I was eating my lunch in a crowded cafeteria. The diners sat elbow to elbow on long benches at polished metal tables arranged in rows. This kid next to me had a bunch of large wooden chess pieces on the table in front of him, laid out in the configuration of a chess problem which he appeared to be intensely contemplating. I leaned over to study the problem for myself when I noticed something curious. “There’s no board!”, I observed. The kid just nodded, still concentrating on the problem. I was impressed. Not only could he analyze all the complex movements and interactions of all the different pieces; he could do it all while visualizing where the pieces belonged on the board entirely in his head.