Enter Your Reply The Comment You're Replying To George Duke wrote on Mon, Nov 3, 2008 05:03 PM UTC:In two pages logicist grounding, Bertrand Russell and A.N. Whitehead prove ''the occasionally useful proposition'' 1 + 1 = 2, in 'Principia Mathematica' 1912 Volume 2 110.643. Within the same year 1913 'History of Chess' A.J.R. Murray recounts the then 400 years of Crazy Queen 64 squares, continuing the then 1300 years of 64 squares. Meanwhile Shogi had expanded to eighty-one and Xiangqi ninety. Mad/Crazy Queen is tantamount in her algebra to 1 + 1 + 1 = 3, as in Rook + Knight + Bishop = Unity by mutual exclusivity of destinations. [''He roller-coaster, he got early warning/ He got muddy water, he one mojo filter/ He say 'One and one and one are three'/ Got to be good-looking cos he's so hard to see...'' --Beatles' Abbey Road 1969] Needless to say, the story has sequel. Because R+N+B+F = unity more primitively, fundamentally, and finally by same principle of mutual exclusivity. 64 squares herself comes a cropper now, fortunately at last, because there is no crowding four elemental logical units onto 8x8 retaining King and Queen. There are still many, many, many, many (infinite?) possibilities for all of 8x10, 8x12 (what fifth piece?), 8x14 (what sixth piece?), 10x10, 9x10, 10x9. No bastion of orthodoxy will take up historic one-of-a-kind debate. Expect nothing from controversial websites like ChessBase with adherents being professed dyed-in-the-wool OrthoChessists. It would take more imagination and learning than any of them happen to have. Edit Form You may not post a new comment, because ItemID ChessboardMath4 does not match any item.