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By Root 3911 0

it could not stop, just as the twice weaker Russian army could not help moving aside. After the shove it had been given, the French army could still roll on as far as Moscow; but there, with no new efforts on the part of the Russian army, it was to perish, bleeding from the mortal wound it had received at Borodino. The direct consequence of the battle of Borodino was Napoleon’s causeless flight from Moscow, the return down the old Smolensk road, the destruction of an invading army of five hundred thousand men, and the destruction of Napoleonic France, upon which had been laid for the first time, at Borodino, the hand of an adversary stronger in spirit.

Part Three

I

For human reason, absolute continuity of movement is incomprehensible. Man begins to understand the laws of any kind of movement only when he examines the arbitrarily chosen units of that movement. But at the same time it is from this arbitrary division of continuous movement into discrete units that the greater part of human errors proceeds.

A well-known so-called sophism of the ancients posits that Achilles can never overtake a tortoise that is walking ahead of him, even though Achilles walks ten times faster than the tortoise: while Achilles covers the distance that separates him from the tortoise, the tortoise will get ahead of him by one tenth of that distance; Achilles covers that one tenth, the tortoise gets ahead by one hundredth, and so on to infinity. The ancients considered this problem insoluble. The nonsensical conclusion (that Achilles will never overtake the tortoise) resulted only from the fact that discrete units of movement were introduced arbitrarily, while the movement of both Achilles and the tortoise was continuous.

By taking smaller and smaller units of movement, we only approach the solution of the problem, but never reach it. Only by allowing for an infinitesimal quantity and the ascending progression from that up to one tenth, and by taking the sum of that geometrical progression, do we arrive at the solution of the problem. A new branch of mathematics, having attained to the art of dealing with infinitesimal quantities in other, more complex problems of movement as well, now gives answers to questions that used to seem insoluble.

This new branch of mathematics, unknown to the ancients, in examining questions of movement, allows for infinitesimal quantities, that is, such as restore the main condition of movement (absolute continuity), and thereby corrects the inevitable error that human reason cannot help committing when it examines discrete units of movement instead of continuous movement.

The same thing happens in the search for the laws of historical movement.

The movement of mankind, proceeding from a countless number of human wills, occurs continuously.

To comprehend the laws of this movement is the goal of history. But in order to comprehend the laws of the continuous movement of the sum of all individual wills, human reason allows for arbitrary, discrete units. The first method of history consists in taking an arbitrary series of continuous events and examining it separately from others, whereas there is not and cannot be a beginning to any event, but one event always continuously follows another. The second method consists in examining the actions of one person, a king, a commander, as the sum of individual wills, whereas the sum of individual wills is never expressed in the activity of one historical person.

Historical science in its movement always takes ever smaller units for examination, and in this way strives to approach the truth. But however small the units that history takes, we feel that allowing for a unit that is separate from another, allowing for the beginning of some phenomenon, and allowing for the notion that all individual wills are expressed in the actions of one historical person, is false in itself.

Any conclusion of historical science, without the least effort on the part of criticism, falls apart like dust, leaving nothing behind, only as a result of the fact that criticism selects as an