Editing 3177: Chessboard Alignment

{{comic
| number    = 3177
| date      = December 5, 2025
| title     = Chessboard Alignment
| image     = chessboard_alignment_2x.png
| imagesize = 397x289px
| noexpand  = true
| titletext = Luckily, the range is limited by the fact that the square boundary lines follow great circles.
}}

==Explanation==
{{incomplete|This page was created BY AN ALIGNED BISHOP. Don't remove this notice too soon.}}
The comic shows an overhead view of three chess boards side by side, with an average of two players facing each other across the boards. Yellow squares (used to show the available or actual movement of a given piece) have been marked leading from the starting position of the middle board's right bishop (F1) to the upper-right. The path continues beyond the edge of the middle board, across four columns of empty space or unseen table, and ends in the top left corner (A8) of the right board. The right board has only one rook (black rectangle) while the other two boards each have two, so it is implied that the bishop has captured the rook, and the player who made the move is now apparently paying attention to (and plausibly co-playing with the neighbouring player on) the board he has moved his piece to. The text below jokingly claims that if you align chess boards exactly, pieces can cross the boundary like this. This is not legal in normal chess,{{Citation needed}} but fits into [[Randall]]'s long history of comics about unusual chess rules or boards.

The position on the left board is from a blitz game played between Judit Polgar and Magnus Carlsen in Madrid in 2022.[https://www.chessgames.com/perl/chessgame?gid=2325478] The middle board's position seems to have followed (up until before this cross-boards move) the game seen in [[3045: AlphaMove]].

The title text refers to the fact that chess boards are normally placed approximately level (parallel to the surface of the Earth). As such there are two different possible interpretations of the title text, whether you are following geodesics on the surface of the Earth (any great circle) or following the geodesics of spacetime (leaving the Earth and going into space).

;    Following great circles
A perfect line of chessboards placed end-to-end on the surface of an Earth-sized sphere (or on perfectly placed tables on that sphere) would form a {{w|great circle}} - the longest possible path around that sphere, as well as only straight path on spheres. This rule would allow chess moves between boards that were kilometers (or even whole countries) apart in any direction, along {{w|great circles}} of the Earth, as any straight line on any sphere or ellipsoid can be extended all the way across. If following the great circle along the ground was considered a straight line, then it would also be possible for each side's rooks, bishops and queen to capture their counterparts in the other color's back row, or, in a later game, they would be able to teleport between left and right sides, or jump onto the other side of any diagonal for pieces that move diagonally, as it would be possible to go around planet following any horizontal, vertical or diagonal line of the chessboard. If no other chessboard were involved it would make it into [https://www.chessvariants.org/shape.dir/torus_standard_board.html Torus chess], but only for pieces that can move an unlimited amount of squares. It would also function differently from Torus Chess for diagonal-movers, because they would move around to the other end of their own diagonal, not loop to the diagonal 4 squares away in a perpendicular direction. There is a caveat to all of this though: the size of a square would have to divide the great circle exactly a rational number of times, with a precision down to micrometers. (The denominator of such number represents how many times that piece would have to go sound the earth.) Quite possibly only one direction would work, if any at all, since Earth is not a perfect sphere, so distance around the Earth would differ in different directions. Notable exceptions would be the South and North Poles, where all great circles are the same. While the North Pole is in the {{w|Arctic Ocean}}, so you won't be able to stay level there easily, at the South Pole there is the {{w|Amundsen–Scott South Pole Station}}, where this variant of chess could be more interesting if you had the correct size of board squares, with both verticals and horizontals working. Alternatively, you could replace squares on the chessboard with rectangles. The difference between vertical and horizontal length would not have to be more than 0.08%, which at regular chessboard size would result in difference of less than 0.5mm, which will be barely noticeable. Replacing squares with rectangles presents a problem, because if you want for chessboard to always be aligned, the required dimensions would depend on the latitude where the chessboard is located, and you would need to put the chessboard at a precise angle on top. Having many different chessboards for different latitudes would not be sustainable.{{Citation needed}}

