THE CHESS UNIVERSE PART 2

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THE CHESS UNIVERSE, PART 2; FORCE AND EXPLORATION

by H.T.Dearden

In the first part of this article, I examined something of the nature of space and time in he chess universe. In this article I consider the meaning of power or force and of exploration. Perhaps these concerns are only of interest to the pedantic, but I find it an intriguing challenge to interpret these matters in a logically consistent manner.

Since in terms of game play the chessmen do not possess mass or momentum, the concept of force in the mechanical sense has no meaning in the chess universe. What then is the nature of force as exhibited by chessmen? The queen is understood to be the `strongest' or `most powerful' piece, but when threatened by the humble pawn she is usually obliged to retreat. There is in fact no contest of strength between chessmen; whichever man lays the latest claim to a square is the victor. The queen exerts the same force on a potential destination square as any other man. The queen does not carry a bigger gun!

The chess force does not diminish with range and has equal effect on all potential destination squares. All men, apart from the king, are equally susceptible to this force, but some may be said to be less vulnerable in that it is harder to approach them without being subject to the force they themselves radiate. It is hard to sneak up on a queen; only the knight may attempt it. Uniquely, the king finds the chess force irresistible, if it cannot be blocked by another man, the king must move; in the chess universe, we may at least answer the age old conundrum `what happens when irresistible force meets immovable object? Checkmate!

The chessmen are simply defined by the moves they make; no separate specification of strength, force or power is required. The chess force is simply the potential to capture a hostile man. (Potential to occupy a square is not quite right, since a pawn may have the potential to occupy a vacant square in front, but it does not have the potential to capture on that square; it does not exert any force over that square). `Most powerful' is virtually synonymous with `most mobile' and in my earlier article the chessmen were correspondingly ranked in terms of their raw (unobstructed) attacking capability. The queen may not have a bigger gun, but she may point it in more directions and threaten its use over a greater range. In common with the other men, she may only use her weapon once with each tempo. A gun is perhaps an inappropriate analogy, since the threat cannot be executed at a distance; a man must move to the occupied square to effect capture. (In passing, we leave the reader to identify the one exceptional circumstance where this is not true*).

The chess force, other than that radiated by the knight (which may be said to be routed via a third dimension), is blocked by any intervening man. Although the knight's force may not be blocked, it can be neutralised by a pin against the king. A pin against any other man would not neutralise the force, but may reduce the control over squares within the knight's influence.

Chess force is related to the concept of control, which is defined in The Oxford Companion to Chess as `the mastery of a square such that if an enemy man moved there it might be captured advantageously'. This is perfectly reasonable, but there is the difficulty of determining whether or not the enemy man may be captured advantageously. This may be a moot point and a game may well turn on the resolution of just this question. As a simple example, consider the illustration.

Who controls e2? If the e3 pawn advances it cannot be captured with advantage to white, who would lose queen for rook + pawn and be left with a lost position. Now give white a bishop on g6, which although it does not bear on e2, allows white to capture the pawn with advantage, with an unstoppable mate on e8 should black exchange on e2. This example, albeit contrived, forcibly demonstrates that positional evaluation may be necessary in assessing who has control of a given square.

All that may be determined absolutely in every case is who may force occupancy after all exchanges are exhausted. (The implication being that occupancy can be maintained for at least three single-moves or ply). This will be the player that can bring the greatest cumulative chess force to bear on the contested square. Note that cumulative force is to be considered, since captures may release latent force from men that are otherwise blocked. Perhaps we might refer to the player with the greater cumulative force as having `ownership' of a square. In the above example, white definitely `owns' e2; whether this is a good thing or not is a different question.

Note that occupancy itself does nothing to enhance ownership except in so far as it restricts the approach of hostile forces that might otherwise contest occupancy. At the moment of occupancy, ownership of a square must diminish, since the occupier no longer exerts any chess force on the occupied square.

