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 influence of the buds. I see only a coincidence of occurrences such as happens with all the phenomena of life, and I see that however much and however carefully I observe the hands of the watch, and the valves and wheels of the engine, and the oak, I shall not discover the cause of the bells ringing, the engine moving, or of the winds of spring. To that I must entirely change my point of view and study the laws of the movement of steam, of the bells, and of the wind. History must do the same. And attempts in this direction have already been made.
To study the laws of history we must completely change the subject of our observation, must leave aside kings, ministers, and generals, and the common, infinitesimally small elements by which the masses are moved. No one can say in how far it is possible for man to advance in this way toward an understanding of the laws of history; but it is evident that only along that path does the possibility of discovering the laws of history lie, and that as yet not a millionth part as much mental effort has been applied in this direction by historians as has been devoted to describing the actions of various kings, commanders, and ministers and propounding the historians' own reflections concerning these actions.
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Book One: 1805 - Chapter XVIII
Book One: 1805 - Chapter XXIII
Book One: 1805 - Chapter XXVII
Book One: 1805 - Chapter XXVIII
Book Two: 1805 - Chapter XVIII
Book Three: 1805 - Chapter III
Book Three: 1805 - Chapter VII
Book Three: 1805 - Chapter VIII
Book Three: 1805 - Chapter XII
Book Three: 1805 - Chapter XIII
Book Three: 1805 - Chapter XIV
Book Three: 1805 - Chapter XVI
Book Three: 1805 - Chapter XVII
Book Three: 1805 - Chapter XVIII
Book Three: 1805 - Chapter XIX
Book Four: 1806 - Chapter VIII
Book Four: 1806 - Chapter XIII
Book Five: 1806-07 - Chapter I
Book Five: 1806-07 - Chapter II
Book Five: 1806-07 - Chapter III
Book Five: 1806-07 - Chapter IV
Book Five: 1806-07 - Chapter V
Book Five: 1806-07 - Chapter VI
Book Five: 1806-07 - Chapter VII
Book Five: 1806-07 - Chapter VIII
Book Five: 1806-07 - Chapter IX
Book Five: 1806-07 - Chapter X
Book Five: 1806-07 - Chapter XI
Book Five: 1806-07 - Chapter XII
Book Five: 1806-07 - Chapter XIII
Book Five: 1806-07 - Chapter XIV
Book Five: 1806-07 - Chapter XV
Book Five: 1806-07 - Chapter XVI
Book Five: 1806-07 - Chapter XVII
Book Five: 1806-07 - Chapter XVIII
Book Five: 1806-07 - Chapter XIX
Book Five: 1806-07 - Chapter XX
Book Five: 1806-07 - Chapter XXI
Book Five: 1806-07 - Chapter XXII
Book Six: 1808-10 - Chapter II
Book Six: 1808-10 - Chapter III
Book Six: 1808-10 - Chapter IV
Book Six: 1808-10 - Chapter VI
Book Six: 1808-10 - Chapter VII
Book Six: 1808-10 - Chapter VIII
Book Six: 1808-10 - Chapter IX
Book Six: 1808-10 - Chapter XI
Book Six: 1808-10 - Chapter XII
Book Six: 1808-10 - Chapter XIII
Book Six: 1808-10 - Chapter XIV
Book Six: 1808-10 - Chapter XV
Book Six: 1808-10 - Chapter XVI
Book Six: 1808-10 - Chapter XVII
Book Six: 1808-10 - Chapter XVIII
Book Six: 1808-10 - Chapter XIX
Book Six: 1808-10 - Chapter XX
