Dr. Slava Gerovitch writes: If two statisticians were to lose each other in an infinite forest, the first thing they would do is get drunk. That way, they would walk more or less randomly, which would give them the best chance of finding each other. However, the statisticians should stay sober if they want to pick mushrooms. Stumbling around drunk and without purpose would reduce the area of exploration, and make it more likely that the seekers would return to the same spot, where the mushrooms are already gone.

Such considerations belong to the statistical theory of “random walk” or “drunkard’s walk,” in which the future depends only on the present and not the past. Today, random walk is used to model share prices, molecular diffusion, neural activity, and population dynamics, among other processes. It is also thought to describe how “genetic drift” can result in a particular gene—say, for blue eye color—becoming prevalent in a population. Ironically, this theory, which ignores the past, has a rather rich history of its own. It is one of the many intellectual innovations dreamed up by Andrei Kolmogorov, a mathematician of startling breadth and ability who revolutionized the role of the unlikely in mathematics, while carefully negotiating the shifting probabilities of political and academic life in Soviet Russia.

As a young man, Kolmogorov was nourished by the intellectual ferment of post-revolutionary Moscow, where literary experimentation, the artistic avant-garde, and radical new scientific ideas were in the air. In the early 1920s, as a 17-year-old history student, he presented a paper to a group of his peers at Moscow University, offering an unconventional statistical analysis of the lives of medieval Russians. It found, for example, that the tax levied on villages was usually a whole number, while taxes on individual households were often expressed as fractions. The paper concluded, controversially for the time, that taxes were imposed on whole villages and then split among the households, rather than imposed on households and accumulated by village. “You have found only one proof,” was his professor’s acid observation. “That is not enough for a historian. You need at least five proofs.” At that moment, Kolmogorov decided to change his concentration to mathematics, where one proof would suffice. [Continue reading…]

The theoretical physicist, Freeman Dyson, writes: Jim Holt’s Why Does the World Exist?: An Existential Detective Story is a portrait gallery of leading modern philosophers. He visited each of them in turn, warning them in advance that he was coming to discuss with them a single question: “Why is there something rather than nothing?” He reports their reactions to this question, and embellishes their words with descriptions of their habits and personalities. Their answers give us vivid glimpses of the speakers but do not solve the riddle of existence.

The philosophers are more interesting than the philosophy. Most of them are eccentric characters who have risen to the top of their profession. They think their deep thoughts in places of unusual beauty such as Paris and Oxford. They are heirs to an ancient tradition of academic hierarchy, in which disciples sat at the feet of sages, and sages enlightened disciples with Delphic utterances. The universities of Paris and Oxford have maintained this tradition for eight hundred years. The great world religions have maintained it even longer. Universities and religions are the most durable of human institutions.

According to Holt, the two most influential philosophers of the twentieth century were Martin Heidegger and Ludwig Wittgenstein, Heidegger supreme in continental Europe, Wittgenstein in the English-speaking world. Heidegger was one of the founders of existentialism, a school of philosophy that was especially attractive to French intellectuals. Heidegger himself lost his credibility in 1933 when he accepted the position of rector of the University of Freiburg under the newly established Hitler government and became a member of the Nazi Party. Existentialism continued to flourish in France after it faded in Germany.

Wittgenstein, unlike Heidegger, did not establish an ism. He wrote very little, and everything that he wrote was simple and clear. The only book that he published during his lifetime was Tractatus Logico-Philosophicus, written in Vienna in 1918 and published in England with a long introduction by Bertrand Russell in 1922. It fills less than two hundred small pages, even though the original German and the English translation are printed side by side. I was lucky to be given a copy of the Tractatus as a prize when I was in high school. I read it through in one night, in an ecstasy of adolescent enthusiasm. Most of it is about mathematical logic. Only the last five pages deal with human problems. The text is divided into numbered sections, each consisting of one or two sentences. For example, section 6.521 says: “The solution of the problem of life is seen in the vanishing of this problem. Is not this the reason why men, to whom after long doubting the sense of life became clear, could not then say wherein this sense consisted?” The most famous sentence in the book is the final section 7: “Wherof one cannot speak, thereof one must be silent.”

