“Victory lies in the legs of the soldier.”—Frederic the Great.
“The principal part of the soldier’s efficiency depends
upon his legs.
“The personal abilities required in all manoeuvres and
in battles are totally confined to them.
“Whoever is of a different opinion is a dupe to ignorance
and a novice in the profession of arms.”—Count de Saxe.
“It is easier to beat an enemy than commonly is supposed,”
says Napoleon, “the great Art lies in making nothing
but decisive movements.”
To the proficient in Strategetics the truth of the foregoing
dictum is self-evident. Nevertheless, it remains
to instruct the student how to select from a multitude of
possible movements, that particular movement or series
of movements, which in a given situation are best calculated
to achieve victory.
Whatever may be such series of movements, obviously,
it must have an object, i.e., a specific and clearly defined
purpose. Equally so, all movements made on such line
of movement must each have an objective, i.e., a terminus.
These objectives, like cogs in a gear, intimately
are connected with other objectives or termini, so that the
project thus formed constitutes always an exact and often
a vast scheme.
Frequently it happens that the occupation of an
objective, valid in a given situation, is not valid in an
ensuing situation for the reasons:
- 1. That the object of the given line of movement is
become unattainable, or,
- 2. Because it has become no longer worth attaining,
or,
- 3. Because such belated attainment may be direct
cause of disaster.
In order to select the decisive movement in a given situation
it is necessary first to determine both the object and
the objective, not merely of the required movement, but also
of that series of movements, which collectively constitute the
projected line of movement; together with the object and the
objective of every movement contained therein.
The mathematician readily will perceive, and the
student doubtless will permit himself to be informed,
that:
Before the true object and the true objective of any
movement can be determined it first is necessary to
deduce the common object of all movement.
As is well known, the combined movements of the
Chess-pieces over the surface of the Chess-board during
a game at Chess are infinite.
These calculations are so complex that human perception
accurately can forecast ultimate and even immediate
results only in comparatively few and simple
situations. Such calculable outcomes are limited to the
earlier stages of the opening, to the concluding phases of a
game; and to situations in the mid-game wherein the
presence of but few adverse pieces minimizes the volume
of effort possible to the opponent.
Consequently, it is self-evident, that:
Situations on the Chess-board require for their demonstration
a degree of skill which decreases as the hostile
power of resistance decreases.
All power for resistance possessed by an army emanates
from its ability to move. This faculty of Mobility is
that inestimable quality without which nothing and by
means of which everything, can be done.
From this truth it is easy to deduce the common object
of all movement, which obviously is:
To minimize the mobility of the opposing force.
The hostile army having the ability to move and consequently
a power for resistance equal to that possessed
by the kindred army; it becomes of the first importance to
discover in what way the kindred army is superior to
that adverse force, which in the Normal Situation on the
Chess-board is its exact counterpart in material, position
and formation.
Such normal superiority of the White army over the
Black army is found in the fact that:
- 1. The former has the privilege of making the
initial move of the game.
- 2. This privilege of first move is the absolute advantage
in Time.
While no mathematical demonstration of the outcome
of a game at Chess is possible, nevertheless there are
rational grounds for assuming that with exact play, White
should win.
This decided and probably decisive advantage possessed
by White can be minimized only by correcting a
mathematical blemish in the game of Chess as at present
constructed; which blemish, there is reason to believe,
did not originally exist.
This imperfection seemingly is the result of unscientific
modifications of the Italian method of Castling;
which latter, from the standpoint of mathematics and of
Strategetics, embodies the true spirit of that delicate and
vital evolution.
To the mathematician and to the Strategist, it is clear
that Chess as first devised was geometrically perfect.
The abortions played during successive ages and in
various parts of the Earth, merely are crude and unscientific
deviations from the perfect original.
Thus, strategetically, the correct post of deployment
for the Chess-King is at the extremity of a straight line
drawn from the center of that Grand Strategic Front
which appertains to the existing formation.
Hence, in the grand front by the right, the King in
Castling K R, properly goes in one move to KKt1, his
proper post. Conversely, in Castling Q R, he also should
go in one move to QKt1, his proper post corresponding to
the grand front by the left.
Again, whenever the formation logically points to the
grand front by the right refused, the King should go in
one move from K1 to KR1. When the formations indicate
the grand front by the left refused, the King
should go in one move from K1 to QR1.
