THE CHESS UNIVERSE PART 1

The convention of placing the board with a white square on the right (as defended by the LASTBUR of addicts' corner), is of course completely arbitrary. The game play is in no way changed should the white square be placed on the left. Nevertheless, the FIDE laws require that a game that is discovered to be played on an incorrectly oriented board must be transferred to a board with the correct orientation. The convention is only relevant to the chequer board with alternating light and dark squares, which is a European invention dating from at least the 11th century. Before then, no distinction in square colour was made. The chequer board does have the virtue of making diagonals more discernable and this is of particular utility in the modern game with the extended diagonal range of the queen and bishop.

It has, of course, always been necessary to arbitrarily distinguish the two armies, nominally black and white. What is not arbitrary is which side has the first move. The convention of white moving first is a relatively recent development from the 19th century. Before then players would draw for colour and for first move, so sometimes black would move first. At that time black was considered the lucky colour (like cats?), and this led to white having the first move as compensation for being left with the unlucky colour.

To avoid confusion, all games from before this convention was adopted have their scores published with the player having the first move being designated as white, regardless of the actual colour of the men.

We have dealt with the orientation of the board and the player colours; there remains the question of the disposition of the men in the array (the term given to the arrangement of men at the start of the game). The pieces are placed symmetrically apart from the king and queen, and we have the convention of the queen being placed on her own colour, which together with the convention of white on the right, places the queen on the white player's left hand side. (And the right of the black player). Note that the FIDE laws require that a game discovered to have been played with the array incorrectly set should be aborted and another game played.

The convention of queen on her own colour allows the king's bishop to always be discerned as the bishop that travels on the king's colour. It is not possible to so discern the king's knight or rook from the queen's and some chessmen have a crown marked on a knight and rook of each army to allow this distinction to be made.

The convention is again arbitrary since all games can equally well be played on the opposite hand. By the simple expedient of designating files a - h starting from the right hand side, all our opening theory and game scores would find application in chess played with the king and queen reversed. The geometry of chess space is unaffected. (As Alice no doubt discovered when she went through the looking-glass).*

A chess set does however exhibit chirality (the condition whereby it is not possible to superimpose a mirror image on the original; a term more usually employed in reference to molecules that have this property); no matter how the looking glass chess set is twisted or turned, it cannot be made to reproduce the orientation of the original. However, since the game play inhabits two dimensional space, the 2D game (as distinct from a 3D chess set), may in theory be turned over to be `bottom up' and rotated through 180 degrees in the plane of the board, to restore the orientation of the original. Chess sets exhibit chirality, but the game does not!

The individual Staunton pattern chessmen have different degrees of symmetry. The pawns are unique in having perfect axial symmetry; their orientation cannot be discerned. The pieces other than the knight are essentially axi-symmetric, but the king's cross, the queen's crown, the rook's crenellations and the bishop's mitre deviate from perfect axial symmetry. The knight has only a single plane of symmetry (as does the bishop) and cannot be said to be essentially axi-symmetric, so the question arises of how it should be oriented on its square.

No stipulations are made, and individual preferences vary. Some players prefer their knights to face the enemy, but this makes handling a little more awkward. Side facing knights are easier to handle and are more visible. Figurine knights in diagrams are shown facing the left, but given the taper towards the nose, the grip feels slightly more natural for the right handed player if the knight faces the right. If you were so minded, you might face the knights in opposite directions and so preserve the distinction between the king's and queen's knights.

The knight is usually said to make an `L-shaped' move, but may also be said to move in straight lines. The knight is technically known as a Ö5 leaper. (Other leapers with different length leaps are used in other variants of the game or in problems). With the unit of physical distance being the length of a square side, the knight moves along a straight line of length Ö5. (Being the length of the diagonal of a rectangle 2 squares by 1 square). The straight lines are in fact at an angle of approximately 27 degrees to the sides of the board.

