What Chess Tells Us About the Value of Perception
As a physics student, I found that I could solve most of the problems simply by looking at derivations and listening carefully to my reactions to the equations. A soft voice inside me would say, “No, that term just doesn’t seem right. Go and find out what went wrong there.” Or, “Ah, these terms hang together and the result feels right. It must be okay.” And it almost always worked out. My piano teacher would do the same when playing an unfamiliar piece of music. She could play it just by making sure it sounded right.
Were these just party tricks? Or was a more fundamental process going on?
The answer is in my favorite study from the field of expertise and expert performance; like the best research in this field, it teaches us general lessons about how one reaches high performance in almost any domain, whether music, chess, poker, mathematics, or teaching.
The study is by Fernand Gobet and the late Herbert Simon, winner of the 1978 Nobel Prize in Economics. They wanted to measure the relative importance of analysis (calculation) and perception (insight) in expert performance. And they thought of a beautiful measurement based on objective data. [“The roles of recognition processes and look-ahead search in time-constrained expert problem solving: Evidence from grandmaster level chess”, Psychological Science 7:52-55 (1996)]
Their subject was Garry Kasparov, chess champion of the world for 15 years (1985-2000). As world champion, he often demonstrated his skill by playing a “simul”: games of chess against several masters and grandmasters simultaneously. Kasparov would have to rotate between games. As soon as Kasparov reached a board, his opponent on that board had to make his or her move. Kasparov would then think for roughly 20 seconds before moving on to the next opponent and game. In contrast, his opponent would think for 3 minutes, until Kasparov’s return from cycling through the other games (typically six others).
At 20 seconds per move, Kasparov mostly used his perception and judgment of chess positions rather than his ability to calculate chess variations (the “I take, he takes, I take, etc.” kind of thinking). Thus, simultaneous chess is a real-life laboratory for measuring the value of perception. How well did Kasparov play, in comparison to his normal strength when playing at the usual tournament rate of 3 minutes per move? His normal strength at the time was 2750 on the Elo scale of chess skill. (To give a feel for the Elo scale, a beginner would be rated about 1000, an average tournament player is rated about 1600, a master is rated at 2200 or above, and a grandmaster is usually above 2400.)
The amazing result: At the rapid “simul” pace, Kasparov performed at a rating of 2650: higher than all but half a dozen players in the world! In other words, most of his world-class expertise comes from how he sees and looks at the chess board, not from his calculation ability. The traditional picture of the chess master as a calculating prodigy is bogus.
This unexpected result explains my (lack of) success playing chess against a friend in college, Adam Lief, who at the time was a very strong master. To make the games even remotely interesting, Adam started with less and less time, eventually reaching 30 seconds to make all of his moves while I had my 5 minutes for all my moves. In my best effort at those odds, I managed, in one game, to get Adam on the run. As I was gloating to myself, he paused for a longer think. As his time was running out, I sensed victory, even if it would come from Adam’s running out of time. After an eternity (7 seconds), he sacrificed his queen and announced “mate in 6”, i.e. that I would be checkmated in 6 moves even if I played perfectly.
Adam had only 5 seconds total for all his moves, so I thought, “I’ll just move fast, so that he doesn’t have time to think while I think, and might then not manage the checkmate.” Bad choice. With my first move, I made a mistake. Adam instantly announced “mate in 2.” And so vanished my victory, the only time I managed to even come close—even though Adam barely even had time to move his piece and hit his chess clock, let alone study the board. For the master, perception and insight are king!
This idea, as I will discuss in a subsequent post, explains the insanity of most mathematics teaching.