The Better Angels of Our Nature: Why Vio - By Steven Pinker Page 0,129

in which statistics are futile. His other analyses counted all wars alike, with World War II no different from, say, a 1952 revolution in Bolivia with a thousand deaths. Richardson’s son pointed out to him that if he divided his data into large and small wars, they seemed to show opposing trends: small wars were becoming considerably less frequent, but larger wars, while fewer in number, were becoming somewhat more frequent. A different way of putting it is that between 1820 and 1953 wars became less frequent but more lethal. Richardson tested the pattern of contrast and found that it was statistically significant.50 The next section will show that this too was an astute conclusion: other datasets confirm that until 1945, the story of war in Europe and among major nations in general was one of fewer but more damaging wars.

So does that mean that mankind got more warlike or less? There is no single answer, because “warlike” can refer to two different things. It can refer to how likely nations are to go to war, or it can refer to how many people are killed when they do. Imagine two rural counties with the same size population. One of them has a hundred teenage arsonists who delight in setting forest fires. But the forests are in isolated patches, so each fire dies out before doing much damage. The other county has just two arsonists, but its forests are connected, so that a small blaze is likely to spread, as they say, like wildfire. Which county has the worse forest fire problem? One could argue it either way. As far as the amount of reckless depravity is concerned, the first county is worse; as far as the risk of serious damage is concerned, the second is. Nor is it obvious which county will have the greater amount of overall damage, the one with a lot of little fires, or the one with a few big ones. To make sense of these questions, we have to turn from the statistics of time to the statistics of magnitude.

THE STATISTICS OF DEADLY QUARRELS, PART 2: THE MAGNITUDE OF WARS

Richardson made a second major discovery about the statistics of deadly quarrels. It emerged when he counted the number of quarrels of each magnitude—how many with death tolls in the thousands, how many in the tens of thousands, how many in the hundreds of thousands, and so on. It isn’t a complete surprise that there were lots of little wars and only a few big ones. What was a surprise was how neat the relationship turned out to be. When Richardson plotted the log of the number of quarrels of each magnitude against the log of the number of deaths per quarrel (that is, the magnitude itself), he ended up with a graph like figure 5–7.

Scientists are accustomed to seeing data fall into perfect straight lines when they come from hard sciences like physics, such as the volume of a gas plotted against its temperature. But not in their wildest dreams do they expect the messy data from history to be so well behaved. The data we are looking at come from a ragbag of deadly quarrels ranging from the greatest cataclysm in the history of humanity to a coup d’état in a banana republic, and from the dawn of the Industrial Revolution to the dawn of the computer age. The jaw drops when seeing this mélange of data fall onto a perfect diagonal.

Piles of data in which the log of the frequency of a certain kind of entity is proportional to the log of the size of that entity, so that a plot on log-log paper looks like a straight line, are called power-law distributions.51 The name comes from the fact that when you put away the logarithms and go back to the original numbers, the probability of an entity showing up in the data is proportional to the size of that entity raised to some power (which translates visually to the slope of the line in the log-log plot), plus a constant. In this case the power is–1.5, which means that with every tenfold jump in the death toll of a war, you can expect to find about a third as many of them. Richardson plotted murders (quarrels of magnitude 0) on the same graph as wars, noting that qualitatively they follow the overall pattern: they are much, much less damaging than the smallest wars and much, much more frequent. But as you