In each and every case the co-operating Rook should
be posted at the corresponding Bishop’s square, in order
to support the alignment by P-B4, of the front adopted.
The faulty mode of castling today in vogue clearly
is not the product either of the mathematic nor of the
strategetic mind.
The infantile definition of “the books,” viz., “The
King in Castling moves two squares either to the right
or to the left,” displays all that mania for the commonplace,
which characterizes the dilettante.
All that can be done is to call attention to this baleful
excrescence on the great Game. Of course, it is useless
to combat it. In the words of the Count de Saxe:
“The power of custom is absolute. To depart from it
is a crime, and the most inexcusable of all crimes is to
introduce innovations. For most people, it is sufficient
that a thing is so, to forever allow it to remain so.”
Says the great Frederic;
“Man hardly may eradicate in his short lifetime all the
prejudices that are imbibed with his mother’s milk; and
it is well nigh impossible to successfully wrestle with
custom, that chief argument of fools.”
Also bearing in mind the irony of Cicero, who regarded
himself fortunate in that he had not fallen victim to
services rendered his countrymen, it suffices to say:
The true Chessic dictum in regard to the double
evolution of the King and Rook should read:
“The King of Castling should deploy in one move to
that point where, as the Base of Operations, it mathematically
harmonizes with that Strategic Front, which is,
or must become, established.”
The change in the present form of Castling, herein
suggested, should be made in the true interests of the
Royal Game.
The instant effect of such change will be:
- 1. Largely to increase the defensive resources both
of White and Black;
- 2. To minimize the handicap on the second player,
due to White’s advantage of first move;
- 3. To permit open play on the Queen’s side of the
board and thus provide a broader and more resplendent
field for Strategetic genius.
In all our modern-day mis-interpretations of the ethics
of Chess and our characteristic Twentieth Century
looseness of practice as applied to Chess-play, perhaps
there exists no greater absurdity, than that subversion
of ordinary intelligence, daily evinced by permitting a
piece which cannot move, to give check.
It is a well known and in many ways a deserved reproach,
cast by the German erudite, that the mind of
the Anglo-Saxon is not properly developed, that it is
able to act correctly only when dealing with known
quantities, and is inadequate for the elucidation of
indeterminate things.
In consequence, they say, the argumentative attempts
of the Anglo-Saxon are puerile; the natural result of a
mental limitation which differs from that of monkeys
and parrots, merely in ability to count beyond two.
Surely it would seem that a very young child readily
would sense that:
A Chess-piece, which by law is debarred from movement,
is, by the same law, necessarily debarred from
capturing adverse material; inasmuch as in order to
capture, a piece must move.
Nevertheless consensus of opinion today among
children of every growth and whether Anglo-Saxon or
German, universally countenance the paradox that:
A piece which is pinned on its own King, can give check
i.e., threaten to move and capture the adverse King.
To argue this question correctly and to deduce the
logical solution, it is necessary to revert to first principles
and to note that:
It is a fundamental of Chess mathematics that the
King cannot be exposed to capture.
Furthermore, it is to be noted as equally fundamental,
that:
- 1. A piece exerts no force against that point upon
which it is posted;
- 2. That whatever power a piece exerts, always is
exerted against some other point than the point upon
which it stands; and that;
- 3. In order to exert such power, it is an all-essential
that the piece move from the point which it occupies to
the point at which its power is to be exerted.
Hence, it is obvious and may be mathematically demonstrated,
that,
- 1. A piece which cannot move, cannot capture.
- 2. A piece which cannot capture, does not exercise
any threat of capture; and
- 3. Consequently, a piece deprived of its right to
move; which cannot capture nor exercise any threat to
capture, obviously and by mathematical demonstration,
cannot give check, inasmuch, as “check” merely is the
threat by a piece to move and capture the adverse King.
Therefore, whatever may be the normal area of movement
belonging to a piece, whenever from any cause
such piece loses its power of movement, then,
It no longer can capture, nor exercise any threat of
capture, upon the points contained within said area; and
consequently such points so far as said immovable piece
is concerned, may be occupied in safety by any adverse
piece including the adverse King, for the reason that:
An immovable piece cannot move; and not being able
to move it cannot capture, and not being able to capture,
it does not exercise any threat of capture, and consequently
it cannot give check.
