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Archive for the ‘philosophy’ Category

Conversation and chaos

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.

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The concept of balance has been on my mind lately, in many different forms. The most recent of them was the fictional (is it?) concept of touka koukan (“Equivalent Exchange”) from the Japanese anime series ‘Fullmetal Alchemist’. The series is, predictably, about alchemy, but as a strict, practical science accompanied by laws and limitations, much like physics or chemistry. Touka koukan is one of these laws, explained at the beginning of every episode with this prologue: “Man cannot gain anything without first sacrificing something else. To obtain anything, something of equal value must be lost. That is alchemy’s Law of Equivalent Exchange.” (This, according to the show, is why the idea of a Philosopher’s Stone is so crucial to alchemy; it would allow the alchemist to bypass touka koukan.)

Outside of fictional worlds, we have the spiritual concepts of karma and the taijitu (yin and yang) and the scientific ones of equilibrium and Newton’s Third Law, all revolving around this general concept of balance. They’re all different interpretations of how it works and where it’s applied, but each reflects the same basic idea: that by nature, something is always equal to something else.

Correct me if I’m excluding anything important here, but it seems to me like these interpretations of balance–spiritual and scientific–can be divided into three types: cause-and-effect balance (touka koukan, Newton’s Third Law, karma), existing balance (yin and yang), and natural balancing (equilibrium). Not the best titles for each type, I know, but I hope the general idea gets across. The first type asserts that every action has an equal reaction, and it refers to action; there must be an initial action to spark the reaction. The second type is the idea that balance already exists, and will always exist; no action is needed, because the balance just is. The third type describes two unequal amounts of something balancing together (eg, the ideas behind carbon-14 dating and economic price theory), and is a sort of blend of the former two (action and pre-existing balance). All three are simply different views on balance.

Interpretations and applications of the balance concept are prevalent in many (if not all) cultures spanning the entire globe and thousands of years of human history. The ancient Egyptian Book of the Dead describes a ceremony called the Weighing of the Heart, in which the heart (believed to contain the soul) of the deceased was weighed against the feather of truth before they could be admitted to the afterlife. A strange example of balance, but an ancient and applicable one nonetheless. Better known is the Chinese idea of yin and yang, probably dating back even earlier than the Book of the Dead and developed independently thousands of miles east. The idea of religious sacrifice, present in early European and South/Central American religions (among others), is similar to touka koukan, because it stems from the belief that whatever is sacrificed will give them a blessing of similar value (hence the sacrificing of the more valuable things–best of the crops, best of the herds, sometimes children–was assumed to yield a better result).

So why is humankind so interested in the idea of balance? Why is it so widely spread out over so many cultures and time periods? “Because it’s true” is a very weak answer, because it’s hard to substantiate that (outside of equilibrium) without religious or philosophical claims. Why do some babies not survive to toddlerhood? They surely can’t have done something equivalently wrong already. It’s impossible to answer that without blaming a past life or claiming that the baby was ‘destined’ to die because his parents did something wrong. Why do bad things happen to good people, and why are murderers running free? Those kinds of questions can’t be answered with touka koukan or yin/yang or whatever form of balance we might think exists.

I haven’t reflected on the concept as much as I’d like (when do I ever?), or assessed my own personal beliefs on the matter, but I have a feeling that a belief in something like touka koukan might come from the urge to control. For most, I think, there’s a comfort associated with the knowledge that every result is deserved. It’s like a blending (balance?) of fate and control. We can’t control the balance itself, but we can control how we use it. If karma were true, whatever terrible thing that happens to us is our own fault. It’s controllable, yet not completely, and that’s what makes it such an appealing idea.

However, until the question of why bad things happen to good people can be actually answered, whether or not the prevalent concept of real balance actually exists can’t be determined. Speculation might or might not help; who knows?

Thoughts?

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