THE BEST OF TIMES

Steven Pinker scruples at the importance of the crimes of the twentieth century. But when these statistics are properly assessed, they bleed through every calculation, forming a ghastly but ineradicable spike in the otherwise humdrum human record of murders.

PART THREE OF THREE

READ PART I HERE

READ PART II HERE

The twentieth century is terrible because, terrible though its warfare has been, its crimes have been worse. Steven Pinker does not, of course, deny the magnitude of these crimes; he scruples at their relative importance. “If I were one of the people who were alive in a particular era,” he asks, “what would be the chances that I would be a victim of violence?”^[2]Pinker, The Better Angels, 47. The question provides its own answer. There is safety in numbers.^[3]For a Zebra eager to evade a lion, being in a herd is better than being alone. The bigger the herd, the better his chances. For a Jew trapped in the Lodz ghetto in 1942, the reverse was as nearly … Continue reading

Is there? Is there really?

An individual x selected at random is a commonplace in the theory of probability, where he may often be found within an urn and waiting to be fished out. Pinker is dealing with a larger canvas, one in which x is who he is and P is the population in which he is embedded. Whatever else he may be, x is a man of the world: it is the world’s population as a whole that is Pinker’s relevant reference class. In the twentieth century, just what risk was he running to—or fleeing from? It was, Pinker affirms, the risk of being “a victim of violence.” This is cant. If the victims of violence are left undefined, they tend to multiply uncontrollably, the more so if violence is treated as a sinister, but shapeless, force. The Holocaust, the Nuremberg court affirmed, was a crime against humanity. The judgment was morally correct because morally unavoidable, but if the entire human race has, for this reason, been a victim of violence, there are no statistical distinctions left to draw. For any x in the twentieth century, the probability that x has been a victim of violence is 1.

When the victims of violence are allowed to lapse, there remains the grisly category of violent deaths. These dead are dead. They can be counted. The world’s population in 1940 stood at roughly two billion. In 1840, it was roughly half as large. If a man selected at random must run the risk of violent death, would he not prefer running it in 1940?

This is Pinker’s question.

And his point.

Violence in the twentieth century has had a lurid, but characteristic, shape both in space and in time. In 2010, Timothy Snyder published a book entitled Bloodlands: Europe between Hitler and Stalin.^[4]Timothy Synder, Bloodlands: Europe between Hitler and Stalin (New York: Basic Books, 2010). The Bloodlands encompassed Poland, the Ukraine, Belarus, Russia, and the Baltic States during the twelve years from 1933 to 1945. It was there, and then, that fourteen million men, women and children were murdered. The gross violence of the Bloodlands was confined to something like an irregular parallelepiped, but whatever the geographical niceties, the Bloodlands comprised a shape with something like a rational boundary. It made (and makes) sense to say of an individual x that either he was within the Bloodlands or beyond them. It is thus that the Bloodlands emerges as a complicated dead zone: large, irregular, bounded, blood red.

Violent deaths make for homicide in the largest sense, and murder in the plainest. Thus a return to a symbol of old in H. What is now at issue is just what statistic might be assigned to x on the assumption that his reference class is the world? If centuries are to be compared, it can only be the ratio H/P of homicides to the world’s population as a whole, with distinctions of time and place allowed to lapse. It is this statistic that measures “the risk of violent death.”

And it is no easy statistic to define. What is wanted is a measure of risk, and in the case of the Bloodlands, serving now as a synecdoche for all of the outrages of the twentieth century, the risk of violent death is singular. Within the Bloodlands it converges to 1; and beyond them, to 0.

To one? Yes, of course. Within the Bloodlands, everyone was at risk of death. Reference class ambiguities lapse: the risk of violent death was very close to the mean, no matter the reference class. It is within the Bloodlands that one sees what in probability theory and economics is referred to as a concentration of measure, a wonderfully elegant euphemism.^[5]In probability theory, one speaks of a concentration of measure, Michel Talagrand remarks, when “a random variable that depends in a Lipschitz way on many independent variables (but not too … Continue reading

To zero? Yes, of course. Someone living in Peru was at no risk of violent death in Poland, the Ukraine, Belarus, Russia, and the Baltic States during the twelve years from 1933 to 1945. The risk of violent death was an all or nothing affair.^[6]An illustration of a zero-one law in probability theory, and so a tail event. That said, it is important to emphasize that an appeal to the theory of probability would make sense only if the … Continue reading

To cross the border into the Bloodlands was to radically change one risk of death—so radically that it is by no means clear that one sample space rationally defined both the Bloodlands and the rest of the world.

