Editing 2465: Dimensional Chess
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
| Latest revision | Your text | ||
| Line 11: | Line 11: | ||
Being good at {{w|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 {{w|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 {{w|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 <i>N</i>-dimensional game thus makes it arbitrarily more difficult, even before Randall's addition of non-uniform dimensionality of the board. | Being good at {{w|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 {{w|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 {{w|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 <i>N</i>-dimensional game thus makes it arbitrarily more difficult, even before Randall's addition of non-uniform dimensionality of the board. | ||
| β | 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 | + | 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 can only experience three spatial dimensions. 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. | 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. | ||
