tapir wrote:
it is far from sure that I can distinguish the local area from the rest of the board
You can: choose a 'locale' (local set / region of intersections) of your choice! (Not randomly, but choose it as suitably as you can.) Next, for the given locale and the hypothesis that you have chosen it well, study what happens inside the locale and what happens outside the locale. If you cannot construct relevant sequences that are only inside, then you notice that you must have chosen your locale badly; alter it to fit it better! If, however, everything local and relevant happens within the locale, then you know to have chosen it well.
Within the suitably chosen locale, you get the local temperature. If you cannot identify it, then maybe because sequences are not local, that is, local = global. In many practical study applications, local <> global.
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or that there is only a single sequence in play at one point.
Why do you care? What matters is whether all relevant sequences / value calculations fit into the / a suitably chosen locale.
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For common usage
Temperature is not for "common usage" but is a concept for usage with some degree accuracy far above that of common usage.
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I don't see any benefits of saying "settling the group cooled down this area and other parts of the board are hotter now" instead of "after settling the group playing elsewhere is larger"
The latter is a common usage conjecture. Expressing things by means of average move values or possibly temperatures has the potential of verifying or refuting such a conjecture.
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or "this move heated up this area over the ambient temperature and there is an even number of moves in the sequence" instead of "this sequence can be played in sente now".
As before.
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Basically people are rephrasing their insights in a metaphoric language, which works for them,
Does it? Can they prove that something can be played "in sente"? If they can, fine. If they can't, then more accurate tools such as local move values or temperatures might have a greater chance of allowing a proof.
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but leaves a visible question mark in the faces of bystanders.
Sure. New (here: more accurate) concepts for them must be learnt before their question marks vanish.
I have made the experience though that CGT-like temperature talk is hopeless overkill in most practical cases. I prefer to speak of pragmatic compromise versions of more accurate concepts. Such that allow you to choose a locale and such that speak of average local move size instead of local temperature etc. Everybody can divide a difference of positional values by a difference of move numbers. Hardly anybody can apply formal CGT definitions during his games. Therefore I would not recommend the latter to bystanders when the former provides already more than enough accuracy.