In “Chess as a Behavioral Model for Cognitive Skill Research,” Mechner writes the following about mental representation of the game by blindfold chess masters:
But the bombshell, which prompts the present reexamination of ‘‘visualization,’’ is this: blindfold chess masters consistently report that what they visualize are not images of pieces or chessboards, but abstractions of these with minimal or no physical features. A typical report is, ‘‘I do not visualize real pieces but I know where they are.’’
The fourteen or so blindfold champions quoted by Hearst and Knott describe what they do in these terms: ‘‘no mental pictures,’’ ‘‘abstract knowledge,’’ ‘‘I know where the pieces are,’’ ‘‘only an abstract type of representation,’’ ‘‘only relationships,’’ ‘‘no real picture,’’ ‘‘the significance of a piece,’’ ‘‘knowing what combination or plan is in progress,’’ ‘‘lines of force,’’ ‘‘pieces are only friend or foe, carriers of particular actions,’’ ‘‘sort of formless visions of the positions,’’ and so forth. Many of the masters report that they have no mental image at all (p.151).
The masters also confirm that blindfold chess improves their performance in normal chess.
Some of the strongest masters find the actual sight of a chess position to be more distracting than helpful when thinking ahead during a game.
Now, normal chess encourages a physical representation, when the game vision is more like geometry than algebra. That's compelling because humans get used to visual models since childhood. But extending the analogy with mathematics, the "algebraic" form is more powerful.
So in normal chess, a player has to make a choice: developing a visual representation or adopting the blindfold chess relationship model. That's the foundation to build chess memory and calculations on.
What approach is more promising in the long run? Which one do top players use?