Robert Jasiek's Go Theory Research

[pwaldron]

There are terms for which
a) I strongly believe my definition to be correct (ko),
b) I have not seen one counter-example since I have written my definition (thickness, if understood to be generalised to include also inside thickness),
c) I try to be a bit better than a random go dictionary entry, but I am aware that more study and quite likely changes to the definition are needed (aji, if understood to be used for the bad possibility variety of the term).

I guess my point would be, if such an informal description is not possible, how can you claim your definition is "correct"? "Correct" in relation to what?
If such a description is possible however, then, since your formal definition cannot be used to prove anything useful, what's the purpose of this level of formality in the first place?

This is the crux of it. It looks like the standard is that Robert thinks it is correct and can't find a counter-example. I suppose that's enough on which to base more work, but it's a pretty flimsy foundation. You'd spend a lot of time on something without any confidence that there isn't some pathological counter-example lurking around the corner.

[RobertJasiek]

For a long time, "ko" has been used for basic ko, triple ko, quadruple ko etc. It has also been used for long cycle shapes with traditional names that accidentally do not carry "ko" in their name: eternal life, moonshine life etc. Certain ko rules have carried ko in their names, e.g., a superko rule.

There has also been an alternative use of calling only basic kos "kos", of denying that "basic ko" would be the name and of denying that triple ko etc. would be a ko at all. Instead the latter might have been called "long cycle shapes" or such. In this sense, I mean both "ko" and "long cycle shapes".

Informal description of "ko": something allowing "interesting" cycles.

Informal description of "ko" for the sake of my ko definition paper: a connected part of the board, so that a cycle involving it is worth playing under suitable circumstances.

Examples: see my papers.

"Correct" in relation to all known ko shapes (given the ruleset, turn, komi etc.) and an interesting selection of counter-examples. The correct thing about my definition is that it determines each known example meant to be a ko as a "ko" and that it does not determine any other known and tested example as a "ko". The definition models the known reality.

My definition has been proven to be useful for
- see above
- explaining the above
- characterising the nature of ko in general
- providing new techniques of theory
- allowing better insight to ko strategy

[RobertJasiek]

pwaldron, this is the fate of models of reality. Until all counter-examples have been proven impossible, a counter-example might possibly be found. Until then, you might share my appreciation of the power of my definition to distinguish ko from non-ko even in all known arcane examples. Or would you question the power of the theory of general relativity because some time a counter-example might be found?

[Bill Spight]

It looks like the standard is that Robert thinks it is correct and can't find a counter-example. I suppose that's enough on which to base more work, but it's a pretty flimsy foundation. You'd spend a lot of time on something without any confidence that there isn't some pathological counter-example lurking around the corner.

pwaldron, this is the fate of models of reality. Until all counter-examples have been proven impossible, a counter-example might possibly be found. Until then, you might share my appreciation of the power of my definition to distinguish ko from non-ko even in all known arcane examples. Or would you question the power of the theory of general relativity because some time a counter-example might be found?

Robert, do I understand correctly that you claim to have a definition of ko that fits all examples of "ko" or "cycle" or other examples to which a ko rule has been applied (like "moonshine life"), under all of the main rule sets, while excluding cycles to which such terms have not been applied? (As far as you know.)

For example, you do not call a one stone sacrifice a ko because no major rule set does, even though it repeats a board position, right? (OTOH, it would be called a ko under a ko rule that prohibited repeating a position of the whole board by means of board plays alone, without passes. Is that what you mean by a pathological counter-example, pwaldron? )

[Bantari]

I obviously have no issue in stepping stones on someones research, but I thought threads in the study journal section are asking for some sort of advice (as a moderator recently noted).

Regarding the formality, I disagree. I think it is in that spot where it is not formal enough to deserve a "go theory research" label and it is too formal to be a useful definition for an amateur. Go theory research is closer to math than to enumerations.

Good points, for sure, and we can certainly discuss that sometime.
Personally, I think that the above is a matter of opinion, and yours is as valid as mine, or RJ's. Certainly no reason to invalidate posts or people.

