Clues

(Occasional Posts)

To achieve play that feels like chess requires:

a formal line of development, with geometrical and logical rigor, that respects the game
the penetration of two paradigm barriers

4/08/26 - If the 2D board is a square of squares (8x8), then the 3D board should be a…?
4/09/26 - A cube of cubes (8x8x8).
4/11/26 - A square has 8 neighbors; 4 connected by sides, 4 connected by corners.
4/13/26 - Rooks move through sides, changing 1 coordinate axis, bishops move through corners, changing 2.
4/15/26 - A cube has 26 neighbors; 6 connected by faces, 12 connected by edges, 8 connected by vertices (corners).
4/19/26 - Rooks move through faces, changing 1 coordinate axis, bishops move through edges, changing 2.
4/20/26 - A new piece is required (the duke); dukes move through vertices changing 3 coordinate axes.
4/21/26 - 3D requires a 3rd base piece, one base piece per dimension.
4/22/26 - How all the other pieces move can be specified by combinations and limitations of the base pieces.
4/23/26 - Changing 1 coordinate axis allows access to all the tiles on the board.
4/24/26 - Changing 2 coordinate axes restricts access to half the tiles on the board.
4/25/26 - Changing 3 coordinate axes restricts access to a quarter the tiles on the board.
4/26/26 - Thus, the duke is to the bishop, like the bishop is to the rook.
4/27/26 - In 2D, there are two line types, two orthogonal (rank & file), and the two diagonals.
4/28/26 - Each allows motion along a single ray in either of two directions.
4/29/26 - Thus, in 2D a piece has at most 8 directions it can move in.
4/30/26 - In 3D, there are three plane types: orthogonal (rook), skew (bishop) and slant (duke).
5/01/26 - In 3D, the number of planes is not constant: rooks move in three, bishops in four, and dukes in six.
5/02/26 - Motion is along a pair of rays, in 4 directions for rook and duke, 6 directions for bishops.
5/03/26 - Thus…