War And Peace: Book 11 - CHAPTER I

作者: Leo Tolstoy

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Author: 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.