This incongruity of permitting an immovable piece to
give check constitutes the second mathematical blemish
in the game of Chess, as at present constructed.
This fallacy, the correction of which any schoolboy
may mathematically demonstrate, is defended, even by
many who would know better, if they merely would take
time for reflection; by the inane assumption, that:
A piece which admittedly is disqualified and rendered
dormant by all the fundamentals of the science of Chess,
and which therefore cannot legally move and consequently
cannot legally capture anything; by some
hocus-pocus may be made to move and to capture that
most valuable of all prizes, the adverse King; and this
at a time and under circumstances when, as is universally
allowed, it cannot legally move against, nor legally capture
any other adverse piece.
The basis of this illogical, illegal, and untenable assumption
is:
The pinned piece, belonging to that force which has
the privilege of moving, can abandon its post, and capture
the adverse King; this stroke ends the game and
the game being ended, the pinning piece never can avail
of the abandonment of the covering post by the pinned
piece to capture the King thus exposed.
The insufficiency of this subterfuge is clear to the
mathematical mind. Its subtlety lies in confounding
together things which have no connection, viz.:
Admittedly the given body of Chess-pieces has the
right to move, but it is of the utmost importance to
note that this privilege of moving extends only to a single
piece and from this privilege of moving the pinned piece
is debarred by a specific and fundamental law of the
game, which declares that:
“A piece shall not by removing itself uncover the
kindred King to the attack of a hostile piece.”
Thus, it is clear, that a pinned piece is a disqualified
piece; its powers are dormant and by the laws of the
game it is temporarily reduced to an inert mass, and
deprived of every faculty normally appertaining to it as a
Chess-piece. On the other hand, as is equally obvious,
the pinning piece is in full possession of its normal powers
and is qualified to perform every function.
To hold that a piece disqualified by the laws of the
game can nullify the activities of a piece in full possession
of its powers, is to assert that black is white, that the
moon is made of green cheese, that the tail can wag the
dog, or any other of those things which have led the German
to promulgate his caustic formula on the Anglo-Saxon.
Hence, artificially to nullify the normal powers of an
active and potential piece which is operating in conformity
to the laws of the game, and artificially to revivify
the dormant powers of a piece disqualified by the
same laws; to debar the former from exercising its
legitimate functions and to permit the latter to exercise
functions from which by law, it specifically is debarred,
is a self-evident incongruity and any argument whereby
such procedure is upheld, necessarily and obviously,
is sophistry.
No less interesting than instructive and conclusive,
is reference of this question to those intellectual principles
which give birth to the game of Chess, per se, viz.:
As a primary fundamental, with the power to give
check, is associated concurrently the obligation upon
the King thus checked, not to remain in check.
Secondly: The totality of powers assigned to the
Chess-pieces is the ability to move, provided the King be
free from check. This totality of powers may be denoted
by the indefinite symbol, X.
The play thus has for its object:
The reduction to zero of the adverse X, by the operation
of the kindred X.
This result is checkmate in its generalized form. In
effect, it is the destruction of the power of the adverse
pieces to move, by means of check made permanent.
By the law of continuity it is self-evident that:
The power to move appertaining either to White or to
Black, runs from full power to move any piece (a power
due to freedom from check), down to total inability to
move any piece, due to his King being permanently
checked, i.e., checkmated.
This series cannot be interrupted without obvious
violation of the ethics of the game; because, so long as
any part of X remains, the principle from which the
series emanated still operates, and this without regard
to quantity of X remaining unexpended.
Thus, a game of Chess is a procedure from total ability
to total disability; i.e., from one logical whole to another;
otherwise, from X to zero.
Checkmate, furnishes the limit to the series; the game
and X vanish together.
This is in perfect keeping with the law of continuity,
which acts and dominates from beginning to end of the
series, and so long as any part of X remains.
Hence to permit either White or Black to move any
piece, leaving his King in check, is an anomaly.
Denial to the Pawn of ability to move to the rear is an
accurate interpretation of military ethics.
Of those puerile hypotheses common to the man who
does not know, one of the most entrancing to the popular
mind, is the notion that Corps d’armee properly are of
equal numbers and of the same composition.
This supposition is due to ignorance of the fact that
the multifarious duties of applied Strategetics, require
for their execution like variety of instruments, which
diversity of means is strikingly illustrated by the differing
movements of the Chess-pieces.
