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War And Peace 492


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mighty arm being stricken powerless, but all the generals and soldiers of his army whether they had taken part in the battle or not, after all their experience of previous battles--when after one tenth of such efforts the enemy had fled--experienced a similar feeling of terror before an enemy who, after losing HALF his men, stood as threateningly at the end as at the beginning of the battle. The moral force of the attacking French army was exhausted. Not that sort of victory which is defined by the capture of pieces of material fastened to sticks, called standards, and of the ground on which the troops had stood and were standing, but a moral victory that convinces the enemy of the moral superiority of his opponent and of his own impotence was gained by the Russians at Borodino. The French invaders, like an infuriated animal that has in its onslaught received a mortal wound, felt that they were perishing, but could not stop, any more than the Russian army, weaker by one half, could help swerving. By impetus gained, the French army was still able to roll forward to Moscow, but there, without further effort on the part of the Russians, it had to perish, bleeding from the mortal wound it had received at Borodino. The direct consequence of the battle of Borodino was Napoleons senseless flight from Moscow, his retreat along the old Smolensk road, the destruction of the invading army of five hundred thousand men, and the downfall of Napoleonic France, on which at Borodino for the first time the hand of an opponent of stronger spirit had been laid. 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, mans 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

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