When you have to pick a single direction that works for looping your own chessboard then there are three options for orienting the chessboard:
* If you choose a horizontal line, then you will get a limited variant of {{w|Cylinder chess}}, where only the Queen and Rooks can utilize the wraparound, and only when moving horizontally.
* If you choose a vertical line, it is technically also a cylinder for Rooks and Queens, but it will create an interesting dynamic, where players would be able to exchange queens and rooks in the first 2 turns (for example, doing this opening: 1. Qxd8+ Kxd8 2. Rxh8 Rxa1).
* If you choose a diagonal, then it will result in Queens and Bishops being able to jump over all pieces (they cannot switch to a different diagonal, as in cylinder chess, as all diagonals will loop on themselves), though they would have to have visibility of one of the edges of the chess board. Also, they cannot jam themselves in-between 2 or more pieces, as they would emerge on the opposite side of the diagonal. Most likely, diagonal works only in one of the two possible directions too, so there is an extra choice there (unless you are at one of the Earth's poles, where you can make both diagonal directions work).

;    Following the geodesics of spacetime
While nearby boards would appear to be in the same plane, the curvature of the Earth would cause boards more distant than 3.57 meters away to be in planes so different that the squares would be more than a micrometer off from the ideal straight lines leading off the board. It is thus implied that each infinite-range piece's valid path is a straight line of virtual squares that eventually leads into space. Straight lines would have to be in the overall spacetime of the universe along a {{w|Geodesics in general relativity|geodesic}}. This would not rule out motion to another board on another celestial body or spaceship, though delivery of a chess piece across this distance would be impractical{{Citation needed}} and other objects in space would move so fast relative to your board that they would be in alignment for only a fraction of a second, unless it is a satellite in a {{w|geostationary orbit}}. If you want to be level with Earth and 'aim' your chessboard at a geostationary satellite, you would have to be at latitude of around 81.4° in either Arctic or Antarctic, because those orbits are so far away from the Earth. So chess games would have to take place at some {{w|List of northernmost settlements|arctic research station}} ({{w|Station Nord, Greenland}} being the optimal) or somewhere on the continent of {{w|Antarctica}} (the best research station there would be {{w|Sobral Base}}, though not as good as Station Nord). If this interpretation is accepted then this can be considered a second comic in a week about [[3174: Bridge Clearance|distances extending past typical boundaries]].

[[:Category:Chess|Chess]] is a common recurring theme on xkcd.

==Transcript==
{{incomplete transcript|Don't remove this notice too soon.}}

:[An aerial view of three chess-games, with six players shown, in each case with white at the near-side of board (towards the bottom of the comic panel) and each having reasonably developed game positions.<!-- which I won't describe, both for brevity and for possible misrecognition of the low-detail depiction of each piece-->]
:[The middle board has yellow highlight on the squares from white's King's Bishop's original position, diagonally forward-right to the respective edge square of the board, then four more squares in the gap between boards until ending on the black Queen's Rook square of the right-hand board, which appears now to have three white bishops, one of them on this rook's starting square.
:[There is just one black rook, elsewhere on the right board, whether or not the other was lost to middle-board's bishop, and the middle board has only one bishop (and is lacking three pawns, with just two others still in their starting positions), for white, with apparently their King sent forward-left by two successive diagonal moves but no other major pieces having noticably relocated.]
:[The middle board's near-side player has now also moved across to pay attention to the right hand board, leaving only his opponent facing his original board.]

:[Text below the main scene's panel:] It doesn't happen often because it requires micrometer precision, but if two chess boards are '''''perfectly''''' aligned, it's actually legal to move pieces between them.

{{comic discussion}}<noinclude>
[[Category:Chess]]
[[Category:Comics with color]]
[[Category:Geometry]]