1. White (Hypatia) plays the standard center initiative (P-K4), which elicits an unusual response (P-Q4) by Black (Hegemony) paving the way for early involvement of Black's most powerful piece.

2. White and Black make obvious capture and recapture moves (PxP, QxP), which leaves Hypatia's forces with a substantial (20%) advantage, because of the wasted moves Black will have to make protecting its exposed Queen.

3. Hypatia adds to her initial tempo advantage by developing a Knight (Kt-QB3) and forcing Black to make another Queen move (Q-QR4) to the edge of the board.

4. On the fourth move, Hypatia begins to diverge from a strategy aimed at winning the game, toward one trying to win and secure a specific objective (in her case advancing knowledge, symbolized by a Pawn in the middle of the board). White develops (Kt-KB3) its other Knight (chosen by about 10% at this stage), which reduces White's advantage among games reaching this position to 15%. Black responds with a standard (Kt-KB3) Knight development move.

5. Hypatia advances her remaining central Pawn (P-Q4) to a protected central square, restoring her statistical advantage to 19%. Black develops a Bishop (B-B4), reducing its statistical disadvantage to 16%.

6. Hypatia departs from the normal "political" move of maximizing attack potential and makes a shortened (defensive) Bishop developing move (B-K2), which produces a "dead even" positional situation. The Hegemony responds with its own short (P-K3) move, which keeps a 50%-50% outcome projection from the resulting position.

7. Hypatia follows through with castling (0-0), instead of making a short Bishop move protecting her pinned Knight. The Hegemony bypasses a popular Pawn move providing a clear line of retreat for its Queen, and instead develops its second Knight (QKt-Q2), creating a situation where White has no statistical chance of victory, and Black is projected to win 50% of the time.

8. In the parallel historical situation, Hypatia of Alexandria faces a choice between defending unpopular minorities or abandoning them and protecting herself. Here, White follows the only option (P-QR3), a foundational move preparatory to pushing back the invading Black Queen. Black leaves White without a winning prior example with a move (B-K2), which leaves the way open to castle in either direction (depending on where White appears weakest).

WHITE: K(g1), Q(d1), R(a1, f1), B(c1, e2), Kt(c3, f3), P(a2, b2, c2, d4, f2, g2, h2);

BLACK: K(e1), Q(a5), R(a8, h8), B(e7, f5), Kt(d7, f6), P(a6, b7, c7, e6, f7, g7, h7).

9. Hypatia mobilizes her Queen Bishop (B-K4) to focus on a key Queen-side Pawn, and the Hegemony castles (0-0) in the opposite direction.

10. White continues with a Queen-side Pawn push (P-Qkt4) and Black retreats its Queen (Q-Kt3) to a square where it attacks White's central Pawn.

11. White moves its King Rook (R-K1) closer to the action in the center, and Black responds with a similar move (QR-Q1) of its Queen Rook.

The deployment of forces thus far parallels the historical battle over the Great Library at Alexandria, which was the center of learning in the 5th century Mediterranean World.

12. Hypatia continues her pressure (Kt-QR4) on Black's Queen, which moves away (Q-B3) to the only safe square.

13. Almost like Hypatia's advanced position in support of freedom of inquiry, White pushed forward (P-B4) with another Queen-side Pawn, and Black moves a Knight (Kt-Kt3) to provide a line of retreat for Black's Queen.

14. Both sides then pull back their Queen-side Knights (Kt-B3, Kt-R1).

WHITE: K(g1), Q(d1), R(a1, e1), B(e2, f4), Kt(c3, f3), P(a3, b4, c4, d4, f2, g2, h2);

BLACK: K(g8), Q(c6), R(d8, f8), B(e7, f5), Kt(a8, f6), P(a7, b7, c7, e6, f7, g7, h7).

At this juncture, Hypatia reaches a "fork in the road" between maintaining a secure position, and seeking to advance the frontiers of knowledge. Here the White Pawn front penetrates into Black's territory and precipitates a clash which costs both sides four points in material.

15. Hypatia moves to reinforce her front line (Q-Kt3) and the Hegemony makes a defensive move (P-QR3) to oppose further advance of White's Queen-side Pawn front.

16. White further bolsters its strong center (QR-Q1) and Black withdraws its Queen away from the path of Hypatia's impending center Pawn advance (Q-K1).

