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EyesCollection

Referenced by
GeneralEyeDefinition

 

Two Corners Kills The Eye
Path: EyesCollection   · Prev: FalseEye   · Next: FalseEyeLife
    Keywords: Life & Death

In GeneralEyeDefinition, it is stated:

[Diagram]
An eye in the centre

For an eye in the center, white stones must not be able to occupy more than one of the four marked points at the same time.

Bignose: I've since fixed the wording at General Eye Definition, hope it makes this clearer.

unkx80: Thanks.



But it seems to me that as soon as White has seized two of the marked points, Black has a false eye:

[Diagram]
False eye #1

[Diagram]
False eye #2

...and so on. Am I crazy or what?

Migeru No, the wording is (arguably) good mathematically but bad linguistically. The statement is that "white must not be able to occupy (the marked point for) at least three of the four marked points"

"White must not be able to occupy" is predicated as a property of "three of the four marked points". It's awful what knowledge of formal logic will do to your English.



unkx80: Pardon my not so good english. When I wrote this I found a lot of difficulty expressing it, and being much more mathematical than linguistic I wrote it the way I did. (Somemore, I had a course on discrete mathematics.) I actually wanted to say "black stones must occupy at least three out of the four marked points", but it is wrong with respect to the diagram below. On hindsight, the statement might be better rephrased "white stones can occupy at most one of the four marked points", but I find it very counter-intuitive. Please tell me if the alternative phrasing is better, and if so, I will start correcting the General Eye Definition page. =)

I didn't mean to sound too critical. As a foreign speaker and mathematician myself, I am best equipped to understand what went wrong, since it happens to me every so often. - Migeru

[Diagram]
"Black stones must occupy at least three out of the four marked points" does not apply.


Bill: To make a false eye, the White stones must live, and at least one of the Black strings must not make another (non-false) eye. It is possible for a group to live with two apparently false eyes (looking only at the points forming the eye).

[Diagram]
False eye #2

Like this? - Migeru


[Diagram]
Two-headed dragon

A much nicer example is the so-called "two-headed dragon" also known as living with two false eyes like the black group in this diagram. These eyes not only look false, they are false in the local context. Only in the global context do they suddenly appear to be real eyes. -- Andre Engels

Beautiful. As a fan of "The Neverending Story", I want to call this diagram "Auryn". - Migeru


Skelley Why don't we just combine the previous two examples :)

[Diagram]
Two headed false eyed dragon


Scartol: Look, my goal is to make Go as easy to understand for beginners as possible (especially since so much of it was so puzzling for me as I was coming up). So I think this way of presenting the idea of real vs. false eyes makes the most sense:

[Diagram]
Real eyes

In general: If black can surround a point with a circle of at least five stones, he has an eye. (In the middle; fewer stones are needed for the sides and corners.) However..


[Diagram]
False eyes

If white fills two of the corner spots in the circle, black's eye becomes false. Note that there are exceptions to this rule; once in a while, a shape can survive that appears to contain false eyes (include above examples).



Skelley: I see what you mean and your effort is very much appreciated. I usually use corner problems to illustrate false eyes to beginners. It seems to me that it is easier for them to understand that way.

[Diagram]
False eye

Something like this.

x is the vital point.

If any of the stones surrounding the eye can be captured then the eye is false.


[Diagram]
False eye

And then this.

x is the vital point.



Path: EyesCollection   · Prev: FalseEye   · Next: FalseEyeLife
This is a copy of the living page "Two Corners Kills The Eye" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.