Temperature and Terminology Discussion
Bill: Brief comment to kick things off.
When people talk about the sizes of plays, they seem to naturally think of them as indicating gain and loss, and to derive gains and losses by adding and subtracting them. That is, they want miai values, but they have learned deiri values. They try to use deiri values like miai values, and end up with confusion. (See Discussion of the value of sente and gote plays for an example of this.)
So I have been on a campaign to promote miai values. That has meant introducing the term, as well as the term, deiri value, for what people have already learned. Whether I have caused more confusion than I have cleared up is another question. ;-)
The discussion on English vs. Japanese go terminology has got me thinking, though. Temperature is a precise English term that conveys the correct meaning. Maybe we should not bother with miai value at all.
Charles Matthews People are surely interested in the idea of gain first and foremost. Motivation to count plays is, for pragmatic players rather theorists, that if you can count better you will gain something by it, and so win more games.
So the introductory concept might have to be this: it is rare to get a pure gain in competent play.
For other types of gains you give your opponent sente, at least once and possibly more often.
Of course you may succeed in killing the opponent's group without any compensation - you hardly have to count to see the gain, there. You do, however, have to expect to lose sente in so doing (death in gote is horrible because that's then not true).
There is more than one way of dealing with the idea that you must set, against a gain you can see, the value of the sente you have lost in taking it. The naive way is to reckon in the opponent's next play. I make a 25 point gote play, she makes a 20 point gote play, I have sente back having gained 5 points. Of course it's not quite the 'same' sente: it matters quite a lot whether the largest gote play on the board is then worth 18 or 12.
I think the theoretical way of doing this, at a more sophisticated level, by introducing an 'intensive quantity' method of counting per play invested (miai counting), and a background number for the 'value of sente' (temperature, in the guise of ambient temperature), does work. If it is presented correctly, one can see it as
- drawing attention that gain must be 'value for money' for the extra stones (balance of past tenuki plays in that part of the board included); and
- admitting that go is a war fought on several fronts.
Bill: Charles, we have to do something about urgency and urgent. The CGT usage, related to temperature, is different from the go usage, related to mainly to shape and the strength or weakness of groups. I have thought about avoiding the CGT usage, but haven't found a happy substitute. They can coexist, OC, but something needs to be done. For instance, the Urgency page refers to the go usage, while the usage on the Hot page and Temperature page is the CGT usage. However, the term on the Hot page is linked to the Urgency page. The link should be eliminated or the urgency page should be revised, no?
Charles Yes, this was my point on Go theory and CGT discussion. It looks like hot should be reserved as formal usage for 'high temperature', since it is otherwise impossibly confusing. And it looks like urgent should be reserved as informal use.
Sebastian: I am still confused. What's the use of the concept of temperature? If it's the same as deiri value, why introduce a new term? Are these two different ways (concepts) to see the same thing? The nice thing about temperature, as I know it, is that it can be quite easily measured. How is temperature measured in Go? Moreover, it seems like miai value is more frequently used on SL, and since it also involves a division by effort it seems this would be closer to the concept of temperature in physics. -- 03-10-05
Charles Temperature is prima facie linked to miai counting, not deiri value. One thing to come up here in discussion is the way that miai values can only really be evaluated when you know 'best play' for each player in a local position. That hardly even makes sense before the endgame, if you think about it: it looks like an artefact of being able to draw some sort of boundary around the implications of a play. An attacking play removing the base of a group can rarely be assessed so neatly.
So we have three working concepts:
Of these temperature actually has the soundest theoretical basis. I'm beginning to think that this might be another case of the still half-baked ideas I put at strategic concepts and mediating concepts..
Sebastian: Thank you for your explanation. Your distinction (in "One thing to come up here ...") is very helpful. Is this the same distinction you call "formal" vs "informal" above? Do you mean, we have three concepts for something like urgency (distinguished by degrees of formality or sheer convenience of speech), and deiri is not one of them, since it measures something else (value?)? It seems, then, the current introductory paragraph of deiri value is misleading when it links deiri to urgency and temperature. I could try my best at editing it if you or another sensei looks at it afterwards.
Unfortunately, I'm not at an expert level, so strategic concepts and mediating concepts is way above my head. Also, I couldn't find a theoretical basis for temperature. The page on "hot" hints at endgame counting - is that what you mean? -- 03-10-05
Charles I really didn't understand this area properly until I thought it through for myself (see miai counting - ratio explanation). Every player of 1 dan level ought to understand deeply deiri value, as the swing (difference) made by a local sequence compared to what the opponent can do there. Every player of 5 dan level ought similarly, I suppose, to understand local tally at gut level. So logically the ratio, which is deiri value/local tally = miai value, should become intuitive for strong amateurs.
