RobertJasiek wrote:2) Li speaks of "open and complex board positions" in a too general manner and, as a side effect, draws a wrong conclusion.
I'm not going address the critical judgement, but I do think the point of terminology is worth hashing out.
In the article a notorious dynamical lepidopterist is invoked. The Wikipedia article on the "butterfly effect" say this was an unnamed meteorologist, invoked by Edward Lorenz (not Mandelbrot, as I and I suppose others lazily thought). In any case, Li says he is talking about fights where a small change makes for largely divergent trajectories of the resulting development.
In other words, for mathematicians, he is talking about a "hyperbolic" situation.
RobertJasiek wrote:Instead - for the context of Li's discussion -, non-local positions must be classified into at least two types: a) a complex local fight involving strings on the open outside (such as the game 1 opening fight on the upper side); b) a complex fight involving large scale to global interaction between different parts of the board (such as the game 4 fight around move 78). By confusing the two types, Li makes the wrong judgement that, in game 1, Lee would have managed to create a global, long-term fight, while it should be called a large local fight, whose tactical complexity is mostly confined locally and whose global judgement can be done at quiet positions after the fight cools down.
I'm going to pass on the matter under debate, not being strong enough to have an opinion. I note though that Robert is making a distinction in an ontology of fights. My current work on Wikidata makes me familiar with co-existing ontologies. Robert's (a) is roughly "open system", and (b) roughly "coupled system".
Let me get my own contribution in now. As a somewhat
faux mathematician these days, I think I can still point out that hyperbolic belongs as an adjective in a family with parabolic and elliptic. Or, in another sense, with Euclidean and elliptic, for geometries. In any case there is a clear antonym, "elliptic", and a boundary case.
We know, roughly, what the antonym to "running fight" is, namely a localised fight that will reach one of a definable list of outcomes (i.e. has a status once you know who will play first). So, e.g. classic life-or-death for a group, capturing race, to name the ones every player has to learn. Or, indeed, come down to endgame plays, though there are some weasel words around that.
So, the parabolic case might be the bone of contention? We know some running fights can be described, for example in
joseki dictionary shorthand, as "both players jump out". It is quite possible that this quasi-evaluation is an artefact, created for example by looking at one corner of the board and arbitarily "ruling out" coupling to other areas, and other fights, on the board now or implicit in frameworks.
It is also quite possible that modern go theory has got beyond this bit of ontology.
"Neither player needs to add a stone to the running fight, for the time being." If playing out the fight further has foreseeable consequences, this might stand up. The game will flow in laminar rather than turbulent fashion, to introduce another metaphor.