Apart from your personal preference, is there any advantage of using "all" instead of "at least one" for the string's initial intersections?

Click Here To Show Diagram Code

[go]$$c
$$ . . . . . . . . . . . . . . .
$$ . . . X X . . . . . . . . . .
$$ . . X . X . . . . . . . . . .
$$ . X . X X X X X X X X X . X .
$$ . X X X O O O O O O O X X X .
$$ , . . X O . X X X . O X , . .
$$ . . . X O O O O O O O X . . .
$$ . . . X X X X X X X X . . . .
$$ . . . . X . . . . X . . X . .
$$ . . . . X . . . . X . . . X .
$$ . . . . . . . . . . . . . . .
$$ , . . . . . , . . . . . , . .[/go]

To me W lives in seki. According to your formulation??

BTW "damit" = "in order that" <> "therewith" = no english ( according to my dictionary )
"damit" = "with it/this/that" <> "therewith" = no english

Personally, I think my command of the English language is not enough to interfere too deeply into these discussions about the rules; I cannot express my thoughts well enough. Also sometimes I face problems in understanding the english of my German friends, which might have other reasons as well.

_________________
I think I am so I think I am.

Well, Cassandra's English might be not the best, also not in his otherwise nice book. (I think he must be Thomas Redecker, author of Igo Hatsuyoron Problem 120.) What matters is factual discussion rather than language knowledge (except where the precise wording does matter, of course).

Cassandra, you claim Japanese style rules, but "all" (for "2-eyed") is not Japanese style. You might call it "my wish for what Japanese rules should be". (Then I would throw in the Simplified Japanese Rules.)

"Advantage" ?

Hmm, I'm not really sure, if "advantage" will be the right term. It might depend on the standpoint you are looking from.

But I'll try to explain.


Motivation 1:

"All" might be more adequate to associate the string with something "alive", despite the fact that the string has been captured. The whole string has been "killed", but is "reborn" in the end (if this end is positive).

You wouldn't call someting "alive" anymore, of which only a small part (let's say 1 of many stones) has been "reanimated". Would be similar to bring a starfish temporarily to death and thereafter reanimate one of his five arms. I think, you wouldn't say that the (primary) starfish lives on.


Motivation 2:

"All" might be simpler during evaluation, because there is only one (1 !) status you have to try to achive for your string.

Let's reclaim the aim of the game:
To get at least one point of territory more than your opponent.

If we let apart the aquivalence of prisoners taken during the course of "Play" with "territory" for this explanation in "Evaluate" and "Count", there is something that temporarily prevents territorial points to be recognised as "empty" during "Score": opponent's "dead" stones.

This class of stones can be associated with "not-2-eyed inside opponents' 2-eyed" or "not-independently-alive inside opponents' independently-alive". Only one (1 !) status (including it's complement) is sufficient to achive this.

As you already know (and have already written in your "User-friendly reading ..." thread), there is no need to have a further status with regard to "Seki". But there is a strong reference to Seki, when introducing "at least one".

"At least one" in only necessary, if you prefer to have an "alive-alive" coexistence of opposing strings in a Seki instead of a "not-alive-not-alive" one. Perhaps this preference is triggered by the fact that the stones in Seki remain on the board (like really, i.e. independently, "alive" strings) during "Count" and so naturally look "more alive than dead".

"At least one" introduces a status in "Evaluate", which will not be of any interest during "Count". And additionally, you might encounter difficulties, when you must explain, why there is no territory in Seki, despite some of the engaged strings look "alive", and some of the opponent's ones "dead".


Anti-Motivation 1:

"Seki" is an element of the game, that has its relevance during "Play".

So it might be difficult to explain, why this important concept is not mentioned or referenced to by the rules.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Robert, you know very well that my English is not the best indeed. Thanks that you are looking behind the curtain.

One advantage of writing in a foreign, unfamiliar language is the need to think longer how to say what one wants to say. Gives the time required to cool down.

For "all" vs. "2-eyed" see my posting above.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Colloquially the position of the coexistence of Black's three stones and the surrounding White string is called "Seki".

