Thursday, October 25, 2012

The Tragedy of Optimality

I have children.  And because I have had them in the era of DVDs and iPods, I have watched all of the Pixar feature films, many of them well over a hundred times.  It's an occupational hazard, although there are some countervailing benefits; for one, my impression of Shark, doing his impression of Woody, is spot on.

Some time ago, as I was watching Finding Nemo for probably about the 267th time, I thought: Now isn't it too bad that Nemo just didn't stay away from the boat (butt)?  All this hassle could have been avoided.  But on the other hand, if they avoided the hassle, Nemo would have spent the rest of his childhood being helicopter-parented around by Marlin.  And it occurred to me that a lot of the other Pixar films had similar moments.  If only Woody hadn't sent Buzz flying out the window.  But then they would never have bonded or saved the neighborhood from a bully.  If only Bob hadn't sent his boss Mr Huph flying through four office walls and gotten fired.  But then he never would have stumbled onto a plot on the lives of the former supers and regained the trust of the people.  And so on.  I think this pattern, as formulaic as it might seem in retrospect, is part of the strength of Pixar stories.

I was reminded of all of this a couple of days ago as I was making my way through James Gleick's Genius, a biography of Richard Feynman that, for a wonder, wasn't written by the man himself.  As a boy, Gleick writes, possibly in reaction to not having been blessed with extraordinary or even ordinary athleticism, Feynman disdained the fine arts—music, drawing, poetry, and so forth—as not being masculine enough, for being too impractical.  You almost want to go back through the decades and slap some sense into the boy...and yet, if he had not disdained those things, would the world have been deprived of the great genius of Feynman?  As the mathematician G.H. Hardy said of the Indian prodigy Ramanujan,
He would probably have been a greater mathematician if he had been caught and tamed a little in his youth; he would have discovered more that was new, and that, no doubt of greater importance.  On the other hand he would have been less of a Ramanujan, and more of a European professor and the loss might have been greater than the gain.
The general notion is one of the trade-off as yet unseen.  We hear all the time about the value of being willing to fail, of being ready to risk substantial loss in search of almost inestimable gain.  But it's easier to be brave, I think, when you know what you might gain.  Few will wholly fault you then.  As both fiction and fact tell us, though, there are plenty of moments when things of value are risked, and seemingly without even the hope of gain, simply through recklessness or stubbornness, and yet things of value too are gained nevertheless.  Under the circumstances, without willful insistence, it seems an error even to call these risks.  More accurate to call it routine imperfection (although certainly also more of a mouthful).

In light of my posts on game theory and the like, it may sound as though I'm advocating for occasionally suboptimal behavior as a way to obtain optimal results.  That's not exactly right; as far as they go, the results of game theory are inviolate.  You can't get optimal results from suboptimal choices.  But what you can do is discover that your measure of what's optimal wasn't quite right.  You can optimize perfectly for dollars (or regular-season wins, or family time, or whatever), and yet thereby miss greatness.

Or, you might miss nothing.  In fact, most of the time, and for the vast majority of people, that's exactly what you miss.  And that's what makes routine imperfection so unappealing on an individual level, because it's regularly unrewarding.  But on a social level, with millions or billions of people operating in general autonomy, it's at once unavoidable and essential.

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