Tuesday, May 17, 2016

[mlawnxpo] Coordinates on a go 囲碁 board

In chess, a reasonably skilled player (or fan) can instantaneously locate a square specified in algebraic notation, without having to refer to coordinates on the side of the board (or counting coordinates if they aren't written) and finding the intersection.  The board seems small enough that each square has its own identity and the coordinates are just names rather than instructions on how to find it.  (Perhaps beginners have such a hard time at this that it is a barrier to entry.)

In 19x19 go 囲碁, the board is too large for each intersection to have such an instantly locatable identity, so we consider ways to refer to a specific intersection, especially for things like commentators discussing a game in progress on a demonstration board.

The most obvious, and already commonly done method, is to have coordinates marked along the side of the board.  However, because the board is so large, following a coordinate line all the way across the board takes time and is prone to error.  (Geometrically, this is an instance of area growing faster than perimeter.)  Only the corner regions are quick.

A simple elaboration would for coordinates to be marked on every intersection, similar to beginner's chess boards.  Assuming letter plus number, we win because the highest number is 19, and the 1 digit does not take much space in a proportional font.  The board does potentially get noisy with a lot of text, especially if each played stone is also annotated with its move number.

Another already commonly done method is for commentators to add marks, e.g., letters, to certain intersections (which may or may not be occupied with a played stone) and refer to the marks in discussion.  The marks are landmarks.

With landmarks, we can ambitiously also consider a standardized language for referring to a point a given offset from a landmark.  The area reachable by N wazir moves is a diamond shaped region given by OEIS A001844.  Exploit approximate 8-way symmetry (understanding that orthogonal and 45 degree diagonal points will have redundant names).  24 letters, perhaps NATO alphabet plus an octant specifier can cover up to 9 wazir moves (A002620).  An offset such as a knight's move will always have the same name (but different octant specifiers) in all 8 possible directions.

Inspiration was two commentators commenting on an online go board.  Though this could be solved better with software: each commentator could have a different colored pointer.

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