Usually it is preferred to assume that these two strings "live", because they cannot be taken off the board.

But it would make no difference to call them "dead", because only "dead" strings inside opposing "alive" ones will become prisoners. This is true also with "2-eyed" vs. "not-2-eyed".

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

I'm sincerely trying to get the meaning behind this sentence. But I fail because I don't understand "therewith". I tried the German "damit", trying to see behind the language, but it didn't help me.
Do you mean: 'Strings in positions colloquially named "Seki" will all get the status not-2-eyed, unless it is inside opposing 2-eyed-strings: '

_________________
I think I am so I think I am.

The white string in my example is inside opposing "alive" ones. If you would call them dead they would become prisoners. I don't believe you want that.

_________________
I think I am so I think I am.

Motivation 1: This is subjective. Concerning subjective opinion, I do not have a preference for either the minimally "at least one" or the maximally "all".

Motivation 2: "all" works also with only one status, see Intermediate Step Rules or Simplified Japanese Rules. So I don't buy this motivation.

The first ruleset with only one life status was a draft in probably 2003, where I permitted only uncapturable. The first traditionally reasonable acceptable ruleset was the Intermediate Step Rules in my J1989 commentary.

Concerning seki, I do not have a personal preference whether the strings are alive or not alive. Alive is the traditional status, of course.



This might be so (Simplified Japanese Rules) but is not needed to be so (Simplified Japanese Rules with independently alive as an additional criterion in the definition of terriory). Anyway, it is only an aesthetic aspect. Having consistent visible surrounding by one colour of an empty string is a more important aesthetic and functional aspect.

Anti-Motivation 1: With the same right one could state thousands of strategic objects that do not play any role for scoring. Seki is just one of them.

cyclops, if Cassandra were more careful in his wording than J1989, then surrounding would be expressed clearly in the topological sense, so the example does not create the problem you fear.

Topological structures are not so simple as they might appear, aren't they, Robert ?

I remember we had this topic years before and you didn't like it.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Cyclops, typological structure often do not behave as they are assumed to do at first sight.

Let me explain, based on your Trojan Horse.

We will start with looking at each string seperately first.

• Black's 3-stone-string in not closed, so the remaining area of the board lies at only one side of it. Colloquially one would say, that everything else lies "outside", but this statement is true only for the string alone.
• White's string (let's name it the horse's stomach) is closed. So there is a smaller area on one side, containing Black's 3-stone-string (colloquially named "inside" White's string) and a larger area on the other side, containing the body of the Trojan Horse (colloquially named "outside" White's string).
• The body of Black's Trojan Horse is closed, too, and has a smaller area on one side (the horse's stomach - colloquially named "inside") and a larger one on the other side (colloquially named "outside").

Combining what we had found above for the single strings, we get:

• Black's 3-stone string (not-2-eyed) remains inside a White string (not-2-eyed), so it will not become prisoners.
• White's stomach-string has Black's 3-stone-string on one side, the horse's body on the other side, so it lies "between" (= "inside", because the bordering is complete, despite the bordering consists of more that only one part) two Black strings, of which one is not-2-eyed. So White's string, not-2-eyed-also, will not become prisoners, too.

In relation to the horse's body, White's stomach is extra-territorial. As a concluding result, one might even say, that it is "outside" Black's string.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

This may be true for the final stage of counting. I think you will not have used "an" = "1" literally.

But during evaluation it would be sufficient to have a visible bordering line of one colour.

This bordering line will be destroyed when using "at least one". It will remain stable when using "all".

