Cycle / Discussion

Sub-page of Cycle

Table of contents Table of diagrams
B6 tenuki/pass

a-b-c-d cycle

Reconstructing 5- and 7-move cycles

RobertJasiek: Several years ago, in the mailing list go-rules, John Tromp found cycles of lengths 5 and 7 with the functional sequences kkkkkp and kkkkkkkp. Does anyone recall the shapes?

Herman: Interesting! Isn't there a mailing list archive?

RobertJasiek: Precisely, there is none (yet). I have a good percentage stored somewhere locally but no time yet to publish it as an archive.

Herman: I assume that terminology here is: k = ko, p = pass? Where ko means basic ko?

RobertJasiek: Yes, for the moves, and in square brackets, but I cannot denote the brackets on Sensei correctly or is there an escape character?

Herman The character ! escapes wiki syntax, so ![kkkkkp] will give: [kkkkkp]

Can [kkkkp] be a cycle?

Herman Hmmm, correct me if I'm wrong, or misunderstand, but if k = basic ko, then every k in the sequence should add one exactly stone and remove exactly one stone? So kkkkkp would:

  • add black, remove white
  • add white, remove black
  • add black, remove white
  • add white, remove black
  • add black, remove white
  • pass

And would have an unbalanced number of additions/removals, leading to one extra black and one less white? (ie: cannot be a cycle)

RobertJasiek: k means ko (in general) - not (necessarily) basic ko (as currently on Sensei's ko page). Sorry, overlooked your earlier question related to basic ko.

Herman: Ok, thanks. Can you clarify for me: k refers to any play on a ko intersection? ie: the 5 move cycle currently named sending three returning two qualifies for the pattern [kkkkkp]?

RobertJasiek: Yes. Or use [kkkkkt] in case of a tenuki.

ThorAvaTahr: Would it even be correct to say that any cycle of length 5 would be [kkkkkp]?

Herman: I can imagine there might be cycles that include (necessary) suicide, don't know if any of them could be 5 long (I highly doubt it).

RobertJasiek: No (unless you do not apply any ko rules). I am currently researching in identifying the ko intersections from the non-ko intersections, so one cannot be precise in general about the distinction of [k] and [t] yet.

Herman: If I understand correctly, your definition currently depends on the term force (mathematical)? So:

B6 tenuki/pass  

This constitutes a 5 move cycle, but since it is voluntary, it isn't [kkkkkp], correct?

Yes. --rj

Bill: Ah! Another case of sending three, returning two, n'est-ce pas? ;)

Herman: Oui! This was the first thing that came to my mind for a 5 move cycle when writing the cycle page, but it's boring because it's not forced :)

Is suicide really a one-move cycle?

Thoravatahr: Does the one move cycle need a tag that it isn't a cycle, there is no force to commit suicide.

Herman: If it is allowed, then a player can use it to avoid passing, and can draw out the game infinitely long with the sequence: Pass, Suicide, Pass, Suicide, Pass, Suicide, etc. So rules must take it into account.

RobertJasiek: Presumably there is some freedom of definition. Either one includes it or one does not. It has already caused some nightmares for me (definitions require care) but probably I will either include or exclude it depending on which is easier or more consistent when formulating the final definitions. Even then one might alter them to suit other research better. - Yes, that a one move cycle can be a surprising means to force something is crucial indeed. Therefore so far I simply exclude it to make my life as a definition finder (a tiny bit) easier. - I was more frightened by the opponent of the one trying to force a cycle though!

Update needed (Jasiek’s research of 2010-01-31)

RobertJasiek: In view of my [ext] recent research, the page needs an update of its contents.

Herman: In the section "Presuppositions and Basic Definitions I", the term cycle is claimed to be defined elsewhere, so presumably this research does not redefine the term cycle?

RobertJasiek: The meaning of positional / situational cycle is well known. (The parent page defines positional cycle only though.) There can be different annotations though. No, I do not mean to redefine cycle in my paper. The parent page Cycle needs a major update though because it is abused to describe some informal generalization of ko. In this respect, there are mistakes. E.g., a ko is not always defined by only one cycle - one might have to consider a set of cycles. E.g., a subtle point is that now answer-force should substitute force. My major concern is, however, that Ko expects the Cycle page to explain general ko. It does not do that well. My paper does do it. - One thing is very clear though: Ko (in general) and cycle are two different concepts. Currently Ko suggests that they were about the same. This is desinforming.

Re: suicide only one-move cycle / legalese

Archived from Cycle: comment added in [ext]

A single-stone suicide is the only possible type of one-move cycle.[3]

[3] Robert Pauli: I disagree to that claim. (PJT: I have edited the contested statement to take account of this objection.)

