The California Chess Reporter
(Volume IX Number 5-6, January-February 1960)
TOPSY-TURVY WORLD OF THE KNIGHT
by Fritz Leiber
The knight is an enchanted and bedeviled piece, a cripple with magic powers.
For him time and space are as jumbled and folded as in the weirdest science-fiction story. Yet - study this strange continuum around the knight, learn its non-Euclidean geometry, and he will work more powerfully for you; his perversity be less apt to thwart you.
For the knight, near is far and far is near.
The next square to the knight is three moves away for him. It takes him that many moves to reach the next square in a rank or file and he must back about like a crab to do it.
Yet he can reach the third square on the diagonal in only two leaps.
But the second square on the diagonal! - that is the knight's poison square, four whole moves away. For the seasoned player the poison squares around the knight glow with a sickly luminescence; the enemy king and queen love to poise there. By some strange warp age of chessboard space the fourth, fifth, and sixth squares on the diagonal are each the same distance away for knight as the poison square - four moves. (Incidentally, a jump of two squares on the diagonal was the move of the ancient bishop, as if he had been created to compensate for this chink in the knight's armor.)
The knight's crooked-seeming move has been described in many ways. Perhaps it is simplest to say he moves two squares - but shorter than the two-square move of the bishop and longer than the two-square move of the rook; anglewise he splits their moves. Or, he moves to all squares two squares away that a queen can't move to.
The longest possible journey a knight can make on the chessboard with wasting moves is from corner to opposite corner - six moves. Any other chessboard journey he can make in five moves or less.
The corners of the board are poison for knights, though. No piece loses as much power in a corner as a knight does - 75 per cent. In the center he has eight moves, in the corner only two. By comparison a king in the corner declines in power by 63 per cent, a bishop by 46 per cent, a queen by 21 per cent, a rook not at all.
Time presses down on the knight more than on any of the other pieces. He cannot lose a move or make a true waiting move - that is, he cannot make a move and still threaten the same square. Each move he must change the color of his square - and the color (the opposite) of the square he threatens; no matter how he tries he can never escape this enforced alternation.
Other weird rhythms spring from this one, maintaining their sorcerous-seeming hold on the knight. Let's trace the minimum number of moves it takes the King's Knight to reach the squares on his file:
King's Knight's second: 3 moves.
Eerie symmetries spring from the Knight's move, forming diamond patterns in the chessboard space around him. The four adjacent squares (three moves away from him - remember?) form the smallest diamond - call it a three-move diamond. The four adjacent squares on the diagonals, each two moves away for the knight, are the midpoints of the sides of a two-move diamond... and on each side of this diamond is based another two-move diamond... try it and see. The fifth squares away from the knight on rank and file are the apexes of a three-move diamond though we would have to enlarge the board to see all of it. Still further off are four and five move diamonds - truly, a strange business.
The number of routes available to the knight in making the same journey are another matter for wonder. For instance, there is only one route available to the King's Knight making a two-move journey from his original square to King's Fifth - or a three-move journey to Queen's Seventh; in these cases the knight moves in a straight line and there is only one of those between two points. A knight journeying three squares away on the diagonal or four squares away on a rank of file has only two alternative routes open to it. But a knight starting the three-move journey to the adjacent square in rank or file has in each case twelve routes it can choose from, while it has fifty-four ways of reaching each "poison square" two squares away on the diagonal!
No wonder the knight's move has fascinated mathematicians! No wonder puzzle artists have delighted in the Knight's Tour (whereby he visits each of the 64 squares of the chessboard in turn without ever visiting one twice) and in creating new forms of the tour, giving them such fantastic names as the Woven Spiral, the Four Stars, the Red Cross and the Toastrack!
No wonder some of us, temporarily exasperated by the knight's perversity; have cried out that only the deep Dostoyevskian mind of an Alekhine or Tchigorin can truly tame the devilish powers of the horse-headed piece!
Yet - know the knight's topsy-turvy chessboard space-time and he fights more resourcefully for you.
But no one can know all his secrets.
An odd piece, the knight, to the very end. It is at least an arguable exaggeration to say that half the magic of chess comes from the knight alone.
Return to Index