Message #3303

From: Roice Nelson <roice3@gmail.com>
Subject: AlphaGo, 4D Go, Hyperbolic Go
Date: Wed, 09 Mar 2016 11:38:43 -0600

Anyone catch the match last night? Melinda and I did, and are
enthusiastically discussing it. It was awesome! You can watch the
remaining games live here
<https://www.youtube.com/channel/UCP7jMXSY2xbc3KCAE0MHQ-A>.

To connect the excitement back to the group, I wanted to mention you can
play Go on the 1-skeletons of 4D polytopes using an early version of
Jenn3D. Head to the very bottom of this page
<http://www.math.cmu.edu/~fho/jenn/> to try. Duoprisms are particularly
interesting, because you can use them to make boards that remove all the
edges of a traditional board but are otherwise the same. Playing on
polytopes feels like it would generally have too much freedom though,
especially if single stones have more than 4 adjacent liberties.

Adapting MagicTile to support Go might work well, since it would keep the
boards as 2D surfaces. A {5,4} tiling would be a natural choice for a
first board, and probably some of Andrea Hawksley’s ideas about
non-euclidean <http://blog.andreahawksley.com/non-euclidean-chess-part-2/>
chess would apply. But I also wonder if hyperbolic Go would be
fundamentally flawed. Random walks in the Poincaré disk inevitably escape
to infinity. For this reason, it is almost impossible to heat a house in
the disk because you can’t stop the heat from escaping (p37 of the book The
Scientific Legacy of Poincare
<http://www.amazon.com/Scientific-Legacy-Poincare-History-Mathematics/dp/082184718X/>).
I wonder then if it would similarly be almost impossible to surround
territory in hyperbolic Go. We need to try this!

Roice