Nothing wrong with Robert asserting that his definition is correct. He aims to provide a precise definition which captures all the uses of a term we all feel like we understand. If he can capture them all, it is natural to say that his definition is correct. If our intuitive grasp of the concept is not sharp enough, it gets trickier, as we may not be able to decide what examples should be captured by our definition. At this point, it becomes harder to speak of an absolutely correct definition, but there may still be ways of deciding that some definitions are closer to being correct than others.

I am not sure where the case of ko falls, but my point is that there are standards for a correct definition, and it seems that Robert is aiming for them.

For more on the subject, try an article from an old professor of mine: http://plato.stanford.edu/entries/definitions/. The first section lays out several types of definition.

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Please don't overlook the 2nd and 3rd paragraphs of leichtloeslich post as I believe they are the most useful advice someone ever gave you in this forum.

For reference:

And now:


I am not sure I agree with this. It would certainly be useful for definitions to be followed by theorems, but they don't need to be, its all a function of aim.

For example: lets look at recent JF's definition/explanation of 'honte' and compare it to RJ's definition/explanation. Since both did not come with any theorems, so according to the above, both are useless? I don't think so. They both aim at answering an implied question: When I see a word 'honte' in a pro commentary, what does it mean? In this sense, I would say both are good and useful, although we can certainly argue which is better.

For other of the definitions I see RJ posting here (Ko, nakade, etc), I see them more of stepping stones in his own research, formalized versions of what we already know, not some generally applicable and finalized papers. To me, its more like he says: look people, here is what I came up with, I find it useful for my purpose, anybody agree, disagree, lets discuss. In this sense - it is a very good thing he does, even if most of us are not interested or find the approach too formal.

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I disagree with that in this context. What you say only applies when somebody defines a brand new concept.

For existing concepts, a definition can either reflect/formalize/agree with what we already know, or not, or only to some degree. And this degree of 'agreement' decides if the definition is correct or not, and to what extend. It is usually this 'degree of correctness' which we discuss here. If the definition is to far off the mark, we call it redefinition instead, and often frown upon that.

Example of bad (incorrect) definition (unless your furniture is really messed up):

• A 'wooden table' is a thing that is furry, has two ears, two eyes, wagging tail, and which needs to be walked every morning or it poops on the carpet.

Example of a better (more correct) definition:

• A 'puppy' is a thing that is furry, has two ears, two eyes, wagging tail, and which needs to be walked every morning or it poops on the carpet.

Hope this helps.

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Nature of my ko definition:

Firstly, see my paper, in which I comment on the scope of understanding and the need of future research:

http://home.snafu.de/jasiek/ko.pdf

Secondly, the ko definition is not of the kind of definitions for which a theorem would map it to the members of the set of all positions, turns, komi, history bans and input rulesets. Instead the ko definition belongs to a weaker kind of definitions: the definition is successfully tested to that subset of all positions, turns, komi, history bans and input rulesets, so that the positions include all known ko shapes (i.e., having been reported somewhere and spread; for details, see the paper). It is like a theory of physics (such as the general theory of relativity viewed on the macroscopic scale excluding quantum mechanics) that has been very thoroughly tested against perceived reality without any counter-example thus far.

Future research should continue to classify all shape classes etc., so that a theorem becomes possible, or a counter-example can be found.

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.



The reason I think your KO definition is useless:
- A KO definition shouldn't be 46 pages long.

If a definition is 46 pages long, then it's no longer a definition but something else. Not even the most complicate english word requires 46 pages to be explained in terms of simpler building blocks.

uPWarrior, if you carefully read my ko paper, you would notice that the definition itself is 1 short line long. It relies on 2 pages of preparatory definitions, of which a half is repeated or enhanced earlier research. The other 44 pages are commentary and examples, which include all known ko shapes, which is necessary to demonstrate that the definition detecs all known ko shapes.

Exercise: the definition of global-ko-intersection includes one superfluous condition added for easing the reader's understanding.

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.

Unless somebody made you *the* authority of what 'go theory research' is or should be. If so, please tell.

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Absolutely. I don't think I did that.

Are you sure? Have you taken a look at his definition? Afaik what "normal people" refer to as "ko", RJ would refer to as "basic ko", the definition of which is fairly trivial. See also here for a discussion along similar lines.

@Robert: could you give a short, informal description of what you are talking about when you refer to "ko"?
Preferably in terms everyone can understand without reading any of your research. (For example I think most people will have a good idea of what a "cycle" is.)

A few illustrative examples would also do.

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?


Either way, I'm still in favour of applying the metric of "usefulness" to definitions, as opposed to "correctness", which is usually an adjactive reserved for theorems.
I made a similar point in my original posting: your definitions can be "incorrect" and counterintuitive, but still useful, and imho that's the property we search for in a definition. An alternative word for "useful" may be "practical".

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.

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

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? )

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Everything with love. Stay safe.

Ok, my bad then. sorry.

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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?

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

+ + + + +

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 ?

+ + + + +

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.

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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.

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.

Are you really sure ?

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" ?

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