Space

Anti-de Sitter space 1 Anti-de Sitter space ¹

Image of (1 + 1)-dimensional anti-de Sitter space embedded in flat (1 + 2)-dimensional space. The t1- and t2-axes lie in the plane of rotational symmetry, and the x1-axis is normal to that plane. The embedded surface contains closed timelike curves circling the x1 axis, though these can be eliminated by "unrolling" the embedding (more precisely, by taking the universal cover) - Description from Anti-de Sitter space from Wikipedia - Image "Hyperboloid of one Sheet" by Krishnavedala, May 23, 2011, CC BY-SA 3.0, Wikimedia Commons ↩︎

Space,
a loosely defined evaluation feature related to square control, in particular center control considered by piece placement dependent on pawn structure. A player controlling more squares than the other is said to have a spatial advantage ¹. Tarrasch's concept of force, space and time ² and their equivalence (to some extend) is considered by material (force), piece placement and center control (space) and roughly by mobility (space and time).

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Implementations

Some programs have explicit evaluation terms concerning space. For instance, Stockfish defines a space area bonus by the number of safe squares for minor pieces on the central four files on ranks 2 to 4, counting twice if on a rearspan of an own pawn. The space area bonus is multiplied by a weight, determined by the number of own pieces minus number of open files ³. Toga II 3.0 gives a non-linear bonus for pieces on the opponent half of the board - the more the better ⁴. Senpai 2.0 considers space by the "glorified" pawn chain piece-square tables ⁵.