Originally published at: https://boingboing.net/2020/10/29/doc-populars-print-on-demand-one-dimensional-chess.html
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Umm, not a topologist, but if one can grab a piece and move it, we’re certainly in three dimensions, right?
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It’s really chess for linear thinkers.
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I am a topologist. The pieces are 3d but, as far as gameplay is concerned, the number of degrees of freedom for their placement on the board is 1. (Sort of, it is a finite discrete lattice in 1d so you could also say that it is 0 dimensional as there are no continuous degrees of freedom, but that’s probably not a useful perspective in this case.)
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This conversation came up a few times during playtesting, with some folks arguing that normal chess was actually 3D not 2D. Thus my One-Dimensional Chess would actually be 2D.
In truth, I am breaking the idea of moving through one-dimension when I describe the Knight as “jumping”, but I feel it’s okay to take liberties with this sort of thing. Much like Edwin Abbott Abbott’s “Flatland” book took three-dimensional liberties when describing life in a two-dimensional world, I’m taking a few liberties in describing chess in one-dimension.
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Since pieces take time to be moved, you could also say it’s four- dimensional.
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Turn the board into a feromagnetic Möbius strip (maybe with a few more than 8 squares) with pieces clinging to its surface. How many dimensions then?
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Still one, right?
BTW, another fun twist I’ve seen on 1D chess is putting it on a loop (or a square in the image below). This effectively plays out as an infinite version of one-dimensional space.
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As a bonus, you can use a regular chessboard for this version
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Since the pieces end up back on the 2d grid at the end of the move, it isn’t clear what information another dimension would add. i.e. if you are always moving from (a,b,0) to (a+i,b+j,0), why write the 0?
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A ‘dimension’ is any measurable scalar. We might simply specify the location of an aircraft as x,y (the coordinates of the surface it’s over); as x,y,z (include elevation); or as t,x,y,z (note a point in space-time). Bet we may also measure its velocity (speed and orientation); the atmosphere’s ambient temperature; the aircraft’s fuel load at that point in space-time and its calculated range; the fatigue level of the pilot; et fucking cetera.
I built a 31D matrix to program a SoundBlasterPro sound card because it has that many settings at any instant. I needed mucho virtual memory on a PC-AT but so what? Maybe I’ll write an AI to play 31D chess. Right.
We tried to invent chess where you could move pieces through time as well as space, but the rules became too complex. Also we were super-high.
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Moving through time? As in, retracting a move? Or jumping ahead x moves? We usually call that ‘cheating’.
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