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WALKING STICK MONOPOD : 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, walking stick monopod Achilles could never catch up with a tortoise he walking stick monopod 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 walking stick monopod has covered another one hundredth, and so on forever. This problem seemed to the ancients insoluble. The absurd answer walking stick monopod 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. walking stick monopod adopting smaller and
WALKING STICK MONOPOD : smaller elements of walking stick monopod we only approach a solution of the problem, but never reach it. Only when we have admitted the conception of the walking stick monopod 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. walking stick monopod 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. walking stick monopod modern branch of mathematics, unknown to the ancients, when dealing with problems of motion admits walking stick monopod 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
WALKING STICK MONOPOD : motion instead of examining continuous motion. walking stick monopod seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable arbitrary walking stick monopod wills, is continuous. To understand the laws of this continuous movement is the walking stick monopod 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 walking stick monopod to any event, for one event always flows uninterruptedly from another. The second method is to walking stick monopod 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
WALKING STICK MONOPOD : 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 walking stick monopod of many men is expressed by the actions of any one historic personage, is in itself false. It needs no critical exertion walking stick monopod reduce utterly to dust any deductions drawn from history. It is merely necessary to walking stick monopod some larger or smaller unit as the subject of observation- as criticism has every right to do, walking stick monopod that whatever unit history observes must always be arbitrarily selected. Only by taking infinitesimally small units for walking stick monopod (the differential of history, that is,
WALKING STICK MONOPOD : the individual tendencies of men) and attaining walking stick monopod 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 walking stick monopod 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 walking stick monopod walking stick monopod 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 walking stick monopod dozen men in a building in the city of Paris,
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