Instructions

Rules

There are two players:

  • X moves first, his spooky marks are subscripted with odd integers.
  • O moves second, her spooky marks are subscripted with even integers.

There are two types of moves:

  • Placement moves: click in two squares to place a pair of spooky marks.
  • Collapse moves; click on a spooky mark on the loop (purple) to collapse that move to that square.
    • The other player makes the collapse selection.
    • All moves entangled with that one will also collapse to classical positions.

Restrictions

  • Spooky marks may be placed in any uncollapsed square.
  • Game is over when either all squares are classical or there is one or more 3-rows of classical marks.

Play Interface

Play:

  • Click in two squares to make a placement move.
    • A partial placement move (a spooky move) can be retracted by clicking again.
  • Placement moves which share squares are entangled.
    • Each entanglement is displayed in a different color (red, green, blue).
  • Upon a cyclic entanglement, click on a purple spooky mark to make a collapse move.

Listings:

  • The list of quantum moves will update automatically.
    • It populates sequentially.
  • The list of classical moves will update automatically.
    • Note that it populates only when moves collapse to classical values.

State string (human/machine readable):

  • A human readable state string will grow in the editable box below the board.
  • The classical ensemble will grow with each placement move.
  • Use this box to save or load games (copy; or paste, then hit the load button).

Classical Ensemble:

  • Placement moves which share squares result in classical realities pruned from the ensemble by contradiction.
  • Collapse moves will be pruned from the ensemble by choice, but highlited in yellow for reference.

Buttons:

  • Typical mix of game buttons.
  • Keyboard shortcuts for the buttons are indicated with underscores.

Illustrative Games

Copy and paste into the state string box (black edit box below the QT3 board), then load.

FeatureGame
Spooky marksX1+(1,2); O2+(5
EntanglementX1+(1,2); O2+(5,2);
Cyclic entanglementX1+(1,2); O2+(2,3); X3+(3,1)[132];
With stemsX1+(1,2); O2+(2,3); X3+(3,2)[23
CollapseX1+(1,2); O2+(2,3); X3+(3,2)[23
Max collapsesX1+(1,2); O2+(2,1)[12]; X2@X1(1)!X1(1)!O2(2); X3+(4,5); O4+(5,4)[34]; X4@O4(4)!X3(5)!O4(4); X5+(7,8); O6+(8,7)[56]; X6@X5(7)!X5(7)!O6(8); X7+(3,6); O8+(6,3)[78]; X8@O8(3)!X7(6)!O8(3);
Max entanglementsX1+(1,2); O2+(2,3); X3+(4,5); O4+(5,6); X5+(7,8); O6+(8,9);
Long stemsX1+(1,2); O2+(2,3); X3+(3,6); O4+(6,9); X5+(8,9); O6+(7,8); X7+(4,7); O8+(7,8)[68
ChronoblocksX1+(1,2); O2+(4,5); X3+(5,4)[23]; O3@O2(4)!O2(4)!X3(5); O4+(3,6); X5+(9,8); O6+(8,7); X7+(7,8)[67
DegenerateX1+(1,2); O2+(2,3); X3+(3,6); O4+(6,9); X5+(9,8); O6+(8,7); X7+(7,4); O8+(4,1)[18765432]; X8@X1(1)!X1(1)!O2(2)!X3(3)!O4(6)!X5(9)!O6(8)!X7(7)!O8(4);
Shared winsX1+(1,2); O2+(4,5); X3+(2,3); O4+(5,6); X5+(3,6); O6+(1,4)[135426]; X6@O6(4)!X1(1)!O2(5)!X3(2)!O4(6)!X5(3)!O6(4); {X=1, O=0.5}
Dual winsX1+(1,2); O2+(2,3); X3+(3,6); O4+(6,9); X5+(9,8); O6+(8,7); X7+(7,4); O8+(4,5); X9+(5,1)[198765432]; O9@X9(5)!X1(1)!O2(2)!X3(3)!O4(6)!X5(9)!O6(8)!X7(7)!O8(4)!X9(5); {X=2, O=0}

My Favorite Game

  • Load this up, then look at the classical ensemble.

    X1+(2,5); O2+(1,5); X3+(3,5); O4+(4,5); X5+(6,5); O6+(7,5); X7+(9,5);

  • Note that by move 7, X has a win in the 3rd column in 5 of the 8 classical games.

  • O needs to make a play that makes all five of these realities self-contradictory, so they are pruned from the classical ensemble by contradiction.

  • Here is one of three moves (move 8 of the game) that accomplishes that objective.

    O8+(3,6)[358|12467];

  • While X gets to collapse this cyclic entanglement, note that neither of his choices prevent O from winning.

    X8@O8(6)!X1(2)!O2(1)!X3(3)!O4(4)!X5(5)!O6(7)!X7(9)!O8(6); {X=0, O=1} X8@O8(3)!X1(2)!O2(1)!X3(5)!O4(4)!X5(6)!O6(7)!X7(9)!O8(3); {X=0, O=1}

  • O wins by attacking X’s past.

  • And that is not even the best part; his wins would have been on move 7, but hers occur on move 6.

    • Moves 2, 4, 6, in the first column.

So let’s review. At timestep 7, we detected an unfavorable outcome, took action after that, at timestep 8, to make the bad thing never happen, replacing it at timestep 6, before it never happened, with an outcome favorable to us. Note the creative use of tense.

Practical, paradox free time travel.