(Occasional Posts)

To achieve play that feels like chess requires:

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

Clues

  • 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, in 3D a piece has at most 60 directions it can move in.
  • 5/04/26 - These directions are called quadrants.
  • 5/05/26 - In 2D, motion is in straight lines.
  • 5/06/26 - In 3D, motion is in flat planes.
  • 5/07/26 - The board has been promoted by a dimension, so must the moves.
  • 5/08/26 - Planar moves preserve the endgames.
  • 5/09/26 - A rook and king can checkmate a lone king – with exactly the same algorithm.
  • 5/10/26 - A one pawn advantage can secure the game.
  • 5/11/26 - The goal was a rule set that yields play which feels like chess.
  • 5/12/26 - So, a piece advances along one ray, then along the other.
  • 5/13/26 - Or, does it advance along the other, then along the one?
  • 5/14/26 - Oops, now every attack has two paths, blocking is busted.
  • 5/15/26 - Planar moves preserved the endgames, but busted the midgame.
  • 5/16/26 - What kind of a rule would allow a single piece to block an attack along two paths?
  • 5/17/26 - A path is an example of a trajectory.
  • 5/18/26 - The very concept of trajectory must be abandoned.
  • 5/19/26 - If a quadrant defines direction then advancement must be into the quadrant.
  • 5/20/26 - Advancement must occur along both rays simultaneously.
  • 5/21/26 - Call this an advancement square.
  • 5/22/26 - For a move to the perimeter to be legal, every tile in the advancement square must be unoccupied.
  • 5/23/26 - In 2D, a piece advances one square at a time.
  • 5/24/26 - In 3D, a piece advances one perimeter at a time.
  • 5/25/26 - Blocking restored, gambits restored, the goal remains, a rule set yielding play which feels like chess.
  • 5/26/26 - Only…what was the path the piece took to move from the soure tile to some specific destination tile on the perimeter?
  • 5/27/26 - No path, no trajectory - those are classical abstractions.
  • 5/28/26 - The piece started here, ended up there, and was never, ever, anywhere in between.
  • 5/29/26 - This is also true of 2D chess, we just never noticed.
  • 5/30/26 - The piece started here, ended up there, and was never, ever, anywhere in between.
  • 5/31/26 - It’s just that the straight line connecting here to there, and the physical act of moving a piece, tricked us into thinking there was a path.
  • 6/01/26 - In between here and there, a piece just kind of spreads out (the advancement square).
  • 6/02/26 - A little like a wave function, just no oscillation - but definitely nonlocal.
  • 6/03/26 - An electron changing state in an atom, starts here, ends up there, and is never, ever anywhere in between.
  • 6/04/26 - This connection with quantum physics is the biggest surprise of these rules.
  • 6/05/26 - And this is just the tip of the iceberg.
  • 6/06/26 - The third dimension has required the addition of a third base piece, the duke.
  • 6/07/26 - So where do we place it in the starting line up?
  • 6/08/26 - Should the bishop stay adjacent to the royal pieces?
  • 6/09/26 - Or should the duke slip into that slot?
  • 6/10/26 - To make room for both a queen side and a king side duke, now requires 10 tiles.
  • 6/11/26 - A 10x10x10 board will yield 1,000 tiles.
  • 6/12/26 - Uninteresting complexity.
  • 6/13/26 - This places the pawns too far apart as well.
  • 6/14/26 - Every game is split strategically, a major piece war, followed by a pawn war.
  • 6/15/26 - There goes the quest, doesn’t feel like chess.
  • 6/16/26 - Pawn engagement can be solved by selecting a 10x8x8 board, that’s only 640 tiles.
  • 6/17/26 - But the lack of symmetry distorts pawn race endgames (king, knight).
  • 6/18/26 - Again, we lose the quest.