《War And Peace》 Book11 CHAPTER I
by Leo Tolstoy
FOR THE HUMAN MIND the absolute continuity of motion is inconceivable. The
laws of motion of any kind only become comprehensible to man when he examines
units of this motion, arbitrarily selected. But at the same time it is from this
arbitrary division of continuous motion into discontinuous units that a GREat
number of human errors proceeds.
We all know the so-called sophism of the ancients, proving that Achilles
would never overtake the tortoise, though Achilles walked ten times as fast as
the tortoise. As soon as Achilles passes over the space separating him from the
tortoise, the tortoise advances one-tenth of that space: Achilles passes over
that tenth, but the tortoise has advanced a hundredth, and so on to infinity.
This problem seemed to the ancients insoluble. The irrationality of the
conclusion (that Achilles will never overtake the tortoise) arises from the
arbitrary assumption of disconnected units of motion, when the motion both of
Achilles and the tortoise was continuous.
By taking smaller and smaller units of motion we merely approach the solution
of the problem, but we never attain it. It is only by assuming an infinitely
small magnitude, and a proGREssion rising from it up to a tenth, and taking the
sum of that geometrical progression, that we can arrive at the solution of the
problem. A new branch of mathematics, dealing with infinitely small quantities,
gives now in other more complex problems of dynamics solutions of problems that
seemed insoluble.
This new branch of mathematics, unknown to the ancients, by assuming
infinitely small quantities, that is, such as secure the chief condition of
motion (absolute continuity), corrects the inevitable error which the human
intellect cannot but make, when it considers disconnected units of motion
instead of continuous motion.
In the investigation of the laws of historical motion precisely the same
mistake arises.
The proGREss of humanity, arising from an innumerable multitude of individual
wills, is continuous in its motion.
The discovery of the laws of this motion is the aim of history. But in order
to arrive at the laws of the continuous motion due to the sum of all these
individual wills, the human mind assumes arbitrary, disconnected units. The
first proceeding of the historian is taking an arbitrary series of continuous
events to examine it apart from others, while in reality there is not, and
cannot be, a beginning to any event, but one event flows without any break in
continuity from another. The second proceeding is to examine the action of a
single person, a sovereign, or a general, as though it were equivalent to the
sum of many individual wills, though the sum of individual wills never finds
expression in the action of a single historical personage.
Historical science as it advances is continually taking smaller and smaller
units for analysis, and in this way strives to approximate the truth. But
however small the units of which history takes cognisance, we feel that the
assumption of a unit, disconnected from another, the assumption of a
beginning of any phenomenon, and the assumption that the individual wills
of all men find expression in the actions of a single historical personage are
false in themselves.
Every conclusion of history can, without the slightest effort on the part of
the critic, be dissipated like dust, leaving no trace, simply through criticism
selecting, as the object of its analysis, a GREater or smaller disconnected
unit, which it has a perfect right to do, seeing that the unit of history is
always selected arbitrarily.
Only by assuming an infinitely small unit for observation—a differential of
history—that is, the homogeneous tendencies of men, and arriving at the integral
calculus (that is, taking the sum of those infinitesimal quantities), can we
hope to arrive at the laws of history.
The first fifteen years of the nineteenth century present the spectacle of an
extraordinary movement of millions of men. Men leave their habitual pursuits;
rush from one side of Europe to the other; plunder, slaughter one another,
triumph and despair; and the whole current of life is transformed and presents a
quickened activity, first moving at a growing speed, and then slowly slackening
again. What was the cause of that activity, or from what laws did it arise? asks
the human intellect.
The historians, in reply to that inquiry, lay before us the sayings and
doings of some dozens of men in one of the buildings of the city of Paris,
summing up those doings and sayings by one word—revolution. Then they give us a
detailed biography of Napoleon, and of certain persons favourably or hostilely
disposed to him; talk of the influence of some of these persons upon others; and
then say that this it is to which that activity is due, and these are its
laws.
But the human intellect not only refuses to believe in that explanation, but
flatly declares that the method of explanation is not a correct one, because in
this explanation a smaller phenomenon is taken as the cause of a GREater
phenomenon. The sum of men's individual wills produced both the revolution and
Napoleon; and only the sum of those wills endured them and then destroyed
them.
“But whenever there have been wars, there have been GREat military leaders;
whenever there have been revolutions in states, there have been great men,” says
history. “Whenever there have been great military leaders there have, indeed,
been wars,” replies the human reason; “but that does not prove that the generals
were the cause of the wars, and that the factors leading to warfare can be found
in the personal activity of one man.”
Whenever, looking at my watch, I see the hand has reached the figure x, I
hear the bells beginning to ring in the church close by. But from the fact that
the watch hand points to ten whenever the bells begin to ring, I have not the
right to infer that the position of the hands of my watch is the cause of the
vibration of the bells.
Whenever I see a steam-engine move, I hear the whistle, I see the valve open
and the wheels turn; but I have no right to conclude from that that the whistle
and the turning of the wheels are the causes of the steam-engine's moving.
The peasants say that in the late spring a cold wind blows because the
oak-buds are opening, and, as a fact, a cold wind does blow every spring when
the oak is coming out. But though the cause of a cold wind's blowing just when
the oaks are coming out is unknown to me, I cannot aGREe with the peasants that
the cause of the cold wind is the opening of the oak-buds, because the force of
the wind is altogether outside the influence of the buds. I see in this simply
such a coincidence of events as is common in every phenomenon of life, and I see
that however long and minutely I might examine the watch hand, the valve, and
the wheel of the steam-engine and the oak-bud, I shall not discover the cause of
the bells ringing, of the steam-engine moving, and of the spring wind. To do
that I must completely change my point of observation and study the laws of the
motion of steam, of the bells, and of the wind. History must do the same. And
efforts have already been made in this direction.
For the investigation of the laws of history, we must completely change the
subject of observations, must let kings and ministers and generals alone, and
study the homogeneous, infinitesimal elements by which masses are led. No one
can say how far it has been given to man to advance in that direction in
understanding of the laws of history. But it is obvious that only in that
direction lies any possibility of discovering historical laws; and that the
human intellect has hitherto not devoted to that method of research one
millionth part of the energy that historians have put into the description of
the doings of various kings, ministers, and generals, and the exposition of
their own views on those doings.
