Forum for False Eye
A different viewpoint [#1171]
Elroch: I believe the concept of a false eye is a historical accident that should be avoided, or corrected. In both the examples of false eyes given, if one of the black groups is extended the "false" eye can be shown to be fully functioning (see diagram below, for example). This shows it is not the eye itself that is faulty, but the upper of the two black groups, which was only in contact with one eye. This confused viewpoint has been perpetuated because of a loose idea of group, including stones that are not properly connected. The diagram below has two black groups, each in contact with two eyes (one of which is shared). See also Recognizing an eye where I have added this viewpoint to the article itself. I know this viewpoint will be seen as controversial to some, but I have no doubt that it is better founded, and encourage discussion on this point.
![[Diagram]](diagrams/33/f3c0ba3dd9064da04e1ee2556be6990d.png)
![[Diagram]](diagrams/21/807227ad0873f1e6227d574c3c538f62.png)
In part the problem is English go terminology. Not to make a fetish of Japanese terms, but early English go terms were translations from Japanese. A better translation for the corresponding Japanese term might be defective eye.
In a sense, you can see the defective quality of the eye at 
by the fact that Black is still alive if it is filled. It does not help to make Black alive.
More important, however, is the fact that many go concepts depend upon the implicit assumption of alternating play.
![[Diagram]](diagrams/16/2d0d9b778f7f3c9ba05b4ceb678d0800.png)
Elroch: It is interesting to see the different emphasis from very experienced contributors. Bill says that the middle eye is defective because if it was filled the new merged chain would be alive. I say it is not defective because it gives both chains life without any more stones being played! I think the concept Bill is describing is more "essentialness" than "defectiveness". It is worth noting that the two headed dragon is an example of a group which is given life by two eyes which have all the characteristics of what are known as "false" eyes, and which are essential as well, in that they may not be filled in without leaving the group dead.
One point that might be useful to emphasis is that a "false" eye appears to be characterised by being made up of more than one chain in such a way that the only way to make the chains into a single chain is to destroy the eye.
Hence I propose the terms "disconnected eye" for one whose border is made up of more than one group. My really wacky example in the second diagram below shows that what appears to be disconnected locally may not be globally. I have no doubt that the deeply embedded traditional terminology will continue to be used by everyone.
![[Diagram]](diagrams/6/ab3f4c2a21d142501a6017c79b44e702.png)
![[Diagram]](diagrams/16/b9595a369def5ae3c379155760b72de8.png)
About essentialness: A defining quality of any eye is one or more open points surrounded by stones of the same color. If the eye may be filled without changing the life or death status of a group, the eye is not essential to that status, because a non-eye will do. In your examples, the connection is essential to the life of the group, the eye itself is not.
The Japanese term, kakeme, which I think would better be translated as defective eye, is a local condition of an eye. It is also an informal notion. A necessary condition is that the stones forming the group do not form a single chain and that they cannot form a single chain without capturing at least one opposing stone or filling the eye. The eyes in the two headed dragon example that you give are kakeme.
As for whether the eyes in a two headed dragon are false or not, usage differs among English speaking players. I would not call them false eyes. Nor would I call the connecting eyes in your other examples false. Other people would.
Elroch: The different ways of thinking (which I think in all cases lead us to the same practical consequences) are mainly to do with a group-oriented idea of life versus a chain-oriented idea of life. Like the Benson's algorithm article which I was pointed towards early in this discussion, my natural inclination is to the chain-oriented concept, mainly because it is simple enough to write down the logic, which is not true if I try to define the life of a group directly. I see groups as collections of chains that are one stone from being solidly connected, and the life of a group is the life of some subset (sometimes all) of its chains. Pattern recognition and reading can identify the life of a group without thinking in this way, but it seems simpler to treat the life of chains as the basic concept.
Your first example says "eye gives life to four groups", but calling that an eye would only confuse I think (just like your earlier examples). So the group in your example has 4 eyes, 1 false eye, and 5 points of territory. Your edit on RecognizingAnEye says "now it's a real eye", in such a case, but I do not agree, and the viewpoint of others in this simple common case is not clear to me yet. The way I've always seen it is: things like your example may be a point of territory, and an illegal place to play for the opponent, but still not an eye, still a false eye. (The discussion about the two-headed dragon is another one.)