In the instant that the rules of chess were first conceived, the entire chess universe was created. Since that moment we have continued to explore that universe. The masters explore the furthest known reaches, whilst the experience of the novice hardly moves from the originating rules. Combinations, correct technique, and theoretical novelties are not created, but are discovered. They have been there since the rules were conceived and are the inevitable, logical consequence of those rules. This in no way detracts from the feat of imagination and vision needed to make these discoveries.

When we are surprised and thrilled by a brilliancy, we reveal our intuitive approach to the game. Brilliancies and curiosities are not perceived as such because of some new twist in the logic of the game, which maintains absolute fidelity with the rules, but because of the limitations of our intuition.

Given the brute force approach to chess employed by computers, in which all legal possibilities are evaluated many ply deep, regardless of their plausibility, it is unlikely that a computer would be surprised even if one were engineered to register such a condition.

The fact that humans can challenge computers at all is testimony to the efficiency, in disregarding the less plausible continuations, of the intuitive approach,. We also have the joy of surprise, elegance, humour, wit, and drama.

The surprises to be found within chess were intriguingly used in support of an argument made by Sir William A.Raleigh (1861-1922) in his work Romance (1917):

“Let him who conceives of high hopes from the progress of knowledge and the pertinacity of thought, tame and subdue his pride by considering for a moment the game of chess.

That game is played with 32 pieces of six different kinds, on a board of 64 squares. Each kind of piece has one allotted move of action, which is further cramped by severe limitations of space. The conditions imposed upon the game, are strict, uniform, and mechanical. Yet those that have made of chess a life-long study are ready to confess their complete ignorance of the fundamental merits of particular moves; one game does not resemble another; and from the most commonplace of developments there may spring up, on a sudden, wild romantic possibilities and vibrations that are like miracles. If these surprising flowers of fancy grow on the chess-board, how shall we set a limit to the possibilities of human life, which is chess with variety and uncertainty many million times increased.”

We may perhaps forgive Sir William his inaccuracies (…..ready to confess their complete ignorance?? One game does not resemble another??) and heartily endorse the sentiment.

* en passant!


