We live in an age of science. In this modern age, we have taken its methods and applied it to every conceivable intellectual discipline. We have a science of politics, a science of engineering, a science of linguistics, a science of economics. We even have a science of philosophy. Any intellectual endeavor is legitimized and trusted if the scientific method supports it.
It is therefore not surprising that scientific methods dominate in both academia and government agencies in their attempts to understand the political and economic world which surrounds them. Because of the unquestioned faith that is placed in these scientific methods, the failure to anticipate the collapse of communism between 1989-1991 in Central and Eastern Europe is difficult to understand for those who put their faith in science. Even given the fact that social science never made the claim to be able to “predict” specific events, a basic understanding of the fragilities of communist societies seems to have been lacking throughout the Cold War period. How could the science of politics and economics have gotten it so wrong?
An excellent summary of the commonly-cited reasons why Western analysts so poorly understood the social and economic conditions of the Soviet Union was provided by Peter Rutland in 1993. Rutland isolates seven factors which surfaced after the collapse of communism that contributed to this failure: 1) The political bias of academics, 2) the isolation of Sovietologists from other core social science disciplines, 3) the absence of language and historical knowledge of the Soviet Union among Sovietologists, 4) the difficulty of research inside the USSR, 5) the fact that emigre scholars were largely ignored, 6) the seduction of leading academics into the role of media pundits (which precluded careful analysis), and 7) excessive dependence on government funding which allowed the Pentagon/CIA to set the academic agenda.
Aside from this last factor, Rutland believes that each factor contains a degree of the truth. While his critique of each assumption is nuanced, he ultimately concludes that all but two of the above-listed factors were mostly irrelevant to the inability of Sovietologists to understand the fragility of the communist system. He supports the argument that there was a general lack of grounding in languages and histories of the area. This was compounded by the inability of scholars to do legitimate field research within the Soviet Union. His analysis of the 87 PhD dissertations that dealt with Soviet domestic politics between 1976 – 1987 is sobering. Among his findings, he discovered that only seventeen of the eighty seven thesis writers had actually studied in the USSR. One-quarter of these dissertations relied exclusively on English-language sources (and only six showed proficiency in a non-Russian language of the Soviet Union). Only a small number did actual field research within the Soviet Union (such as interviewing officials). While he is sympathetic to the challenges associated with research of such a closed society, he writes, “Given the quality of the primary material feeding in to the base of the Sovietological discipline, it is hardly surprising that much of its high theorizing turned out to be nonsense on stilts.” Ultimately, he concludes, “… the root of the problem, which I see as the emergence of a ‘disciplinary groupthink’ which stifles creative thinking and controversial ideas.”
This paper takes one more step away from “disciplinary groupthink” in considering that the scientific method itself may be flawed in understanding social and political phenomena. Further, it looks to a novel written in the 1860’s for an explanation as to why our scientifically-based understanding of social phenomena may be flawed. Ultimately, it suggests that Tolstoy’s illustration of the tendencies embedded within the scientific method may, when recognized as such, help academic and government analysts to avoid certain errors in understanding the international environment.
Tolstoy’s Critique of Investigative Scientific Reasoning
Tolstoy’s first critique of science aims at the fundamental principles of what we may call investigative scientific reasoning. Investigative scientific reasoning involves activities which seek to advance our understanding of the observable world through empirical, measurable observations. These observations are measurable in so far as they isolate segments or variables of observable reality in an attempt to understand specific outcomes. The ultimate goal of this activity is the understanding of causal inference.
In War and Peace, Tolstoy questions the viability of this sort of investigatory activity and draws upon Zeno’s Paradox to illustrate its fundamental weakness. In this paradox, the reader is encouraged to imagine a race between the legendary Achilles and a tortoise. In order to simplify the understanding of how the race will proceed, the paradox forces the reader to parse the race into small time segments. The race begins with a ten-unit advantage for Achilles due to the fact that he can run ten times faster than the tortoise. Once the race begins, measurements are taken each time Achilles reaches the point where the tortoise was at the end of the preceding time segment. The result is that Achilles always comes closer to closing the gap between himself and the tortoise, but never quite catches him. Achilles never wins the race.
