kitchen table math, the sequel: chunking

Thursday, April 24, 2008

chunking

[P]ractice changes the way a task is perceived. A chess master, for example, can look at a game in progress for a few seconds and then perfectly reconstruct that same position on a blank chessboard. That’s not because chess masters have great memories (they don’t have the same knack when faced with a random arrangement of pieces) but because hours and hours of chess playing have enabled them to do what psychologists call “chunking.” Chunking is based on the fact that we store familiar sequences—like our telephone number or our bank-machine password—in long-term memory as a single unit, or chunk. If I told you a number you’d never heard before, though, you would be able to store it only in short-term memory, one digit at a time, and if I asked you to repeat it back to me you might be able to remember only a few of those digits—maybe the first two or the last three. By contrast, when the chess masters see the board from a real game, they are able to break the board down into a handful of chunks—two or three clusters of pieces in positions that they have encountered before.

In “The Game of Our Lives,” a classic account of the 1980-81 season of the Edmonton Oilers hockey team, Peter Gzowski argues that one of the principal explanations for the particular genius of Wayne Gretzky was that he was hockey’s greatest chunker. Gretzky, who holds nearly every scoring record in professional hockey, baffled many observers because he seemed to reverse the normal laws of hockey. Most great offensive players prefer to keep the rest of the action on the ice behind them—to try to make the act of scoring be just about themselves and the goalie. Gretzky liked to keep the action in front of him. He would set up by the side of the rink, or behind the opposing team’s net, so that the eleven other players on the ice were in full view, and then slide the perfect pass to the perfect spot. He made hockey look easy, even as he was playing in a way that made it more complicated. Gzowski says that Gretzky could do that because, like master chess players, he wasn’t seeing all eleven other players individually; he was see ing only chunks. Here is Gzowski’s conclusion after talking to Gretzky about a game he once played against the Montreal Canadiens.... :
What Gretzky perceives on a hockey rink is, in a curious way, more simple than what a less accomplished player perceives. He sees not so much a set of moving players as a number of situations. . . . Moving in on the Montreal blueline, as he was able to recall while he watched a videotape of himself, he was aware of the position of all the other players on the ice. The pattern they formed was, to him, one fact, and he reacted to that fact. When he sends a pass to what to the rest of us appears an empty space on the ice, and when a teammate magically appears in that space to collect the puck, he has in reality simply summoned up from his bank account of knowledge the fact that in a particular situation, someone is likely to be in a particular spot, and if he is not there now he will be there presently.

The Physical Genius

This is what Carolyn meant when she talked about math being a seamless whole. (I think.)