If this is so, what statistic should be assigned a randomly selected x as a measure of his risk of violent death? Not H/B, which measures homicide rates within the Bloodlands, since this would assign to anyone beyond B the risk of death of everyone within it—namely 1. Not H/Bc, which measure homicide rates beyond the Bloodlands, since this would assign to anyone within B the risk of death of everyone beyond it—namely 0. But any x chosen at random finds himself either within the Bloodlands or beyond it. It would thus seem that no x chosen at random receives anything like the statistic he deserves.

It is this oddity that provokes the hope for a statistical compromise. An average, perhaps? Violent deaths are, by definition, concentrated in B. The risk of violent death is a zero-one property; and the statistics for such properties admit of no intermediate cases. The contrast to infection in epidemiology is very stark. Homicides within the Bloodlands were not like vectors of disease. There is no consistent way in which to assign to an x chosen at random a rational statistic measuring his risk of death within the Bloodlands. This should hardly be a surprise.^[7]I assume throughout that any set S used in these in calculations can be replaced by its cardinal meaure |S|. They are sets embodying populations, after all. The attempt to provide a statistic for an individual drawn from the world’s population at large represents the friction engendered when an ill-posed problem encounters a reference class ambiguity. So far as homicides go, as Albert Reiss was heard to remark, what is required is “a measure of [the] population that is exposed to the events, or is at risk of being involved in events, such as offenders or victims.”^[8]Cited in Fahui Wang and Van O’Brien, “Constructing Geographic Areas for Analysis of Homicide in Small Populations: Testing Herding-Culture-of-Honor Proposition,” in Geographic Information … Continue reading

This eliminates H/B^C as a rational statistic, and with it any appeal to safety in numbers. They are an irrelevance.

A lighthouse in Italy, Albertus Magnus remarked, does not affect a lighthouse in England.

There remains an empirical point, and so a matter of fact. According to Pinker’s own source, the proportion of excess deaths to the world’s population was far smaller in the nineteenth than in the twentieth century.^[9]Pinker’s conclusions to the contrary would make sense only if victims were homogeneously distributed. This is not the case. The underlying issue of statistical homogeneity is by no means trivial. … Continue reading

All formulas were tried to still
The scratching on the window-sill,
All bolts of custom made secure
Against the pressure on the door,
But up the staircase of events
Carrying his special instruments,
To every bedside all the same
The dreadful figure swiftly came.^[10]H. Auden, New Year Letter [1940].

In the face of its crimes, what can one say about the twentieth century beyond what Elias Canetti said: “It is a mark of fundamental human decency to feel ashamed of living in the twentieth century.”^[11]Quoted in Simon Leys, The Hall of Uselessness: Collected Essays (New York: New York Review Books Classics, 2013), p. 408. What one is not prepared to say, and still less to encounter, largely because it is, at once, absurd and obscene, is the view that the great crimes of the twentieth century were, all things considered, not so bad. This is the view that Pinker defends: The crimes of the twentieth century were not among the greatest of crimes because other crimes were greater. In The Better Angels of Our Nature, Pinker offers a list of the worst atrocities in human history.^[12]Pinker, The Better Angels, pp. 235–36. His source is Matthew White, a librarian with a morbid interest in atrocities and a marked talent for publicity. White has deduced his conclusions by an assiduous survey of secondary sources, each citing the other for authority, an undertaking otherwise known as a circle jerk. The greatest of the great atrocities, White argues, is the An Lushan revolt in eighth-century China. Thirty-five million Chinese lost their lives. This is the figure cited originally on White’s website, but on more diligent reflection, White revised thirty-five to thirteen million, almost a threefold reduction. This might have suggested to a more scrupulous scholar than Pinker that White is no reliable source.^[13]See Mathew White, Statistics of Wars, Oppressions and Atrocities of the Nineteenth Century. Both White and Pinker would have been better served by considering the nineteenth-century Taiping … Continue reading

Whatever the truth, it is incontestable that the times were bitter.

“Earth fades, Heaven fades, at the End of Days. But Everlasting Sorrow endures always.”^[14]Yang Gufei, “The Song of Everlasting Sorrow.”