Book Six: 1808-10 - Chapter XXI
Book Six: 1808-10 - Chapter XXII
Book Six: 1808-10 - Chapter XXIII
Book Six: 1808-10 - Chapter XXIV
Book Six: 1808-10 - Chapter XXV
Book Six: 1808-10 - Chapter XXVI
Book Seven: 1810-11 - Chapter I
Book Seven: 1810-11 - Chapter II
Book Seven: 1810-11 - Chapter III
Book Seven: 1810-11 - Chapter IV
Book Seven: 1810-11 - Chapter V
Book Seven: 1810-11 - Chapter VI
Book Seven: 1810-11 - Chapter VII
Book Seven: 1810-11 - Chapter VIII
Book Seven: 1810-11 - Chapter IX
Book Seven: 1810-11 - Chapter X
Book Seven: 1810-11 - Chapter XI
Book Seven: 1810-11 - Chapter XII
Book Seven: 1810-11 - Chapter XIII
Book Eight: 1811-12 - Chapter I
Book Eight: 1811-12 - Chapter II
Book Eight: 1811-12 - Chapter III
Book Eight: 1811-12 - Chapter IV
Book Eight: 1811-12 - Chapter V
Book Eight: 1811-12 - Chapter VI
Book Eight: 1811-12 - Chapter VII
Book Eight: 1811-12 - Chapter VIII
Book Eight: 1811-12 - Chapter IX
Book Eight: 1811-12 - Chapter X
Book Eight: 1811-12 - Chapter XI
Book Eight: 1811-12 - Chapter XII
Book Eight: 1811-12 - Chapter XIII
Book Eight: 1811-12 - Chapter XIV
Book Eight: 1811-12 - Chapter XV
Book Eight: 1811-12 - Chapter XVI
Book Eight: 1811-12 - Chapter XVII
Book Eight: 1811-12 - Chapter XVIII
Book Eight: 1811-12 - Chapter XIX
Book Eight: 1811-12 - Chapter XX
Book Eight: 1811-12 - Chapter XXI
Book Eight: 1811-12 - Chapter XXII
Book Nine: 1812 - Chapter VIII
Book Nine: 1812 - Chapter XIII
Book Nine: 1812 - Chapter XVII
Book Nine: 1812 - Chapter XVIII
Book Nine: 1812 - Chapter XXII
Book Nine: 1812 - Chapter XXIII
Book Ten: 1812 - Chapter XVIII
Book Ten: 1812 - Chapter XXIII
Book Ten: 1812 - Chapter XXVII
Book Ten: 1812 - Chapter XXVIII
Book Ten: 1812 - Chapter XXXII
Book Ten: 1812 - Chapter XXXIII
Book Ten: 1812 - Chapter XXXIV
Book Ten: 1812 - Chapter XXXVI
Book Ten: 1812 - Chapter XXXVII
Book Ten: 1812 - Chapter XXXVIII
Book Ten: 1812 - Chapter XXXIX
Book Eleven: 1812 - Chapter II
Book Eleven: 1812 - Chapter III
Book Eleven: 1812 - Chapter IV
Book Eleven: 1812 - Chapter VI
Book Eleven: 1812 - Chapter VII
Book Eleven: 1812 - Chapter VIII
Book Eleven: 1812 - Chapter IX
Book Eleven: 1812 - Chapter XI
Book Eleven: 1812 - Chapter XII
Book Eleven: 1812 - Chapter XIII
Book Eleven: 1812 - Chapter XIV
Book Eleven: 1812 - Chapter XV
Book Eleven: 1812 - Chapter XVI
Book Eleven: 1812 - Chapter XVII
Book Eleven: 1812 - Chapter XVIII
Book Eleven: 1812 - Chapter XIX
Book Eleven: 1812 - Chapter XX
Book Eleven: 1812 - Chapter XXI
Book Eleven: 1812 - Chapter XXII
Book Eleven: 1812 - Chapter XXIII
Book Eleven: 1812 - Chapter XXIV
Book Eleven: 1812 - Chapter XXV
Book Eleven: 1812 - Chapter XXVI
Book Eleven: 1812 - Chapter XXVII
Book Eleven: 1812 - Chapter XXVIII
Book Eleven: 1812 - Chapter XXIX
Book Eleven: 1812 - Chapter XXX
Book Eleven: 1812 - Chapter XXXI
Book Eleven: 1812 - Chapter XXXII
Book Eleven: 1812 - Chapter XXXIII
Book Eleven: 1812 - Chapter XXXIV
Book Twelve: 1812 - Chapter II
Book Twelve: 1812 - Chapter III
Book Twelve: 1812 - Chapter IV
Book Twelve: 1812 - Chapter VI
Book Twelve: 1812 - Chapter VII
Book Twelve: 1812 - Chapter VIII
Book Twelve: 1812 - Chapter IX