17. Hypatia's expected push for open inquiry and preservation of knowledge starts off as anticipated (P-Q5) and Black initiates an exchange with a Pawn capture (PxP).

18. White continues by recapturing with its Knight (KtxP), which Black captures with its own Knight (KtxKt). At this point Hypatia is able to restore the Great Library as a center of learning.

19. White's recapture of Black's Knight with a Pawn (PxKt) brings forward Black's most powerful piece (Q-Q2). In our historical parallel, this move is equivalent to Alexandria's Bishop Cyril taking charge of the attack on Hypatia and her civic activists.

WHITE: K(g1), Q(b3), R(d1, e1), B(e2, f4), Kt(f3), P(a3, b4, d5, f2, g2, h2);

BLACK: K(g8), Q(d7), R(d8, f8), B(e7, f5), Kt(a8), P(a6, b7, c7, f7, g7, h7).

20. Hypatia "doubles down" on her aggressive defense of the Great Library at Alexandria by sending her remaining Knight into the heart of the battle (Kt-K5), thereby occupying the other 5th rank central square and driving Black's Queen back to its eighth rank (Q-B1).

21. White's Knight moves (Kt-B4) to a square where it can support the further advance of Hypatia's Pawn (which symbolizes the Great Library at Alexandria). Black replies by moving its King Rook to the base of the center open file (KR-K1).

22. White's Queen moves (Q-Kt3) to where it reinforces support for Hypatia's Bishop whose line of attack bolster's Hypatia's advancing Pawn. Black responds by moving its Bishop (B-B3) to allow its Rook to attack along the open central file.

23. Hypatia continues (P-Q6) with a move that symbolizes the advance of knowledge in the center of learning (the Great Library) and the Hegemony responds with an attack (P-QKt4) on one of the Library's key defenders.

WHITE: K(g1), Q(g3), R(d1, e1), B(e2, f4), Kt(c4), P(a3, b4, d6, f2, g2, h2);

BLACK: K(g8), Q(c8), R(d8, e8), B(f5, f6), K5(a8), P(a6, b5, c7, f7, g7, h7).

24. Hypatia moves back her Knight facing imminent capture by a Pawn (Kt-K3) to a square where it challenges Black's light-square Bishop. The Hegemony responds with a Knight move (Kt-Kt3) out from its back-rank purely defensive position.

25. Next, White makes a bold Bishop move (B-Kt4) which will lead to a substantial loss of material by both sides and Black accepts the challenge and captures White's Bishop (BxB).

26. The "Blood Bath" continues as White uses its Queen (QxB) to capture Black's Bishop, and Black uses its own Queen (QxQ) to capture its opposite number.

27. White restores material parity by capturing Black's Queen (KtxQ) and Black escalates the "carnage" by initiating an exchange of Rooks (RxR+).

28. White is compelled to capture the Rook checking its King (RxR) and this Rook move gives up protection of White's advanced Pawn, which Black then captures (PxP).

29. White is able to restore parity by capturing Black's Pawn (BxP), because Black would have to allow a checkmate on the next move, if it captured White's Bishop. Having already accomplished a key Hegemony objective (destruction of the Great Library), Black moves its Knight (Kt-B1) to create a double attack on White's Bishop.

WHITE: K(g1), R(e1), B(d6), Kt(g4), P(a3, b4, f2, g2, h2);

BLACK: K(g8), R(d8), B(f6), Kt(c8), P(a6, b5, f7, g7, h7).

30. Hypatia's forces continue the pressure by posting a Bishop (B-B5) on a square where it has strong Pawn support, Black responds with a preliminary move (B-K2) toward trading off Bishops.

31. White declines to delay the Bishop exchange (BxB), even though allowing Black to capture first would have generated a passed Pawn. Black now has no choice but to recapture (KtxB) and thereby present White with the same choice of giving up its King for a minor piece, which Black had earlier declined.

32. At this juncture, the historical Hypatia of Alexandria did not flinch and continued her aggressive defense of freedom of inquiry and civic tolerance. Here, her forces accept Black's challenge (RxKt!) because it offers the only opportunity to advance her cause in the long run. At this point, Black has only one viable response (R-Q8#+).

WHITE: K(g1), R(e7), Kt(g4), P(a3, b4, f2, g2, h2);

BLACK: K(g8), R(d1), B(f6), Kt(c8), P(a6, b5, f7, g7, h7).

33. After White's obligatory King removal(K:Off), Black needed to create an escape hatch (P-B3), to prevent an immediate checkmate.