It is the absurdity of this conclusion that illustrates why fragmenting reality into ever smaller units of analysis leads to error. For Tolstoy, this is why contemporary historians, who seek to understand the international environment by dissecting it, err in their attempts to understand the “laws of historical movement.” Indeed, as he examines how historians have attempted to explain Napoleon’s invasion of Russia in 1812, he writes, “The deeper we go in search of causes, the more of them we find, and each cause taken singly or whole series of causes present themselves to us as equally correct in themselves, and equally false in their insignificance in comparison with the enormity of the event, and equally false in their incapacity (without the participation of all other coinciding causes) to produce the event that took place.” Tolstoy summarizes this notion in one sentence: “Human science fragments everything in order to understand it, kills everything in order to examine it.”
What makes this all the more pernicious for Tolstoy is the tendency toward certainty with which scientists apply these methods to their investigative activities. It is the first source of misunderstanding he provides in illustrating the errors of historians to isolate individual causes which led to Napoleon’s invasion of Russia. He writes, “What produced this extraordinary event? What were its causes? Historians say with naïve assurance that the causes of this event were the offense inflicted upon the Duke of Oldenberg, the non-observance of the Continental system, Napoleon’s love of power, Alexander’s firmness, diplomatic mistakes, and so on.” This “naïve assurance” (or naïve certainty) ultimately results in a closed-mindedness that precludes the consideration of additional explanations to be considered.
How does Tolstoy suggest we understand events such as Napoleon’s invasion of Russia? Rather than dissect individual variables in our attempt to understand causality, we must understand the “uniform strivings of people.” He writes that, “ . . . billions of causes – coincided so as to bring about what happened. And consequently none of them was the exclusive cause of the event … Millions of men, renouncing their human feelings and their reason, had to go from west to east and kill their own kind, just as, several centuries earlier, hordes of men had gone from east to west, killing their own kind.”
In other words, no single variable or person can account for the French invasion of Russia in 1812. Similarly, no single variable or person can account for a specific military victory or defeat. Prince Andrei understands this and states just before the battle of Borodino, “Success never did and never will depend on position, or on ammunition, or even on numbers . . . [but] on the feeling that’s in me, in him .. in every soldier.” It was the “spirit” of the French nation which ultimately resulted in the initial success of the invasion of Russia. It was the “spirit” of the Russian nation that allowed it to push them out.
For Tolstoy, the root of the problem of investigative scientific reasoning, therefore, can be found in the “parsing of the whole”. It is due to this error that social scientists are unable to understand the “spirit” of a nation and of its individual men and women which is so crucial to understanding international events. Tolstoy illustrates the “spirit” of the French and Russian fighting man by examining a multitude of the book’s characters. Only in this way does the reader learn of their motivations and actions. No single variable can account for any particular action. As human beings, they are complex creatures with myriad variables contributing to their individual animating spirits. Understanding these individuals is time-consuming labor. For Tolstoy, however, it is necessary if we are to understand the larger picture.
Tolstoy’s Critique of Applied Scientific Reasoning
Clearly Tolstoy is concerned about the errors of investigative science. For the most part, these errors are brought to light in War and Peace through the voice of the historical narrator. In terms of volume, this is a very small portion of the novel. It is through the actions and thoughts of the characters in the novel (which make up most of the book), that we find another set of criticisms of the scientific method. For Tolstoy, it is the application of the findings of investigative science that aggravates or accelerates the errors made in the investigative process. He illustrates this most clearly as it relates to the medical field.
Tolstoy presents his strongest critique of applied medical science in Volume III by recounting Natasha’s remorseful depression following her attempted elopement with Anatole Kuragin and the subsequent collapse of her engagement with Prince Andrei. Tolstoy writes,
“She was so ill that is was impossible to think of how much she was to blame in all that had happened, while she did not eat, did not sleep, grew noticeably thinner, coughed, and was, as the doctors let it be felt, in danger. They had to think only of how to help her. Doctors visited Natasha both singly and in consultation, spoke a good deal of French, German, and Latin, denounced one another, prescribed the most varied medications for all the illnesses known to them; but the simple thought never occurred to any of them that they could not know the illness Natasha was suffering from, as no illness that afflicts a living human being can be known: for each human being has his peculiarities, and always has his own peculiar complex illness, unknown to medical science . . .”