The coordination of crimes over centuries requires some consideration of their natural reference classes. “For comparisons across vast ranges of times and places (such as comparison of the atrocities of the 20th century with those of earlier centuries),” Pinker writes, “I generally use the population of the entire world at the time.”^[15]See Pinker’s website. In assessing the An Lushan revolt, Pinker accepts the figure of thirty-five million dead. Thirty-five million dead in the eighth century, he argues, is comparable to 429 million dead in the mid-twentieth century. Calculations are straightforward. H1/W1 ≈ H2/W2, where H1 designates death tolls in the An Lushan rebellion, and H2 refers to presumptive death tolls had the An Lushan rebellion taken place in the mid-twentieth century. W1 and W2 are eighth-century and mid-twentieth-century population totals. Following White (blindly, as it happens), Pinker assumes that H1/ W1 = 1/6, whereupon there is H2 = 429,000,000.^[16]Stop, I am tempted to say, laying an avuncular hand on Pinker’s shoulder. Ratios scale as a matter of arithmetic, but homicide statistics do not. Two deaths in a hamlet of one hundred, two thousand … Continue reading This is a figure intended to shock, and, of course, it does. Had the An Lushan taken place today, Pinker remarks, it could “hold its head high amidst twentieth century atrocities.”^[17]Pinker, The Better Angels, p. 234. There is a sort of savage nobility about his firm reliance on his own bad taste, as A. E. Housman said of Eric Bentley. A sense for the tone appropriate to his subject is not among Pinker’s stylistic accomplishments. These meditations must now be interrupted by an obvious question: If the An Lushan rebellion had taken place today, would the ensuing death toll be greater than it was or would the world’s population be smaller than it is? Both counter-factual claims are compatible with the assumption that H1/W1 ≈ H2/W2.^[18]If Julius Caesar = Richard Nixon, would Caesar have spoken English or Nixon Latin? Nelson Goodman raised many pertinent questions of this type in Fact, Fiction, and Forecast (Cambridge, MA: Harvard … Continue reading This macabre argument goes backwards as well as forwards. Six million Jews were murdered in the Holocaust. The world population in 1940 stood at roughly two billion; and the world’s population in 1300, at roughly one hundred million. Had the Holocaust taken place in 1300, would death tolls have stood at 300,000 or would the world’s population have been two billion? In response to the objection that the world’s population in 1300 was not two billion, there is the counter-response that neither did the Holocaust take place in the fourteenth century. Which is it to be? There is no way of telling: evidence, if any were needed, of the homicidal projection is intrinsically unstable because it is unavoidably counterfactual.^[19]Alan Hájek, “The reference class problem is your problem too,” Synthese 156 (2007): 563–85. Hájek’s paper is, except for its conclusions, correct in its diagnoses. That the An Lushan revolt killed thirty-five million people is, or may be, a fact; that the An Lushan would have killed 429 million people in the twentieth century is not. The Holocaust, the Atlantic slave trade, and the An Lushan revolt cannot be projected into the past or into the future. They are what they are. We are left with what we always knew.

The An Lushan revolt killed, or may have killed, thirty-five million Chinese; and the Holocaust most certainly killed six million Jews.

Both were terrible.

A correlative error at once follows, this one closer to frank fallacy. “If the population grows,” Pinker affirms,

so does the potential number of murderers and despots and rapists and sadists. So if the absolute number of victims of violence stays the same or even increases, while the proportion decreases, something important must have changed to allow all those extra people to grow up free of violence.^[20]Steven Pinker, “Frequently Asked Questions.” Pinker misses the reality that the crimes of the twentieth century were unprecedented in scope and that those committing them were officials of the … Continue reading

Nothing of the sort is true in the case of homicide statistics; and nothing of the sort is true in the case of atrocities either. The supposition is backwards. The correct question is rather what changed in Nazi Germany, or Stalin’s Russia, or Mao’s China, or Pol Pot’s Cambodia, to allow crimes never before seen to take place there?

If the question is obvious, so, too, the answer. We have no idea.

In contemplating the twentieth century, contemporary criminologists enjoy or, at any rate, evince, a sense of optimism somewhat at odds with their immersion in the inky details of their professional calling—murder, after all. Like El Dorado in a somewhat different context, London in 1950, Eisner argued, “may serve as a benchmark for the lowest level of interpersonal lethal violence as yet attained in any known Western society.”^[21]Eisner, “Long-Term Historical Trends in Violent Crime,” p. 106. Interpersonal lethal violence? What Eisner had in mind is murder; and what he observed was that, for a time in London, there was not much of it going around.

Whereupon that sense of optimism.

Given the correlative assumption that the homicide rate is a quantifiable indicator of the degree of violence, criminologists might be forgiven a sense of giddiness.

Historians of the twentieth century, like anyone with his eyes open, might wonder about interpersonal lethal violence elsewhere in Europe just a few years earlier. From Eisner’s buoyant “long term declining trend in homicide rates,” one would expect the data to reflect a series of homicide rates converging sedately to H/P ≈ 1/100,000. They did nothing of the sort. Look to Kyiv, Amsterdam, Westerbork, Salonika, Treblinka, Majdanek, Chelmno, Sobibor, Krakow, Lachwa, Zazlaw, Potulice, Soldau, Stutthof, Lublin, Kelice, Wilnow, Bedzin, Bialystock, Nowogrodek, Ponary, or Warsaw, and another picture emerges, one in which homicide rates converged to the near certainty of death.

