I occasionally have a-ha moments too, but they’re usually more like the dreams where you look down and realize that you forgot to put on pants this morning.
Recently I was trying to make some theological point in conversation, and I found myself using metaphors from the game of chess. I thought that was a little odd, because although I played a lot of chess in high school, I’ve barely touched the game in thirty years. Still, I thought, it makes a good metaphor for what I’m trying to say.
And then I thought: In fact, it makes a good metaphor for my whole worldview.
And then I thought: It makes a really, really good metaphor for my whole worldview.
That’s when the a-ha moment hit.
Back in college, after I had given up chess the way an addict gives up his drug (and consequently had the time to pass my courses), I did a lot of reading in the philosophy of science. A quote from the early twentieth century astrophysicist Arthur Eddington impressed me so much that I have remembered it ever since: “Some men went fishing in the sea with a net, and upon examining what they caught they concluded that there was a minimum size to the fish in the sea.”
Like Jesus, Eddington intended his little parable to be interpreted on many levels. In the simplest interpretation, he was just pointing out how dependent scientists are on their tools. You see what your instruments pick up, you don’t see what they don’t pick up, and if you’re not careful you’ll wind up basing your theory on the limits of your equipment rather than on the external world. (If the fishermen were a little more thoughtful, they might notice that the smallest fish their theory allowed was about the same size as the holes in their net.)
But Eddington wasn’t just talking about telescopes and microscopes, or even about sailors who imagine that the world must end just beyond the range of their ships. He was also talking about our philosophical “equipment”—the concepts and frames that we bring to whatever phenomenon we’re examining. The conclusions we arrive at depend not just on objective reality, but also on the questions we’re able to ask and the answers we’re able to imagine.
If we’re not careful, it’s easy to wind up “proving” (diligently and laboriously, sometimes) that the world fits the unconscious template that we had before we looked at any evidence at all. It’s not a question of honesty or sophistry. By the time the fishermen get around to sorting and measuring and theorizing about their fish, they have long forgotten about the nets. They aren’t politicians spinning an issue or accountants trying to fool the IRS. The conclusion they come to is really there, in their catch.
They just didn’t think hard enough about how it came to be there.
Now let’s go back to my a-ha moment. In my teens, at precisely the time when I was learning how to think hard about things, what I thought hardest about was chess. Decades later, after a long and winding spiritual journey, I arrive at conclusions that fit neatly into the metaphor of chess.
Interesting coincidence, don’t you think?
Maybe I was just lucky in the game I happened to take up in high school. But I think it’s more likely that I was weaving my nets back then, and it has taken all these years to examine my catch and find the conclusions that were woven in.
Here’s what I wove: My best friend and main rival on the chess team had a second love: computers. Those were the early days of artificial intelligence, when chess-playing programs were written by lone geniuses rather than corporate teams with cutting-edge supercomputers. Any smart high school student with a computer account could dream, as my friend did, about having the key insight that unlocked the problem.
And so we had long conversations not just about the game, but about what was really going on when players thought about their next move. Unlike practically every other teenage American chess player of that era, our hero was not Bobby Fischer but Mikhail Botvinnik, the Russian ex-world-champion whose book Computers, Chess, and Long-Range Planning was the Bible of ambitious chess programmers.
Just like today, the seemingly limitless potential of computers fed the fantasy of transcending the limits of the human mind. And that led to a thought experiment: What if you had an infinite mind, so that memory and calculation stopped being the limiting factors? How would you play then?
With a little thought, the answer was obvious: You’d completely ignore all the received wisdom in the human chess manuals. Instead, you’d picture a vast graph that game theorists called “the game tree.”
Each game (like checkers or go or backgammon) has its own game tree, and chess’s tree looks like this: At the base is a dot that represents the situation at the beginning of the game. At the second level are dots representing all the positions that could result from white’s opening move. The dots on the third level represent all the positions resulting from black’s response to that move. And so on, with lines connecting dots if there is a move that gets you from one position to the other. Far up the tree are the leaves—final positions where the game has been won or lost or drawn.
Once you’ve imagined the game tree, then any particular chess game is just a path from the base to a leaf. They’re all in there somewhere. The Tree, if you think about it, is a God of sorts. Not the kind you would pray to before making a risky move, but a ground-of-being sort of God. In the Game Tree (I have to capitalize it now, in recognition of its divinity) all the individual games of chess live and move and have their being.
The Tree is vast, of course, but it’s finite, it has limits. If your mind had no limits, it would be no trick to picture the whole thing. And that’s how you’d play: At any point in the game, you’d see where you were in the Game Tree and all the paths that branch out from there. You’d look all the way up to the leaves, and then you’d work backwards, planning your future moves until you had eliminated every path that leads to a loss and minimized the number that lead to a draw.
Conceptually, it’s a simple strategy, but the possibilities multiply so rapidly as you go up the tree that even a supercomputer would need eons to decide on its first move.
Impractical as it is, the Game Tree remains a compelling idea. Once you’ve envisioned the Game Tree all the learn-to-play-chess books look completely different. They’re filled with concepts and principles that are stated as confidently as if they were rules of the game: Bishops are worth three pawns; rooks are worth five; the purpose of the opening is to develop your pieces and control the center of the board; and on and on and on. Those principles have value, in the sense that human beings who understand them are likely to outplay human beings who don’t. But from an absolute perspective, from the point of view of the Tree, it’s all just human nonsense. The Tree just Is. It knows nothing of all our concepts and point values and principles of development. They are just rules of thumb we made up to kluge around the limitations of our tiny human minds.
And they only take you so far. The great players know that. Every now and then, one of them gets a vision of some unusually large chunk of the Game Tree and goes completely off script. For ten or fifteen moves at a time, grandmasters will violate every known principle of wise play—trading queens for pawns, letting threatened pieces sit, dismantling their own king’s defenses—and then come out the other side with an advantage. That’s what makes them grandmasters.
It’s been decades since I thought seriously about any of this. I had to check Wikipedia for the spelling of Botvinnik and the title of his book. And yet, mysteriously, I have taken a long circuitous path to wind up with a chess player’s worldview.
I know exactly what I’d do if I had an infinite mind. I’d live by the Game Tree. I’d foresee all the consequences of my actions, all the ways that my choices affect the world out to the End of Time, and I’d pick the path I liked best.
I can’t do that, so instead I try to live by high-minded principles. Relative to other high-minded principles I’ve heard, I think mine are pretty good. I believe that people who live by my principles will probably do better in life and have a more beneficial impact on the world than people who live by other principles or by none at all.
And yet . . . I have little patience with people who take their principles too seriously, even if they have the same ones I do. It’s all just human nonsense, rules of thumb, kluges that work around the limitations of our tiny minds.
Until recently, I thought I had decades of experience to prove that point. But now I have to wonder even about that.
Maybe it’s just taken me this long to get around to measuring the holes in my net.