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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.
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