War and Peace

bsolute continuity of motion is not comprehensible to the human mind.
Laws of motion of any kind become comprehensible to man only when he
examines arbitrarily selected elements of that motion; but at the
same time, a large proportion of human error comes from the arbitrary
division of continuous motion into discontinuous elements. There is a
well-known, so-called sophism of the ancients consisting in this, that
Achilles could never catch up with a tortoise he was following, in spite
of the fact that he traveled ten times as fast as the tortoise. By
the time Achilles has covered the distance that separated him from the
tortoise, the tortoise has covered one tenth of that distance ahead
of him: when Achilles has covered that tenth, the tortoise has covered
another one hundredth, and so on forever. This problem seemed to
the ancients insoluble. The absurd answer (that Achilles could never
overtake the tortoise) resulted from this: that motion was arbitrarily
divided into discontinuous elements, whereas the motion both of Achilles
and of the tortoise was continuous.

By adopting smaller and smaller elements of motion we only approach a
solution of the problem, but never reach it. Only when we have admitted
the conception of the infinitely small, and the resulting geometrical
progression with a common ratio of one tenth, and have found the sum of
this progression to infinity, do we reach a solution of the problem.

A modern branch of mathematics having achieved the art of dealing with
the infinitely small can now yield solutions in other more complex
problems of motion which used to appear insoluble.

This modern branch of mathematics, unknown to the ancients, when dealing
with problems of motion admits the conception of the infinitely small,
and so conforms to the chief condition of motion (absolute continuity)
and thereby corrects the inevitable error which the human mind cannot
avoid when it deals with separate elements of motion instead of
examining continuous motion.

In seeking the laws of historical movement just the same thing happens.
The movement of humanity, arising as it does from innumerable arbitrary
human wills, is continuous.

To understand the laws of this continuous movement is the aim of
history. But to arrive at these laws, resulting from the sum of all
those human wills, man’s mind postulates arbitrary and disconnected
units. The first method of history is to take an arbitrarily selected
series of continuous events and examine it apart from others, though
there is and can be no beginning to any event, for one event always
flows uninterruptedly from another.

The second method is to consider the actions of some one man—a king or a
commander—as equivalent to the sum of many individual wills; whereas the
sum of individual wills is never expressed by the activity of a single
historic personage.

Historical science in its endeavor to draw nearer to truth continually
takes smaller and smaller units for examination. But however small the
units it takes, we feel that to take any unit disconnected from others,
or to assume a beginning of any phenomenon, or to say that the will of
many men is expressed by the actions of any one historic personage, is
in itself false.

It needs no critical exertion to reduce utterly to dust any deductions
drawn from history. It is merely necessary to select some larger or
smaller unit as the subject of observation—as criticism has every
right to do, seeing that whatever unit history observes must always be
arbitrarily selected.

Only by taking infinitesimally small units for observation (the
differential of history, that is, the individual tendencies of men) and
attaining to the art of integrating them (that is, finding the sum of
these infinitesimals) can we hope to arrive at the laws of history.

The first fifteen years of the nineteenth century in Europe present an
extraordinary movement of millions of people. Men leave their customary
pursuits, hasten from one side of Europe to the other, plunder and
slaughter one another, triumph and are plunged in despair, and for some
years the whole course of life is altered and presents an intensive
movement which first increases and then slackens. What was the cause of
this movement, by what laws was it governed? asks the mind of man.

The historians, replying to this question, lay before us the sayings and
doings of a few dozen men in a building in the city of Paris, calling
these sayings and doings “the Revolution”; then they give a detailed
biography of Napoleon and of certain people favorable or hostile to him;
tell of the influence some of these people had on others, and say: that
is why this movement took place and those are its laws.

But the mind of man not only refuses to believe this explanation, but
plainly says that this method of explanation is fallacious, because in
it a weaker phenomenon is taken as the cause of a stronger. The sum of
human wills produced the Revolution and Napoleon, and only the sum of
those wills first tolerated and then destroyed them.

“But every time there have been conquests there have been conquerors;
every time there has been a revolution in any state there have been
great men,” says history. And, indeed, human reason replies: every time
conquerors appear there have been wars, but this does not prove that the
conquerors caused the wars and that it is possible to find the laws of
a war in the personal activity of a single man. Whenever I look at my
watch and its hands point to ten, I hear the bells of the neighboring
church; but because the bells begin to ring when the hands of the clock
reach ten, I have no right to assume that the movement of the bells is
caused by the position of the hands of the watch.

Whenever I see the movement of a locomotive I hear the whistle and see
the valves opening and wheels turning; but I have no right to conclude
that the whistling and the turning of wheels are the cause of the
movement of the engine.

The peasants say that a cold wind blows in late spring because the oaks
are budding, and really every spring cold winds do blow when the oak
is budding. But though I do not know what causes the cold winds to blow
when the oak buds unfold, I cannot agree with the peasants that the
unfolding of the oak buds is the cause of the cold wind, for the
force of the wind is beyond the influence of the buds. I see only a
coincidence of occurrences such as happens with all the phenomena of
life, and I see that however much and however carefully I observe the
hands of the watch, and the valves and wheels of the engine, and the
oak, I shall not discover the cause of the bells ringing, the engine
moving, or of the winds of spring. To that I must entirely change my
point of view and study the laws of the movement of steam, of the
bells, and of the wind. History must do the same. And attempts in this
direction have already been made.

To study the laws of history we must completely change the subject of
our observation, must leave aside kings, ministers, and generals, and
study the common, infinitesimally small elements by which the masses are
moved. No one can say in how far it is possible for man to advance
in this way toward an understanding of the laws of history; but it is
evident that only along that path does the possibility of discovering
the laws of history lie, and that as yet not a millionth part as much
mental effort has been applied in this direction by historians as has
been devoted to describing the actions of various kings, commanders,
and ministers and propounding the historians’ own reflections concerning
these actions.