Gérard TAILLE wrote:
Cassandra wrote:
This implies that ALL points that are neighboured to (also surrounded by, even eye-points) STONE(s) that are in SEKI are DAME.
But I do not understand this implication.
Dame is defined by the two following sentences:
Empty points surrounded by the live stones of just one player are called "eye points." Other empty points are called "dame."You see that for defining a
dame you need only to know if stones are alive or not. The status of
seki for these living stones is irrelevant for defining an
eye point or a
dame.
As a consequence I do not see a recursivity here because the status of an
empty point (
eye point or
dame) is determined immediately and unambigously with only one stage (with recursivity we would have several stages for determining the satus of an empy point).
Dear Gérard,
"eye point" is nothing that serves the definition of TERRITORY.
When determining TERRITORY, empty points of the board can have one of ONLY TWO status:
-- DAME
-- TERRITORY
STONE(s) that are in SEKI (= SEKI STONE(s)) cannot surround TERRITORY, so every empty point in their neighbourhood must be DAME.
Please note that the primary definition of DAME (= "ANYTHING BUT surrounded by alive STONE(s) of only one colour") is derived from "eye point". But the definition of "eye point" seems to be declarative only (probably for better understanding? probably a reference to the "real" world?); there is NO, ABSOLUTELY NONE, further reference on this term in the rules (with the exception of the definition of the temporary opposite). Therefore, "eye points" have nothing to do with TERRITORY.
STONE(s) that are in SEKI might be neighboured to an "eye point", but "eye point" does not exist when you determine TERRITORY. If an empty point is DAME, it cannot be TERRITORY, and vice versa.
+ + + + + + + + + + + + + + + + + + +
Yes, indeed, we have two pairs of terms:
-- eye point / DAME, and
-- DAME / TERRITORY, but
both pairs have to be seen in different context.
The first pair serves the easy detection of a first amount of "DAME", with which can be started in the second pair, for determining "SEKI STONE(s)", and probably a second amount of "DAME".
The term "DAME" exists in both pairs, but this does NOT imply that "eye point" = "TERRITORY".
_________________
The really most difficult Go problem ever:
https://igohatsuyoron120.de/index.htmIgo Hatsuyōron #120 (really solved by KataGo)