Absolutely. I don't think I did that.

Ok, my bad then. sorry.

[RobertJasiek]

Bill, 1-stone suicide: in my paper, I mention that the ko definition can be altered to include 1-stone suicide. This is simply a matter of study purpose whether to exclude or include 1-stone suicide.

My definition of ko fits all examples and - I think - counter-examples, (almost) regardless of the chosen input ruleset, which can have some ko-ruleset. It need not be a main ruleset, but can be any go ruleset. (Well, almost any. E.g., a ruleset with a tournament-rules-like 4-pass-game-end condition needs to be modelled by a 3-pass-game-end condition in order to work as an input ruleset and not create a conflict with the design of the default restriction rules.)

More generally, history bans, turn and komi may be given in addition to the ruleset. (Maybe I was too courageous with allowing history bans, even under superko in the input ruleset?:) I have not studied this carefully in practice yet.)

I have not checked the lost example with a 7 plays cycle. If you recall the example, which somebody presented in the mailing list go-rules, please present it here and verify.

Moonshine life is trivial: it consists of basic-ko-intersections. The interesting question, however, is: when does a moonshine-life consist of global-ko-intersections?

[Cassandra]

My definition has been proven to be useful for
* snip *
- allowing better insight to ko strategy

Dear Robert, I must admit that I have studied your Ko-paper partially only. So -- at the moment -- I have just minor annotations.

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If I understand it correctly, "Basic-Ko" is defined as a cycle, wherin each player captures the just played single stone of the opponent, which has captured a single stone of the player.

"Local-Ko" seems to be defined as a cycle that one player starts, and the opponent participates in, but only because the opponent wants to pre-empt a local loss.

"Global-Ko" seems to be defined as a cycle that one player starts, and the opponents participates in, but only because the opponent wants to pre-emt the loss of the game.

However, I am afraid that this classification follows from (Ko) strategy. So, where should the "better insight" come from ?

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I was very confused about your usage of the term "Triple-Ko" (may be that similar problems would arise with your usage of "Double-Ko").

In my understanding, "Triple-Ko" is used to name the combination of three "Basic-Ko" on the board (mostly related to one formation, but this is not mandatory).

In your paper, you used "Triple-Ko" also for the combination of a "Two-Stage-Ko" (would this also be a "Double-Ko" in your terminology ?), and a "Round-Robin"-shape.

I doubt this usage, because the characteristics of a "Three-Basic-Ko"-formation are quite different from those of a "Three-Stage-Ko"-formation.

[Boidhre]

This is the crux of it. It looks like the standard is that Robert thinks it is correct and can't find a counter-example. I suppose that's enough on which to base more work, but it's a pretty flimsy foundation. You'd spend a lot of time on something without any confidence that there isn't some pathological counter-example lurking around the corner.

Well this is how most theory is developed. One researcher proposes something testable. They do some tests to show its got some merit. Other people do their best to find examples that contradicts the test. The researcher goes back to tinker or abandon depending on what is found and so on.

It's fine, so long as the first researcher isn't going around saying "it's correct" before there's been confirmation from independents that they couldn't find a counter example either.

[RobertJasiek]

Cassandra, a basic-ko consists of the two intersections related to what you describe.

Local-/Global-ko-intersection: The players do not have free will (your "wants to"), but obey the definitions of prevent or answer-force. It depends on a set of cycles (which might consist of one cycle), not necessarily of just one cycle.

An intersection can be a basic-, local- OR global-ko-intersection. Notice that it is not XOR. Therefore, a ko can have intersections that are, e.g., local- AND global-ko-intersections.

If you think that the classification follows from ko strategy, please cite any text preceding my paper and providing such a classification.

Triple-ko: Put one on the board. Then, for each of its (fake) basic-kos, capture and recapture a single stone. Impossible! A triple-ko does not consist only of basic-kos.

Triple-ko is a somewhat ambiguous term, sometimes referring to different shapes involving three kos.

