Virtual groups

A useful way of approaching framework theory is to think of possible invasions as 'virtual groups' - groups that exist in your head rather than (yet) on the board.

So virtual groups have a life cycle:

1. any real framework (not secure territory) has some virtual group or groups inside it;
2. an actual invasion creates a weak group from a virtual group;
3. virtual groups may live, if an invasion lives;
4. virtual groups may die, if (a) the framework is reinforced in such a way as to prevent an effective invasion, or (b) the invasion takes place but the group created dies (mochikomi).

If a framework is turned into territory, that means all the virtual groups inside it are now dead. Often the final play consolidating the territory is very efficient; the translation of that in virtual group terms may be that it kills two virtual groups at once.

Iron pillar  

For example Black plays 1 (the iron pillar) in the hope of reducing to nothing White's aji to live around a, and around b.

The terminology of virtual groups is just a way of discussing aji for life. It is quite graphic and suggestive. I learned it in seminars of Matthew Macfadyen. Charles Matthews

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Comments

When I looked at the title I thought virtual groups were random black and white groups spontaneously appearing out of the blank go board and then annihilating again, like virtual particles and antiparticles appearing and disappearing in space. (added anonymously on 2011-02-04)