Bear with me, for today is the day I deviate (sort of) from my usual liberal arts/humanities subject matter and venture into the world of math and non-social sciences. Gasp! Will I be any good at it? Will I utterly fail? We shall see, my friends, we shall see.

I’ll start with an anecdote: last weekend, I had an English project. It wasn’t just any old English project; it was asking me to do what I engage in every single day–critical analysis of a written work. Actually, it was seven written works, and all had to be analyzed to a very specific list of seven non-engaging questions to be applied to every one of them, and the answers would preferably be in paragraph form. I tend to procrastinate on assignments that I see no value in, so I left this all to the very last night: seven written works and 49 paragraph-answer questions. In retrospect, it was pretty stupid, even for me… at three in the morning with more than twenty questions left to go, for some reason, I went searching through my contact list to find someone online to talk to. After I explained my situation, the person asked why I was starting a conversation when I obviously had a lot of work to do, and mindlessly, I replied with something similar to this: “I need to keep my mind alert, and conversation just works that way… it’s unpredictable, it makes me think… it works like chaos.”

And just about when I pressed ‘send’, even in my feverishly caffeinated state of mind, I thought: *oh my God, it is chaos*.

Mathematical chaos, I mean. It’s a real-life example of chaos theory in action.

First, I offer this incredibly simplified and probably not perfectly sound explanation from what I understand of chaos theory. Here it goes: in chaos theory mathematics, chaos comes as a result from something called nonlinear feedback occuring in dynamic equations. That means that when you have a constant and a variable with a power greater than one (eg, a number squared) that changes with feedback (the result being inserted back into the equation as a variable) in the same equation (eg, x^2 + c = r, where r becomes the next x), you start to get chaotic results like this graph that was derived from a nonlinear dynamic equation for population growth. One of the more classic examples of nonlinear feedback is the three-body problem of physics. It’s impossible to plot the *long-term* paths of, say, two moons that revolve around the same planet, because the long-term results eventually get chaotic. That doesn’t mean that three orbiting structures don’t suddenly fly erratically off into space (we wouldn’t have our own Sun-Earth-Moon system if that was the case); it just means that the three orbiting paths start to slowly change in ways we can’t predict beforehand. This is because the three masses each have their own nonlinear gravitational force that effects the two others.

Complicated? Try this oversimplified (possibly too much so?) summary:

(dynamic number with a power greater than one) + (unchanging constant) + (result that becomes the new first number with a power greater than one) + (optional: dynamic variables that all effect the others) = unpredictable (chaotic) results

One of the curious traits of chaotic systems is a sensitivity to initial conditions–the butterfly effect. In fact, the butterfly effect was discovered by Edward Lorenz, who placed an approximated value of 0.506 into one of the variables of his chaotic system instead of the full number, 0.506127, and ended up with wildly different results. (He went on to discover the famous Lorenz attractor, which is still the poster child of chaos theory and the butterfly effect.)

Now, to tie all of this back to conversation–and hopefully, some readers are already starting to see the connection (I’m not just crazy, am I?). I think that conversation is an example of chaos theory. At this point, I think I have to admit that I lied a bit at the start of my post. I don’t have the knowledge or skill to prove beyond reasonable doubt via scientific or mathematical method that conversation is chaotic… just logic and speculation. So it’s actually philosophy, not science or math. (Consequently, if one of you can explain it mathematically, there’s a lovely little ‘Comment’ link at the bottom of this post, and I would really appreciate hearing about it.)

Firstly, it’s not that hard to establish the fact that conversation is very dependent on initial conditions. What those initial conditions are, though, is harder to determine. There are probably a lot of them. The personalities, interests, and knowledge base of the people involved, where the conversation takes place, the initiating line from either party, first impressions, what each person was doing earlier that day, how long they have to talk, etc. I happen to think that the most crucial of the initial conditions is the first: the personalities, interests, and knowledge base of the participants. Feel free to disagree.

This is where my lack of math/science expertise becomes a problem: proving the existence of nonlinear feedback. The feedback part isn’t an issue, because of course conversation is feedback; that’s more or less the point. The problem is proving that this feedback is nonlinear (represented in an equation by a number with a power greater than one). How does one prove that kind of thing? For me, at least, philosophy has to take over and fill in the rest.

Instead of arguing for the nonlinearity of conversation (which I can in no way prove), I’d like to try and prove things through analogy. This is why I introduced the three-body problem in my original explanation; because I think I can use it to prove my point. In the three-body problem, we see that the long-term paths of three orbiting bodies of mass (think planets) are impossible to accurately predict–they’re chaotic–because each of the bodies exerts a (nonlinear) force on the other two. Chaos comes as a result of these three variables that each effect the others; that’s the feedback. If we apply this to conversation, where at least two people are listening and reacting to each other (the feedback), we might be able to prove the same chaotic results. Even if there are only two people (not enough to fit the proper three-body problem), I would argue that there are at least four variables that effect all the others: what person A says and thinks, and what person B says and thinks.

Why are what the participants say and think two different variables? Because people claim, rightly or not, that a huge percentage of communication (the actual number varying from source to source) is non-verbal. If this is true, than in a conversation, what you think matters as much or more than what you actually say. In circumstances where one of the participants says one thing and is shown by their body language to be thinking something completely different, the conversation is likely to go in a different direction than if only the content of the person’s speech had been considered. There may be other variables to consider as well (tone? context?), but I think these are the two big ones. Four variables that depend on feedback from the others is enough to satisfy the three-body problem (which is actually the greater-than-or-equal-to-three body problem, but that sounds cluttered). It would be optimal if I could prove that the variables effected each other in a nonlinear way, but unfortunately, I can’t.

As for the constant that I mentioned in my explanation, well–that can be a number of things. If I had to guess, it would be who the participants actually are; what a person says and thinks can change during a conversation, but I haven’t seen someone spontaneously change into someone else during any conversations I’ve had. If the variables determining who the participants are were dynamic and depended on feedback, we would see that sort of thing happening. It doesn’t. Therefore, it’s reasonable to believe that the participants themselves are the constants.

At the end of all this, I conclude that conversation is an example of chaos theory because (a) it is highly sensitive to initial circumstances, (b) the result is constantly being fed back into dynamic variables, (c) it contains dynamic variables that depend on (possibly nonlinear) feedback from other variables, (d) it contains at least one constant, and (e) it displays unpredictable behavior. If I’ve lost you somewhere in the middle of all of this… well, I’ve lost myself several times while writing this, so you’re not alone.

Thoughts and criticism are accepted and appreciated.

(Tags: chaos, chaos theory, conversation, math, philosophy, science, thought)

on April 3, 2007 at 12:18 pm |DaveHey there, I’ve been tossing around some similar thoughts myself. I was a Philosophy and English double major in college, and got to wondering how nonlinear dynamics could apply to literature. Most literature in the Western world follows a more or less standard arc where the plot is introduced, a problem arises, and is fixed in the “deneounement”(French for I always spell this wrong). Since nonlinear interplay seems more the norm than the exception in most naturally occurring events, it stands to reason that literature should be changing to reflect this. I believe that the best writers already do this, although not explicitly. Also, in literature the three-plus body problem is unavoidable. Wherever there is plot there is at least two characters(or character vs. nature, etc.), but then the reader makes a third. In this sense, every time a book is read, the resulting experience is utterly unpredictable. So for any authors who overthink their works, just relax and be true to yourself.