WAR AND PEACE

CHAPTER I

" HE human intellect cannot grasp the idea of ab

solutely uninterrupted motion. Man can begin

to understand the laws of any kind of motion only when

he takes into consideration arbitrarily selected units of

such motion . But at the same time from this arbitrary

division of unbroken motion into measurable units flows

the greater part of human errors.

Take, for instance, the so- called " sophism " of the

ancients, to prove that Achilles would never overtake a

tortoise which had the start of him, even though Achilles

ran ten times more swiftly than the tortoise. As soon

as Achilles had passed over the distance between them ,

the tortoise would have advanced one-tenth of that dis

tance ; Achilles runs that tenth , the tortoise advances a

hundredth, and so on ad infinitum .

This problem seemed to the ancients unsolvable. The

fallacy of the reasoning that Achilles would never over

take the tortoise arose from this : simply, that inter

mitted units of motions were arbitrarily taken for

granted, whereas the motion of Achilles and the tor

toise were continuous.

By assuming ever smaller and smaller units of motion,

we only approach the settlement of this question, we

never really attain to it . Only by assuming infinitesi

mal quantities, and the progression up to one-tenth, and

by taking the sum of this geometrical progression, can we

attain the solution of the question. The new branch of

Mathematics which is the science of reckoning with in

finitesimals enables us to deal with still more compli

cated problems of motion, and solves problems which to

the ancients seemed unanswerable.

This new branch of mathematics, which was unknown

to the ancients, and applies so admirably to the problems

of motion, by admitting infinitesimally small quantities,

---that is, those by which the principal condition of

motion is reëstablished, -- namely, absolute continuity,

in itself corrects the inevitable error which the human

mind is bound to make when it contemplates the sepa

rate units of motion instead of continuous motion .

In searching for the laws of historical movements

precisely the same things must be observed . The prog

ress of humanity, arising from an infinite collection of

human wills, is continuous.

The apprehension of the laws of this onward march

is the aim of history.

But in order to discover the laws of continuous motion

in the sum of all the volitions of men, human reason

assumes arbitrary and separate units. History first

studies an arbitrary series of uninterrupted events,

and contemplates it separate from the others, albeit there

is and can be no beginning of an event, but every event

is the direct outgrowth of its predecessor.

Secondly, history studies the deeds of a single man,

a tsar, a colonel, as representing the sum of men's voli

tions, when in reality the sum of men's volitions is

never expressed in the activities of any one historical

personage.

The science of history is constantly taking ever

smaller and smaller units for study, and in this way

strives to reach the truth . But, however small the

units which history takes, we feel that the assumption

of any unit separate from another, the assumption of a

beginning of any phenomenon whatever, and the assump

tion that the volitions of all men are expressed in the

actions of any historical character, must be false per se .

Every deduction of history falls to pieces, like powder,

without the slightest effort on the part of criticism, leaving

nothing behind it , simply in consequence of the fact

that the criticism chooses as the object of its observa

tion a more or less interrupted unit ; and it has always

the right to do this, since every historical unit is always

arbitrary.

Only by assuming the infinitesimal unit for our obser

vation, -as the differential of history, —in other words,

the homogeneous tendencies of men, and by attaining

the art of integrating (calculating the sum of these

infinitesimal differentials ), can we expect to attain to

the laws of history.

The first fifteen years of the nineteenth century in

Europe exhibit an extraordinary movement of millions

of men. Men abandon their ordinary vocations, rush

from one end of Europe to the other, rob, slaughter

one another ; they are filled with triumph and with

despair, and the whole course of their lives is for a

number of years changed, and undergoes a powerful

movement, which at first goes on increasing and then slackens.

" What is the cause of this movement, or by what

laws did it take place ? " asks the human mind.

The historians, replying to this question , bring to our

notice certain acts and speeches of certain dozens of

men, in one of the buildings of the city of Paris, and

call these acts and speeches " the Revolution " ; then

they give a circumstantial account of Napoleon, and of

certain sympathizers and enemies of his, tell about the

influence which certain of these individuals had upon

the others, and they say :

" This was the cause of this movement, and here are

its laws."

But the human mind not only refuses to put credence

in this explanation , but declares, up and down, that this

manner of explanation is fallacious, for the reason that,

according to it, a feeble phenomenon is taken as the

cause of a mighty one. The sum of human volitions pro

duced both the Revolution and Napoleon , and only the

sum of these volitions sustained them and destroyed them .

" But in every case where there have been conquests

there have been conquerors ; in every case where there

have been revolutions in a kingdom there have been

great men ," says history.

• Indeed, in every case where conquerors have ap

peared, there have been wars," replies human reason ;

but this does not prove that the conquerors were the

cause of the wars, or that it is possible to discover the

laws of war in the personal activity of a single man.

In every case when I , looking at my watch, observe

that the hand points at ten , I hear the bells ringing in

the neighboring church ; but from the fact that in every

case when the hand reaches ten o'clock, the ringing of

the bells begins, I have no right to draw the conclusion

that the position of the hands is the cause of the motion in

the bells.

Every time when I observe an engine in motion, I

hear the sound of the whistle, I see the valves open and

the wheels in motion ; but from this I have no right to

conclude that the whistle and the movement of the

wheels are the cause of the movement of the engine.

The peasants say that in late spring the cold wind

blows because the oak tree is budding, and it is a fact

that every spring a cold wind blows when the oaks are

in bloom . But, although the cause of the cold wind

blowing during the blossoming-time of the oaks is un

known to me, I am unable to agree with the peasants in

attributing the cause of the cold winds to the bur

geoning buds on the oaks, for the reason that the force

of the wind is wholly outside the influence of the oak

buds. I see only a coincidence of conditions, which is

found in all the phenomena of life, and I see that, no

matter how carefully I may contemplate the hands of the

watch, the valves and wheels of the engine, and the

oak buds, I shall never learn the cause that makes the

church -bell chime, the engine to move, and the wind to

blow in the spring. To discover this, I must entirely change

my point of view, and study the laws that regu

late steam, bells, and the wind.

History must do the same thing

And experiments in this have already been made.

For, studying the laws of history, we must absolutely

change the objects of our observation, leave kings, min

isters, and generals out of the account, and select for

study the homogeneous, infinitesimal elements that reg

ulate the masses. No one can say how far it is given

to man to attain by this path an understanding of the

laws of history ; but evidently on this path only is there

any possibility of grasping the laws of history, and the

human intellect has not, so far, devoted to this method

the one-millionth part of the energies that have been

expended by historians in the description of the deeds

of individual tsars, colonels, and ministers, and in the

elucidation of their combinations, resulting from these

deeds.