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To the men of both sides alike, worn out by want of food and rest, it began equally to appear doubtful whether they should continue to slaughter one another; all the faces expressed hesitation, and the question arose in every soul: “For what, for whom, must I kill and be killed?... You may go and kill whom you please, but I don’t want to do so any more!” By evening this thought had ripened in every soul. At any moment these men might have been seized with horror at what they were doing and might have thrown up everything and run away anywhere.
But though toward the end of the battle the men felt all the horror of what they were doing, though they would have been glad to leave off, some incomprehensible, mysterious power continued to control them, and they still brought up the charges, loaded, aimed, and applied the match, though only one artilleryman survived out of every three, and though they stumbled and panted with fatigue, perspiring and stained with blood and powder. The cannon balls flew just as swiftly and cruelly from both sides, crushing human bodies, and that terrible work which was not done by the will of a man but at the will of Him who governs men and worlds continued.
Anyone looking at the disorganized rear of the Russian army would have said that, if only the French made one more slight effort, it would disappear; and anyone looking at the rear of the French army would have said that the Russians need only make one more slight effort and the French would be destroyed. But neither the French nor the Russians made that effort, and the flame of battle burned slowly out.
The Russians did not make that effort because they were not attacking the French. At the beginning of the battle they stood blocking the way to Moscow and they still did so at the end of the battle as at the beginning. But even had the aim of the Russians been to drive the French from their positions, they could not have made this last effort, for all the Russian troops had been broken up, there was no part of the Russian army that had not suffered in the battle, and though still holding their positions they had lost ONE HALF of their army.
The French, with the memory of all their former victories during fifteen years, with the assurance of Napoleon’s invincibility, with the consciousness that they had captured part of the battlefield and had lost only a quarter of their men and still had their Guards intact, twenty thousand strong, might easily have made that effort. The French who had attacked the Russian army in order to drive it from its position ought to have made that effort, for as long as the Russians continued to block the road to Moscow as before, the aim of the French had not been attained and all their efforts and losses were in vain. But the French did not make that effort. Some historians say that Napoleon need only have used his Old Guards, who were intact, and the battle would have been won. To speak of what would have happened had Napoleon sent his Guards is like talking of what would happen if autumn became spring. It could not be. Napoleon did not give his Guards, not because he did not want to, but because it could not be done. All the generals, officers, and soldiers of the French army knew it could not be done, because the flagging spirit of the troops would not permit it.
It was not Napoleon alone who had experienced that nightmare feeling of the 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 Borodin. 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 Borodin. The direct consequence of the battle of Borodin was Napoleon’s senseless flight from Moscow, his retreat along the old Smolnsk road, the destruction of the invading army of five hundred thousand men, and the downfall of Napoleonic France, on which at Borodin for the first time the hand of an opponent of stronger spirit had been laid.
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.