34. Hypatia's Kingless army starts (R-K6) with an immediate Rook attack on a Black Pawn which cannot safely move away. The Hegemony replies with a Rook challenge (R-Q5) to a White Knight with no safe escape square.

35. White's next move (P-R3) defends its endangered Knight and opens an escape hatch at the same time. Black pushes the same Pawn forward another square (P-B4) to again threaten White's Knight.

36. White moves its Knight (Kt-K3) away from the Pawn threat, but Black renews the threat by another advance of its Bishop Pawn (P-B5).

37. White then moves its Knight back to its position three moves previously (Kt-Kt4), and Black challenges it with another Pawn move (P-KR4).

38. White then moves its Knight to its recently established escape square (Kt-R2) and Black challenges an unprotected Pawn (R-Q7), which cannot be moved without jeopardizing another unprotected Pawn.

WHITE: R(e6), Kt(h2), P(a3, b4, f2, g2, h3);

BLACK: K(g8), R(d2), P(a6, b5, f4, g7, h5).

39. Instead of switching its Rook to a defensive posture (which would let the Black King "get out"), Hypatia's army captures a rival Pawn (RxP). Black replies by executing its threatened Pawn capture (RxP).

40. White finds a move (R-KKt6) which defends its threatened Pawn and prevents Black from linking up its King-side Pawns. Black replies by moving its King (K-B2) to force White's Rook off of the intersection of the 6th rank and King-Knight file.

41. White pulls back its Rook one rank (R-Kt5), thereby attacking two Black Pawns while still defending its King-Knight Pawn. Black then advances its King to force White to give up the defense of its King Knight Pawn (K-B3).

42. White opts to capture (RxRP) the Black Pawn which might be supported by a Pawn advance, and Black captures the White Pawn (RxP) left en prise.

43. White checks the Black King (Kt-Kt4+) by moving its Knight to a defended square, and Black's King (while moving out of check) threatens White's Rook (K-Kt3).

WHITE: R(h5), Kt(g4), P(a3, b4, h3);

BLACK: K(g6), R(g2), P(b5, f4, g7).

The basic problem for Black's effort to vindicate its checkmate is thta it has only one piece with substantial mobility, versus two White pieces actively involved in the battle and able to concentrate their fire on a single contested square.

50. With Black's Rook tied up defending its advanced Pawn, White is free to start its Rook Pawn on a march to promotion (P-R5). Black responds by going behind its Knight Pawn (K-Kt1) to try to get at White's Rook.

51. However, White moves its Rook four squares (R-B4), putting it out of the range of Black's King, so the Hegemony attacks Hypatia's main piece with a Pawn (P-Kt4).

52. However, White moves the Rook (R-Kt4) to attack Black's Knight Pawn, and Black has to move its Rook (R-R4) to the only square where it can defend its Knight Pawn.

53. White then moves its Rook Pawn forward (P-R6), in the "breathing space" while Black moves its King (K-Kt2) toward where it can protect its fourth-rank Pawn.

54. White continues to advance its Rook Pawn (P-R7) as Black's King reaches (K-B3) its trailing Pawn.

55. White's advancing Pawn reaches its eighth rank (P-R8 = B) and becomes a Bishop, while Black's King advances (K-B4) to challenge White's Rook (which is easy to protect because White now has three pieces).

WHITE: R(g4), B(a8), Kt(d3), P(b4);

BLACK: K(f5), R(h5), P(f3, g5).

Just as social progress goes hand in glove with freedom of inquiry and tolerance of diversity, so the main focus of Hypatia's forces at this juncture is to contain destructive tendencies (prevent the promotion of either of the Hegemony's two Pawns.

56. White moves its Knight to protect its Rook by occupying the penultimate square in the promotion pathway for Black's sixth-rank Pawn (Kt-B2). Black responds by attacking Hypatia's White Knight (R-R7).

57. White responds by checking Black's King (B-K4+), which is forced to give up its attack on White's Rook as it moves (K-B3) to the one square where it can provide the only protection for Black's fourth-rank Pawn.

58. White moves away its challenged Knight (Kt-Q3), which allows Black's advanced Pawn to move to its seventh rank (P-B7).

59. White offers an exchange of Rooks (R-Kt2) which Black cannot accept because this would leave Hypatia's forces with a clear pathway to a forced mate. Black moves its Rook away (R-R5) to where it challenges White's undefended Bishop.