Using the word 'eye' like you do, would confuse me, anyway :) Say there is a life and death problem, consisting of two strings, one of which has an eye, the other half an eye, connected by a false eye. With your usage of the word eye, you'd say the group has become a 3-eyed group after making the second eye. That just sounds odd to me.
In this light I also propose changing your piece on RecognizingAnEye, but I'm curious about the opinion of others first :)
My poor use of terminology may have misled. I should have said four strings or four chains. Each string or chain has one proper eye and shares an eye which would traditionally be called false. As a result all four chains are alive. When you look at it logically, it is the chains that live and die, and the chains that need to border two eyes. The Benson's algorithm page elaborates this better.
Thinking in this way immediately indicates the status of the group in your example, as one string has an eye of its own and borders a "false" eye, so is not under threat, but the other string only borders the shared eye. Hence that string is vulnerable. If that string is killed the first string becomes vulnerable. I would _not_ say the group has become a 3-eyed group. I only count eyes for strings, as this is necessary and sufficient.
This clarifies the use of the string-oriented viewpoint in life and death problems. If each string has two eyes (without an intersection not touching the string) then the strings are all safe, hence the group is safe. If there is a string that does not, it is vulnerable to attack, and if it is killed, one needs to repeat the analysis, as other strings sharing an eye with the dead string may be compromised.
In response to your comment I have edited RecognizingAnEye to avoid confusing people with a non-standard use of the term "real eye".
A few even more extreme examples
![[Diagram]](diagrams/48/0ee6dfab0f87a0eeef4b1b4fe441ec19.png)
![[Diagram]](diagrams/13/992248ae1e8129d969641220070b4f6d.png)
You are right ofcourse, that 'real' and 'false' eyes are not very strictly defined. Examples like the Two Headed Dragon show that eyes that seem to be false can be real eyes.
However, false eyes are a very useful concept for teaching. It gives us an easy way to show beginners when surrounded spaces are eyes and when they are not. We would only confuse most people with formal definitions, two headed dragons, etc. Such things are useful and interesting, but should not stop us from using the term 'false' eye.
For an even more formal definition, you might look at Benson's Algorithm, which also handles the case of bigger eyes where the opponent can still play inside (which you have touched upon on the recognizing an eye page).
Elroch: Thanks for your knowledgeable input, Herman. On a little more consideration, I have realised that the crucial issue is related to the point about eyes really being needed by solidly connected groups. In most cases where there are two almost connected groups, and one has a proper eye and shares a second eye with the second group, there is a way to join the groups together and form a single group. All examples of "false" eyes have the property that there is no way to connect the groups without filling the "false" eye. Of course with my modified example, the need to solidly connect the groups disappears, since each group lives alone, by sharing the "false" eye.
I suppose the only thing I object to about the established nomenclature is that the falseness of an eye is only properly clarified when the groups that create it become consolidated, so the "falseness" is not a property of the eye, but rather of the final state of the groups that share it.
I find thinking of the individual solidly connected groups makes a lot of life and death situations very clear, such as "living small" situations with two or more groups in the corner.
![[Diagram]](diagrams/6/f0601b005835ac6d06a31dd037500025.png)
![[Diagram]](diagrams/7/1eb403ff71d2c0f7a60579cf552af638.png)
Hi Elroch, many thanks for your viewpoint. In fact this has been a subject having lots of debate, and I believe Dieter did a lot of work to wiki master edit all these mess into the presently readable pages. A summary of the discussion can be found at formal definitions of eye.
Another way is to use a simpler approach to define eyes, and then defer the precise meaning of life and death to a level that is beyond the description of eyes. What this means is that we can define eyes as described in the more accurate section of recognizing an eye, so a simple heuristic is to disregard the number of false eyes and count the number of real eyes, and say since the group have two or more real eyes, it lives. So such a definition of eye will defer the determination of life by having only two false eyes, or two headed dragon, to other means. As far as I understand, the Chinese players tend to see things this way. In fact, a common Chinese name to two headed dragon can be directly translated to "false eye life", which seems to be quite telling on how Chinese players define eyes. However, I do not dare to claim that all Chinese players define the term "false eye" unambiguously or in the same manner.
