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War and Peace

by Leo Tolstoy/Tolstoi

BOOK ELEVEN: 1812

CHAPTER I

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

by Leo Tolstoy/Tolstoi

BOOK ELEVEN: 1812

CHAPTER I

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

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