The influence quantity of pieces is defined by their number of unique moves with respect to their from- and to-square coordinates, the cardinality of the set of all possible moves, or potential, globalmobility^{[1]}. It might be used to enumerate and encode all those moves, i.e. associating each move, per piece and in total, with a unique number for minimal perfect hashing opposed to intermittent Butterfly boards.

For instance a pawn (including promotions) has 48 (8*6) single pushes and 84 (2*7*6) captures, plus 8 possible double pushes on each file, which results in a influence quantity of 140 of either white or black pawns.The influence quantities of all pieces are divisible by four times seven (28), excluding pawn and king even by sixteen times seven (112). While obviously the number of queen quantities is the sum of rook- and bishop quantities, it is at the first glance somehow surprising that the rook quantity is the sum of bishop- and knight quantities.

Following table gives the distinct number of moves per piece and origin square and their sums from the lower left quarter of a board (a1-d4) and in total for the whole board:

The mentioned move quantities of pawns and pieces only roughly correlate with their point values since the static enumeration of all moves with distinct coordinates does not take into account the reachability of all origin-squares. Only queen and rook can reach any square in at least two moves on the otherwise empty board. Bishop quantities cover all light and dark colored from-squares. While a single bishop is bounded to one square color, its individual influence quantity is therefor divided by two. Also, pawns can only move forward and can not reach each enumerated origin square, which decreases their individual influence accordantly. King and knights can reach every square on the otherwise empty board, but may take more time with respect to distance and knight-distance.

Divisibility by Seven

All influence quantities are divisible by four times seven, thanks to the double pushes. For a rook it is quite obvious, since each of the 64 from squares covers one rank and file each with seven squares left.

If we only consider pieces with disjoint moves (excluding pawns and king), and the queen as superset of bishop and rook, the influence quantities are even divisible by seven times sixteen, where the remaining quotients from knight to queen are Fibonacci numbers as shown by the Fibonacci spiral ^{[3]}^{[4]} .

In his esoteric and pseudo scientific touched Encyclopedia of Chess-Prehistory, Peter Orantek ^{[6]} mentions a possible connection to astronomy, related to the orbital period of Earth and Venus. The influence quantity of a queen is equivalent to about 4 years (4 x 364 days), while the influence quantity of a rook is equivalent to 224 days x 4 Venus rotations.

In his German text sample ^{[7]} , Orantek further elaborates that queen quantities of the four center squares (four times 27) represent four earth moon rotations, while the three concentric rings around the center might related to various synodic periods of the four terrestrial planets. He associates following prime numbers with planets or objects orbiting the Sun^{[8]} :

^Kelly Fisher Lowe (2006). The Words and Music of Frank Zappa. Praeger Publishers, pp. 119 The lyrics to "Inca Roads" are absurdist in the extreme. They veer wildly from spacey - "Did a vehicle / Come from somewhere out there / Just to land in the Andes?," which both Watson and Courrier claim Zappa's satire on the popular-at-the-time book Chariots of the Gods? ...

Home * Chess * Pieces * Influence Quantityinfluence quantityof pieces is defined by their number of unique moves with respect to their from- and to-square coordinates, the cardinality of the set of all possible moves, or potential, global mobility^{[1]}. It might be used to enumerate and encode all those moves, i.e. associating each move, per piece and in total, with a unique number for minimal perfect hashing opposed to intermittent Butterfly boards.For instance a pawn (including promotions) has 48 (8*6) single pushes and 84 (2*7*6) captures, plus 8 possible double pushes on each file, which results in a influence quantity of 140 of either white or black pawns.The influence quantities of all pieces are divisible by four times seven (28), excluding pawn and king even by sixteen times seven (112). While obviously the number of queen quantities is the sum of rook- and bishop quantities, it is at the first glance somehow surprising that the rook quantity is the sum of bishop- and knight quantities.

^{[2]}## Table of Contents

## Moves per Origin

Following table gives the distinct number of moves per piece and origin square and their sums from the lower left quarter of a board (a1-d4) and in total for the whole board:## Whole Board Diagrams

Whole board tables cover pawn, knight, king and sliding pieces, and their file-, rank and total sums:## Board Circles

The concentric "circles" around the center with their respective influence sums of sliding pieces:## Quantities and Point Values

The mentioned move quantities of pawns and pieces only roughly correlate with their point values since the static enumeration of all moves with distinct coordinates does not take into account the reachability of all origin-squares. Only queen and rook can reach any square in at least two moves on the otherwise empty board. Bishop quantities cover all light and dark colored from-squares. While a single bishop is bounded to one square color, its individual influence quantity is therefor divided by two. Also, pawns can only move forward and can not reach each enumerated origin square, which decreases their individual influence accordantly. King and knights can reach every square on the otherwise empty board, but may take more time with respect to distance and knight-distance.## Divisibility by Seven

All influence quantities are divisible by four times seven, thanks to the double pushes. For a rook it is quite obvious, since each of the 64 from squares covers one rank and file each with seven squares left.## Fibonacci Spiral

If we only consider pieces with disjoint moves (excluding pawns and king), and the queen as superset of bishop and rook, the influence quantities are even divisible by seven times sixteen, where the remaining quotients from knight to queen are Fibonacci numbers as shown by the Fibonacci spiral^{[3]}^{[4]}.^{[5]}## Analogy in Astronomy

In his esoteric and pseudo scientific touchedEncyclopedia of Chess-Prehistory, Peter Orantek^{[6]}mentions a possible connection to astronomy, related to the orbital period of Earth and Venus. The influence quantity of a queen is equivalent to about 4 years (4 x 364 days), while the influence quantity of a rook is equivalent to 224 days x 4 Venus rotations.In his German text sample

^{[7]}, Orantek further elaborates that queen quantities of the four center squares (four times 27) represent four earth moon rotations, while the three concentric rings around the center might related to various synodic periods of the four terrestrial planets. He associates following prime numbers with planets or objects orbiting the Sun^{[8]}:number

or Objects

in days

in days

White Knight

The Crazy Bishop

224.70069(579–589)

Terra

365.256366(764–811)

## See also

Move Enumeration

## Publications

1876).On the Relative Values of the Pieces in Chess. Philosophical Magazine, Series 5, Vol. 1, pp. 221-2291940).Mathematical Recreations and Essays. from the original by W. W. Rouse Ball, Macmillan1968).A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares. Machine Intelligence Vol. 21990, 1999, 2010, 2015).The Positional Elements of Chess. Russell Enterprises2008).Encyclopedia of Chess-Prehistory - Programming Language Chess.## Forum Posts

## External Links

^{[9]}^{[10]}^{[11]}Frank Zappa, George Duke, Napoleon Murphy Brock, Chester Thompson, Tom Fowler, Ruth Underwood, Captain Beefheart

## References

1990, 1999, 2010, 2015).The Positional Elements of Chess. Russell Enterprises1876).On the Relative Values of the Pieces in Chess. Philosophical Magazine, Series 5, Vol. 1, pp. 221-229 as reported in H. S. M. Coxeter (1940).Mathematical Recreations and Essays. pp. 162-165, from the original by W. W. Rouse Ball, Macmillan, as reported by Jack Good (1968).A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares. Machine Intelligence Vol. 22006).The Words and Music of Frank Zappa. Praeger Publishers, pp. 119The lyrics to "Inca Roads" are absurdist in the extreme. They veer wildly from spacey - "Did a vehicle / Come from somewhere out there / Just to land in the Andes?," which both Watson and Courrier claim Zappa's satire on the popular-at-the-time book Chariots of the Gods? ...## What links here?

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