  1. It is common to take a pass as a special kind of move: at least AGA rules and SGF do. SGF even counts passes just like any other move.
  2. The definition at the top could use board play instead of move to exclude passes, but does not.

Therefore, following that definition (to which I also disagree), a single pass also is a one-move cycle. Unfortunately this then prevents us to call two consecutive passes a cycle, despite that being the most rule-relevant cycle of all.

PJT: Robert, I did not want to change your text, but may I suggest you change “disagree to” to “disagree with” (and remove this suggestion)? P.S. Thank-you for the corrections of the slips in my last edit.

Herman: Can we stop slaughtering this poor article already? It does not need more mathematical legalese. It is an informal high level overview of the subject, and the ambiguity it contains is absolutely fine.

Discussion on cycle length

In reference to the introductory paragraph:

A cycle is a move sequence that starts and ends at the same position.[1] If at the end of the cycle it is the same player’s turn as at the start, it is also a situational cycle[2] (repeats the same situation).

Robert Pauli, who prefers the definition in Cycle / Alternative definition by Robert Pauli, wrote:

Meaning(s) of ‘cycle’

Robert Pauli:

[1] Ignoring the Cycle Completion Law valid throughout the rest of the world.

[2] Ridiculous. Not truth, fake has to be (dis)qualified (i.e. positional "cycle").

RobertJasiek: Explain what you think is ridiculous / fake. See, e.g., Cycle Balance Law?.

RP: Hi, Robert! I explained it now at Cycle Completion. The fake is calling a board repetition "cycle" before the cycle completed. This false use should be (dis)qualified with positional. To instead qualify a sound cycle with situational is, sorry, ridiculous.
(Let me ignore your reference to Cycle Balance Law?: off topic and wasting a term.)

Herman: The current page qualifies nothing, it simply notes that a particular subset of cycles are also situational cycles. Other cycles are positional cycles only. All of them are cycles. Redefining a term to exclude a subset previously included will not do. If you feel the need to make a distinction, feel free to come up with a new term not already in use.

Robert Pauli: This page misuses the general term cycle. All cycles in Go are of an even length. The claimed-to-be cycles of an odd length need a further pass to complete (did you read it?). Until that, they only qualify as repetition of a position, as not-yet cycles, as almost cycles, as positional cycles, as could-be cycles, or whatever you want to call them. What you, Herman, call subset — the "situational" cycles — is the whole set, and its members don’t need a, sorry, stupid qualification.

RobertJasiek: We understand your point that playing recurring cycles requires even numbers of moves. However, historical use has been more tolerant and made the positional / situational distinction. More importantly, cycles can be described as sequence of a) moves, b) positions, c) moves / positions, d) subsequences etc. It depends on study purposes which kind of description one uses. Your preference must not prohibit a richer use and application.

Herman: @RP: Cycle is an existing term used with an existing meaning within go theory, objecting that it misuses a general term is pointless. You might equally object that the term temperature as used in CGT is fake because it has nothing to do with the vibration of atoms. If you feel the need to write go theory on cycles of even length only, by all means call them "loops" or something, and go wild. (BTW, you claim about "the Cycle Completion Law valid throughout the rest of the world" is particularly odd. Searching google for "cycle completion law" gives me literally zero results).

Robert Pauli: Herman, Robert, the term cycle is not at your disposal. As I said over and over again, if the cycle can't start again, it isn't yet finished (complete). It therefore is ridiculous to state that, say, a S2R1 is a cycle of length 3 when everyone knows that if you let it spin, the [ext] period is FOUR. Not I'm wild, you are. You are hi-jacking an established term for what really is whole-board repetition. I make a distinction, you level out. All cycles in Go are even, simply because they have to complete before they can start again. The almost cycles you desperately want to include are exactly that, almost cycles. One further pass, and they are complete. Before that they only are whole-board repetitions (BTW, is this term superfluous? Can't you use it?). Please understand that I'm not pursuing my own agenda. Take [ext] Sine or whatever. 55 Minutes don't make an hour. You should brush off your preoccupation and start to think about it.

Herman: Nobody owns the term cycle. Sensei's library documents the usage of terms. The term cycle as used in the go community includes cycles of both odd and even length. No matter how much that goes against your ideas about what cycles are, the term is not yours to redefine.

Robert Pauli: Here's a little challenge. How many cycles do you count in the [ext] graph below? First Herman, then Robert.


P.J.T.: ¿What is the point of this question? – It is a [ext] Directed_graph; since graph-theory definitions are notoriously idiolectic[42], I see arguments for an answer ``in { 1, 4, 2, 8, aleph_0}`` in order of decreasing plausibility (but not for ``2^(aleph_0)``).