While Tolstoy explains that the doctor’s activities, in of themselves, provided some moral comfort to Natasha’s parents, the actual treatment was ineffectual. Natasha’s condition was peculiar to her. The illness that afflicted her could not be known using the scientific method. Thus, the doctors were simply wasting their time (and hers) when they, ” . . . came every day, felt her pulse, looked at her tongue … [but they paid] … no attention to her grief-stricken face.” Indeed, had they taken the time to ask, they would have learned that Natasha’s condition was linked to an emotional depression caused by the collapse of her engagement to Prince Andrei.
An almost identical story, with a different set of characters, is provided in Anna Karenina. The story begins with a depiction of Kitty’s health after she had spurned Levin in favor of Vronsky (who, in turn, spurned her). Tolstoy writes, “She was ill, and as Spring approached her health was growing worse. The family doctor gave her cod-lever oil, then iron, then common caustic, but as neither the one nor the other nor the third was of any help, and as he advised going abroad for the spring, a famous doctor was called in.” Although Kitty’s father did not approve of this new approach, the fact that a “famous” doctor was called provided comfort to Kitty’s mother. After a humiliating examination in which Kitty was examined naked, the doctor presented his findings to the family. After determining how much time he had available on his large gold pocket watch, he prescribes “Soden” waters. This approach is different from that of the family doctor who insisted that, ” . . . there are always some hidden moral and spiritual causes” to such conditions and that perhaps a trip abroad could remove conditions which are provoking painful memories. Eventually, the famous doctor agrees to the idea of travel abroad. After another look at his gold pocket watch, he then asks to examine Kitty one last time. This is almost more than the humiliated Kitty can take. Tolstoy writes,
“Her whole illness and treatment seemed to her such a stupid, even ridiculous thing! Her treatment seemed to her as ridiculous as putting together the pieces of a broken vase. Her heart was broken. And what did they want to do, treat her with pills and powders?”
As with the case of Natasha, Kitty’s famous doctor does not take the time to talk with Kitty to ascertain any peculiarities in her life. It is almost as if the examination of Kitty’s naked body should suffice to uncover any such peculiarity of her inner self. Ultimately, the doctor’s certainty in applied science leads him to improperly diagnose the source of Kitty’s illness.
While there are slight differences between the two Tolstoyan stories, they both illustrate a tendency of medical science to arrive at incorrect conclusions in two related but distinct ways: 1) the assumption that there are no peculiarities between seemingly identical subjects/objects of analysis, and 2) the absolute certainty that scientifically-derived theory can explain the whole of reality. Thus, the doctors treating Natasha and Kitty’s conditions were concerned with finding symptoms which conformed to known medical theory. Because of the belief that the theory is scientifically sound – and universally applicable – the doctors adhered to the assumption that there was no need to determine any unique circumstance surrounding the life situations of either patient. In both cases, the doctors took no time to delve deeper into their life circumstances which would have explained their conditions. Because they had absolute confidence in the accuracy of the scientific theory, they operated in complete certainty. This, in turn, led them to conclude their analysis in a very short period of time. This paved the way to error as a result of limited examination.
In essence, this tendency of applied science functions to abbreviate the process of the understanding of reality and to reach premature, false conclusions. For all intents and purposes, these doctors could have conducted their “examinations” at great distance by simply reading a description of the patients’ symptoms, coming to conclusions about the disease, and proscribing medication that provided a cure in what they view as similar circumstances.
