are inherently chaotic, defying predictions and expectations. And Klaas largely addresses the failures of social sciences (politics, economy, sociology, psychology) to effectively predict outcomes, which are all reliant on human emotions to a large extent. Does this mean humans are chaotic? Well, certainly that they’re complicated, while not in any way defying the laws of physics or determinism. For instance, I don’t like the color red, and who knows why this might be? It could potentially be due to my astigmatism, and how the lenses in my eyes don’t focus red as well as other colors, but the result might be that, in a decision that depends on whether I choose red or blue, blue is going to be the case most often – even though, on average, humans prefer red over blue. You could only predict this if you knew this trait about me (and now you are so armed.)
This overall dependence on wildly variable human input, however, is why there’s a distinction of ‘social’ sciences versus ‘physical,’ and you can argue – I would, anyway – that the word ‘science’ shouldn’t be applied to the former, because there have never been any results in such fields that tell us we have this down to a science. Here, chaos theory has due application – to a degree, anyway.
Because chaos theory doesn’t determine when a system will depart expectations or ‘become non-linear,’ nor does it provide a method to prevent this – it’s just something we can point to after it happens, a name we can apply. In scientific terms, a theory is an explanation for the known facts – a strong theory predicts results, given the right factors, and this is what chaos theory does not do. And this is also where the article was ultimately disappointing, because while it showed how and where chaos might erupt, it didn’t provide any advancements that have been made since the theory was first coined – I was kind of hoping that, given our enormous computing power and the decades of observations, someone might have been on track for finding any key factors that would help predict when this non-linearity could appear, but so far, we appear to have nothing.
The aforeblasted book by James Gleick was notorious for accusing scientists for not accepting chaos theory, though it never became clear where this was taking place, nor what exactly was supposed to be done about it, and Klaas makes the same error, though to a lesser degree, For instance:
The problem is that social scientists don’t seem to know how to incorporate the nonlinearity of chaos.
I’ll bite: how do you incorporate chaos theory? If it can arise at any time, especially in certain disciplines, what are we supposed to do about it? Simply shrug and say, “I dunno,” and then go play video games? Giving a name to unpredictability isn’t exactly a huge accomplishment – we’d embraced unpredictability before we had language. Ignorance is our default state; our goal is to reduce that as much as possible.
Klaas also targets natural selection (which of course raised my hackles,) but this is more of a straw man argument than anything informative. He shows that genetic variations were largely random, which is perfectly true; the problem is, virtually no one claimed otherwise, and the key part in there is natural selection. Evolution is how the environment favors the variations that best support survival and reproduction, but it has always depended on which variations arise, and many of the weird things we see in species are because an optimal variation did not, so something else that could barely fit the bill was adapted instead. I hate to tell him this, but this was known before chaos theory was coined (and didn’t leap forward after that, either.)
I still have to give the article credit in that it never attempts to deny or misuse determinism, never implies that our knowledge of physics is somehow flawed, which is certainly the overriding impression that I kept receiving from Gleick’s book. Nor does it attempt to elevate chaos theory into something remarkable and innovative, though Klaas does seem to believe that the social sciences cannot recognize it; I have seen no direct examples of this myself, though I never put stock into economics and poli-sci and don’t know how many people do.
But what I will say is that the article sparked a couple of ideas, and rather than make this post inordinately long, I’ll go into them a little later on. Lucky us, eh?