	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 MATRIX THE CHESS UNIVERSE, PART 2; FORCE AND EXPLORATION by H.T.Dearden In the first part of this article, I examined something of the nature of space and time in he chess universe. In this article I consider the meaning of power or force and of exploration. Perhaps these concerns are only of interest to the pedantic, but I find it an intriguing challenge to interpret these matters in a logically consistent manner. Since in terms of game play the chessmen do not possess mass or momentum, the concept of force in the mechanical sense has no meaning in the chess universe. What then is the nature of force as exhibited by chessmen? The queen is understood to be the `strongest' or `most powerful' piece, but when threatened by the humble pawn she is usually obliged to retreat. There is in fact no contest of strength between chessmen; whichever man lays the latest claim to a square is the victor. The queen exerts the same force on a potential destination square as any other man. The queen does not carry a bigger gun! The chess force does not diminish with range and has equal effect on all potential destination squares. All men, apart from the king, are equally susceptible to this force, but some may be said to be less vulnerable in that it is harder to approach them without being subject to the force they themselves radiate. It is hard to sneak up on a queen; only the knight may attempt it. Uniquely, the king finds the chess force irresistible, if it cannot be blocked by another man, the king must move; in the chess universe, we may at least answer the age old conundrum `what happens when irresistible force meets immovable object? Checkmate! The chessmen are simply defined by the moves they make; no separate specification of strength, force or power is required. The chess force is simply the potential to capture a hostile man. (Potential to occupy a square is not quite right, since a pawn may have the potential to occupy a vacant square in front, but it does not have the potential to capture on that square; it does not exert any force over that square). `Most powerful' is virtually synonymous with `most mobile' and in my earlier article the chessmen were correspondingly ranked in terms of their raw (unobstructed) attacking capability. The queen may not have a bigger gun, but she may point it in more directions and threaten its use over a greater range. In common with the other men, she may only use her weapon once with each tempo. A gun is perhaps an inappropriate analogy, since the threat cannot be executed at a distance; a man must move to the occupied square to effect capture. (In passing, we leave the reader to identify the one exceptional circumstance where this is not true). The chess force, other than that radiated by the knight (which may be said to be routed via a third dimension), is blocked by any intervening man. Although the knight's force may not be blocked, it can be neutralised by a pin against the king. A pin against any other man would not neutralise the force, but may reduce the control over squares within the knight's influence. Chess force is related to the concept of control, which is defined in The Oxford Companion to Chess* as `the mastery of a square such that if an enemy man moved there it might be captured advantageously'. This is perfectly reasonable, but there is the difficulty of determining whether or not the enemy man may be captured advantageously. This may be a moot point and a game may well turn on the resolution of just this question. As a simple example, consider the illustration. Who controls e2? If the e3 pawn advances it cannot be captured with advantage to white, who would lose queen for rook + pawn and be left with a lost position. Now give white a bishop on g6, which although it does not bear on e2, allows white to capture the pawn with advantage, with an unstoppable mate on e8 should black exchange on e2. This example, albeit contrived, forcibly demonstrates that positional evaluation may be necessary in assessing who has control of a given square. All that may be determined absolutely in every case is who may force occupancy after all exchanges are exhausted. (The implication being that occupancy can be maintained for at least three single-moves or ply). This will be the player that can bring the greatest cumulative chess force to bear on the contested square. Note that cumulative force is to be considered, since captures may release latent force from men that are otherwise blocked. Perhaps we might refer to the player with the greater cumulative force as having `ownership' of a square. In the above example, white definitely `owns' e2; whether this is a good thing or not is a different question. Note that occupancy itself does nothing to enhance ownership except in so far as it restricts the approach of hostile forces that might otherwise contest occupancy. At the moment of occupancy, ownership of a square must diminish, since the occupier no longer exerts any chess force on the occupied square. In the instant that the rules of chess were first conceived, the entire chess universe was created. Since that moment we have continued to explore that universe. The masters explore the furthest known reaches, whilst the experience of the novice hardly moves from the originating rules. Combinations, correct technique, and theoretical novelties are not created, but are discovered. They have been there since the rules were conceived and are the inevitable, logical consequence of those rules. This in no way detracts from the feat of imagination and vision needed to make these discoveries. When we are surprised and thrilled by a brilliancy, we reveal our intuitive approach to the game. Brilliancies and curiosities are not perceived as such because of some new twist in the logic of the game, which maintains absolute fidelity with the rules, but because of the limitations of our intuition. Given the brute force approach to chess employed by computers, in which all legal possibilities are evaluated many ply deep, regardless of their plausibility, it is unlikely that a computer would be surprised even if one were engineered to register such a condition. The fact that humans can challenge computers at all is testimony to the efficiency, in disregarding the less plausible continuations, of the intuitive approach,. We also have the joy of surprise, elegance, humour, wit, and drama. The surprises to be found within chess were intriguingly used in support of an argument made by Sir William A.Raleigh (1861-1922) in his work Romance (1917): “Let him who conceives of high hopes from the progress of knowledge and the pertinacity of thought, tame and subdue his pride by considering for a moment the game of chess. That game is played with 32 pieces of six different kinds, on a board of 64 squares. Each kind of piece has one allotted move of action, which is further cramped by severe limitations of space. The conditions imposed upon the game, are strict, uniform, and mechanical. Yet those that have made of chess a life-long study are ready to confess their complete ignorance of the fundamental merits of particular moves; one game does not resemble another; and from the most commonplace of developments there may spring up, on a sudden, wild romantic possibilities and vibrations that are like miracles. If these surprising flowers of fancy grow on the chess-board, how shall we set a limit to the possibilities of human life, which is chess with variety and uncertainty many million times increased.” We may perhaps forgive Sir William his inaccuracies (…..ready to confess their complete ignorance?? One game does not resemble another??) and heartily endorse the sentiment. * en passant!