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Re topology: It does not need to get more complicated than J2003. But finding local-2 required real effort. I needed ca. 8 months of non-stop work until I found it. Luckily it turned out to be simpler than what I had in between - it went up to capturable-5 :)

I assume you mean topological. It is the first time I see topology introduced in the discussion about go-rules. Because "connectedness" is a topological term I'm not surprised that it might play a role in rule formulation. It is used in topology in the same sense as in the connectedness of strings. But what I remember from my topology courses in the seventies is that finite unions of closed sets are closed, the same with open sets. So I would expect that all strings are all open or closed depending on the closedness or opennes of the single stoned string. I guess you have used the topological term "closed" in a non-topological sense. I understand that you call a string closed if the set of points not belonging to the string ( lets call it the complement ) is topological disconnected. You might split up the complement in maximal connected parts. The parts touching the border belong to the colloquial outside of the string. The remaining points of the complement belong to the colloquial inside of the string. Apart from your not topolical use of the term "closed" I think I can read your reply. If I totally misunderstand your concepts than can you please define your topological structure i.e. your topological space or give a link to such a definition.

edit: connected -> disconnected

_________________
I think I am so I think I am.

I think you are on the right way.

I'm afraid that I perhaps might not use "topological" as it is used in "topology" as major area in modern mathematics.

Might be more aquivalent to looking on a map, containing several different objects, from above, rather something like Euler's "Seven bridges of Königsberg" than questioning if "Möbius strip" has only one edge.

And from so far above that one cannot identify single stones in strings and may become busy about special move sequences.

I'll have to search in my archives for some older materials.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

Please find attached "topology1.pdf" from the time when I was interested in eyes more than in strings. I hope that the used symbols are self-explanatory.

Perhaps you will recognise that I used a similar methodology in "classification3.pdf" from Robert's "User-friendly Reading ..." tread, here uploaded again for your convinience.

One aim of this structure is to shorten evaluation. It is build from "easy" shapes (i.e. two taboo-points = two one-point eyes only) to more complex ones. So you may stop evaluation at the moment when you recognise that you have reached a structure that can be transformed in an already known one, from which you know the status.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

ok, in mathematical term we are talking about graphs. I will forget about topology. Your included documents will keep me quiet for a while, but at least I am able to follow your discussion for a while.

_________________
I think I am so I think I am.

Hi, cyclops,

May be that some ideas are borrowed from Graph Theory, some ideas from Topology, combined with the concept of "Inheritance" from Object-Oriented Programming.

What follows, is the first written version of my idea. So it is possible that some wording may need some sharpening.



A set of board points, that consists of points with the same property, which are connected along the lines of the board, will be referred to as "area". In the following text "connected along the lines of the board" will be referred to as "line-connected".

Let "string" be defined as "area that is occupied by stones of only one colour".

Let the property "object.closed" be defined as "there are two distinct areas, which are line-connected to the object".
If object.closed is "TRUE", you have to decide on one of the divided parts of the board for further evaluation of the object.

Let's have a function "inside()", which identifies the respective board-points as "inside(object, point) = TRUE". This function will be expanded several times in the course of the text below.



Single string with - colloquially spoken - 2 eyes


Let "minimum" be defined as extension of string. Let it have 2 not line-connected board-points with "inside(string, point) = TRUE".
(1) Its property "string.territory" is TRUE.

To simplify the following text, "board-points with "inside(object, point) = TRUE"" will be referenced to as "inside" points of the object.
The set of line-connected inside points will be referred to as "inside area".

Let the property "object.clumsy" be defined as "there is only one area, which is line connected to the object and does not include the whole edge of the board".


Let "larger" be defined as extension of minimum. Let the number of inside-points be greater than 2.

The inside points can be empty or occupied by opposing strings ("string.empty = TRUE" / "string.empty = "FALSE").

(1a) If they are empty, the property string.territory remains TRUE.
All but two not line-connected inside points can be filled with stones of the string's colour.

(1b) If they are not empty, the opposing strings can be .clumsy or not.

(1b1) If they are .clumsy, they cannot fill all inside points of the string. So the string will remain on the board.
The string's owner can fill inside points, so that the .clumsy opponent's strings will be taken off the board. The inside points will become empty.

(1b2) If the opponent's strings are not .clumsy, the string's owner can either take them off the board or not.

(1b2a) If he can take the opponent's strings off the board, the inside points are empty again.

(1b2b) If he cannot take the opponent's strings off the board, the property "string.territory" will be set to "FALSE".



