Area vs Territory Go Rules

[Bill Taylor] The following Go example shows a safe set of stones with two eyes:

. . . . . .
. . o o . .
. o o . o .
. o . o o .
. . o o . .
. . . . . .

Would this set be called a single group even though it is composed of two disconnected halves?

Most players would call it a single group. In area rules it doesn't matter what you call it. In territory rules it could conceivably matter what you call it, (though it doesn't in practice), because territory rules, in all their artificial absurdity, have to refer to groups from time to time in order to define what is considered "dead" and what is considered "alive".

In territory rules, this matters(!). In area rules, it doesn't matter - if there is any dispute you just play it out (and with no cost) until a group or groups is removed from the board.

Logically speaking, you should call the above two separate groups, each helping to keep the other alive. But people never speak so precisely in practice.

There is even a worse situation. The following group has only one true "eye"; the other one, in the NW corner, is a so-called "false eye", and can eventually be filled and the whole lot captured.

. x x . o .
x o o o o o
x x x x o .
x . x x o o
x x x x o .

Territory rules actually have to define the concept of eyes, false eyes, and the rest. It is lunacy. (Area rules define nothing - you just play it out to the grim end if necessary). Territory rules, with their defined false eyes, come to grief in this famous sort of position:

. x x x x x | Here, black has TWO false eyes, and not a single true one!
x o o o o x | And yet, both separate groups, or parts of a group, are
x o o . o x | keeping one another alive; rather like your above example.
x o . o o x |
x o o o o x | And even the Japanese admit that black is alive, in spite of
x x x x x . | what their rule books say!

Basically, territory rules are an abortion. Computers cannot handle them because they are essentially logically flawed.