Pinker's quantitative analysis seems to based on the assumption that violence should be expected to scale linearly with population size. So he compares the Mongol invasion to recent wars by counting deaths, as a proportion of the population at the time. His trick has the effect of making the Mongol invasion seem much more deadly than it was.
This assumption seems dubious. If we have a population of N people, and we assume that each pair of people has a 1% chance of being enemies, then we expect about 0.01N2 pairs of enemies. If violence occurs between enemies, then we might expect violence to grow quadratically in N.
However civilization would be impossible if violence grew that rapidly. Maybe it makes more sense to assume that potential friendships grow quadratically in N. Then maybe societies can use those friendships to self-organize into peaceful communities, and violence would grow sublinearly in N. Maybe violence only grows like the square root of N, or even the logarithm of N.
Pop psychologist John Gray reviews Pinker:
While Pinker makes a great show of relying on evidence — the 700-odd pages of this bulky treatise are stuffed with impressive-looking graphs and statistics — his argument that violence is on the way out does not, in the end, rest on scientific investigation. He cites numerous reasons for the change, including increasing wealth and the spread of democracy. For him, none is as important as the adoption of a particular view of the world: “The reason so many violent institutions succumbed within so short a span of time was that the arguments that slew them belong to a coherent philosophy that emerged during the Age of Reason and the Enlightenment. The ideas of thinkers like Hobbes, Spinoza, Descartes, Locke, David Hume, Mary Astell, Kant, Beccaria, Smith, Mary Wollstonecraft, Madison, Jefferson, Hamilton and John Stuart Mill coalesced into a worldview that we can call Enlightenment humanism.”This is an odd list of thinkers to credit. Baruch Spinoza was big hero to Jewish atheists. Hardly anyone else has even heard of him. He was a Dutch Jew who believed that God was the universe, and that intuition was the highest kind of knowledge. Immanuel Kant was an unreadable German philosopher whose biggest achievement was to find a non-Christian rationale for the Golden Rule. Thomas Hobbes and David Hume were religious skeptics who were accused of being atheists. Cesare Beccaria wrote a book arguing that crimes should only be punished to the extent necessary, and that people should have access to guns to prevent crime. Thomas Jefferson is revered by Americans for writing the declaration that justified armed revolution against the British. So why does Pinker make him non-violence leader? My guess is that Pinker likes the Jefferson Bible, which was an attempt to remove the religion from the Gospels. (It removed God and miracles, and left the moral teachings.)
What do these have in common? It seems to me that Pinker has cherry-picked some intellectuals in a vain attempt to support his anti-Christian thesis. The Age of Enlightenment was very important, but it happened entirely within Christian Europe. The political leaders, peasants, and intellectuals were nearly all Christians. Christianity taught a message of peace. There were Jews and other groups, but their numbers and influence were far too small to have a significant effect on the violent crime rate or the war-making policy. If violent wars and crimes were declining, it seems crazy to argue that Christianity was not the major reason for the decline.
There are many Christian historians who know this subject much better than Pinker or me. I would like to see a serious rebuttal, as Pinker's book seems like anti-Christian propaganda to me.