Is there a mathematically rigorous description of the geometry and properties of an eye?
As it were: “A point of series of points surrounded by stones of a single colour which…”
It seems odd that a game which looks at first sight so self-evidently based on simple geometry turns out to behave in such peculiar ways of that it’s described in a language all its own.
The first thing is to agree about what is an eye and that seemed to be unclear in a recent post (sorry that was not long ago but OGF search is not always easy to use)
Ok I got it
Eye is not fundamental rule of Go, its useful way to explain which groups are impossible to capture (when there are 2 eyes). But, there are also things like seki, which sometimes don’t have any eye, but not possible to capture too.
I think eyes are the result of the self-capture (“suicide”) rule. While seki is about human behaviour not rules. Whoever plays first into a seki has the disadvantage and the other has the advantage. But an eye is an eye, and no one can play into a 1-space eye according to the rules. (except in rulesets that allow self-capture…).
rule is about number of liberties, not about eyes or no eyes
So an interesting property of an eye is that you have to surround it first to have any chance (if any) to capture it.
Then we have to agree on more of what is an eye. Are we speaking only of real eye as we call something “fake eye”?
… and closely so, so as to take away its liberties. Just surrounding it from a distance doesn’t work.
Thus, again, it is about liberties.
Yes but not only.
I’d rather go into the teacher view. You lie a living simple shape with 2 eyes, give the name “eye” and then search with other configuration if those holes are eyes or not, meaning what we call eye has to be real.
Then the usual conclusion is you need to have 3 of the 4 angles points to be protected, be with a stone or another eye.
There are still some shortcuts like the 2 head dragon but anyway you don’t have to be exhaustive to the learner unless you like confusion and headache.
This may still be different if you are not teached but researching a définition for programming purpose for example. We say for example that a group has 2 eyes even when it’s not yet unveiled on the board. This assume that you can’t force your opponent to let you play twice like in a ko fight although you may have a position in which this is even not a thing to consider.
Yeah, one of the appeals of Go is its elegance: how simple rules create an intricate, deep, strategic, emergent, engaging, game
Do we have any mathematically rigorous description of any concepts in Go?
Other than endgame, of course, since endgame is all mathematics.
Do the rules count as “concepts”? because they’re definitely rigorously defined for simple undirected unweighted graphs in Tromp-Taylor Rules
I’m curious to know what this is…
Hmm this is difficult since “eyes” are part of both “concepts” and “rules”…
“eyes” aren’t part of Tromp Taylor rules
It’s even possible to have shapes with only (seemingly) false eyes to be alive
Benson’s algorithm would consider them real eyes
https://www.govariants.com/game/67fd6714c6f9d78cfd7d2fee
Basically, a graph has some vertices and edges, where edges represent connections between two vertices.
The grid on a normal go board is one example for a graph. The rules can be applied to any graph though.
Yes, I’d say we could fairly easily define a group of stones, for instance, or a tiger’s mouth.
Real ones. (A false eye could be any shape that deceives someone into thinking that it’s a real one!)
