By Jill Russell,2014-11-27 12:23
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     BOOK ELEVEN: 1812


     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 inf