[42] ‘idiolectic’ = ‘pertaining to an idiolect’, i.e. to the form of a language employed by one individual, i.e. every author defines the terminology the way they like it best.

Herman: Please, this is pointless nonsense. The topic at hand is documenting on SL how this term is being used in the go community. Going of on tangents about how a term is used in other fields is not productive.

Robert Pauli: Herman, please do me a favor, and answer nevertheless. To me the nonsense is on your part and the alleged crowd you are hiding behind. The point of my question will be revealed as soon you do.

Herman: You're unable to reveal the point of your question without an answer from me? If you have no further relevant input, I guess we can end this discussion and restore this page to its original form.

Robert Pauli: Herman (and Robert as well), could you please give me an answer. I’ll hopefully agree with you, and then ask you the next question (What’s its period?). I want to see how far we can get with agreeing. And I certainly want to keep this discussion somewhere!

RobertJasiek: For at least half a year, I am too busy with work for such detailed discussion about cycles, sorry.

Herman: @RP you seem to be under the misapprehension that logic matters in this discussion. I understand quite well why you feel it is logical that cycles should be even length, it is not a hard argument to make. What I'm saying, and what I will keep coming back to, is this: SL documents how the term is used in the go community. This is not a matter of logic, it is a matter of reference. Do you disagree that the term cycle has been used, for many years by a variety of authors, to refer to any positional repetition, i.e. of both odd and even length?

Robert Pauli: Herman, you still owe me an answer (How much cycles do you see up there, and what are their periods?). A discussion is an exchange, you know, and I’ll come to my point.
I too understand your point of view:

Crowd talks crap, and we follow (descriptive).

But if things are as stupid as here (pass is a cycle but double pass isn’t even mentioned), we should tell the crowd that it is going astray and that we will not follow! How else could we improve?
What would be the consequences? Search "positional cycle" and you’ll find not much: 3 hits (the same for "situational cycle"). One is Force Mathematics. Look into it. The culprit isn’t the crowd, it’s Robert Jasiek. He makes bad choices and we have to suffer? Come on, that’s ridiculous. Look at his Cycle Balance Law? (another hit). If you look into it you’ll discover that it requires a what he calls situational cycle. But tell me, why didn’t he then call his baby Situational Cycle Law? Was it that he prefers the term cycle over the term situational cycle? Well, me too.

Herman: PJT has given a reasonable answer on the possible answers to the number of cycles in your graph, IMO, but let’s go with the simple cycle definition according to [ext], which uniquely defines a cycle by its set of edges, and say 1 cycle, OK? As to previous authors, we can find cycles of both odd and even lengths mentioned in e.g. Ing-Spight Ko Rule (by Bill Spight), the [ext] Computer Olympiad Rules (by Erik van der Werf) or the Kee Rules Of Go (by Wilton Kee) or Long Cycle Seki Rule (by myself). This is not just something only Robert Jasiek uses.

RobertJasiek: Matti Siivola created the terms position / situation around 1997 and I frequently applied them in various phrases, such as those for cycles. Since I have been the most active researcher by far on related topics, you find the terms mainly in my texts. Regardless of the qualifiers, cycle has often been used by Western and Eastern players in the positional sense because most are concerned with positional recreation and not with enabling infinite recurrence of a situational cycle. Bad luck for you. Go usage does not conform to graph theory. We understand that but do not abandon the qualifiers. For more details, no time for at least 6 months.

Robert Pauli: I'll look at what you refer to, but note that Ing-Spight Ko Rule has:

Cycle: A sequence of board plays that may repeat.

And, how can Bill object if he doesn't show up?
No, Herman, you forgot the period.

Bill: Hi, Robert. C'est moi. :) It's true that I did not sign in, but I have not signed in for years.

RP: Hi, Bill, even if we disagree! :-)

Herman: Ing-Spight Ko Rule specifically mentions that even cycles may repeat immediately, while odd cycles cannot. Bill's objection was added by Bill himself. I think this discussion has run its course and the consensus is clear.

Robert Pauli: Bill's definition there does not agree with the one given on this page either. His "cycles" do not include passes. BTW, he is dealing with local repetitions, not whole-board repetitions.

Robert Pauli: Herman, I started the discussion, and I will end it. I replaced all alleged names with their IP address. If someone wants to participate, he should openly sign up. And now stop being silly and answer my question. What is the period of my 4-arrow cycle you took painfully long to identify (to which I OC agree)?


