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_ Absolute 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 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. _
Read next: Book Eleven: 1812: Chapter 2
Read previous: Book Ten: 1812: Chapter 39
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