Matt Gokey wrote:
alain Baeckeroot wrote:
Le jeudi 22 février 2007 14:11, Matt Gokey a écrit :
The only thing that matters is the graph topology. A corollary is
that on any board that is completely balanced at the beginning with
identical number of neighbors for all nodes, any 1st play is
equivalent and therefore optimal.
Yes. But the round board at http://www.youdzone.com/go.html is not
isotropic, it is a cylinder. You can build it with a square garden
wire netting cut at 45°, and add one wire on each border to have 4
neighbors everywhere. If you start from any point and go "straight"
you end on a border. If you start from a border and go straight you
stay on the border.
I don't understand. I think everyone is thinking too visually. What
does "straight" mean in the context of go? Only liberties are
meaningful. It is isotropic if you stop visualizing the shape and only
consider the graph.
You are right it is not isotropic - sorry - I didn't look at it closely
enough.
Here is a thought experiment to test: define the board only logically
using a graph (nodes and neighbor nodes). No topological shape and no
mesh layout over any shape is needed. If all nodes have exactly four
neighbors, there is no method or algorithm that you can run to find an
edge. All nodes will look equivalent.
I was assuming the board was uniform or isotropic I guess when I wrote
this. Mea culpa.
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