In terms of physical distance covered, the knight moves further than a piece that moves 2 squares along a file or rank. In moving one square diagonally, the king, queen, bishop and pawn all move further than a rook moving a single square. Given the extended range of the modern line piece (a piece that can be moved any distance along an unobstructed line) the men may be ranked in order of maximum speed (physical distance/tempo) where the tempo is the unit of time in the chess universe:

The different physical speeds with which diagonal moves, and moves along rank or file, are made in chess space explains why sometimes counter intuitive possibilities arise, particularly in king and pawn endgames. In the chess universe, space may also be said to be discrete rather than continuous, since the unit of chess space, the square, is indivisible (you cannot move half a square). Chess men move through square chess space at the same speed in all directions; diagonal `distances' are the same as those along rank and file. It is in bringing expectations from our physical universe to the chess universe that our intuition is defeated. With this interpretation the knight is truly a leaper, for if a move through square chess space is obstructed, the knight must temporarily leave the dimensions of chess space to execute his move.

The knight is the only piece that cannot `lose the move', effectively `marking time' by losing a tempo, and bringing about the same position but with the move transferred to the opponent. This is because he can only return to a given square in an even number of moves. He is always on a square of the same colour with either an odd or even number of moves.

Although there are often references to `dynamic' play, this is a complete misnomer; in terms of game play, the men do not possess momentum (or mass, or inertia). It follows that an attack cannot possess momentum either, except in terms of human psychology. Psychology aside, the means by which a given position is arrived at is irrelevant. Like playing cards, chessmen have no memory.

*Curiously, as Alice might herself have said, the chess board illustration in the book `Through the Looking-Glass' is the wrong way round; in the looking-glass world black would be on the right and the white queen's pawn (Alice) would be on the right hand side of the board.