Single string with - colloquially spoken - 1 eye


Let "not-yet" be defined as extension of string. Let it have at least 1 board-point with "inside(string, point) = TRUE".

(2a) "not-yet" can be forced to become "larger" >>> see above.
(2b) "not-yet" can be forced to become "minimum" >>> see above.
In both cases, the property not-yet.territory will be "TRUE".

(2c) Else: nothing can be concluded about the string alone.



Single strings with - colloquially spoken - more than 2 eyes


Let "more" be an extension of "minimum". Let the number of not-line-conneted inside points be 3 (more than "3" can be processed similar).
(3) more.territory = TRUE.

To enlarge the number of inside points of "more" will be widely similar to the procedure with "larger" above.

(3a) "string.empty = TRUE" is as above.

(3b1) "string.empty = FALSE" with opposing "string.clumsy = TRUE"" is as above.

(3b2) Let only 2 of the three inside areas become empty. This forces "inside(string, points)" for the points of the third area to became "FALSE", let us expand the inside-function for this purpose. The property "string.territory" will remain "TRUE" (with impact on the other two inside areas).

(3b3) Let at most 1 of the three inside areas become empty. The property "string.territory" will be set to "FALSE".



Two strings with - colloquially spoken - 2 eyes


Let "diagonally-touched" be defined as "not line-connected, but occupying two diagonally adjacent board points".

Let "stringstring" be defined an extension of string as "set of strings, which are diagonally touched or of which one is positioned inside another one".
The usage of "or" is not exclusive.

Let's expand the function "inside" now again. "inside(set of objects, point)" shall identify the board-points as "TRUE", for which "inside(set of objects, point)" or at least one "inside(single object, point)" becomes "TRUE".

Let "group" be defined as compound of stringstring and string. Let it have 2 not line-connected board-points with "inside(group, point) = TRUE".
(4) Its property "group.territory" is TRUE.

Let "s_minimum" be defined as extension of "stringstring". Let it have 2 not line-connected board-points with "inside(stringstring, point) = TRUE".
(4a) Its property "stringstring.territory" is TRUE; the property "string.territory" of both strings of stringstring is TRUE also.

"s_minimum" behaves like "minimum".



Not diagonally touched


For example, this is Nakade and circles.

(4b1) The two strings can be transformed to "minimum" together >>> see above.
(4b2) The two strings can be transformed to "g_minimum" together >>> see above.
.territory will become "TRUE".

(4b3) Else: nothing can be concluded about the two strings in conjunction.



Diagonally touched


Let "diagonally connected" be defined as "diagonally touched and there cannot be established a permanent stone of opposing colour on both of the two other "cutting points" at at least one diagonally touching.


Let one of the two strings be "minimum".

(4c1a) If the two strings are diagonally connected, "string.territory" of the other string will be "TRUE" also.

(4c1b) If the two strings are not diagonally connected, nothing can be concluded about the other string from "minimum".


Let none of the two strings be "minimum".

(4c2a) The two strings can be transformed to "minimum" together >>> see above.
(4c2b) The two strings can be transformed to "s_minimum" together >>> see above.
.territory will become "TRUE".

(4c2c) Else: nothing can be concluded about the two strings in conjunction.



Two strings with - colloquially spoken - 1 eye


(5a) The two strings can be transformed to "minimum" together >>> see above.
(5b) The two strings can be transformed to "g_minimum" together >>> see above.
.territory will become "TRUE".

(5c)Else: Else: nothing can be concluded about the two strings in conjunction.



Two strings with - colloquially spoken - more than 2 eyes.

Let "s_more" be an extension of "s_minimum". Let the number of not-line-connected inside points be 3 (more than "3" can be processed similar).

(6) "g_more" behaves like "more".



More than two strings with - colloquially spoken - 2 eyes


(7a) Let at least one of the two strings be "minimum".
.territory will become "TRUE".
See above.

(7b) Let at least one pair of strings be "g_minimum".
.territory will become "TRUE".
See above.



More than 2 strings


(8) More that 2 strings can be treated similar to above, by referring to pairs of strings.

_________________
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)