Cut Topology

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    Keywords: Theory

evpsych: Here is an idea for representing a fundamental aspect of a go position, but I am still working out the notation. I'm itching for comments.

My understanding of topology is that you can stretch something without changing the fundamental properties of the thing itself. There seems to be something in that with a cut. Perhaps games can be analyzed by looking only at the cuts, and by idealizing the groups being cut or doing the cutting. Then it is easier to figure out which groups need to be killed, etc.

[Diagram]

Two cuts, one with 4 groups and one with 3 groups, pared down to the essentials by representing each group as one stone. One group is shared between the cuts. There are 6 groups on this board.

There are 3 basic kinds of cuts: one player cuts (resulting in 3 groups), the other player cuts (resulting in 3 groups), or they both cut (resulting in 4 groups). A cut can be erased or converted to a different kind of cut by killing a group or when two groups wrap around to connect. A global position can be canonicalized into a pattern of these types of cuts to inform strategic insight about what groups are important.

We can also note the status of each group with a standard way to represent a live (or seki), dead, unsettled, or unknown-status group that is doing the cutting or being cut. For example, not shown in this diagram, circled and squared groups can mean live and dead, respectively, while unmarked groups are unsettled or unknown. (We would use a triangle for the unsettled groups if there were a triangle.)

There are a max of 4 groups per cut and 4 states per group, resulting in 4*4=16 basic patterns for a single cut. This dramatically reduces the problem space. Then, of course, we have multiple cuts on the goban.

(We could get fancier by adding more statuses (e.g. separating out seki or including the details about the ko and sente statuses) and potential connections and miai and so on, but that would probably be too complicated for most purposes. Note also that some of the cuts might share a group.)

Perhaps this idea is useful for computer go and go databases: you can search for canonical positions without worrying about the exact positions.

Perhaps it is useful here on SL, in that you can post a game diagram that shows only the cut topology. We could say "your BQM canonicalizes into this pattern with 2 cuts".


evpsych Hmm, no comments yet. Is the explanation clear enough?


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