Le jeudi 22 février 2007 01:16, David Doshay a écrit : > It is pretty clear to me that, if the analogy to MC simulations in > magnets > is of any value, the temperature of the Go game you show is hotter than > optimal. > > If the temperature were at the transition temperature, then each of the > renormalized lattices would look just like a piece that size cut from > the > original. Because the details all get smaller, the original lattice > is on the > random, or hotter, side of the transition. > > Thank you very much for this work. I am mulling this over ... how to > cool the Go simulation slightly from the pure MC that you did. >
Your analogy with physics encourage me to share other physical analogies. 1/ Cooling the simulation could be done by controlling the mixing rate and the density of stones. -Beginners'games are too cold, not enought mixed (=overconcentrated or very high viscosity, nearly solid state, not ignitable) -Professionnal games are probably near critical state (explosive conditions, gaz state) -MC-players are nearly random = too hot, too mixed, plasma state. 2/ Soap Bubbles = potential territory In addition to previous fluid state, i see hypothetical bubbles: - beginners makes some (less than 10) big bubbles, and their size and place are early known. (still too cold and too high viscosity) - professional can makes lots of bubbles (20+), but they are changing and turning very often and quickly - nearly-random makes a foam 3/ Solidification and cristal growth often comes to mind. Cristal growth need a "seed" to begin, generally it is a defect or some impurity. In go the defect are the corners: - they need less material to build a frontier (like soap bubbles) so corners are the beginning of the process of "solidification" or cristal growth. - the topology of the corner (2 libs, 3 libs and 4 libs) imposes the size and shape of a living group. - impurity is a captured stone/group 4/ shape/size resonance (un)fortunately the 19x19 size is just the critical size to have problems. -17x17 is too small, corners influence is too strong, it is quickly possible to take the border. (= 3 bubbles) -21x21 is too wide, it is not possible to quickly prevent easy invasion. (= 4 bubbles) (a strong go player told me: both are boring to play) -19x19 is critical, just in between, that's why it's fun (=3.1415 bubbles ;) I made very slow progress to formalize this, except density which is rather trivial, and a kind of temperature, but it needs a lot of go knowledge to work (something like gnugo internals), so it is not (yet) very suitable for a fast MC simulator. But the whole stuff is rather coherent in my mind. Alain _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