Of course one can understand these concepts theoretically much earlier, if one is the thoughtful kind of player. A fighting player will pick up the importance of urgency much earlier than that: maybe by 10 kyu level. And temperature comes out of CGT, which isn't integrated into go thinking so far. These major differences tell one that this area has a number of aspects, of different characters.
 Well, not for example in the case of mochikomi, loss-making threats and so on; but these are notoriously bad play. Sente gains nothing, in the sense that sente plays are one side's prerogative and get counted into the overall 'state of the game'.
 The rule of thumb being that if the largest gote play remaining is worth n points deiri, starting the endgame is worth n/2, i.e. the miai value of the largest play left. This may be why Bill thinks we could elide the miai counting concept entirely. But I don't agree. A better name would help: 'point density'?
- Bill: Actually, it's worth N/4, half the miai value, which is the same as the temperature.
 Bill: And, in terms of what they intend, they are probably using deiri counting, and so their gain is only 2.5 points. If you are 4 points behind and then you make a 25 point move (deiri) and your opponent makes a 20 point move (deiri), you are not 1 point ahead, you are still behind by 1.5 points.
- Charles Ah yes, point taken, because the 'swing' in deiri isn't taken from the mid-point, but between 'Black plays' and 'White plays'.
 Sebastian: In physics, temperature is defined by 1/T = -dS/dE, which is the derivative of entropy by energy. I'm not sure how this translates to go terms - this could translate to something like how the number of possible moves changes for a given effort. I'm not saying that this would be a useful definition, but since I assume that the number of possible moves does play a role in go I am unhappy about misusing this term for something completely different.
Charles The most helpful physics analogy I know is this: it is theoretically possible to model go by considering how to modify the game so that the temperature decreases extremely slowly. On a very large board, one can say, players will 'get round' to playing endgame plays in their due turn, marked out by the local temperature. The reason for thinking about the very slow cooling that goes on, is that one can then drop from consideration the distribution of plays of lower value than one is currently looking at.
Charles Not what I was intending. What I have called the stacks of coins model shows the limitations of thinking in terms of temperature alone; but it is worth factoring out those effects caused by uneven distribution of the sizes of plays in the 'tail' of the game.
Karl Knechtel Interesting that you should mention "entropy" here; I have recently been thinking about entropy as a way of unifying eye and liberty counts. Not sure if I'm really on to anything though.
Bill: Sebastian, the term temperature comes from combinatorial game theory, where it is central to thermography. It is a metaphor, and the central function in thermography is called cooling. John Conway defines cooling with another metaphor, tax.
The basic idea is this: You cool a position (game) by putting a tax on each play in the position. There is a certain tax such that, for every tax higher than it, neither player can gain from playing in the position, while for any tax slightly lower than it, at least one player can gain from playing. That tax is equal to the temperature of the position. It is also equal to the miai value of a play in that position.
The classical definition of temperature does not readily apply to kos. Elwyn Berlekamp managed to derive thermographs for kos using the idea of komaster. I extended thermography to multiple kos by redefining temperature in terms of Berlekamp's idea of a universal enriched environment. Instead of taxing plays, you provide alternative plays in the environment.
You can also talk about the temperature of the environment (although, to avoid circular logic, I did not). That temperature is the temperature (miai value) of the hottest play in the environment. It is this notion of temperature that, after some discussions on rec.games.go, caught on with go players. So people will talk about the temperature of the board, or of the rest of the board. This relatively informal sense of temperature is relevant to some go terms. For instance, you can think of tedomari as the last play before a temperature drop. You can think of sente in one sense as raising the local temperature?, and in another sense as playing to a position that is hotter than the ambient temperature of the rest of the board.
Sebastian: Thank you for your explanations. Unfortunately, I haven't read CGT yet, so I'm not sure about the difference to simulated annealing. From your description, it seems that CGT temperature is not just falling, but can as well rise, such as after a sente move. Is this the root of the difference?
Thanks especially for the last paragraph. This clarification is necessary because this definition of ambient temperature as a maximum flies in the face of the (linear) concept of temperature in physics.
jfc: you call a sente play one that moves to a position that is hotter than the rest of the board. Is there a CGT term for this temperature increase?
Is it the difference in sente temperature increases that account for the phenomena when one pro plays a sente move and her opponent tenukis to play a sente sequence of his own before responding to her sente move? (is that confusing enough?)
might we call sente plays exothermic (chuckle) and borrow some chemistry term to name the resulting increase in temperature?
Bill: The analogous term to sente in Winning Ways is excitable. The analogous term to gote is equitable.
IMO, not exactly a happy pair.