The inability of the Pawn to move backward strategically
harmonizes with its functions as a Corps of Position,
in contradiction to the movements of the pieces,
which latter are Corps of Evolution.
This restriction in the move of the Pawn is in exact
harmony with the inability of the Queen to move on
obliques, of the Rook to move on obliques or on diagonals,
of the Bishop to move on obliques, verticals and
horizontals, of the Knight to move on diagonals, verticals,
and horizontals, and of the King to move like any
other piece.
Possessed of the invaluable privilege of making the
first move in the game, knowing that no move should
be made without an object, understanding that the true
object of every move is to minimize the adverse power
for resistance and comprehending that all power for
resistance is derived from facility of movement, the
student easily deduces the true object of White’s initial
move in every game of Chess, viz.:
To make the first of a series of movements, each of which
shall increase the mobility of the kindred pieces and correspondingly
decrease the mobility of the adverse pieces.
As the effect of such policy, the power for resistance
appertaining to Black, ultimately must become so insufficient
that he no longer will be able adequately to
defend:
- 1. His base of operations.
- 2. The communications of his army with its base.
- 3. The communications of his corps d’armee with
each other, or,
- 4. To prevent the White hypothetical force penetrating
to its Logistic Horizon.
To produce this fatal weakness in the Black position
by the advantage of the first move is much easier for
White than commonly is supposed.
The process consists in making only those movements
by means of which the kindred corps d’armee, progressively
occupying specified objectives, are advanced,
viz.:
- I. To the Strategetic Objective, when acting against the
communications of the adverse Determinate Force and its
Base of Operations.
- II. To the Logistic Horizon, when acting against the
communications between the adverse Determinate and the
adverse Hypothetical Forces.
- III. To the Strategic Vertices, when acting against the
communications of the hostile corps d’armee with each other.
To bring about either of these results against an opponent
equally equipped and capable, of course is a
much more difficult task than to checkmate an enemy
incapable of movement.
Yet such achievement is possible to White and with
exact play it seemingly is a certainty that he succeeds in
one or the other, owing to his inestimable privilege of
first move.
For the normal advantage that attaches to the first
move in a game of Chess is vastly enhanced by a peculiarity
in the mathematical make-up of the surface of the
Chess-board, whereby, he who makes the first move may
secure to himself the advantage in mobility, and conversely
may inflict upon the second player a corresponding
disadvantage in mobility.
This peculiar property emanates from this fact:
The sixty-four points, i.e., the sixty-four centres of the
squares into which the surface of the Chess-board is divided,
constitute, when taken collectively, the quadrant of a circle,
whose radius is eight points in length.
Hence, in Chessic mathematics, the sides of the Chessboard
do not form a square, but the segment of a circumference.
To prove the truth of this, one has but to count the
points contained in the verticals and horizontals and in
the hypothenuse of each corresponding angle, and in
every instance it will be found that the number of points
contained in the base, perpendicular, and hypothenuse,
is the same.
For example:
Let the eight points of the King’s Rook’s file form the
perpendicular of a right angle triangle, of which the
kindred first horizontal forms the base; then, the hypothenuse
of the given angle, will be that diagonal which
extends from QR1 to KR8. Now, merely by the processes
of simple arithmetic, it may be shown that there
are,
- 1. Eight points in the base.
- 2. Eight points in the perpendicular.
- 3. Eight points in the hypothenuse.
Consequently the three sides of this given right angled
triangle are equal to each other, which is a geometric
impossibility.
Therefore, it is self-evident that there exists a mathematical
incongruity in the surface of the Chess-board.
That is, what to the eye seems a right angled triangle,
is in its relations to the movements of the Chess-pieces,
an equilateral triangle. Hence, the Chess-board, in its
relations to the pieces when the latter are at rest, properly
may be regarded as a great square sub-divided into sixty-four
smaller squares; but on the contrary, in those calculations
relating to the Chess-pieces in motion, the
Chess-board must be regarded as the quadrant of a circle
of eight points radius. The demonstration follows, viz.:
Connect by a straight line the points KR8 and QR8.
Connect by another straight line the points QR8 and
QR1. Connect each of the fifteen points through which
these lines pass with the point KR1, by means of lines
passing through the least number of points intervening.