Perhaps of interest to Bill, the Chinese term 假眼 may be directly translated to "fake eye" or "false eye". A Chinese name for two headed dragon is 假眼活, or "false eye life".
![[Diagram]](diagrams/46/c79feca3f1ea2909ea83b1446ea3dbe7.png)
Thanks, unkx80, for the translation of the Chinese terms. :-)
I think that the question of eyes could benefit from rigorous treatment, and perhaps new terminology. False eyes, for instance, are not entirely irrelevant for life.
![[Diagram]](diagrams/34/0c93df75102ae330c7c0dd9bc633a5ba.png)
![[Diagram]](diagrams/30/9bbcee0c83cd6c19078399d384d74974.png)
I suspect the Chinese players do not really have an agreed view on your examples. All should agree that these are in seki, but whether these eyes are false or not, possibly no agreement. Quite often I see statements to the effect of "this eye looks false but...". =)
John F. Bill, I realise there is a pursuit of some sort of mathematical elegance behind the discussion, and so I am walking on quicksand, but I have some trouble in accepting your example here as a false eye, on two levels. (1) Oriental definitions all seem to centre on the fact that a false eye is a shape that looks like an eye but is not because it eventually has to be filled. The point you marked does not have to be filled, so it is a real eye. (2) This is just a re-statement of 1, I think, but it seems to me that an eye is any point that cannot be filled in without prejudicing the life of the group. Anything else is a point of territory (worth 0 or 1 depending on the seki rule) or a false eye, i.e. a point that has to be filled.
Your (1) and (2) do not seem equivalent to me: Imagine two strings with an eye connected by a 'false eye'. According to your (1), the false eye is now an eye (so it's using the language of Elroch), but using your (2), the 'false eye shape' is no eye.
Well, John, for years I used to define a false eye as one that had to be filled to save some of the stones forming it (or the equivalent). However, since the discussions on SL some years ago I have kept a look out for usage, and found references to the eyes in a two headed dragon as kakeme, for instance.
Perhaps, as in English, usage differs among Japanese players. Now, if you have an authoritative definition, I would be glad if you would share it us. Thanks. :-)
John F. Bill, resorting to a dictionary I see that the Japanese do define a false eye as one that will have to be filled in eventually, but then the next entry refers to kakemeiki, which effectively contradicts that definition. Still, I can't imagine that the person who originally coined the term kakeme and the people who followed him were looking for mathematical rigour. I'm really just saying that I think there's a danger in trying to make vernacular words bear a rigid meaning. Maybe we should follow Linnaeus and define oculus spp..
Thanks, John. :-)
I think there's a danger in trying to make vernacular words bear a rigid meaning.
I agree. For instance, see my recent comment about group.
As for both kakeme and false eye, I think that we want at least two definitions, to reflect differing usage.
However, as with sente and gote, I think that there is a place for rigorous, formal treatment of various kinds of eye, in addition to the informal notions. And perhaps we will need some new terms, just as a rigorous treatment of sente and gote showed the need for an ambiguous classification.
To my way of thinking, the conventional use of "false eye" is very useful from a practical viewpoint. If a group has two eyes, neither of them "false", then it's definitely alive. If an eye is "false" (in the conventional sense), then it's necessary to look carefully at the position. I think this attitude is invaluable for beginners learning the basics of life and death.
Even though I recognise the logical validity of the discussion above, it still feels easier and more useful to give the name "false eye" to the local shape, and then remember look at the context every time a "false eye" occurs.
Reviving old subjects is a good thing on a Wiki and it shows that for new users it is not entirely clear that we've been there, done that and hence we perhaps have not fully been there neither done it satisfactorily.