	Llandudno Chess Club \| home WHY PLAY CHESS? \| MANHANDLING; \| BOARD MEETINGS \| ACHIEVEMENT SCORING; \| DESCRIPTIVE NOTATION; A LOST ENDGAME? \| THE CHESS UNIVERSE PART 1 \| THE CHESS UNIVERSE PART 2 \| CHESS COMBAT \| THE REAL MATRIXTHE CHESS UNIVERSE PART 1 THE CHESS UNIVERSE PART 1: SPACE, TIME & SYMMETRY by H.T.Dearden The convention of placing the board with a white square on the right (as defended by the LASTBUR of addicts' corner), is of course completely arbitrary. The game play is in no way changed should the white square be placed on the left. Nevertheless, the FIDE laws require that a game that is discovered to be played on an incorrectly oriented board must be transferred to a board with the correct orientation. The convention is only relevant to the chequer board with alternating light and dark squares, which is a European invention dating from at least the 11th century. Before then, no distinction in square colour was made. The chequer board does have the virtue of making diagonals more discernable and this is of particular utility in the modern game with the extended diagonal range of the queen and bishop. It has, of course, always been necessary to arbitrarily distinguish the two armies, nominally black and white. What is not arbitrary is which side has the first move. The convention of white moving first is a relatively recent development from the 19th century. Before then players would draw for colour and for first move, so sometimes black would move first. At that time black was considered the lucky colour (like cats?), and this led to white having the first move as compensation for being left with the unlucky colour. To avoid confusion, all games from before this convention was adopted have their scores published with the player having the first move being designated as white, regardless of the actual colour of the men. We have dealt with the orientation of the board and the player colours; there remains the question of the disposition of the men in the array (the term given to the arrangement of men at the start of the game). The pieces are placed symmetrically apart from the king and queen, and we have the convention of the queen being placed on her own colour, which together with the convention of white on the right, places the queen on the white player's left hand side. (And the right of the black player). Note that the FIDE laws require that a game discovered to have been played with the array incorrectly set should be aborted and another game played. The convention of queen on her own colour allows the king's bishop to always be discerned as the bishop that travels on the king's colour. It is not possible to so discern the king's knight or rook from the queen's and some chessmen have a crown marked on a knight and rook of each army to allow this distinction to be made. The convention is again arbitrary since all games can equally well be played on the opposite hand. By the simple expedient of designating files a - h starting from the right hand side, all our opening theory and game scores would find application in chess played with the king and queen reversed. The geometry of chess space is unaffected. (As Alice no doubt discovered when she went through the looking-glass).* A chess set does however exhibit chirality (the condition whereby it is not possible to superimpose a mirror image on the original; a term more usually employed in reference to molecules that have this property); no matter how the looking glass chess set is twisted or turned, it cannot be made to reproduce the orientation of the original. However, since the game play inhabits two dimensional space, the 2D game (as distinct from a 3D chess set), may in theory be turned over to be `bottom up' and rotated through 180 degrees in the plane of the board, to restore the orientation of the original. Chess sets exhibit chirality, but the game does not! The individual Staunton pattern chessmen have different degrees of symmetry. The pawns are unique in having perfect axial symmetry; their orientation cannot be discerned. The pieces other than the knight are essentially axi-symmetric, but the king's cross, the queen's crown, the rook's crenellations and the bishop's mitre deviate from perfect axial symmetry. The knight has only a single plane of symmetry (as does the bishop) and cannot be said to be essentially axi-symmetric, so the question arises of how it should be oriented on its square. No stipulations are made, and individual preferences vary. Some players prefer their knights to face the enemy, but this makes handling a little more awkward. Side facing knights are easier to handle and are more visible. Figurine knights in diagrams are shown facing the left, but given the taper towards the nose, the grip feels slightly more natural for the right handed player if the knight faces the right. If you were so minded, you might face the knights in opposite directions and so preserve the distinction between the king's and queen's knights. The knight is usually said to make an `L-shaped' move, but may also be said to move in straight lines. The knight is technically known as a Ö5 leaper. (Other leapers with different length leaps are used in other variants of the game or in problems). With the unit of physical distance being the length of a square side, the knight moves along a straight line of length Ö5. (Being the length of the diagonal of a rectangle 2 squares by 1 square). The straight lines are in fact at an angle of approximately 27 degrees to the sides of the board. In terms of physical distance covered, the knight moves further than a piece that moves 2 squares along a file or rank. In moving one square diagonally, the king, queen, bishop and pawn all move further than a rook moving a single square. Given the extended range of the modern line piece (a piece that can be moved any distance along an unobstructed line) the men may be ranked in order of maximum speed (physical distance/tempo) where the tempo is the unit of time in the chess universe: Queen, Bishop Ö98 (approx 9.90) Rook 7 Knight Ö5 (approx 2.24) King, Pawn Ö2 (approx 1.41) Note that in the chess universe, time is discrete, not continuous, since individual tempi cannot be subdivided. The different physical speeds with which diagonal moves, and moves along rank or file, are made in chess space explains why sometimes counter intuitive possibilities arise, particularly in king and pawn endgames. In the chess universe, space may also be said to be discrete rather than continuous, since the unit of chess space, the square, is indivisible (you cannot move half a square). Chess men move through square chess space at the same speed in all directions; diagonal `distances' are the same as those along rank and file. It is in bringing expectations from our physical universe to the chess universe that our intuition is defeated. With this interpretation the knight is truly a leaper, for if a move through square chess space is obstructed, the knight must temporarily leave the dimensions of chess space to execute his move. The knight is the only piece that cannot `lose the move', effectively `marking time' by losing a tempo, and bringing about the same position but with the move transferred to the opponent. This is because he can only return to a given square in an even number of moves. He is always on a square of the same colour with either an odd or even number of moves. In terms of raw attacking capability (number of squares subject to unobstructed attack) the men may be ranked as follows: Max Min Queen 27 21 Rook 14 14 Bishop 13 7 King 8 3 Knight 8 2 Pawn 2 1 Although there are often references to `dynamic' play, this is a complete misnomer; in terms of game play, the men do not possess momentum (or mass, or inertia). It follows that an attack cannot possess momentum either, except in terms of human psychology. Psychology aside, the means by which a given position is arrived at is irrelevant. Like playing cards, chessmen have no memory. *Curiously, as Alice might herself have said, the chess board illustration in the book `Through the Looking-Glass' is the wrong way round; in the looking-glass world black would be on the right and the white queen's pawn (Alice) would be on the right hand side of the board.