RobertJasiek: I do not always bother to log in but just to confirm that I can log in I am - again - signing my discussion texts. Please do not expect the worst from other people but expect the best: that signing one's text means that it is one's own text. Accidental wrong signing sometimes occurs especially when a third person enters his opinion amidst somebody else's opinion. This, however, is not the case in this discussion so far. Every block of somebody's opinion has been signed by its writer. Note to Herman and Bill: you might want to restore your signatures where Pauli has replaced them by IPs. Note to Pauli: an IP alone does not identify a writer because IPs can be, and in fact often are, dynamic.

Herman: @RP: Official warning: Editing other people's contributions/signatures is very unacceptable, doubly so in this case because you are explicitly casting doubt on the honesty of other users. If you do so again, I will ban you.

Robert Pauli: Other people should sign on if the don’t want to be treated as anonymous (since, as Robert correctly remarked, IPs do not identify someone). We can expect that, especially in a discussion. I did not put my words into others mouth (as Patrick Traill does, e.g. a fortiori), I replaced the alleged names with the actual IPs. That’s nothing but the truth, Herman. If you don’t like the truth, Herman, then ban yourself.

Herman: We have had thousands of conversations on SL with participants who do not sign in. That is why they sign their contributions. Additionally, their IP can be found in the change log, if needed. Removing the signature is not "truth". It hides information. If you do not like how SL works, you can find another platform.

RP: That’s nonsense, Herman. If you want to show your flag, you sign in. If we don’t keep that up, why should anyone sign in?

PJT Sorry you did not like “a fortiori” – I felt it read better, did not alter (but clarified) the sense and that a page Cycle was not expected to be the intellectual property of one person. But since it was in your proposed and signed text, maybe it was out of place; on the other hand that status could only reasonably be temporary in a wiki article not clearly the responsibility of one person.

Now back to my question, Herman, I want to finish this nonsense.

What’s the period of my simple 4-arrow cycle you agreed on to be one?

Herman: I had a look at [ext], but it does not mention the term period anywhere. Googling for "cycle period" gives me only results on menstruation. This does not seem to be an existing term?

Uberdude: Is this discussion a cycle? ;-)

fractic: I'll guess I'll extend this cycle. I think Robert is confused between cycles and periodic processes. Despite my background in mathematics, I've never heard any kind of demand that a cycle must be able to be restarted. This whole idea of Cycle Completion is non-standard.

The term cycle is generally applied to discrete mathematical objects. Cycles typically have lengths not periods. The term period is more commonly applied to things like periodic functions or repeating processes.

If we consider a path in a graph, we can ask things like "does it contain a cycle?". You can then ask for the length of that cycle but not for it's period. It also doesn't make sense to ask if the path could have restarted the cycle. It's just an object under consideration. It can't "do" anything.

Even when considering the path within a bigger class of paths (e.g. paths where both players alternate plays), and there is no other path within that class that immediately restarts the cycle. It still makes sense to say that the original path contains a cycle.

Now of course even and odd move cycles within go are different. And it's fine to study them separately. Sending two returning one is a perfectly valid cycle within the graph of board positions. If you instead consider the graph of board positions + player to move then it's not a cycle there. There is absolutely no reason to restrict the word cycle to cycles in that second graph.

Robert Pauli:
No, fractic, I’m not confused. If ABC is called a cycle, then I expect ABC to be able to follow again and again. Quote

If cycles are allowed without restrictions on them, it is possible for a game to go on indefinitely.

And if someone tells me, hey, that’s not the case, but look, DABC can follow again and again, then I’ll tell this nut that then ABCD is the cycle. Mathematics is without time, right, but moves in a board game certainly take time, so I feel period to fit, its unit OC is move, not hour. So there is a 24-hour cycle (day) as well as a 2-move cycle (ko). The period (. . . length, if you want) of the first is 24 hours, that of the second 2 moves. But even Mathematics uses the term period. Go to [ext] repeating decimal, scroll to the Table of values, and admire the column Period.

Herman, you’re funny (sorry). Adding "-menstrual" might help (but note that the female cycle isn’t really off topic. :-)

Anyway, call it period length, Herman. Just give me the number. I don’t want to put my number into your mouth.

And, Robert, Bill, you too could count the cycles in my diagram and their period lengths and tell us what you found — OC only if your precious time allows that (and don’t forget to sign on).

Herman: If you want a number on the period of a cycle in a graph from me, you'll have to give me a definition in the context of graph theory. But according to graph theory, the length of that cycle is 4. Is that the number you're looking for?

fractic: Robert, do you deny that sending two returning one is a cycle in the graph of board positions? You end in the same position you began. I suppose you can repeat it in that graph if you wanted. Yes, that would be two black moves in a row. But that is not a concept in that graph.