During the German occupation of France, the French police, demonstrating an efficiency never revealed in the pursuit of their daily activities, deported 50,000 Jews from Paris to their deaths.^[22]Jacques Semelin, writing in Persécutions et entraides dans la France occupée (Paris: Édition du Seuil, 2013), remarks with some satisfaction that “puisque environ trois cent trente mille … Continue reading La rafle is today well-remembered in French political history, but la rafle was one incident in a series of deportations, les rafles. Let me see. The population of Paris in 1940 stood at P ≈ 1,000,000. Neglecting entirely the ordinary Parisian murder in which a drunken sot at last settled the score with his nagging wife, H/P ≈ 1,250/100,000 per annum.^[23]The French Wikipedia page is of an extraordinarily high quality, and contains an exhaustive list of French references. It could only have been written by a senior scholar in the Centre National de la … Continue reading The presumptive homicide rate in Oxford in 1343 was 121/100,000. In the middle of the morally improved twentieth century, Parisian homicide rates were ten times higher than they were in mid-fourteenth century Oxford. Almost all Jews in Paris lacking French citizenship were killed.

There were roughly nine million Jews living in Europe in 1939. Of these, six million were murdered, making for a homicide rate H/P ≈ 66,000/100,000, or 14,000/100,000 per annum for each of the four years between 1941 and 1945. A refinement in reference class so that it refers only to Jews murdered in various cities, such as Lachwa, Zazlaw, Potulice, Soldau, Stutthof, Salonika, Budapest, or even Amsterdam, yields a homicide rate much higher than the overall European homicide rate, even as the overall European homicide rate during these years was higher than the European homicide rate at any time in the history of Europe.

Should these dead not be included in European homicide figures?

Are they not dead?

Were they not murdered?

Criminologists understand that terrible crimes took place in the twentieth century. They are disposed to ignore them. Homicide is one thing, genocide, another.^[24]“Most criminologists don’t consider themselves competent,” Manuel Eisner wrote, “to analyze these kinds of levels of killings, believing that genocides and civil wars are something entirely … Continue reading Their business is the first; let others deal with the second. The distinction is entirely artificial. Homicide is murder, and genocide, mass murder. When the statistics pertaining to mass murder in the twentieth century are acknowledged, they bleed through every calculation, forming a ghastly but ineradicable spike in the otherwise humdrum human record of murders undertaken in some sordid hotel room or in the alleyway behind the Bannhof or in a field of winter wheat.

“If thou doest well, shalt thou not be accepted? and if thou doest not well, sin lieth at the door. And unto thee shall be his desire, and thou shalt rule over him.”^[25]Genesis 4:7.

If mass murders are not included in the homicide rate for the twentieth century, then the homicide rate is no very good measure of violence; and if they are included, then the homicide rate does not indicate a long-term declining trend in violence.

It indicates the opposite.

It is by virtue of its crimes that the twentieth century has achieved a terrible form of immortality. “It is in the very nature of things human,” Hannah Arendt observed, “that every act that has once made its appearance and has been recorded in the history of mankind stays with mankind as a potentiality long after its actuality has become a thing of the past.” No matter how remote, great crimes have a living power to influence the future. Tradition and taboo are unavailing.^[26]“Whatever is the cause of human corruption,” Dr. Johnson observed, “men are evidently and confessedly so corrupt, that all the laws of heaven and earth are insufficient to restrain them from … Continue reading “No punishment,” Arendt wrote, “has ever possessed enough power of deterrence to prevent the commission of crimes.” On the contrary, “whatever the punishment, once a specific crime has appeared for the first time, its reappearance is more likely than its initial emergence could ever have been.”^[27]Hannah Arendt, Eichmann in Jerusalem (New York: Penguin Books, 1994), 273. This remark seems to me far more pregnant than Arendt could have imagined.

It is in this sense that the twentieth century, having introduced into human history crimes never before imagined, or if imagined, never before undertaken, is immortal, and will, like the crucifixion, remain a permanent part of the human present.

It is simply there, an obelisk in human history: black, forbidding, irremovable, and inexpugnable.

Interviews with the author:

• CRITICAL THEORY AND THE SLINGSHOT
• THE NARCISSISTIC MARK

David Berlinski is Claire Berlinski’s father. This is a revised version of an essay originally published in the volume Human Nature.