Rubilia/ Excitation

Excitation

The greatest height of a purple point in the thermograph.

Incitation

The lowest height of a purple point in the thermograph.

Properties:

• Tex >= T >= Tin. In strictly sente, gote or ko cases, they`re all equal. In ambiguous positions, the excitation is often greater than the temperature, and the incitation may be smaller (limited by a floor or minus infinity).^[1][2]
• In particular, the excitation of what appears above zero as a mere mast in the thermograph can still be positive.
• The excitation of a sum of games is the greatest excitation of one of its summands. Therefore in a miai situation, the total excitation equals the one of its single parts.
• This results in comparatively shallow trees, because sente "ends sooner": With reference to excitation rather than temperature, ambiguous plays can conveniently be treated as gote. As soon as the actual excitation is smaller than or equal to the initial excitation, play is assumed to continue anywhere, i. e. usually not locally.
  This complies with the precondition of a rich environment, since there is no specific reason to prefer the local continuation over the many other, equally urgent plays.

In the calculation of normal values, I use the excitation as second component (jiàn hé value). Thereby it can differ from the temperature in ambiguous cases.

Note: My late night`s claim of continuity was wrong. Like temperature and incitation, the excitation obviously can be discontinuous for finite values as well.

E. g.

lim(Tex({{2|{0|-2}}+a|{-1|-5}}) (a-->0) ==  1    <>   3/2   == lim(Tex({{2|{0|-2}}+a|{-1|-5}}) (0<--a)

blubb: Are there common terms for this already? If so, please, forgive me my cranky definitions. I am hardly in touch with cgt research and certainly don`t know a lot of the recently established conventions.

Bill: Excitation and incitation are indeed new terms. :-) I have written something about purple masts on Colored Mast.

见合 (jiàn hé) corresponds to 見合い (miai) in Japanese. I do not know if the Chinese talk about jiàn hé values, or, if they do, whether they correspond to excitations.

blubb: I don`t think they do, just as the Japanese, to my knowledge, traditionally didn`t talk about "miai values", either. (I figure if they did, White would be treated as positive in their calculation, as well.) "Jiàn hé values" use Chinese scores, expressed in zĭ.
The use of excitation vs. temperature (ok, let`s use that term here) appears to me as a subordinate difference, and I am still not sure whether or not the advantages of excitation are big enough to justify the complication of the otherwise quite simple conversion jiàn hé value <-> miai value.

[1]

Bill: Not so in the original sense of ambiguous position, which is ambiguous between sente and gote. It is true that colored masts raise questions about the meaning of miai value, but that is a different kind of ambiguity.

In ambiguous positions (as originally defined), the excitation is occasionally greater than the miai value, but the incitation is never smaller.

[2]

Bill: Thermographs have a floor of -1. Thermographs for area scoring have a floor of 0. They do not go down to negative infinity.

blubb: Hmm ... Does that mean that below those lines, nothing interesting happens?

chinese scoring, komi 2 zi  

Including komi, this, as it stands, is a tie. But what if we put the game under a negative tax of more than 1.5 zi per board play?

Bill: A tie? Assuming no ko ban, this is a hot position. If there is a ko ban, it has no thermograph under current theory. You can assign it a score, but then you can do anything.

blubb: Oooops, my bad. Apparently, this example does not comply with what I meant - sorry. My incredible reading keeps on surprising even myself.
I intended to provide a position where no non-losing moves were left, but at least one player could buy another move (net) with a loss bigger than 1 moku. Here, Black doesn`t lose anything at all, so I have to make up another example. Not so easy to find one ... (later): See this post in the discussion about the "Relation between Area and Territory Miai Values and Counts", as well as Rubilia/EnvironmentalNoPassGo, for more on this.

Bill: Anyway, Black to play can win the ko as follows.

B wins ko  

W has no move  

White to play can take the ko and achieve a similar result.

blubb: I don`t understand which ko you are referring to. Do you think of a ko elsewhere or of a local superko?

W takes ko  

Bill: This ko.

blubb: I see - thanks. :)

Bill: OK, let's back up and give the players a bonus of 1.5 zi per play in addition to the area score.

area plus  

area plus  

, = pass

Result: 5 for Black

But how about this variation at ?

var. 1  

var. 1  

, , = pass. @

Result: 8 for Black

Score this?  

So what is the score for this board? (And, hence, its thermograph.) It depends upon the history of play. (It could have been reached for a score of 5 for Black if Black had played at .) That is a result of giving a bonus for a board play under area scoring.

blubb: I agree. Extending the tax backwards may ambiguate the score. Even area scoring then depends on off-board statuses, like territory scoring generally does due to captures.