I found the book enlightening and liberating. It said that philosophy is simple and has limited scope. Philosophy is concerned with logic and the correct use of language. All speculations outside this limited area are mysticism. Section 6.522 says: “There is indeed the inexpressible. This shows itself. It is the mystical.” Since the mystical is inexpressible, there is nothing more to be said. Holt summarizes the difference between Heidegger and Wittgenstein in nine words: “Wittgenstein was brave and ascetic, Heidegger treacherous and vain.” These words apply equally to their characters as human beings and to their intellectual output.

Wittgenstein’s intellectual asceticism had a great influence on the philosophers of the English-speaking world. It narrowed the scope of philosophy by excluding ethics and aesthetics. At the same time, his personal asceticism enhanced his credibility. During World War II, he wanted to serve his adopted country in a practical way. Being too old for military service, he took a leave of absence from his academic position in Cambridge and served in a menial job, as a hospital orderly taking care of patients. When I arrived at Cambridge University in 1946, Wittgenstein had just returned from his six years of duty at the hospital. I held him in the highest respect and was delighted to find him living in a room above mine on the same staircase. I frequently met him walking up or down the stairs, but I was too shy to start a conversation. Several times I heard him muttering to himself: “I get stupider and stupider every day.”

Finally, toward the end of my time in Cambridge, I ventured to speak to him. I told him I had enjoyed reading the Tractatus, and I asked him whether he still held the same views that he had expressed twenty-eight years earlier. He remained silent for a long time and then said, “Which newspaper do you represent?” I told him I was a student and not a journalist, but he never answered my question.

Wittgenstein’s response to me was humiliating, and his response to female students who tried to attend his lectures was even worse. If a woman appeared in the audience, he would remain standing silent until she left the room. I decided that he was a charlatan using outrageous behavior to attract attention. I hated him for his rudeness. Fifty years later, walking through a churchyard on the outskirts of Cambridge on a sunny morning in winter, I came by chance upon his tombstone, a massive block of stone lightly covered with fresh snow. On the stone was written the single word, “WITTGENSTEIN.” To my surprise, I found that the old hatred was gone, replaced by a deeper understanding. He was at peace, and I was at peace too, in the white silence. He was no longer an ill-tempered charlatan. He was a tortured soul, the last survivor of a family with a tragic history, living a lonely life among strangers, trying until the end to express the inexpressible. [Continue reading…]

Steven Pinker claims we are living in the most peaceable era of human existence. In a review of The Better Angels of Our Nature: Why Violence Has Declined, Timothy Snyder challenges Pinker’s thesis.

The central psychological virtue of modern civilization, Pinker claims, is “self-control.” Over the centuries, after people are pacified by the state, they learn to think ahead, to see the perspectives of others, and to pursue their ends without immediate violent action. Violence becomes not only impractical but also taboo. Nazi Germany, as Pinker seems to sense, represents a tremendous problem for this argument. Germany in the 1930s was probably the most functional state of its time, with low homicide rates and a highly literate population. Mastery of self was not the Nazis’ problem; self-control was in fact a major element of the SS ethos, as preached by Reinhard Heydrich and Heinrich Himmler. Even Adolf Hitler practiced his emotive speeches. Lack of self-control was also not the problem for Joseph Stalin’s executioners, or for Stalin and Stalinists generally. Individual Soviet NKVD men killed hundreds of people, one by one, in a single day; this can hardly be done without self-control of a very high order.

To rescue his argument from the problem posed by the mass killings of the mid-twentieth century, Pinker resorts to claiming that a single individual, in the German case Hitler, was “mostly responsible.” Here, he misrepresents the historians he cites. It is true that most historians would subscribe to some version of “no Hitler, no Holocaust.” But what they mean is that Hitler was a necessary condition for such a calamity, not that he was a sufficient one. There were many other necessary conditions for Nazi racial imperialism. Take, for example, worries about the food supply. In the 1930s, food was highly valued in both Berlin and Moscow. This fact did not dictate which ideologies would define the two states. But in practice, both Hitler and Stalin were obsessed with mastering and exploiting fertile soil, the former to transform Germany into a self-sufficient, racially pure empire, the latter to finance the industrialization of the Soviet Union.

