Book Eleven: 1812 - Chapter I

by Leo Tolstoy

　　Absolute continuity of motion is not comprehensible to the humanmind. Laws of motion of any kind become comprehensible to man onlywhen he examines arbitrarily selected elements of that motion; butat the same time, a large proportion of human error comes from thearbitrary division of continuous motion into discontinuous elements.There is a well known, so-called sophism of the ancients consisting inthis, that Achilles could never catch up with a tortoise he wasfollowing, in spite of the fact that he traveled ten times as fastas the tortoise. By the time Achilles has covered the distance thatseparated him from the tortoise, the tortoise has covered one tenth ofthat 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 (thatAchilles could never overtake the tortoise) resulted from this: thatmotion was arbitrarily divided into discontinuous elements, whereasthe motion both of Achilles and of the tortoise was continuous.

　　By adopting smaller and smaller elements of motion we onlyapproach a solution of the problem, but never reach it. Only when wehave admitted the conception of the infinitely small, and theresulting geometrical progression with a common ratio of one tenth,and have found the sum of this progression to infinity, do we reacha solution of the problem.

　　A modern branch of mathematics having achieved the art of dealingwith the infinitely small can now yield solutions in other morecomplex problems of motion which used to appear insoluble.

　　This modern branch of mathematics, unknown to the ancients, whendealing with problems of motion admits the conception of theinfinitely small, and so conforms to the chief condition of motion(absolute continuity) and thereby corrects the inevitable errorwhich the human mind cannot avoid when it deals with separate elementsof motion instead of examining continuous motion.

　　In seeking the laws of historical movement just the same thinghappens. The movement of humanity, arising as it does from innumerablearbitrary human wills, is continuous.

　　To understand the laws of this continuous movement is the aim ofhistory. But to arrive at these laws, resulting from the sum of allthose human wills, man's mind postulates arbitrary and disconnectedunits. The first method of history is to take an arbitrarilyselected series of continuous events and examine it apart from others,though there is and can be no beginning to any event, for one eventalways flows uninterruptedly from another.

　　The second method is to consider the actions of some one man- a kingor a commander- as equivalent to the sum of many individual wills;whereas the sum of individual wills is never expressed by the activityof a single historic personage.

　　Historical science in its endeavor to draw nearer to truthcontinually takes smaller and smaller units for examination. Buthowever small the units it takes, we feel that to take any unitdisconnected from others, or to assume a beginning of anyphenomenon, or to say that the will of many men is expressed by theactions of any one historic personage, is in itself false.

　　It needs no critical exertion to reduce utterly to dust anydeductions drawn from history. It is merely necessary to select somelarger or smaller unit as the subject of observation- as criticism hasevery right to do, seeing that whatever unit history observes mustalways be arbitrarily selected.

　　Only by taking infinitesimally small units for observation (thedifferential of history, that is, the individual tendencies of men)and attaining to the art of integrating them (that is, finding the sumof these infinitesimals) can we hope to arrive at the laws of history.

　　The first fifteen years of the nineteenth century in Europepresent an extraordinary movement of millions of people. Men leavetheir 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 anintensive movement which first increases and then slackens. What wasthe cause of this movement, by what laws was it governed? asks themind of man.

　　The historians, replying to this question, lay before us the sayingsand doings of a few dozen men in a building in the city of Paris,calling these sayings and doings "the Revolution"; then they give adetailed biography of Napoleon and of certain people favorable orhostile to him; tell of the influence some of these people had onothers, and say: that is why this movement took place and those areits 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, andonly the sum of those wills first tolerated and then destroyed them.

　　"But every time there have been conquests there have beenconquerors; every time there has been a revolution in any statethere have been great men," says history. And, indeed, human reasonreplies: every time conquerors appear there have been wars, but thisdoes not prove that the conquerors caused the wars and that it ispossible to find the laws of a war in the personal activity of asingle man. Whenever I look at my watch and its hands point to ten,I hear the bells of the neighboring church; but because the bellsbegin to ring when the hands of the clock reach ten, I have no rightto assume that the movement of the bells is caused by the positionof the hands of the watch.

　　Whenever I see the movement of a locomotive I hear the whistle andsee the valves opening and wheels turning; but I have no right toconclude that the whistling and the turning of wheels are the cause ofthe movement of the engine.

　　The peasants say that a cold wind blows in late spring because theoaks are budding, and really every spring cold winds do blow whenthe oak is budding. But though I do not know what causes the coldwinds to blow when the oak buds unfold, I cannot agree with thepeasants that the unfolding of the oak buds is the cause of the coldwind, for the force of the wind is beyond the influence of the buds. Isee only a coincidence of occurrences such as happens with all thephenomena of life, and I see that however much and however carefully Iobserve the hands of the watch, and the valves and wheels of theengine, and the oak, I shall not discover the cause of the bellsringing, the engine moving, or of the winds of spring. To that Imust entirely change my point of view and study the laws of themovement of steam, of the bells, and of the wind. History must dothe same. And attempts in this direction have already been made.

　　To study the laws of history we must completely change the subjectof our observation, must leave aside kings, ministers, and generals,and the common, infinitesimally small elements by which the masses aremoved. No one can say in how far it is possible for man to advancein this way toward an understanding of the laws of history; but itis evident that only along that path does the possibility ofdiscovering the laws of history lie, and that as yet not a millionthpart as much mental effort has been applied in this direction byhistorians as has been devoted to describing the actions of variouskings, commanders, and ministers and propounding the historians' ownreflections concerning these actions.