Dimensional Chess
Dimensional Chess
[A chessboard is depicted in the middle of a stack of boards. All pieces visible on the middle board are in their starting positions, except the white knight from a2 at d1 and the black pawn from g2 at e2. There are three boards each above and below the original, missing columns a and h. On columns c & f on each board, there are clear cubes with a small pedestal on each square. Columns d & e are similar, except with multiple cubes on each square. No chess pieces are visible, except for a white piece -- not clearly visible, but implicitly the white king's knight -- on the second board above the middle on b2 and a black pawn on the top board on f3. Below the chessboards is a caption] [Caption below the panel]: The problem with N- dimensional chess is that N is a constant across the board. In my new variant, every row has one more dimension than the one behind it.

Being good at chess is often regarded as a sign of high intelligence. A skilled player must be able to consider possibilities several moves in advance, which can be represented as an exponentially growing tree of possibilities.  The branching factor of chess, the approximate number of legal moves available at any given time, is about thirty-five, although most players (human and computer) will use heuristics to prune the trees to regard only likely or promising moves.  Expanding the playing field by generalizing to three-dimensional chess (or beyond) will increase the branching factor even further, and so someone who is able to competently play three-dimensional chess could be regarded as even more intelligent than someone who can only play two-dimensional chess. Making chess into an N -dimensional game thus makes it arbitrarily more difficult, even before Randall's addition of non-uniform dimensionality of the board.
Regarding Randall's rule that "every row has one more dimension than the one behind it," it is easiest to see how this is applied with the first two rows on each end. The first row on each end is a like a row on a traditional two-dimensional chess board (albeit played with three-dimensional pieces): you can go from left to right, or forward into the next row. The second row then becomes a two-dimensional row of a three-dimensional space: you can go left to right, forward to back, and now top to bottom. Note that there are seven spaces (represented by "shelves") from top to bottom, as opposed to the typical eight rows from left to right/front to back. This is likely to make sure there is symmetry between how many additional spaces are on top versus on the bottom (three, in this case). Moving another row would presumably add movement in some other direction to make it more complicated/interesting. This escalates until somehow the middle two rows require moving pieces in five dimensions (the middle two rows are four-dimensional rows + moving to other rows as fifth dimension), despite humans only being able to experience three spatial dimensions. [ citation needed ] This could potentially be accomplished via playing on a computer.
There are eight squares on the first row, 56 on the second row and presumably 504 on the third and 1512 on the fourth, thus making the total number of squares 4160 rather than the 64 of a traditional chess board. The drawing shows apparently five squares (or boxes) stacked on the third row and if this is also formed symmetrically, there are four hidden out of sight. The middle rows are already quite convoluted but it seems as if Randall drew three boxes along this dimension. Due to this dimensionality increase, there is plenty of free space in the middle board, drastically changing the game dynamics such that shadowing plays very little role and that movement is very unrestricted.
The title text refers to the practice of writing down what happens throughout the game, so that it is possible to review how the game progressed later. Recording moves in this fashion is required in most tournament situations. There are several common forms of Chess notation used for this purpose, and as well as indicating the moves, players may add annotations indicating their opinions about whether a particular move was good, bad, or peculiar. According to the title text, every annotation is followed by "?!"—which indicates a questionable move, of dubious value but not obviously a blunder either. The joke is that the variable-dimensional game is so complicated that any move will answer this description.
There appears to be the normal chess pieces (so no Fairy chess pieces ), but the game has already started (there are white and black pawns in one of the middle squares, and both white and black knights have moved.
Note that "in dimensional chess" may be a pun on " N -dimensional chess."
[A chessboard is depicted in the middle of a stack of boards. All pieces visible on the middle board are in their starting positions, except the white knight from a2 at d1 and the black pawn from g2 at e2. There are three boards each above and below the original, missing columns a and h. On columns c & f on each board, there are clear cubes with a small pedestal on each square. Columns d & e are similar, except with multiple cubes on each square. No chess pieces are visible, except for a white piece -- not clearly visible, but implicitly the white king's knight -- on the second board above the middle on b2 and a black pawn on the top board on f3. Below the chessboards is a caption] [Caption below the panel]: The problem with N- dimensional chess is that N is a constant across the board. In my new variant, every row has one more dimension than the one behind it.