It is remarkable that Tolstoy chooses to critique medical science in this way. Indeed, of all the intellectual disciplines which apply the scientific method in the modern world, none is trusted more than the science of medicine. The same may be said for the application of the scientific methods to military strategy and tactics. In fact, throughout the novel, Tolstoy is critical of the (mostly German) generals who rely upon a “science of war” or “strategy” to win battles. He famously writes, “Pfuel was one of those hopelessly, permanently, painfully self-assured men as only Germans can be, and precisely because only Germans can be self-assured on the basis of an abstract idea – science, that is, an imaginary knowledge of the perfect truth.” The non-scientific Russian, on the other hand, does not have this problem. Tolstoy writes that a Russian, “. . . is self-assured precisely because he does not know anything and does not want to know anything, because he does not believe it possible to know anything fully.” This lack of certainty in the notion that anything can really be fully understood was, for Tolstoy, one of the key factors leading to the Russian victory over Napoleon.
This naïve certainty is complicated by yet another factor. Tolstoy calls this the “fog of war.” In his depictions of a whole variety of battles – particularly the battles of Austerlitz and Borodino – he illustrates the physical impossibility of commanders to understand all the events occurring on the battlefield. It is not just that there are too many variables (there are), but the “fog” prevents knowing some variables that might be known in other scenarios. He gives voice to this through Prince Andrei who concludes, “What theory and what science could there be in a matter of which the conditions and circumstances are unknown and cannot be determined, in which the strength of those active in war can still less be determined?” 
Compensating for the Flawed Tendencies of Science
Tolstoy does not confine himself to only illustrating the errors of science, but provides clues as to how the errors can be avoided. The first step in understanding this can be seen in a conceptual tool famously given to us by Isaiah Berlin in his essay The Hedgehog and the Fox: An Essay on Tolstoy’s View of History. In this essay, Berlin argues that intellectuals can be split into two types: hedgehogs and foxes. The hedgehogs, he writes, “ . . . relate everything to a single central vision”, while the foxes, “ … pursue many ends, often unrelated and even contradictory.” He famously concludes that Tolstoy, “ … was by nature a fox, but believed in being a hedgehog.”
This analogy is helpful in understanding the characters of the novel as well. Pierre and Natasha are clearly foxes while Nikolai and Marya are clearly hedgehogs. It is no coincidence that the two foxes end the novel in marriage (as do the two hedgehogs). The foxes share a common approach to life – an approach which is varied and pluralistic. The hedgehogs, on the other hand, share a common notion that life should be lived according to a single, central vision. This makes a successful marriage a possibility for both couples.
While this fox/hedgehog distinction can be useful in understanding lifestyle choices, it is less useful in understanding how the characters process the information presented to them by the outside world. It is here that we can turn to Gary Saul Morson’s depiction of the character of Pierre. He writes, “Pierre Bezukhov – Peter Earless – cannot hear the particular, indistinct signals of daily life by which more prudent folk govern their lives, because he is always attending to some distant call, some indistinct voice from Heaven that will answer not just this or that but all questions of importance.” He continues,
“Truth for Pierre cannot be tentative local or merely practical. It must be as universal as mathematical logic and as certain as Descartes and Leibniz claimed their systems were. The truth about the world must be timeless, not varying with age or culture; absolute, in principle explaining everything worth knowing; theoretical, not a mere series of generalizations from experience; and perfectly clear and convincing to all who see it.”
Morson argues that a key purpose of Tolstoy, in writing War and Peace, is to get away from a purely theoretical way of thinking about the world. He concludes, “Away with the ethereal purity of ideas; back to the rough ground!”
Indeed, Pierre Bezukhov is a theorist in his attempt to understand the world. When asked about the abuses of the French revolution, Pierre responds, “These were extremes, to be sure, but the whole meaning wasn’t in them, the meaning was in the rights of man, emancipation from prejudice, the equality of citizens; and Napoleon kept all these ideas in all their force.” Later in the novel, he attempts to apply the principles of Freemasonry to his unhappy life and broken marriage. This is followed by a phase in which he attempts to apply principles of numerology to his planned assassination of Napoleon. He ends the novel as a political activist who is moderately liberal, but also supportive of the Tsar. In essence, Pierre is continually in pursuit of a new theory while ignoring the day-to-day details of most people’s lives.
