# Quantum Tic-Tac-Toe

 Site Map Path: Novatia . Paradigm Puzzles . QT3 . For Teachers . Ascertainity

### The Ascertainity Principle

Consider the Quantum Tic-Tac-Toe game shown to the right. On move one, X has staked out the center and a corner, a good strategy based on what works in Classical Tic-Tac-Toe. O does similarly, taking advantage of the fact that X is not yet deterministically in control of the center square, and at the same time preventing X from ever getting a 3-row down the anti-diagonal. Moves three and four proceed for similar tactical reasons. On move five X makes a very threatening play that O must respond to. Her decision to create a cyclic entanglement gives selection of the collapse to X, but any other move would allows X to force a win. X chooses to collapse the entanglement such that he ends up with a single horizontal 2-row, even though this gives O two 2-rows. X can force a win, 1 to ½ from here by playing in squares 4 and 8.

However, the classical listing of moves (shown to the right of the game board) makes no tactical sense at all. O could have easily won the classical game on move six simply by playing in square 4, and X should have played there previously on move five to prevent it, but neither X nor O could force these outcomes in the Quantum game. These are not the only poor moves in the classical version. O should have played her first move in the center, and when she didn’t, X should have played his second move in either remaining corner. Of the first six moves in the implied classical game, four of them were tactically dumb.

If all an observer has access to is the classical listing, this is a very mysterious result. If the observer is persuaded that X and O are both competent Tic-Tac-Toe players intent on winning, he must conclude that the classical game he witnessed was actually played under quantum rules. Thus it is possible in general, just from the classical listings, to ascertain whether a game of Tic-Tac-Toe was played under quantum or classical rules.

Although we usually take it for granted, it is actually a little remarkable that we have been able to deduce that we live in a quantum universe and not a classical one. As it is, this revelation is less than 100 years old. Call this the ascertainity principle.

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