Briggs: Continuity of motion. Achilles and the tortoise. Image of the locomotive.
Maude: Continuity of motion. Achilles and the tortoise. The method of history, its explanation of events compared with explanations of the movement of a locomotive.
Pevear and Volokhonsky: Achilles and the tortoise. The search for the laws of historical movement.
Translation:
Part the Third.
I.
For the human mind is incomprehensible the absolute continuity of movements. To a person became understandable the laws which would be those movements only so when he examines the arbitrarily taken units of these movements. Yet together with those of these arbitrary divisions of continuous movements into discontinuous units, stems a big part of human delusions.
A famous so called sophism of the ancients, taking place in how Achilles will never catch up with the ahead going turtle, despite that how Achilles is going at nine times faster than the turtle: as only Achilles will pass the space separating him from the turtle, the turtle will pass ahead of his one tenth of this space; Achilles will pass this tenth, the turtle will pass one hundredth and etc. to infinity. This task presented to the ancients as insoluble. The meaninglessness of the decision (that Achilles will never catch up with the turtle) flowed from this alone, how arbitrarily were the admitted discontinuous units of movements, as the move of Achilles and the turtle was committed as continuous.
Taking all more and more small units of movements, we only move closer to the decision of the issue, but never reach it. Only allowing an infinitely small magnitude and ascending from it progression to one tenth, and taking the amount of this geometric progression, we reach the decision of the issue. A new branch of mathematics, having reached the art to handle with infinitely small quantities, and in other more complex questions of movements give now answers to questions seeming insoluble.
This new, unknown to the ancients, branch of mathematics, in considering the issues of movements, allowing infinitely small magnitudes, i.e. such, in which recovers the main condition of movements (absolute continuity) by that very much correct that inevitable mistake, which the mind of a human may not do, looking at instead the continuous movements of separate units of movements.
Finding the laws of historical movements is going on completely the same.
The movement of humanity, flowing out from the countless quantity of human arbitrariness, is committed continuously.
The comprehension of these laws of movements is the objective of history. Yet so that to comprehend the laws of the continuous movements of the sum of all the arbitrariness of people, the mind of a human allows arbitrary, discontinuous units. The first reception of history jokes so that to take an arbitrary row of continuous events, to discern it separately from others, then as may or may not be the beginning of events, but always one event continuously follows from another. The second reception consists so that to discern the action of one human, a tsar, a commander, as the amount of the arbitrariness of people, as amounts the arbitrariness of humanity never expresses in the activities of one historical face.
Historical science in the movement constantly accepts all smaller and smaller units for consideration and by this path strives to approach to truth. Yet how small the units which accept the story, we feel that the assumption of units, separated from others, the assumption beginning some phenomena and the assumption of how the arbitrariness of all people express in the actions of one historical face, is false in itself.
Any conclusion of history, without the slightest effort to the parties of critics, breaks up as ash, leaving nothing behind by itself, only owing to how the criticism elects for the subject of security of more or smaller discontinuous units; in that it always has the right, as the taken historical unit is always arbitrary.
Only allowing the infinitely small unit for security — the differential history, i.e. homogeneous attraction of people and having reached the art to integrate (to take the sum of these infinitely early), can we hope to comprehend the laws of history.
—————
The first 15 years of the XIX century in Europe presents the extraordinary move of a million people. The people leave their ordinary lessons, strive with one party of Europe to another, rob, kill one another, triumph and despair, and all move life in a few years change and represent the enhanced move, which first is increasing, then weakening. — How was caused these movements, or by which laws was it happening? — asks the mind of a human.
Historians, answering to this question, set out to us the deeds and speeches of several dozens of people, at one of the buildings of the cities of Paris, calling these deeds and speeches the word revolution; then give a detailed biography of Napoleon and some sympathetic and hostile to him persons, telling about the influence of one of these persons to others and speak: here is from what happened this movement, and here are the laws of it.
Yet the mind of a human not only refuses to believe this explanation; but all speak that the reception of explanations is not true, because of how in this explanation the weakest phenomenon is taken for the cause of the strongest. The amount of human arbitrariness made the revolution and Napoleon, only the amount of this arbitrariness suffered them and destroyed them.
"Yet any time when were conquests, were conquerors; any time, when were made coups in state, were great people," speaks the story. Really, any time, when revealed conquerors, was war, responds the mind of a human, but this is not proof, so that the conquerors were the reason for war, and so that to possibly find the laws of war in the personal activities of one human. Any time, when I, looking at my watch, see that the arrow has come up to 10, I hear that at the neighboring churches begins a toll, but from that at any time, that the arrow comes to the 10th hour then it begins to toll, I do not have the right to conclude that the position of the arrow is the cause of the movements of the bells.
Any time, as I see the movement of an engine, I hear the sound of a whistle, I see the opening of the valve and the movement of the wheels; but from this I do not have the right to conclude that the whistling and movement of wheels is the crux cause of the movement of the engine.