As already mentioned, it makes a great deal of sense that Tolstoy has Pierre marry Natasha due to their shared fox-like natures. However, Natasha plays the role of bringing Pierre to the “rough ground” in terms of the way he processes information. Indeed, there is nothing theoretical about Natasha. She lives for the moment in the here and now. Perhaps the most famous scene depicting Natasha, at her spontaneous best, occurs in her “Uncle’s” little village of Mikhailovka. After a day’s hunting on horseback, the family gathers for dinner and music. Once “Uncle” begins to play the guitar, Natasha jumps up to dance. Tolstoy writes,
“Where, how, and when had this young Countess, brought up by an émigré Frenchwoman, sucked this spirit in from the Russian air she breathed, where had she gotten these ways, which should have been long supplanted by the pas de chale? Yet that spirit and these ways were those very inimitable, unstudied Russian ones which the uncle expected of her. . . . She did it exactly right, and so precisely, so perfectly precisely, that Anisya Fyodorovna, who at once handed Natasha the kerchief she needed for it, wept through her laughter . . .”
There is nothing Cartesian or ethereal in her behavior. She imbibes every moment and masters every detail whether it is a European or a Russian dance. While charming, there is a price to pay for this. Shortly after this scene, she attempts to elope with Anatol Kuragin and breaks her engagement with Prince Andrei. For Tolstoy, Natasha’s “rough ground” must ultimately be balanced by Pierre’s abstract musings.
This same distinction between abstractness and concrete reality can be seen in the marriage of Nikolai and Marya. Like Pierre, Marya also attempts to live her life according to a central principle; in her case, a life based upon the Christian message found in the Gospels. This principle finds its roots not in daily life, but from the example of mystical, wandering pilgrims. One of the key passages which illustrates this is found as Tolstoy writes,
Once, when in the dark room, by the light of the icon map, Fedosyushka [a religious pilgrim who had wandered from one religious shrine to another barefoot in chains] was telling about her life, the thought that Fedosyushka alone had found the right way of life suddenly came to Princess Marya with such force that she herself decided to go wandering. When Fedosyushka went to bed, Princess Marya thought about it for a long time, and finally decided that, however strange it was, she had to become a wanderer. She confided her intention only to her father confessor, the monk Akinfi, and the monk approved of it. Under the pretext of a gift for the wanderers, Princess Marya provided herself with a full wanderer’s outfit: a shirt, bast shoes, a kaftan, and a black kerchief. Often, going to the secret chest, Princess Marya would pause, unable to decide whether the time had come to fulfill her intention.
Just as Pierre meets near catastrophe in his attempt to live according to purely abstract notions, Marya narrowly avoids disaster in her attempts to deal with her peasants according to the principles of the Gospel during their retreat from Bald Hills. Of course, it is the “rough ground” Nikolai who saves Marya in this scenario. Once married, he continues to save her from these scenarios.
Much like his sister Natasha, Nikolai is categorically a-theoretical. He is a man who lives for the moment; a man with a military spirit and tradition, who appreciates the comradery of military life and the spirit of devotion to the Tsar. He is also a man who has a weakness for gambling – a vice one might expect from an individual who lives for the moment. It is gambling which results in financial catastrophe for Nikolai and his family; it is Marya who proves to be their savior.
Tolstoy intentionally ends the novel with all four characters living together in the same house. Under the influence of their spouses (and each other), the focus and method that each individual has for understanding the real world is adjusted in a manner which helps to check the other’s tendency toward error. Pierre and Marya are never on the same “rough road” as their spouses, however they do become more aware of the daily details of life. At the same time, Natasha and Nikolai remain on this “rough road” of day-to-day life, however their dangerous impetuosity is moderated by their theoretically-oriented spouses.
Avoiding The Errors of Scientific Certainty
The notion that opposites attract is commonplace in the world of romance. However, Tolstoy is not merely attempting to reinforce this commonplace notion of love and marriage in War and Peace. He is also pointing out that the notion that diverse methods and outlooks can help to avoid errors of analysis. How does this diversity help to avoid error?