[Cassandra]

Triple-ko: Put one on the board. Then, for each of its (fake) basic-kos, capture and recapture a single stone. Impossible! A triple-ko does not consist only of basic-kos.

Are you really sure ?

The Basic Ko Rules
*...*
Definition : (basic) ko : Two board points are a (basic) ko if on them a move of one player followed by a move of the other player repeats the configuration of stones.

Italics inserted.

It seems to me that there are three spots in a "usual" Triple-Ko, where this definition applies.
Without the "Basic-Ko"-rule, capture and recapture of a single stone would be possible, as a matter of course.

An example:
Black captures one to these Ko, White plays a Ko-threat, Black answers the Ko-threat, White recaptures the "one of these" Ko.
No "Basic Ko" ?

[RobertJasiek]

Cassandra, read the paper to its end, or put stones on a board and test each "basic-ko" of a standard triple-ko (no outside liberties). You CANNOT recapture a single stone in each of the three.

[Cassandra]

Cassandra, read the paper to its end, or put stones on a board and test each "basic-ko" of a standard triple-ko (no outside liberties). You CANNOT recapture a single stone in each of the three.

With a "standard" "Triple-Ko":

B1 captures W1.
W3 captures B3. This is a Ko-threat, related to B1 / W1.
B2 captures W2. This is a Ko-threat, related to W3 / B3. This answers White's Ko-threat, related to B1 / W1.
W1 captures B1. This is a Ko-threat, related to B2 / W2. This answers White's Ko-threat, related to W3 / B3.
B3 captures W3. This is a Ko-threat, related to W1 / B1. This answers White's Ko-threat, related to B2 / W2.
W2 captures B2. This is a Ko-threat, related to B3 / W3. This answers White's Ko-threat, related to W1 / B1.

The "Triple-Ko-"cycle is completed.

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With regard to Ko #1:

B1 captures W1.
This is a Ko-threat, related to B1 / W1.
This answers White's Ko-threat, related to B1 / W1.
W1 captures B1.
This is a Ko-threat, related to W1 / B1.
This answers White's Ko-threat, related to W1 / B1.

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With regard to Ko #2:

W3 captures B3.
This is a Ko-threat, related to W3 / B3.
This answers White's Ko-threat, related to W3 / B3.
B3 captures W3.
This is a Ko-threat, related to B3 / W3.

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With regard to Ko #3:

B2 captures W2.
This is a Ko-threat, related to B2 / W2.
This answers White's Ko-threat, related to B2 / W2.
W2 captures B2.

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Each of B1, W3, B2 has become re-captured !!!

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What do I have overlooked ?

[hyperpape]

Good God people, we have diagrams and eidogo!

[RobertJasiek]

$$B
$$ +-----------+
$$ | X X X X X |
$$ | . X . X O |
$$ | X O X O . |
$$ | O O O O O |
$$ +-----------+

Click Here To Show Diagram Code

[go]$$B
$$ +-----------+
$$ | X X X X X |
$$ | . X . X O |
$$ | X O X O . |
$$ | O O O O O |
$$ +-----------+[/go]

$$B
$$ +-----------+
$$ | X X X X X |
$$ | . X . X O |
$$ | X O X O 1 |
$$ | O O O O O |
$$ +-----------+

Click Here To Show Diagram Code

[go]$$B
$$ +-----------+
$$ | X X X X X |
$$ | . X . X O |
$$ | X O X O 1 |
$$ | O O O O O |
$$ +-----------+[/go]

$$B
$$ +-----------+
$$ | X X X X X |
$$ | . X . X . |
$$ | X . X . X |
$$ | . . . . . |
$$ +-----------+

Click Here To Show Diagram Code

[go]$$B
$$ +-----------+
$$ | X X X X X |
$$ | . X . X . |
$$ | X . X . X |
$$ | . . . . . |
$$ +-----------+[/go]

Now a recapture is impossible;)

[Cassandra]

Now a recapture is impossible;)

This fake posting is far, far below your level.

Is this your "new" way, when you have run out of arguments with regard to contents ?

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