It's fine that you only care about the graph of (board position + player to move) but other people are also interested in the graph of just board positions (as evidenced by several examples that have already been linked). You do not get to restrict the use of the general term cycle to merely that second graph. It would be just as silly as demanding we only study the graph of game states according to Japanese rules. At least that one is nicely acyclical.

Robert Pauli: Thank you, Herman (one cycle of length four). I’ll wait a little for the others (Robert, Bill, fractic) to agree to you. fractic, you can use the term almost cycle for your purpose. There is no need to spoil the term cycle. Cycles are the beasts that prevent the game from ending, that’s what this is about. Does two for one (without the pass) prevent no-pass Go to end? Don’t get your claim that Japanese rules give an acyclic directed graph. Position, player, and prisoner difference certainly can repeat.

fractic: I'll agree with the fact that the cycle you drew has length four. You cannot force other people to use a term like almost cycle for a generic graph theory term. You didn't answer my question about whether or not you think sending two returning one is a cycle in the graph of board positions.

As for my comments on the Japanese rules gamestate graph. Obviously prisoner count is part of the game state not just prisoner difference. But even then the graph is acyclic. Repetitions of that kind move the game to a no-result state. And two passes move the game to a scoring state.

Patrick Traill: As far as the game state is concerned, there are different possible ways of modelling the game which yield equivalent results, except for the issue of which cycles they forbid, and I think this is true of the “prisoner difference/counts” distinction. I do not find it “obvious” that either model is better, though to me minimising the amount of information retained has an appeal that supports “difference” rather than “counts”. Both approaches make the number of states infinite, which is unfortunate, as forbidding repetition then no longer guarantees termination. For that reason I would rather consider only the state on the board itself (and the history of such states), and so, in principle, use area scoring. In practice, like many of us, I use the prisoners as a convenience to reduce area scoring to territory scoring, and of course the bowls show us counts rather than the difference. When you say the Japanese state graph is acyclic, I am not sure you are not begging the question: the point is surely that we have a state/transition-definition of a game which does allow cycles and then transform this into an acyclic game by introducing one or more rules forbidding cycles; one may also introduce new components to the state (e.g. “Black has requested adjudication by the Nihon Ki-in”). I am not familiar enough with the Japanese rules to say whether they succeed in eliminating cycles, but I wonder about triple ko.

fractic: I agree there are more nuances to the whole thing than I initially mentioned. But it was just meant as an example to indicate that restricting the term cycle to some specific graph is silly. This ultimately tells you more about what graph you chose rather than true meaning of the word cycle. (PJT: Fair point)

I thought triple ko was rather explicitly a no-result under japanese rules though. (PJT: I think you are right.) But the Japanese rules have been historically underdefined so perhaps it wasn't the best example.

Robert Pauli: fractic, thank you for agreeing with Herman. Let’s see if the other two follow him (one, four).

To almost cycle. They can change that to positional repetition of an odd length if they want, but I deny them to spoil the term cycle, e.g. odd cycle which pretends to be a special kind of cycle.

Since we want the game to end, the only directed graph that matters is the one that is equivalent to the game (with no rules about repetition or ending yet). You arbitrarily shrink those arrows in it that represent passes to achieve your goal. Would you follow me if I’d look at ``sf1//sf13 ={:sf076923:}`` and declare its period length to be ``sf5`` instead of ``sf6`` because I refuse to count the digit zero? Ridiculous. So, not I am choosing whatever graph I like, you are.

"But even then [with prisoner difference] the graph is acyclic" simply is wrong and lets me wonder. Just take and (immediately) retake a ko — the cycle has completed. Since this cycle is frequent, they banned it. The other frequent cycle is the trivial cycle (however, I may not call it that because, remember, this page ridiculously calls a pass a cycle). That cycle would end the game. Two for one is no cycle under Japanese rules in a strict sense (prisoner difference grows) and therefore needs not be aborted (see foolish cycle). But, Japanese rules are off topic, so let’s stop to discuss them.

Have a nice Valentine’s day!

Herman: This page does not call a pass a cycle.


"Since we want the game to end, the only directed graph that matters is the one that is equivalent to the game".

No! This is the crux of this discussion. It is the only graph that you are interested in. As demonstrated other people care about other kinds of cycles.

And you still have not answered my question about sending two returning one in the graph of "board positions". Simply claiming that it's me who wants shift focus on a different graph from the one that matters is once again your own bias. Sure, you dress it up as it being the only graph that matters because it is somehow equivalent to the game.