Tolstoy’s critique of the scientific method is a convincing one. It is difficult to refute that investigative science is prone to error as a result of the “parsing” of reality or that applied science is prone to error as a result of the rush to judgement based upon preconceived notions of what the data should indicate. What is most troubling about these errors is that they persist; embedded in both forms of scientific activity is the tendency to consider only one approach and to preclude others. For Tolstoy, science is epistemologically hegemonic.
By “marrying” the theoretical thinkers to the “rough grounders”, Tolstoy is functionally weakening the hegemony of any single approach. A Soviet-era example, provided by Leszek Kolakowski, provides an illustration of how a Pierre-like tendency (an over-reliance upon theory) can be only be corrected by a Natasha-like attention to day-to-day details. He writes,
“When I visited Moscow in October of 1990, a Russian friend called my attention to a simple fact, the significance of which I had failed to notice. It was known that under Khrushchev a relatively large-scale housing construction program had been developed in the cities; people in great numbers secured their family dwellings. However small and inferior in standard, they gave people space for privacy, little nooks to breathe in. My Russian friend told me that without these modest but individual flats no opposition movement would have been possible. How foolish of Khrushchev! People crammed like sardines in miserable workers’ barracks or in small flats shared by several families, hating each other and spying on each other, jostling all the time and deprived of all moments of privacy, were unlikely to think about anything but sheer survival. The improvement of living conditions turned out to be politically dangerous. Far from appeasing people, making them more docile, as certain Sovietologists expected, such measures slowly opened up a space for critical thinking, ultimately for rebellion.”
This on-the-ground reality undermining theory is augmented by a similar story provided by a then-unknown young economist in the 1980’s named Grigory Yavlinsky. After carefully observing Soviet workers, he concluded, “The people don’t want to work. The people have no incentives. The economy inside which the people have no incentives [they] have no future.” A former Norilsk factory manager confirmed this sentiment in this context. He stated, “People come to work and just go through the motions. They doze off, read papers, do crosswords. The state goes on paying them, the state gets poorer, the people get corrupted, then bankruptcy. And that’s what happened – the collapse of a great empire.”
Both Yavlinksy and Kolakowski began with very logical assumptions based upon abstract theories: both were disproven by on-the-ground reality. Importantly, both social scientists gained a certain understanding of reality through direct observation and reflection within a larger context which led them to understand the fragility of the Communist system. For both, it was the “spirit” of the Soviet citizen/worker that was observed; this in turn, led to a more precise understanding of reality.
This same evolution can be seen in the thinking of Bernard Lewis touching upon a very different analytical failure – the 9/11 terrorist attacks. In his book, What Went Wrong: Western Impact and Middle Eastern Response, Lewis argues that, “For many centuries the world of Islam was in the forefront of human civilization and achievement. In the Muslims’ own perception, Islam itself was indeed conterminous with civilization, and beyond its borders there were only barbarians and infidels.” This all changed in the 17th and 18th centuries with a series of military defeats to Western powers. These defeats eventually led to a collective sense of shame and humiliation that provided the context for al Qaeda’s ideological justification for the 9/11 attacks. Indeed, it is only in this context that Western analysts could understand Osama bin Laden’s statements after the 9/11 attacks that the Americans were only then feeling the shame and humiliation that Muslims had felt for years.
Lewis’ historical approach is buttressed by an attentive listening to the currents of thought circulating among Muslim intellectuals in the years leading up to 9/11. In an interview given after the publication of What Went Wrong, he explained that his regular travels to the region were augmented by regularly listening to news programs directly broadcast from the Middle East – news programs unfiltered by Western news agencies. He explained that in this way, he got, “Day-to-day detail and a lot of small things, which are not even mentioned in the [Western] media.”
In Tolstoyan terms, by placing events within the larger historical context, Lewis avoids the error of fragmenting reality. At the same time, in attentively and regularly listening to his target audience, he avoided the error of prematurely coming to conclusions as a result of an over-reliance upon “established” scientific findings or assumptions. He did this by “marrying” his theoretical knowledge derived through a careful reading of history with his on-the-ground observations.