Without recognizing the importance of scarce resources, it is impossible to understand the very different plans for agrarian colonization that the Nazi and Soviet ideologies sanctioned. But Pinker dismisses any claim that resources (rather than bad ideas) were related to the bloodiest conflicts in modern history as a “nutball conspiracy theory.” This is an odd position for him to take, since his own history begins in a premodern world of conflict over resources. By insisting that ideas alone were to blame, he oversimplifies the issue. A more rigorous explanation would explain how political ideas interacted with scarcity, rather than insist that either one or the other must have been the problem.

Modern ideologies were not, as in Pinker’s metaphors, “toxic” forces that “drove” people to do this or that. They provided narratives to explain why some groups and individuals had better access to resources, and appealing visions of the future after an aggressive reordering. Nazi Germany and the Soviet Union were ideological states, but they cannot be dismissed from history simply because they were organized around the wrong ideas. Each of them had plans for economic development that were meant to privilege one group at the expense of others — plans that were inextricably entangled with justifications for why some people deserved more, others less, and others nothing but death (the extreme and unprecedented case being the Holocaust). These ideologies were effective in part because they motivated, and they motivated in part because they delivered, if not plenty, then at least visions of plenty.

We are different from the Nazis and the Soviets not because we have more self-control — we don’t. We are different largely because postwar improvements in agricultural technology have provided the West with reliable supplies of food, our massive consumption of which says much about our limited self-control. But what if food were to become scarcer and more expensive, as seems now to be the trend? What if unfavorable climate change were to outrun our technical capacities? Or what if melting glaciers leave societies such as China without fresh water? Pinker claims, unpersuasively, that global warming poses little threat to modern ways of life. But it hardly matters whether he is right: states are already taking action to minimize its consequences. China, for example, is buying up land in Africa and Ukraine in order to compensate for its own shortage of arable soil. The fresh water of Siberia must beckon. If scientists continue to issue credible warnings about the consequences of climate change, it would be surprising if leaders did not conjure up new reasons for preemptive violent action, positioning their states for a new age of want.

Treating Nazi Germany as a historical aberration also allows Pinker to sidestep the question of how Germans and central and western Europeans became such peaceful people after the demise of Nazism. This is a strange oversight, since European pacifism and low European homicide rates are where he begins the book. Today’s Europe is Pinker’s gold standard, but he does not ask why its levels of violence are the lowest in all of his charts. If, as he contends, the “pleasures of bourgeois life” prevent people from fighting, Pinker should also consider the place where these are most fully developed, and how they became so. Pinker persuasively relates how postwar economic cooperation among European states led to a pacifying interdependence, but he fails to stress that the postwar rebirth of European economies was a state-led enterprise funded by a massive U.S. subsidy known as the Marshall Plan. And he says very little about the concurrent development of redistributive social policy within those states. State power goes missing in the very places where states became preoccupied with welfare rather than warfare.

David Africa writes:

As South Africans celebrate the birthday of their national hero Nelson Mandela all the accolades again praise him as a peacemaker, moderate, and a saint. This image of Mandela is one that has been aggressively cultivated since his elevation from prisoner to president with the first democratic election in 1994, and is a curious part of a political project with the twin objectives of moderating one of the primary symbols of the South African liberation struggle on the one hand, and appropriating this ‘new Mandela’ for a moderate or even conservative political project.

The saint-like status that Mandela has acquired in the West, traditionally hostile to Mandela’s politics and that of his organisation the African National Congress (ANC) is mirrored in the false adulation showered upon him by the local parliamentary opposition party the Democratic Alliance. The Democratic Alliance is mainly a coalition of former liberals and the remnants of the National Party that ruled South Africa until 1994. The capture of the Mandela icon and his transformation from militant to moderate saint is now almost complete.

And yet, this is not the Mandela that black South Africans know. The Mandela we know has always been a militant, from his days as a fiery youth leader in the 1940s, through leading the ANC Defiance Campaign against the Apartheid government in 1952 and being the first commander of that organisation’s armed wing when it turned to violent resistance in 1961.

His speech to the court in April 1964, as he and his fellow ANC comrades faced the real risk of the death penalty, is an articulation of a militancy that is at once reasonable and defiant. Throughout his long imprisonment Mandela refused offers of personal freedom in exchange for abandoning violent resistance to the Apartheid government.