Head Space

I've been talking about these maps we have in our heads. Some of them are literal projections of the surface of our bodies onto a surface in the brain, but we also have maps of a more plastic kind. Most of us, I think, have a sort of mental map of our house, good enough to walk around in the dark unless somebody has left a chair or toy in an unusual place. Similarly, I can call up images of sorts of my neighborhood and my town in which I can roughly place the major landmarks, but some details are missing. For example, if I want to figure out how many houses are between my house and the corner, I have to go through them one by one, mapping them to numbers. I can't even do that for houses a block or two away.

A slightly more abstract kind of map comes up in chess. If you wish to visualize consequences of future moves, you need to be able to mentally project those moves on the chessboard, moving the pieces in your head. Blindfold chess is slightly more difficult, since you play without sight of a board, and rely on verbally expressed chess notation (e4, say, or in older notation popular in my youth, P-K4 - moving the white pawn in front of the king to the fourth square in front of the king).

This skill is impressive when you first see it (or at least it impressed me), but virtually every player of expert strength or above can do it, and some grandmasters can play dozens of such games at once. Weaker players like me often can play one, though not very well. When I was in practice, after a few beers I could ocassionally be persuaded to play a game with my back to the board, sometimes impressing the barmaids.

So how good is/was my mental map of the board? Not very good at all. I can see what's happening pretty well in a 3x3 block of squares, but I find it hard to see much further - and knights are particularly a pain. In order to see how a bishop on, say, g5 affects the rest of the board, I need to mentally trace its path and see what is in the way. Did my opponent develop his knight to f6, or e7, for example? Is there a pawn on h6 or f6 to capture me? Is his queen still on d1? It's hard work, and it would be a lot easier if I could mentally see the whole board at once. Can masters? How about grandmasters?