Distance

    Keywords: Theory

(Sebastian:) How could we define "distance" on a goban?

[Diagram]
Is x Further than c from the Marked Stone?  

In the discussion of one opening (unfortunately I forget which one) it was argued that x is further from black+circle than c - or was it the other way round? Anyway, is there an empirical way to compare distances? Intuitively, one might say that a is further than c, and c is further than b.

But since the only valid connections in Go are the rectangular lines of the goban, it appears we should use Manhattan distance, which would regard a and c as equally far from black+circle.

HolIgor: [...] please, look if you can combine [the two pages].
(Sebastian:) Gladly, if someone can confirm that Manhattan distance (and the Bronx variant mentioned there) is the agreed way to measure distances in Go.

[Diagram]

Which Connection is Closer?

On the other hand, it is said that the black stones are connected more safely than the white stones - should they be considered closer?

kritz Not to complicate the discussion, but "relatively," aren't two stones on the third line "closer" than two on the fifth line? By this I mean - easier to connect/defend.

(Sebastian:) You're right, this makes it hard to define distance simply as the difficulty to connect. For large distances (such as in the opening diagram), a distance concept should in some way fit to strategical considerations. Another pitfall this could introduce is dependency on direction relative to the shape of formations. I was looking for a simple concept, and was hoping that the behaviour of two single stones is at least a reasonable guideline for estimating other distances. But maybe that would be hopelessly misleading?

Bill: In any event, a kosumi (on an otherwise empty board) is connected, while a one-space jump is, in general, not, although the Manhattan distance of both is 2.

Diagonal jump kosumi kogeima ogeima daidaigeima nobi ikken tobi niken tobi three-space extension
[Diagram]
Connections by Distance  

(Sebastian:) Maybe it helps to rank distances in this diagram. The idea is to fill it with all connections to the marked stone, arranged in alphabetical order of strength.


See also:


Distance last edited by 128.220.39.254 on January 28, 2006 - 01:07
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