Ultimately, Tolstoy provides a clear depiction of the flawed tendencies of the scientific method. Importantly, he does not reject science in its entirety. He does not reject the importance of empirical observation, nor does he reject the need to address causal inference. He does, however, argue that the illusion of certainty is a fundamental tendency of science; it is this tendency that can lead to error. By accepting uncertainty in this light, an analyst of our modern political and economic world may very well be further propelled down the road of perpetual assessment and re-assessment that helps to avoid the errors of applied and investigative science. For Tolstoy, uncertainty is a virtue; through it, we avoid a common error of science. Without it, we are doomed to error.
 His analysis is equally as applicable to inability of Western analysts to accurately assess the weakness of the communist systems in Central Europe as well. See Peter Rutland, “Sovietology: Notes for a Post-Mortem,” The National Interest No. 31 (Spring 1993), pp. 109-122.
 Ibid., p. 112.
 Ibid., p. 115.
 Ibid., p. 116. For an excellent discussion of the application of science to politics see: Gary King, Robert O. Keohane, and Sidney Verba, Designing Social Inquiry: Scientific Inference in Qualitative Research (Princeton: Princeton University Press, 1994) and the subsequent “Special Issue” of The American Political Science Review (Vol. 89, No. 2) which appeared in June of 1995.
 See John P. Moran, The Solution of the Fist: Dostoevsky and the Roots of Modern Terrorism (Lanham, MD: Lexington Books, 2009), 18 – 19.
 He admits that modern mathematics has solved this paradox by allowing for infinitesimal quantities to be dealt with. He thus must grant that it is theoretically possible to understand the whole through a process of examining the infinitesimal parts. However, he does not believe that this can be done in understanding how history unfolds. See Leo Tolstoy, War and Peace, trans. Richard Pevear and Larissa Volokhonsky (New York: Alfred A. Knopf, 2007), pp. 821 – 823.
 Ibid., p. 604.
 Ibid., p. 442.
 Ibid., p. 603.
 Ibid., p. 822.
 Ibid., pp. 604-605.
 Ibid., p. 773.
 Interestingly, the day before the battle of Austerlitz, Tolstoy has Kutuzov tell Prince Andrei that they will lose the up-coming battle because of a total absence of the appropriate fighting spirit. See Ibid., p. 260.
 Ibid., p. 655.
 Ibid., p. 657.
 Leo Tolstoy, Anna Karenina, trans Richard Pevear and Larissa Volokhonsky (New York: Penguin Books, 2002), p. 117.
 Ibid., p. 118.
 Ibid., p. 119.
 Leo Tolstoy, War and Peace, p. 639.
 Ibid., p. 639.
 Ibid., p. 643.
 Isaiah Berlin, The Hedgehog and the Fox: An Essay on Tolstoy’s View of History (London: Phoenix, 1988).
 Ibid., p. 3.
 Ibid., p. 5.
 Gary Saul Morson, War and Peace Tolstoy, (ed. Donna Orwin) Cambridge University Press, p. 66
 Ibid., p. 67.
 Ibid., p. 68.
 For more on this see John P. Moran, “Tolstoy’s Hedgehog: Violence, Conflict, and the Deification of Reason,” Perspectives on Political Science, 43(3), 2014.
 Leo Tolstoy, War and Peace, p. 20.
 Ibid., p. 512.
 Ibid., p. 687.
 Ibid., pp. 734 – 735.
 Leszek Kolakowski, “Amidst Moving Ruins,” Daedalus (Spring 1992), p. 46.
 https://www.pbs.org/wgbh/commandingheights/shared/minitext/tr_show02.html. Downloaded on 9 April 2019.
 Bernard Lewis, What Went Wrong: Western Impact and Middle Eastern Response (Oxford: Oxford University Press, 2002), p. 3.
 http://booknotes.org/FullPage.aspx?SID=167924-1 (downloaded 12 January 2020)