60. White captures Black's advanced Pawn (KtxP) and simultaneously defends its Bishop. Black responds with a King move (K-K4) that doubles its attack on White's Bishop.

61. Hypatia's forces capture Black's last Pawn (RxP+) and simultaneously check the Black King. The Hegemony must deal with the check (K-B5) and cannot capture White's Bishop.

62. White moves its Rook (R-KB5+) to a square defended by its Bishop, where it checks Black's King and defends its Knight, which defends its Bishop. All Black could do is to move its King out of check (K-K6) to the only square where it continued the double attack on White's Bishop.

63. White moved its Rook (R-B3+) to renew its check, while maintaining its defense of White's Knight. Black then moves out of check (K-Q5), while still continuing the double attack on White's Bishop.

64. White moves its Bishop out of the Black King's range (B-B6), and the Black King goes to the one square (K-B5) where it can attack White's remaining Pawn.

65. Hypatia's remaining Pawn then moves forward (P-Kt5) into a mutually supporting relationship with White's Bishop. From this point forward there was nothing the Hegemony could do to thwart the continued accumulation of knowledge (i.e., the promotion of White's fifth-rank Pawn). All Black could do was to move its King (K-B4) to where it could delay the advance of White's Pawn for a few moves.

WHITE: R(f3), B(c6), Kt(f2), P(b5);

BLACK: K(c5), R(h4).

At this juncture, Hypatia's forces have an aggregate strength of 12 points, versus 9 points for the Hegemony. Hypatia's "freedom fighters" consist of four components versus only two for their "oppressors." This leaves Black with little room to maneuver.

66. White checks Black's King (Kt-Q3+), forcing the Black King to retreat (K-Kt3).

67. White moves its Rook (R-B6) to set up a discovered check, and Black picks the best dark square (White's Bishop which will move to create a check by White's Rook, travels on light squares) (R-R1) to stay out of harm's way.

68. White does not need to be concerned about where it moves its Bishop in creating a discovered check(B-K8(+)), since Black must move its King out of check (K-Kt2) and cannot use its Rook to capture.

69. White moves up its Knight (Kt-B5+) to deliver another check, and Black struggles to avoid being forced to the edge of the board (K-B2).

70. White is able to renew its check again with a Pawn push (P-Kt6+), and Black has no choice but to withdraw its King to its back rank (K-Q1).

71. Hypatia's forces make a Bishop move (B-Q7) which is supported by a White Knight to force the Black King away (K-K2) from the side of the board where their remaining pawn must advance to promotion.

72. White then renews its check of the Black King (R-K6+), and Black's King is confined (K-B2) to only six squares on its King side back two ranks.

WHITE: R(e6), B(d7), Kt(c5), P(b6);

BLACK: K(f7), R(h8).

From this point onward, the Hegemony can do little more than to avoid loss of material from some sort of two-pronged attack. About half-way through the next seven moves, Hypatia's forces are augmented by a second Bishop, covering all the squares on the board between them. This leaves very few secure squares for Black, as its chances of avoiding a second checkmate (and restoration of both Kings) diminish.

73. White moves its Pawn forward to the seventh rank (P-Kt7), and Black moves its Rook from one safe back-rank square to another (R-KB1).

74. White then moves its Rook onto the file where its Pawn will be promoted (R-QKt6), and Black has nothing better than moving back to the square is vacated on the previous move (R-KR1).

75. White marches its Pawn to promotion (limited to a minor piece by Four Dimensional Chess Rules) as a Bishop (P-Kt8 = B), and Black moves its Rook away from the action (R-R5).

76. White moves its newly minted Bishop (B-K5) to where it further diminishes the Black King's range of movement, and Black sends its Rook as far as possible (R-R8) from the section of the board dominated by Hypatia's forces.

77. White uses the support of its new Bishop to check Black's King (R-KB6+) and almost surround it. Black tries to avoid being forced toward the corner (K-K2).

78. White moves its other Bishop (B-B5) to eliminate the Black King's only alternative to retreating to its back rank. Black avoids a King move by shifting its Rook to another square on the opposite side of the board from the other five chessmen (R-KKt8).

79. White moves its Knight (Kt-K6) to put all of its pieces into a tight cluster, and Black's Rook continues to keep its distance from the action (R-KKt8).

WHITE: R(f6), B(e5, f5), Kt(e6);

BLACK: K(e7), R(g1).

