War And Peace полностью

We all know the fallacy (a ‘sophism’ to the ancients) whereby a tortoise that has a start on Achilles will never be caught up by him, even though Achilles is walking ten times faster than the tortoise. While Achilles is busy covering a certain distance between him and the tortoise, the tortoise leading the way will have covered another one-tenth of that distance. Achilles covers that tenth, by which time the tortoise has covered another hundredth, and so on ad infinitum. This problem was considered by the ancients to have no solution. The absurdity of the conclusion (that Achilles will never overtake the tortoise) arises from the arbitrary decision to sub-divide the motion into discrete units, whereas the motion of both Achilles and the tortoise was continuous.

By adopting smaller and smaller units of motion all we do is get closer and closer to a solution to the problem without ever reaching it. Only by allowing for an infinitely small quantity and a progression rising from it up to a tenth, and by taking the sum of that geometrical progression, can we arrive at a solution of this problem. A new branch of mathematics taking account of infinitely small quantities can now consider other more complex problems of motion and provide solutions to problems that once seemed insoluble. When applied to these problems of motion, this new branch of mathematics (unknown to the ancients) allows for infinitely small quantities and by doing so creates the basic condition of motion – absolute continuity – thus correcting the inevitable mistake that the human intellect is bound to make when it rejects continuous motion in favour of discrete units of motion.

In the search for laws of historical movement exactly the same thing occurs.

The movement of humanity, arising from a countless series of actions arbitrarily performed by many individuals, is a continuous phenomenon.

The aim of history is to work out what laws lie behind this movement. But in its attempt to establish the laws behind the continuous movement that arises from all those arbitrary individual actions taken together, the human mind accepts a sub-division into arbitrarily determined discrete units. The first thing history does is to take an arbitrary series of continuous events and examine it separately, whereas in fact no event can ever have a beginning, because an individual event flows without any break in continuity from another. The second thing history does is to treat the actions of a single person, king or commander, as the sum total of everybody else’s individual will, whereas in fact the sum of individual wills never expresses itself in the actions of a single historical personage.

In the development of historical science, smaller and smaller units are selected for analysis, as if this is the path that leads to truth. But however small the units determined by history, we feel that the acceptance of any discrete unit, or of a beginning to any phenomenon, or the idea that multiple individual wills express themselves in the actions of any one historical personage, is intrinsically wrong.

Criticism can effortlessly ensure that every conclusion of history gets blown away like dust, leaving no trace behind, simply by selecting a greater or smaller discrete unit for analysis – and criticism has every right to do this, because the selection of historical units is always an arbitrary business.

Only by adopting an infinitely small unit for observation, the differential in history otherwise known as human homogeneity, and perfecting the art of integration (the adding up of infinitesimals) can we have any hope of determining the laws of history.

The first fifteen years of the nineteenth century in Europe present an extraordinary spectacle – millions of men in movement. Men drop their normal occupations and rush from one end of Europe to the other, plundering, slaughtering one another, experiencing triumph and despair, and the whole business of life is disrupted for years to come as the movement accelerates and builds up before tailing off again. What was it that caused all this movement? By what laws did it develop? This is what human intelligence wants to know.

When historians reply to these questions they present the sayings and doings of a few dozen men in one building in the city of Paris, and sum up these doings and sayings in a single word – revolution. Then they launch into detailed biographies of Napoleon and one or two persons for and against him; they also tell us how some of these persons were influenced by others, and they conclude by saying this is what caused all the movement, and these are the laws that governed it.