Basically, earlier attempts to structure the discussion had the following purpose:
- Presenting a few pages on the eyes subject, with beginner? difficulty, which cover the subject in a comprehensible, natural way, which corresponds to the basic human treatment of life & death situations. I think the eye, false eyeand recognizing an eye do a good job in that respect.
- Moving the discussion about false eye life, two-headed dragon and seki to appropriate (discussion) pages, with their appropriate difficulty level.
Compare it to encyclopaedic entries versus books on a subject. It must be possible to write an entry about a computer, without diving into the intricacies of Von-Neumann architecture or Turing machines.
If we set completeness of the subject as a goal for a descriptive page, we're bound to fail in presenting a readable article to an average reader. I'm sure this is common Wiki-sense. In practice, neither seki, false eye life or the linguistic issues on translating Japanese, Chinese or Korean terminology for the subject should be on the descriptive page of false eye.
We must obviously improve on the linking between these pages and the path of eyes collection (a path title I have never liked) which tries to present all these pages with their relative content and relationships.
Well, going back to a long ago discussion, I thought that we reached agreement about introductory material. I notice that this page is labeled introductory, but is a terminology page. My impression at the time was that such a page would be titled False eye - Introductory or the like. To say that a false eye is something that looks like an eye but isn't one is fine for an introductory page, but inadequate for a terminology page, IMHO.
I agree that a terminology page should not aim at completeness. That's why we have hypertext links. :-) I notice that at one time this page had several links to related pages, but not now. What happened? Have those other pages disappeared?
I want to warn for a possible flaw in thinking. The circled point can indeed be said not to be an essential eye?, because filling it does not change the status of the group.
![[Diagram]](diagrams/29/4108faf0e45651c32721731e471d272a.png)
However, neither is the group's status affected when filling the circled eye here, and yet the eye is real. So filling the eye does not change the group's status is not a sufficient but a necessary condition for a false eye. BUT, ...
In my opinion it is not efficient, axiomaticallly, to derive an eye's nature from the status of the group to which it belongs. It is much more efficient to give a local definition of the nature of an eye, and then derive a group's status from it:
- groups with two real eyes (locally defined) live
- groups can live in seki
- groups can live with false eyes (locally defined), in false eye life, under certain (global) conditions
Such an approach stays close to a go player's learning curve and is logically well built (but perhaps not elegant enough to some).
![[Diagram]](diagrams/22/d5daae59e4d6fbc8179515a3429cd629.png)
Consider this situation. You want to tell something in this stage of the game about the eyes' nature. Locally, all black eyes are false. All white eyes are real.
Due to the unusual whole board situation, the life of the Black group is decided by the point a. If White takes it, Black dies. If Black takes it, he lives, with false eye life. The nature of the eyes hasn't changed, the status of the group has.
It is not very helpful, IMO, to say that the nature of the eyes depends on who plays a. Essentially, the concepts of life and death and eye, coincide in such an approach, making either of the concepts void of significance.
The chain viewpoint makes it easy in both examples. In my diagram with the two chains with one real eye each, sharing an "inessential" eye, each chain is unconditionally alive as it borders two eyes which may not be invaded.
In the other example on the 6x6 board, if black plays at 'a' she has four chains with 2 eyes each, and if white plays at 'a' two of the chains are not safe,as they border only one eye. The knock-on effect is that all the black chains are vulnerable.
What I have been lately teaching to beginners is that an eye is a place where a chain of stones has a liberty that the opponent cannot ever remove unless all the other liberties have been removed before.
This feels like the defining property of an eye, since now it is easy to explain independent life: "two eyes live" follows from exactly from the fact that there are two distinct liberties that both would need to be removed last.
Of course, if one were to use this as a general definition of an eye, then the pair of kos in a double ko seki might get defined as an eye while it clearly is not; it merely behaves like one.
-Bass
I strongly disagree with the original argument. It is a complete misunderstanding to think that there are two black groups in the proposed example. This simply is one group with two eyes. The false eye here is just a special sort of connection between the two chains. Especially with area scoring, it has no importance whatsoever. (With territory scoring such a connection is worth 1 more point than a plain connection, but that's all there is.)
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