Monday, August 16, 2010

More on Paths

I introduced the notion of the Path in "A bit more introspection." This is an idea that, in some form, influences areas of physics, philosophy, policy, and — sometimes — more personal issues. This is going to be a bit of a meandering post that winds through all of those things.

I’ll start, as I sometimes do, with physics. I mentioned in "A bit of introspection" that I have a certain fascination with variational principles, the most famous of which is the principle of least action. This is a physical principle that allows us to figure out what the motion of a particle—its path through space and time—is going to look like. If you want to do something like that using Newton’s laws (e.g. Force = mass x acceleration) you’d look at all the forces on the particle at any given time and see that “oh, it’s getting nudged this way, and then it’s going to get nudged that way…” and so on. It can get a bit clumsy and you have to add up all kinds of forces—you have to deal with vectors and things can get very messy depending on your coordinate system.

The principle of least action gives you another way to figure out how a particle’s going to move and this way turns out to be completely equivalent to doing things Newton’s way. But the calculation is very different. Instead of figuring out the net results of all the pushes and pulls acting on the particle, we instead focus on the path. We take the starting point and the ending point of the particle’s path and we find that the real path it takes between those two points is the path for which a certain quantity that we know how to calculate—“action”—is the smallest. If you think about it, conceptually that seems like a big difference. As Richard Feynman put it in his Lectures on Physics:

There is quite a difference in the characteristic of a law which says a certain integral from one place to another is a minimum—which tells something about the whole path—and of a law which says that as you go along, there is a force that makes it accelerate. The second way tells how you inch your way along the path, and the other is a grand statement about the whole path.

One of the philosophical points raised in response to this, historically, was that it seemed to introduce teleology into the universe. Telos (“the end term of a goal-directed process”) assumes a certain underlying purpose, some kind of meaningful connection between a beginning and an associated end. If our physical calculations involve knowing a certain starting and ending point for a particle to determine the path it will take between them, does that mean the particle “knows” where it will end up when it starts out? As Wikipedia notes in the “apparent teleology” section of its page on least action :
In particular, the fixing of the final state appears to give the action principle a teleological character which has been controversial historically. This apparent teleology is eliminated in the quantum mechanical version of the action principle.

The quantum mechanical version they mention—invented by Feynman—is called the path integral formulation and resolves the question by essentially postulating that the particle takes all possible paths to all possible endpoints and things just sort of average out to reflect the classical picture of a set path between set points:

Classical action principles are puzzling because of their seemingly teleological quality: given a set of initial and final conditions one is able to find a unique path connecting them, as if the system somehow knows where it's going to end up and how it's going to get there. The path integral explains why this works in terms of quantum superposition. The system doesn't have to know in advance where it's going or what path it'll take: the path integral simply calculates the probability amplitude for any given process, and the path goes everywhere. After a long enough time, interference effects guarantee that only the contributions from the stationary points of the action give histories with appreciable probabilities.

That may explain the source of the apparent teleology but I’m not convinced it eliminates it. But teleology as a concept isn’t limited to this physical example, it (or the lack thereof) also has implications for society as a whole. Teleology plays a key role in Alasdair MacIntyre's arguments in his book After Virtue.

MacIntyre, in exploring questions of ethics and the virtues, points to the centrality of telos to the Aristotelian conception of ethics and morality. Man has a proper end toward which the path of his life winds and only by living a virtuous life can man satisfy that telos and reach that intended end. But the concept is even broader than that. Far from simply informing ethical choices and shaping a person’s actions, telos actually defines one’s social role (and all interactions between the individual and society) and one’s personal identity. Consider this bit from the book in which MacIntyre discusses the concept of ancient heroic societies (the sort you read about in the Illiad or Beowulf):

What I hope this account makes clear already is the way in which any adequate account of the virtues in heroic society would be impossible which divorced them from their context in its social structure, just as no adequate account of the social structure of heroic society would be possible which did not include an account of the heroic virtues...For the given rules which assign men their place in the social order and with it their identity also prescribe what they owe and what is owed them and how they are to be treated and regarded if they fail and how they are to treat and regard others if those others fail.

Without such a place in the social order, a man would not only be incapable of receiving recognition and response from others, not only would others not know, but he would not himself know who he was. It is precisely because of this that heroic societies commonly have a well-defined status to which any stranger who arrives in the society from outside can be assigned.

In such a society, whether they actually ever existed or not, a person has a set role to play. They have an end toward which they are striving (recognized and decided not just by them but by everyone) and, as such, their social and personal lives have purpose (and, I daresay, some sort of meaning). Ethical principles by which to live one’s life—the virtues—thus emerge from this teleology-oriented cosmology fairly naturally. Ethics and morality are those principles that will best enable the individual to fulfill his social role and arrive at the destination intended for him.

In our own post-Enlightenment Western society, the emphasis is on the supremacy of the individual. Individuals do not derive their identify from society, they carry it with them into society, which is itself an emergent structure that arises from the myriad interactions of countless individuals. No one is fulfilling a telos that determines his position or role in society, no one really has any particular reason (beyond a personal preference) to live by a given set of ethical or moral principles, and many of us face a recurring—and sometimes debilitating—sense of purposelessness. To the extent that our intense focus on individuality prompts us to attempt to define ourselves, our reality, our values, etc (i.e. to the extent we don’t get these definitions from religious, cultural, or familial cues), it robs us of the possibility of some external driver shaping our paths with some endgame—some telos—in mind.

And so we fit into society awkwardly, with an oft-shifting and meaningless role that invites and requires few ethical principles to sustain it and anchor our metaphysical selves. We stagger haphazardly through the wilderness instead of following a path. There is no destination, there is no purpose, there is no path. This is the state in which our listless society finds itself today. Or at least, this is the philosophical view of existence that has come with with our self-centric cosmologies, whether we intended for it to or not. But as I mentioned in "A bit more introspection," my philosophical/physical understanding of the nature of time suggests to me that our lives are not being written but in fact are written, with a defined end point out there waiting for us. Yet this doesn’t necessarily suggest purpose and an end goal (although I don’t think it can be said to preclude that possibility either). Rather, it’s a statement about limitations. If tomorrow has already happened, I can no more deviate from the path I took through it than I can deviate from the path I took through yesterday. What happened yesterday has happened and what happens tomorrow will happen and I experience events at least as much as I shape them.

This notion of limitations brings us to another manifestation of paths: the policy (or, more generally, social scientific) concept of path dependence. Where you can go is constrained by where you’ve been. That’s why, for example, the current political and policy climate is generally assumed to preclude an abrupt shift to a single-payer health care system. Certainly this is the way Obama has approached the question:

“If you’re starting from scratch,” he says, “then a single-payer system”—a government-managed system like Canada’s, which disconnects health insurance from employment—“would probably make sense. But we’ve got all these legacy systems in place, and managing the transition, as well as adjusting the culture to a different system, would be difficult to pull off. So we may need a system that’s not so disruptive that people feel like suddenly what they’ve known for most of their lives is thrown by the wayside.”

All this serves as an exclamation point on the suggestion that the past and future of the path can’t be viewed in isolation but must be viewed as a seamless whole. Or, to borrow the phrase Feynman used in discussing least action principles, we should be prepared to make “a grand statement about the whole path.” If we try and take that whole-path perspective, we might stumble over some interesting thoughts about the physical universe, the social universe, political developments, and even our own lives. But as the Oracle once said, everything that has a beginning has an end. And since I'm getting tired, I think this post has just about fulfilled its telos. May we all be so fortunate.

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