Schrodinger's cat

What is Schrödinger's cat?

A Schrödinger's cat is a special case of an unsettled group. Sometimes a group is "both alive and dead" at the same time, and we can call it a "Schrodinger's cat". How can this happen? It usually occurs when killing (or saving) a group is not big enough -- and both players tenuki. Such group(s) remain unsettled until a later point in the game. Usually, such ignored & unsettled groups happen in the corner.

Note that the following are requirements to serve as Schrodinger's cat:

1. The weak group must have the opportunity to live and in the meantime, the other player has the opportunity to kill it. (thus both "alive and dead" or "unsettled")
2. The value of this saving or killing is not big enough so both player choose to tenuki (until there are no big moves elsewhere: this is Whole Board Thinking); but if either player is not strong enough to understand this point and choose to save or kill this group, then this cat suddenly "collapses" into a settled group.

What's the difference from "unsettled"?

When you bring up "unsettled", I think you mean the first meaning from below:

1. In life and death, a group is unsettled when its status depends on the player who gets to play first.
2. In the middle game, a group is unsettled when it is weak and lacking eyeshape. This is in contrast to strong and settled groups.

I would argue that a Schrodinger's cat is more specific in that both players "intentionally" do not settle the group for the better good, so Schrodinger's cat is a specific case of "unsettled". When we say "unsettled", we don't take "intentionality" into consideration.

For example, a Ten Thousand Year ko is also a ko, but it is much more specific than a general ko.

Examples

Example #1:

This is a Pandanet game of 4k+ vs. 4k+, please go to the position of 56.

See Dia. 1: Is black 57 rectifying the corner necessary?

See Dia. 2: The life and death of the corner group is an "approach ko" and for white to kill the group, black can play 4 moves elsewhere (note: see the calculation below), therefore, both sides tenuki the corner for now (until there are no more big moves on the board) Before the corner group is settled, it is both alive and dead, therefore, it is a "Schrodinger's cat".

Calculation of the value per move for the ko:

• This ko has 5 states (positions), including both ends (the states where the ko is ended, with black-win-the-ko and white-win-the-ko respectively).
• The score difference on the board (black's score minius white's score) for the black-win-the-ko state is +7.
• The score difference on the board for the white-win-the-ko state is -19.
• The total value of the ko is |+7-(-19)| = 26
• This ko has 5 states, so for each move to fight the ko, the value is: 26/(5-1)=6.5 points.
• The value of fighting the ko is only 6.5 points, which is very small in the opening stage, so both players tenuki the corner.

Example #2:

This is the famous "Kejie-Alphago joseki".

See Dia. 1: This is the sequence of the complete joseki.

See Dia. 2: Both the 3 black stones and the 4 white stones are Schrodinger's cats; of course, black can kill white immediately by cutting, but it's a 20-points-gote yose only (not big enough); moreover, there are still some ajis to leverage later, so both sides tenuki and it ends up with 2 Schrodinger's cats.

Example #3:

This is a Fox game of 9d vs. 9d, please go to the position of 55.

See Dia. 1: In the actual game, white plays 56 to live the upper-left corner, but if the players think it is more urgent for white to play A to destroy black's center moyo or play B to rectify the white groups at the right side; and in this case both players tenuki the upper-left corner group, then that group becomes a Scrodinger's cat.

As a go term (if accepted)

English: Schrodinger's cat

Japanese: シュレディンガーの猫 (Shuredingā no neko)

Korean: 슈뢰딩거의 고양이 (Syureoding-geo-ui goyang-i)

Traditional Chinese: 薛丁格的貓 (Xuē dīng gé de māo)

Simplified Chinese: 薛定谔的猫 (Xuē dìng è de māo)

References:

• Origin of the term: In quantum mechanics, Schrödinger's cat refers to the thought experiment in that a cat is both alive and dead before the box is opened, a phenomenon that dominates the microscopic world. When the cat is both alive and dead, it is called in a superposition state, and when it is confirmed to be either alive or dead, the superposition state collapses.
• Category in Sensei's library: under "Strategic Concept" section of the strategy page.
• Proposal of the term: A post on 1 Mar. 2023 at Facebook group "Go (Baduk, Weiqi) Players on Facebook" Schrodinger's Cat of Go:; also a post on 7 Mar. 2023 at Forum for Go Terms at Sensei's Library To propose a new go term: Schrodinger's Cat #13672.