Then the line KR8 and QR8 will represent the segment
of a circle of which latter the point KR1 is the center.
The lines KR1-KR8 and KR1-QR1 will represent the
sides of a quadrant contained in the given circle and
bounded by the given segment, and the lines drawn from
KR1 to the fifteen points contained in the given segment
of the given circumference, will be found to be fifteen
equal radii each eight points in length.
Having noted the form of the Static or positional surface
of the Chess-board and its relations to the pieces at
rest, and having established the configuration of the
Dynamic surface upon which the pieces move, it is next
in sequence to deduce that fundamental fact and to give
it that geometric expression which shall mathematically
harmonize these conflicting geometric figures in their
relations to Chess-play.
As the basic fact of applied Chessic forces, it is to be
noted, that:
The King is the SOURCE from whence the Chess-pieces
derive all power of movement; and from his ability to
move, emanates ALL power for attack and for defence
possessed by a Chessic army.
This faculty of mobility, derived from the existence of
the kindred King, is the all essential element in Chess-play,
and to increase the mobility of the kindred pieces
and to reduce that of the adverse pieces is the simple, sure
and only scientific road to victory; and by comparison
of the Static with the Dynamic surface of the Chess-board,
the desired principle readily is discovered, viz.,
The Static surface of the Chess-board being a square,
its least division is into two great right angled triangles
having a common hypothenuse.
The Dynamic surface being the quadrant of a circle,
its least division also is into two great sections, one of
which is a right angled triangle and the other a semi-circle.
Comparing the two surfaces of the Chess-board thus
divided, it will be seen that these three great right angled
triangles are equal, each containing thirty-six points;
and having for their common vertices, the points KR1,
QR1 and R8.
Furthermore, it will be seen that the hypothenuse
common to these triangles, also is the chord of that
semi-circle which appertains to the Dynamic surface.
Again, it will be perceived that this semi-circle, like
the three right angled triangles, is composed of thirty-six
points, and consequently that all of the four sub-divisions
of the Static and Dynamic surfaces of the Chess-board
are equal.
Thus it obviously follows, that:
- 1. The great central diagonal, always is one side of
each of the four chief geometric figures into which the
Chess board is divided; that:
- 2. It mathematically perfects each of these figures
and harmonizes each to all, and that:
- 3. By means of it each figure becomes possessed of
eight more points than it otherwise would contain.
Hence, the following is self-evident:
That Chessic army which can possess itself of the great
central diagonal, thereby acquires the larger number of
points upon which to act and consequently greater facilities
for movement; and conversely:
By the loss of the great central diagonal, the mobility of
the opposing army is correspondingly decreased.
It therefore is clear that the object of any series of
movements by a Chessic army acting otherwise than on
Line of Operations, should be:
Form the kindred army upon the hypothenuse of the right
angled triangle which is contained within the Dynamic surface
of the Chess-board; and conversely,
Compel the adverse army to act exclusively within that
semi-circle which appertains to the same surface.
Under these circumstances, the kindred corps will be
possessed of facilities for movement represented by thirty-six
squares; while the logistic area of the opposing army
will be restricted to twenty-eight squares.
There are, of course, two great central diagonals of the
Chess-board; but as the student is fully informed that
great central diagonal always is to be selected, which
extends towards the Objective Plane.
Mobility, per se, increases or decreases with the number
of squares open to occupation.
But in all situations there will be points of no value,
while other points are of value inestimable; for the reason
that the occupation of the former will not favorably affect
the play, or may even lose the game; while by the occupation
of the latter, victory is at once secured.
But it is not the province of Mobility to pass on the
values of points; this latter is the duty of Strategy. It is
sufficient for Mobility that it provide superior facilities
for movement; it is for Strategy to define the Line of
Movement; for Logistics, by means of this Line of
Movement, to bring into action in proper times and
sequence, the required force, and for Tactics, with this
force, to execute the proper evolutions.
Mobility derives its importance from three things
which may occur severally or in combination, viz.:
- 1. All power for offense or for defense is eliminated
from a Chess-piece the instant it loses its ability to move.
- 2. The superiority possessed by corps acting offensively
over adverse corps acting defensively, resides in
that the attack of a piece is valid at every point which it
menaces; while the defensive effort of a piece, as a rule,
is valid only at a single point. Consequently:
Increased facilities for movement enhance the power of
attacking pieces in a much greater degree than like facilities
enhance the power of defending pieces.
