WHEN: 8:45am EST, September 21st, 2013
WHERE: In my apartment in Portland, ME
FORMAT: DVD on a 24” Philips CRT television
MENTAL STATE: Tired. Headache. Stuffy Nose.
IAN MALCOLM, AMBASSADOR OF CHAOS THEORY:
There is a decent chance that if, like me, you are an average movie-loving schlub, you first heard about chaos theory from Jurassic Park‘s Ian Malcolm. It may be the only place you’ve encountered the concept. This is unfortunate, because for all his odd laughs and snazzy outfits, Ian Malcolm appears to know shit-all about chaos.
Today we’re going to take a quick look at what Ian Malcolm has to say about chaos theory, and what, if any, resemblance it has to the fascinating area of study in which he so suavely claims an expertise.
Because intensity + leather = science.
“CHAOTICIAN” ISN’T A REAL WORD:
It’s never a good sign when your expert identifies himself using a made-up term. Chaos theory is a field of study within mathematics, which can be applied to a multitude of different disciplines. A mathematician might look at the general behavior of chaotic systems. A biologist might study chaotic behavior in the fluctuations of elk populations. A fluid dynamicist might consider chaos theory when studying air flow problems. There are not, however, a group of scientists called chaoticians going around warning people that systems are unpredictable.
“Excuse me, ma’am, I hear that your refrigerator has a fractal problem?”
This never happens.
“THE BEHAVIOR OF THE SYSTEM IN PHASE SPACE”:
Malcolm’s one and only reason for tagging along to Jurassic Park is his claim that chaos theory proves the park to be unstable. But, during the course of the entire movie, he presents no evidence to support this. The closest he comes is when, on the helicopter, he tells Hammond that his concerns are based on “the behavior of the system in phase space.” Hammond dismisses this as “a load of fashionable number crunching.” So is Hammond right? Is Malcolm talking out of his ass here?
I’m afraid that if I tried to give a proper, in-depth explanation of phase space, it would turn into a case of the layman leading the layman. I can, however, tell you the bare basics. (You can trust me! I read a pop science book on chaos). Firstly, it’s important to note that phase space is not some sort of magical diagnostic test. It’s much more of a visual/conceptual aid. Secondly, there’s no way that something as complex as the operation of a theme park/zoo could reasonably be represented in a phase space diagram.
To understand what I mean by this, take a look at this phase portrait of the Lorenz attractor.
Why Malcolm thought Sattler would be familiar with this type of attraction is beyond me.
The above image represents a surprisingly mundane phenomenon: the circulation of a thin layer of liquid being heated from above and cooled from below. This seemingly simple motion displays, when plotted, amazing complexity. Entire books have been written on it, and it only comprises the four dimensions of physical space and time.
If the above “simple” example of chaotic behavior is that complicated, how has Malcolm been able to plot out all the variables involved in an entire amusement park? Even assuming he had total access to the park, down to the last microbe (he doesn’t), a long period of time to observe it (also no), and the computational power to look at a phase space diagram for this data (such power does not exist), he would only be able to see patterns in how the system behaves, not make specific predictions about its imminent collapse. He might, under those ideal but non-existent circumstances, be able to point out potential mathematical outcomes for the park, but he certainly wouldn’t be able to point out what’s going to go wrong, or when.
Either Malcolm is passing off some horribly simplistic mathematical model of the park as accurate, or he’s a big fat liar.
THE WATER DROP EXPERIMENT:
Malcolm drops some water on Sattler’s hand; it rolls off. He drops another drop; it rolls off in a different direction. Behold: chaos!
The problem is that this experiment, as explained by Malcolm, creates an entirely false impression of chaos. The point that he appears to be trying to make is that even under perfect conditions, the drop would roll down two different, unpredictable paths; that the result will be, by its very essence, random.
In reality, two identical drops of water, dropped on two identical surfaces, would take two identical routes down. The reason they never do in practice is that we are incapable of creating identical starting conditions. In other words, complex systems (flowing water, in this case) are deterministic, but are sensitive to initial conditions. Two identical drops of water, dropped on two surfaces with only microscopic differences, could take two wildly different routes down. Approximately similar starting conditions do not create approximately similar results.
To be fair, Malcolm comes very close to hitting this correctly. He does mention the microscopic differences in the skin, etc. But his wording messes things up. He says, “I’m going to do the same thing, start at the same place again,” implying identical starting conditions. It’s just a little difference in wording, but a chaos expert, of all people, should know that a little difference can have huge consequences.
THE ESSENCE OF CHAOS:
“The Tyrannosaur doesn’t obey any set patterns, or park schedules; it’s the essence of chaos,” Malcolm says triumphantly. Unfortunately, he’s missed the point entirely. Yes, the Tyrannosaur is going to do what the Tyrannosaur is going to do, but according to chaos theory, all of its future patterns are set, they are deterministic. We just can’t tell what they are, because we are unable to see the precise combination of initial conditions that caused them. We don’t know the exact firing pattern of every neuron in the Tyrannosaur’s brain, or every wind current whooshing by it, or any of the other billions of factors involved. Even if we were able to approximate these, we wouldn’t be able to predict its behavior, because approximations are not good enough.
Malcolm could more accurately have said, “We are unable to compute the factors that guide the Tyrannosaur’s patterns, so we could never predict its behavior. That’s the essence of chaos.”
But he didn’t say that.
It might seem like I’ve been nitpicking here, but when Malcolm gets major concepts wrong, significantly misspeaks when talking about others, and then has the gall to make up a name for the specialty he’s been fumbling, I think there’s room for criticism. Chaos theory is really really cool, but sadly, two hours with Ian Malcolm doesn’t leave the viewer with a solid idea of what it is. That’s a real shame. I probably haven’t done much better myself, but hopefully I’ve succeeded in pointing out that there’s much more to this topic than Malcolm lets on. And at least I’m not claiming to be a “chaotician.”
For more information on chaos, check out James Gleick’s Chaos: Making a New Science. It’s a fun read, and it’s what drove me to write this article. You’ll start reading it as a layman, and you’ll finish it as a layman who knows slightly more about chaos than Ian Malcolm. So, get to it, and you too can tell Hammond he’s a shithead without any legitimate justification!