Let's look at IngSpightKoRule. This is one of the many ways to address cycles in rules of go. It explicitly mentions odd cycles and those have real rule relevance. Now sure, most of us don't use this particular version of the ko rule. But that doesn't invalidate the whole thing or render it less interesting. Note how clearly the page defines its terms and distinguishes between even and odd cycles. It even has a comment about how odd cycles can't directly repeat. Also note how Robert Jasiek and Herman pointed out the existence of the terms positional cycle and situational cycle. This is how terminology should be. Well defined, precise and applicable to the situation at hand. If you want to write something, say an article on this wiki, and you only care about even length cycles. All you have to do is write a small comment or footnote saying something like "In this article we only consider even length cycles." And everything is clear.

Instead you are trying to lay a claim to the definition of the term cycle. And do so in a manner that disagrees with its existing usage. And furthermore you would have others to use terms like "almost cycle" for things they already had perfectly well defined terms for. Should we just update all existing works to use your new term? Insisting on that would be arrogant in the supreme. Like you said, I choose what graph to consider and apply the general term cycle to. But unlike you, I am not denying you your right to apply the term to whatever graph you want.

fractic: As an aside, regarding your question about whether or not a pass would constitute a cycle. I would say it depends on what graph you are considering. In the graph where vertices are board positions and edges are moves or passes. Then yes it is a cycle. In a graph where the vertices record the board position and the player to move. Then no, it is not a cycle.

fractic: As another aside, regarding to your response to my example of the graph of gamestates according to Japanese rules. Your counter example to my acyclicity claim doesn't work. Taking a ko and retaking a ko is not a cycle in this graph. For the simple reason that the retaking the ko is not an edge in that graph because the rules forbid it. (Or perhaps it moves the game to an "invalid move you lose" state. I will concede that my example was not properly specified. The vagueries of the Japanese rules are indeed off topic.)

I mentioned it as an analogy to what you are doing. You say (heavily paraphrased): don't look at the "board position" graph look at the "board position + player to move" graph instead. And you justify this by appealing to the game rules. I merely took this to an absurd extreme by saying: forget about both of those graphs and look at the "Japanese gamestate" graph instead. Using the same appeal to game rules.

Robert Pauli: It does, Herman. The very first sentence on this page was, quote:

A cycle is a move sequence that starts and ends at the same position.

Remember? Let’s additionally quote the [ext] Official AGA Rules of Go, 1991:

A move consists in playing a stone of one’s color on an empty intersection (including edges and corners), or in passing.

So, this page indeed calls a pass a cycle. If you as me should not like this, don’t worry, fractic will explain us in detail why we should.

fractic: You somewhat misunderstoond my stance Robert. I'm not forcing you to call a pass a cycle. But it is entirely reasonable to consider a pass a cycle. Context is the key here.

The word cycle means many things. In graph theory a cycle is a path that starts and ends in the same vertex. In group theory it refers to certain elements of symmetric groups, but it also is about things going in circles. The water cycle is a whole other thing all together. The connection with the earlier uses of the word is still there but more vague. Yet people also talk about a cycle of novels where the relation to the other uses of the word cycle is tenuous. Yet none of this somehow "spoils" the word cycle. Context is essential.

And so it is with the word cycle in go. It can mean something different in different circumstances. This is why people like Bill and Robert Jasiek use terms such as positional/situation cycle and odd/even length cycle. Nothing is stopping you from using the word cycle in a way that only considers even length cycles. All you have to do is define your terms.

So I wouldn't even object to you adding your view to this page. Feel free to add lines about how cycles can only be directly repeated after an even number of moves, or link to your pages about cycle completion. But you don't get to call the other uses of the word deprecated because you made the trivial observation that you can't repeat sending two returning one right away. This page is about cycles in go in general. The word can mean more than you want it to, in fact it already does. This page should reflect that.

Herman: You don't have to refer to the AGA rules, you can just read the move page on SL to see that move is an ambiguous term which sometimes includes passes and sometimes does not. What is clear, however, is that this page does not mention a pass as a one move cycle, instead mentioning only a single stone suicide.

Robert Pauli:

  1. How long will you keep us in the dark, Herman? The meaning of move in the definition of cycle has to be resolved, one way or the other.
  2. fractic, if you draw those odd cycles, isn’t one arrow the first and another the last?