Book Twelve: 1812 - Chapter XI
Book Twelve: 1812 - Chapter XII
Book Twelve: 1812 - Chapter XIII
Book Twelve: 1812 - Chapter XIV
Book Twelve: 1812 - Chapter XV
Book Twelve: 1812 - Chapter XVI
Book Thirteen: 1812 - Chapter I
Book Thirteen: 1812 - Chapter II
Book Thirteen: 1812 - Chapter III
Book Thirteen: 1812 - Chapter IV
Book Thirteen: 1812 - Chapter V
Book Thirteen: 1812 - Chapter VI
Book Thirteen: 1812 - Chapter VII
Book Thirteen: 1812 - Chapter VIII
Book Thirteen: 1812 - Chapter IX
Book Thirteen: 1812 - Chapter X
Book Thirteen: 1812 - Chapter XI
Book Thirteen: 1812 - Chapter XII
Book Thirteen: 1812 - Chapter XIII
Book Thirteen: 1812 - Chapter XIV
Book Thirteen: 1812 - Chapter XV
Book Thirteen: 1812 - Chapter XVI
Book Thirteen: 1812 - Chapter XVII
Book Thirteen: 1812 - Chapter XVIII
Book Thirteen: 1812 - Chapter XIX
Book Fourteen: 1812 - Chapter I
Book Fourteen: 1812 - Chapter II
Book Fourteen: 1812 - Chapter III
Book Fourteen: 1812 - Chapter IV
Book Fourteen: 1812 - Chapter V
Book Fourteen: 1812 - Chapter VI
Book Fourteen: 1812 - Chapter VII
Book Fourteen: 1812 - Chapter VIII
Book Fourteen: 1812 - Chapter IX
Book Fourteen: 1812 - Chapter X
Book Fourteen: 1812 - Chapter XI
Book Fourteen: 1812 - Chapter XII
Book Fourteen: 1812 - Chapter XIII
Book Fourteen: 1812 - Chapter XIV
Book Fourteen: 1812 - Chapter XV
Book Fourteen: 1812 - Chapter XVI
Book Fourteen: 1812 - Chapter XVII
Book Fourteen: 1812 - Chapter XVIII
Book Fourteen: 1812 - Chapter XIX
Book Fifteen: 1812-13 - Chapter I
Book Fifteen: 1812-13 - Chapter II
Book Fifteen: 1812-13 - Chapter III
Book Fifteen: 1812-13 - Chapter IV
Book Fifteen: 1812-13 - Chapter V
Book Fifteen: 1812-13 - Chapter VI
Book Fifteen: 1812-13 - Chapter VII
Book Fifteen: 1812-13 - Chapter VIII
Book Fifteen: 1812-13 - Chapter IX
Book Fifteen: 1812-13 - Chapter X
Book Fifteen: 1812-13 - Chapter XI
Book Fifteen: 1812-13 - Chapter XII
Book Fifteen: 1812-13 - Chapter XIII
Book Fifteen: 1812-13 - Chapter XIV
Book Fifteen: 1812-13 - Chapter XV
Book Fifteen: 1812-13 - Chapter XVI
Book Fifteen: 1812-13 - Chapter XVII
Book Fifteen: 1812-13 - Chapter XVIII
Book Fifteen: 1812-13 - Chapter XIX
Book Fifteen: 1812-13 - Chapter XX
First Epilogue: 1813-20 - Chapter I
First Epilogue: 1813-20 - Chapter II
First Epilogue: 1813-20 - Chapter III
First Epilogue: 1813-20 - Chapter IV
First Epilogue: 1813-20 - Chapter V
First Epilogue: 1813-20 - Chapter VI
First Epilogue: 1813-20 - Chapter VII
First Epilogue: 1813-20 - Chapter VIII
First Epilogue: 1813-20 - Chapter IX
First Epilogue: 1813-20 - Chapter X
First Epilogue: 1813-20 - Chapter XI
First Epilogue: 1813-20 - Chapter XII
First Epilogue: 1813-20 - Chapter XIII
First Epilogue: 1813-20 - Chapter XIV
First Epilogue: 1813-20 - Chapter XV
First Epilogue: 1813-20 - Chapter XVI
Second Epilogue: 1813-20 - Chapter I
Second Epilogue: 1813-20 - Chapter II
Second Epilogue: 1813-20 - Chapter III
Second Epilogue: 1813-20 - Chapter IV
Second Epilogue: 1813-20 - Chapter V
Second Epilogue: 1813-20 - Chapter VI
Second Epilogue: 1813-20 - Chapter VII
Second Epilogue: 1813-20 - Chapter VIII
Second Epilogue: 1813-20 - Chapter IX
Second Epilogue: 1813-20 - Chapter X