Here are the next six moves in post-checkmate play in this Level IV game. For a complete explanation of Four Dimensional Chess Rules, with illustrations, please contact Michael.Halliwell@csulb.edu

In this Larsen vs Deep Blue (1993) continuation, Black cannot bring its Rook too close to its King without getting forked or pinned, but it does help slow down White's march toward checkmate, by eliminating the use of zugwang (forcing Black's King to choose among damaging moves). However, White has sufficient material to force checkmate with a series of checks.

80. White starts by pulling back its Knight (Kt-B4) to a point where it can check from two different locations. Black responds by attacking White's undefended Bishop with its Rook (R-K8). White does not have to deal with this challenge, because it can force mate without ever allowing Black's King any respite (in the continuous five-move assault to come).

81. White's checking Knight move (Kt-Q5+) forces the Black King to its back rank (K-K1).

82. White renews its check with a Knight move (Kt-B7+) to a square where it is supported by a Bishop. Black takes this opportunity to get back to its second rank (K-K2).

83. Hypatia's forces maintain the pressure with a Rook check (R-K6+), and Black moves its King sideways (K-B2), to stay off its back rank.

84. Because its Knight now protects its Rook, White moves its light square Bishop to check Black's King (B-Kt6+). Black then makes one last move out of check (K-Kt1).

85. When Whiite administers this second checkmate (R-K8 ), the game does not end (and will not until both Kings are back on the board and a third checkmate occurs).

WHITE: R(e8), B(e5, g6), Kt(c7);

BLACK: K(g8), R(e1).

There are a number of special symbols in Four Dimensional Chess notation relating to checks and checkmates: (+) indicates a discovered check; ## indicates a conclusive checkmate, with a +9 margin without removal of the opposing King; #+ indicates that the checkmated King must be removed and that play will continue if the post-removal margin is less than +9; is reserved for a second checkmate, where the Kingless side and the checkmated side both put their Kings back on the board and play continues. When the Kingless side restores its King, this restoration is always marked with !!. When a King is restored to the board, it may be placed on its original square, or any square adjacent to it.

85. ..., Black is forced to use up it post-checkmate move to remove its King (K:Off).

86. Since Black has a place to bring back its King, White can reinstate its King and chooses to place it a diagonal move from its original square (King to (d2)!!). Black cannot move its Rook out of harms way, but must instead reinsert its King (King to (d7)).

87. White's King acts immediately to capture Black's Rook (KxR). At least Black's King has an opportunity to break out (K-B3) of its encirclement by White's pieces.

88. White begins the process of driving the Black King to the edge of the board with a preliminary move (B-B5) to set up a "Bishop bracket." Black's King responds by moving closer to the center of the board (K-B4).

89. White then checks Black's King (Kt-K6+), which moves further away (K-B5) from its previous encirclement.

90. White completes its "Bishop bracket" (K-K4), which forces Black to move its King (K-Kt4) toward the edge of the board.

91. White's Knight no longer takes an active role in forcing Black's King to the sideline, but its control of key squares allows more aggressive Bishop moves (B-Q4). Black's King responds with the only move it has (K-Kt5), without going to the edge of the board.

92. White re-establishes a "Bishop bracket" (B-Q3) one file closer to the edge of the board and Black's King again makes its only move (K-Kt6) which stays away from the edge.

93. At this point, Hypatia's forces use a Rook move to check Black's King (R-QKt8+), leaving it no option but to go to the edge (K-R5).

94. If White's restored King were actually Hypatia, come back after a protracted period in limbo, this leader would be pleased to watch White's pieces bring the Hegemony to its knees with a tightening mating net (B-B5). Black's King then makes its only legal move (K-R4).

95. Another Bishop move (B-B4) re-establishes White's "Bishop bracket", leaving Black's King no option but to go back to its previous square (K-R5). White's King has never participated in "bringing the opposing monarch to justice", appropriate enough in a demonstration that ideas can be immortal, without a further contribution from their originator.

96. It has taken twice as many moves for Hypatia's forces to ultimately prevail as the entire game up to the point where White's King was removed from the board (R-QR8##). Dr. Martin Luther King often noted, "The arc of the moral universe is long, but it bends toward justice."

WHITE: K(e1), R(a8), B(c4, c5), Kt(e6);

With only six pieces on the board at this point, nearly all the remaining moves are self-evident.