Herman: The text is informal, and that's fine. The definition of pass itself is ambiguous. Under some rule sets it is an actual move, under others it simply foregoes the right to make a move, and the only moves that exist are board plays (See e.g. the discussion at The meaning of a pass). In a graph where each vertex is a position, one could either add an edge from a vertex to itself to represent a pass, or one can keep track of "player to move" outside the graph. Either way, graph theory defines a cycle as having at least two vertices, so under that definition an edge from a vertex to itself is not a cycle either. But in the end, the point of this page is that rule sets have different mechanisms for preventing some or all cycles. No common rule sets prohibit cycles of only passes, therefore trying to define such sequences as cycles is not productive and does not reflect real world usage of the term.

fractic: I'm going to have to stop you there Herman. The definition of cycle on wikipedia you are going by does allow cycles from one vertex to itself. That definition is based on the definition of a path where the beginning and ending vertex are the same. A length 3 cycle between vertices a, b, and c would be notated as (a, b, c, a) in this convention. And (a, a) would be valid.

fractic: Regarding point 1: Once again you show your complete unwillingness to consider different contexts. The meaning of the word 'move' does not need to be resolved one way or the other. It can mean different things in different contexts and consequently the word 'cycle' can mean different things too.

I'm not going to type up a a whole nuanced response to your second point. I know where you are coming from suggesting that odd lengths cycles have a first and last move. I fully understand your position and consider it a valid position. But this is not going to stop me from calling it a cycle. I could show you that there are contexts in which such a cycle cannot be said to have a first or last move. You would probably not consider them valid. Quite frankly I don't care about your opinion on them. I have already said you are free to use your definition of what a cycle is in whatever text you write as long as you define your terms.

To avoid further wasting my time I'm going to state a fact and an opinion.

  • fact: People use the term cycle to apply to more things than what your definition would entail.
  • opinion: The Cycle page should be inclusive to all uses of the word cycle as it relates to go.

Together this fact and opinion lead me to the conclusion that it would be wrong for the Cycle page to only hold your view. The fact you cannot deny. And if you disagree with the opinion I don't think you understand what a wiki is. The fact that you consider other peoples' use of the word cycle somehow wrong doesn't matter.

Robert Pauli:
Herman, what for is a definition if it is ambiguous, is not finite (in the context his page, fractic)? Since all examples are without a pass, why don’t you follow Bill and replace move with board play in it?

fractic, before you leave, explain us your positions-only drawings. My best guess is that an arrow from position A to position B is to been drawn if either

  1. A = B, or
  2. a black board play in A leads to B, or
  3. a white board play in A leads to B.

Is this correct?

fractic: Yes, that's basically the graph I'm thinking about. Although including edges from a position to itself is optional. You do it if you want to include passes.

Bill: I have not been following this discussion, but I am a bit alarmed at my name coming up. The definition of cycle I gave with regard to the Ing rules was idiosyncratic and specific to those rules, not anything general. My opinion, FWIW, is that the idea of cycles that includes passes leads to unnecessary complications. That puts me in a minority, but I don't think that I can add anything useful to the idea of cycles that do include passes.

fractic: I'm sorry for any alarm caused on my part Bill. I hope I didn't misrepresent your viewpoints. I merely took your version of the Ing ko rules as an example of a use of the term cycle that is broader than what Robert Pauli is suggesting.

Bill: Oh, I was not worried about being misrepresented, thanks. But that definition is so broad as to be unrecognizable in other contexts. It really is peculiar to my treatment of the Ing rules.

Robert Pauli:
fractic, take an empty 4×4. Add a black stone, add three white stones, add a black stone, add three white stones, and so on. Following your drawing, you would call this a cycle of length four, right? I don’t have to tell you or Bill that not only do I call this a cycle of length six, it is a cycle of length six. Why? Because this is a board game and not some abstract nonsense. The two players alternate. Black passes after White’s first and second stone. A pass is a perfect move (just like zero is a perfect digit). Must I remind you, Bill, about pass stones? Must I remind anybody about hitting the clock even if they pass? Look at rules beast 1. After the ko threat and its follow-ups, the cycle starts with taking one, continues with a pass (!), continues with offering two, and would complete with taking two.
Herman, "no common rule sets prohibit cycles of only passes", right, but they neither ignore them. As you can read at the end of cycle completion, a cycle not only can trigger a loss, it also can trigger game end or even a win.
Bill, you're not in the minority, you join the narrow minded I see wherever I look.

Herman: Anyway, I don't think there's much point in continuing here. RP's proposed change received no support, only opposition, and has been rejected. I'll do some necessary clean-up when I have some time.

fractic: Bill, of course your use of cycle in your take on the Ing ko rules is very specific to that context. That is exactly why I used it as an example. I am after all arguing for the word cycle to be viewed in different contexts.