The peasants speak that the late spring blows the cold wind because of how the bud oak is deployed, and really all spring blows the cold wind, when is the deployed oak. Yet although the cause of the blowing in the deployment of the oak cold wind is unknown to me, I cannot agree with the peasants in that the cause of the cold wind is the deployment of the bud oak because only how the power of the wind is located beyond the influences of the bud. I see only the coincidence of those conditions, which there are in every life phenomenon and I see that, how much I would and would in detail watch the arrow of the watch, the valve and the wheels of the engine and the oak bud, I do not recognize the cause of the toll, the movements of the engine and the spring wind. For this I should change completely the location of security and the study of the laws of the movements of time, the bells and the wind. That same should be done to history. And these attempts are now being made.
For studying the laws of history, we must change completely the subject of security, left only in the tsar, ministers and generals, but study the homogeneous, infinitely small elements which lead the masses. No one may say, in how much the given person reaches by this path the understanding of the laws of history; but it is obvious that in this way only lies the opportunity to catch historical laws; and that in this way did not lay another mind of a human one millionth share of those efforts that historians put in the description of the deeds of the institutions of the tsar, generals and ministers, and in the exposition of their considerations by the occasion of these deeds.
Mentioned: the first fifteen years of the nineteenth century, ten o'clock, late spring
Locations: undefined
Mentioned: Europe, Paris
Pevear and Volokhonsky Notes: "For human reason, absolute continuity of movement is incomprehensible."
The problem of Achilles overtaking the tortoise for ancient philosophers is discussed and then used as an analogy for the problem of human reasoning (one that is solved by advanced mathematics).
"The movement of mankind, proceeding from a countless number of human wills, occurs continuously. To comprehend the laws of the movement is the goal of history."
Line break after "can we hope to comprehend the laws of history."
We then move from the abstract philosophical to the slightly more concrete and seemingly relevant "first fifteen years of the nineteenth century in Europe." Historians try to understand why this "extraordinary movement of millions of people" happened. "The sum of individual human wills produced the revolution and Napoleon, and only the sum of those wills endured them and then destroyed them."
Tolstoy provides the analogies of looking at your watch every time the bells ring (though this isn't the cause of it), the movement of a locomotive "caused" by its whistle, and a cold wind blowing (in a peasant's estimation) because the leaf buds are sprouting.
Characters (characters who do not appear, but are mentioned are placed in italics. First appearances are in Bold. First mentions are underlined. Final appearance denoted by *):
Napoleon
(Achilles is discussed but is a reference, not a character, as is the turtle. The people of Europe in general are discussed, as are historians. Tolstoy also references himself as "I" and peasants, kings, ministers, and generals.)
Abridged Versions: Start of Part the Eleventh in Wiener. Line break after "to grasp the laws of history." Line break in the same spot in Maude, Mandelker, Dunnigan, Edmonds, and Briggs.
Start of Volume 3, Book Eleven in Maude.
Start of Part 3 in Briggs, Dunnigan, Edmonds, and Mandelker. Start of Part Eleven in Garnett.
Start of Chapter 9 in Bell with no break.
Gibian: Start of Book Eleven 1812. Date of Principal Historical Event
Old Style New Style
Sept. 1 Sept. 13 Kutuzov orders retreat through Moscow.
Chapter 1: line break after "arrive at the laws of history."
Fuller: Entire chapter is cut.
Komroff: Entire chapter is cut.
Kropotkin: Entire chapter is cut.
Bromfield: No apparent corresponding chapter.
Simmons: Start of 1812 Book Eleven: entire chapter is cut and replaced with: "Tolstoy repudiates the conventional notion of historians that the actions of some one man--a king or a commander--are equivalent to the sum of many individual wills. On the contrary, Tolstoy declares, the sum of individual wills is never expressed by the activity of a single historic personage."
Additional Notes: Garnett: "The philosopher Zeno of Elea (c.495-430 B.C.) used paradoxes such as this one about Achilles and the Tortoise to prove that a continuum is not made up of multiple points--that is, that time not a sum of movements."
"Tolstoy refers to calculus, a branch of mathematics Sir Isaac Newton (1642-1727) and Gottfried Wilhelm Leibniz (1646-1716) discovered that is concerned with change and continuity over time."
Letters (Christian): Page 620: “Something new is bound to come out of the combination of these two phenomena, but what it will be I can’t even guess, and I think nobody can foresee, since history never repeats itself.”
The Peasant in Nineteenth-Century Historiography by Michael B. Petrovich:
Page 197: Sergei M. Solovyov...In Hegelian fashion…”History deals only with that which visibly moves, which acts and manifests itself, and thus history has no way of dealing with the popular masses; it deals only with representatives of the people, no matter in which form the government may express itself; and even when the popular masses are set in motion, it is the leaders, the directors of that movement, who are of primary interest and with whom history is and should be primary concerned.”
Troyat/Amphoux: Page 328: "As the historian Shebalsky has said, this is "historcal nihilism." But since individuals have no control over events, how does one explain war? After all, the people who are not the ones who are lusting to cut each other's throats! An embarrassing question for the novelist. To admit that Napoleon is capable of setting a massacre in motion is to admit that he possesses some power over history, and the attractive theory of the total ineffectiveness of the hero no longer holds water. To insist that a lone man cannot "compel five hundred thousand to die" is to admit that the five hundred thousand have determined, more or less consciously, to invade a neighboring country; and so another, no less attractive theory--that of the fundamental goodness of the people--must also fall by the wayside. Tolstoy took the easy way out of his dilemma in his article, Some Words about War and Peace: fatality..."
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