Such increasing facilities for movement ultimately
render an attacking force irresistible, for the reason that
it finally becomes a physical impossibility for the opposing
equal force to provide valid defences for the numerous
tactical keys, which at a given time become simultaneously
assailed. Hence:
Superior facilities for occupying any point at any time
and with any force, always ensure the superior force at a
given point, at a given time.
The relative advantage in mobility possessed by one
army over an opposing army always can be determined
by the following, viz.:
1. That army whose strategic front of operations is
established upon the Strategetic Center has the relative
advantage in Mobility.
2. To utilize the advantage in Mobility extend the
Strategic Front in the direction of the objective plane.
3. To neutralize the relative disadvantage in Mobility
eliminate that adverse Corps d’armee which tactically
expresses such adverse advantage; or so post the Prime
Strategetic Point as to vitiate the adverse Strategic front.
Advantage in Mobility is divided into two classes, viz.:
- I. General Advantage in Mobility.
- II. Special Advantage in Mobility.
A General Advantage in Mobility consists in the
ability to act simultaneously against two or more vital
points by means of interior logistic radii due to position
between:—
- 1. The adverse army and its Base of Operations.
- 2. Two or more adverse Grand Columns.
- 3. The wings of a hostile Grand Column.
- 4. Two or more isolated adverse Corps d’armee.
Such position upon interior lines of movement is
secured by occupying either of the Prime Offensive Origins,
i.e.:
- 1. Strategic Center vs. Adverse Formation in Mass.
- 2. Logistic Center vs. Adverse Formation by Grand
Columns.
- 3. Tactical Center vs. Adverse Formation by Wings.
- 4. Logistic Triune vs. Adverse Formation by Corps.
Special Advantage in Mobility consists in the ability
of a corps d’armee to traverse greater or equal distances
in lesser times than opposing corps.
“Never interrupt your enemy when he is making a
false movement.”—Napoleon.
In the year (366 B.C.) the King of Sparta, with an
army of 30,000 men marched to the aid of the Mantineans
against Thebes. Epaminondas took up a post with his
army from whence he equally threatened Mantinea and
Sparta. Agesilaus incautiously moved too far towards
the coast, whereupon Epaminondas, with 70,000 men
precipitated himself upon Lacedaemonia, laying waste
the country with fire and sword, all but taking by storm
the city of Sparta and showing the women of Lacedaemonia
the campfire of an enemy for the first time in six
hundred years.
Flaminius advancing incautiously to oppose Hannibal,
the latter took up a post with his army from whence he
equally threatened the city of Rome and the army of the
Consul. In the endeavor to rectify his error, the Roman
general committed a worse and was destroyed with his
entire army.
At Thapsus, April 6, 46 B.C., Caesar took up a post
with his army from whence he equally threatened the
Roman army under Scipio and the African army under
Juba. Scipio having marched off with his troops to a
better camp some miles distant, Caesar attacked and
annihilated Juba’s army.
At Pirna, Frederic the Great, captured the Saxon
army entire, and at Rossbach, Leuthern and Zorndorf
destroyed successively a French, an Austrian and a
Russian army merely by occupying a post from whence
he equally threatened two or more vital points, awaiting
the time when one would become inadequately defended.
Washington won the Revolutionary War merely by
occupying a post from whence he equally threatened the
British armies at New York and Philadelphia; refusing
battle and building up an army of Continental regular
troops enlisted for the war and trained by the Baron von
Steuben in the system of Frederic the Great.
Bonaparte won at Montenotte, Castiglione, Arcola,
Rivoli and Austerlitz his most perfect exhibitions of
generalship, merely by passively threatening two vital
points and in his own words: “By never interrupting an
enemy when he is making a false movement.”
Perfection in Mobility is attained whenever the
kindred army is able to act unrestrainedly in any and
all directions, while the movements of the hostile army
are restricted.
NUMBERS
“In warfare the advantage in numbers never is to be
despised.”—Von Moltke.
“Arguments avail but little against him whose opinion is
voiced by thirty legions.”—Roman Proverb.
“That king who has the most iron is master of those who
merely have the more gold.”—Solon.
“It never troubles the wolf how many sheep there are.”—Agesilaus.