Robert, I'm not entirely clear about your example. I'm assuming you meant something like the following on a 2x2 board?

a-b-c-d cycle  

The sequence a-b-c-d is obviously a 4 cycle. But it does not correspond to a sequence that can happen in a game. You called this a 6 cycle. That is simply not correct. You can call the sequence a-pass-b-pass-c-d a 6 cycle of course. And I believe that that is what you meant. You somehow still dodged the sending two returning one question I have posed many times. The sequence of B1-W2-B3 constitutes a 3 cycle. And it is a sequence that can happen in a game. Of course you are free to only consider the B1-W2-B3-pass cycle instead.

Now I don't think this a-b-c-d cycle is particularly relevant for studying the game. But perhaps there is a context where someone would want to study these kinds of cycles. And they would be totaly justified in using the word cycle for these kinds of things, as long as they properly define their terms.

But at this point I find myself in agreement with Herman. I don't think there is any point in continuing this discussion. We will not change your mind. And your insinuation that everyone else is narrow-minded doesn't bode well for how the conversation would turn out.

Bill: Robert Pauli, you do not have to remind me about pass stones, after all, I was one of those who (independently) came up with the idea. :)

Robert Pauli: Hush, don’t confuse the poor SGF client. Watch it do my cycle on a 2×2:

  1     2     ?   4     ?   6     7     8     ?   10    ?   12    13

Why the heck did it give the second black stone the number 7? Crazy, only 5 stones were played, right? Maybe we should tell it that we’re in the context of a cycle. What also confuses me is that SGF dares to call the value after property 'B' or 'W' a move even if a pass move is shown as '[]' . Come on, doesn’t that overstretch the term move a little?

Another far fetched analogy is to compare

``sf1//sf13 = 0.sf076923076923ldots ={:sf076923:}``


[ba] [ab] [] [aa] [] [bb] [ba] [ab] [] [aa] [] [bb] . . . = ``bar{: sf"[ba] [ab] ["\ sf"] [aa] ["\ sf"] [bb]" :}``

Come on, aren’t we in a different field?

Bill, if that is the case, why would you then ignore passes in a cycle? We’re handling stones, we’re hitting the clock — looks pretty much like any other move to someone not narrow-minded. Which length would you or fractic then give to the cycle in rules beast 1 that starts with taking one? Tell me. Are you telling me it is not a cycle? Are you telling me not to count the pass?

Herman, I’m still waiting for you to clarify your definition, and spare me the blabla. Didn’t Bill tell you not to include passes? Well, then change move to board play or explain us why this would be wrong.

Bill: First, I did not tell Herman or anybody to do or not to do anything. Second, including passes in go cycles can complicate the application of the rules of go. I have not seen any advantage for doing so. Other people may have different opinions. That's OK with me.

Robert Pauli: Bill, I gave you an example of a cycle with a pass inside, see rules beast 1 as explained above. I didn’t include the pass on purpose, you know, it is there. Likewise the two passes in the cycle on the 2×2 above. Wouldn’t you call each of those examples a cycle?

Hi Robert Pauli

What you say makes perfect sense. A cycle as we have defined it here, can't be cyclical with an uneven number of moves, in the sense there's no way to repeat the cycle (and as such being truly cyclical) unless someone passes, hence making the number of moves effectively even.

However, despite the overwhelming logic of your argument, the sequences with odd number of moves as described over here, resulting in the same position, however not with the same player to move next, have been called "cycles" by those who discuss the game and have been documented as such on Sensei's Library. There's nothing we can do about it, or rather, want to do about it.

Herman's analogy of "temperature" is quite apt but if you allow me to give an even more blatant example: American Football is played with anything but the feet. It's ridiculous they call it football and in return call the real football game "soccer" but that's the way it is. We will not convince the fans of the Patriots or the Rams that they should stop calling the game "football". They will laugh in the face of the overwhelming evidence. And I wish you the best of luck trying to change the Wikipedia lemma into "American handball".

Sometimes, words are used in ways they shouldn't. It is better to accept that, grudgingly, and move on.


Bill: On the question of odd or even cycles, regular English does allow us to talk about recurrent cycles which are not periodic, i.e., which do not repeat immediately. Definition 1 from the online OED: "A series of events that are regularly repeated in the same order." The second example sentence is this: ‘Between 7 and 10 days later, the whole cycle is repeated.’ Obviously, this indicates a gap between repetitions.

Robert Pauli:

Dieter, a subtle correction of the cycle definition almost nobody cares about (let’s face it) is not comparable with changing the stupid name of a stupid game used by those millions with the most stupid date format. But does SL define cycle at all? Tell me, is a single pass a cycle?

So, Bill, a triple ko starts with a subcycle of length 5, right?

Cycle / Discussion last edited by PJTraill on March 30, 2019 - 19:25
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