[computer-go] Big board, ++physics

[alain Baeckeroot]

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