Mon Apr 30th, 2012 at 05:06:35 AM EST
There was a somewhat interesting discussion on war and European civilisation (such as it is) and colonialism in the comments to a recent diary by afew on the French presidential election. In it featured:
- the argument by Steven Pinker that we have become "more civilised" since WWII and so the kind of genocidal warfare of the 1930s and 40s is unlikely to be repeated
- the question of whether large wars should be considered as a fraction of total world population (in which case WWII ranked only 6th according to wikipedia - and estimates about older conflicts were called into question in the comments) or in absolute numbers.
In that context, I compared WWII to the 30 years' war in terms of how "traumatic" it had been to the peoples of Central Europe, as well as making the rather cryptic comment "complex systems have lulls, diary tomorrow". This is that diary, with a little delay.
frontpaged with minor edit - Nomad
The discussion, especially the bit about the recurrence of large wars, reminded me of Carl Sagan's Cosmos which, in the last chapter of the book version, referred to some Englishman's statistical investigation of large conflicts. This is Richardson's curve as printed on my own copy of the Spanish edition of Cosmos:
Here's the discussion of Richardson by Carl Sagan:
L. F. Richardson was a British meteorologist interested in war. He wished to understand its causes. There are intellectual parallels between war and weather. Both are complex. Both exhibit regularities, implying that they are not implacable forces but natural systems that can be understood and controlled. To understand the global weather you must first collect a great body of meteorological data; you must discover how the weather actually behaves. Our approach must be the same, Richardson decided, if we are to understand warfare. So, for the years between 1820 and 1945, he collected data on the hundreds of wars that had then been fought on our poor planet.
Richardson's results were published posthumously in a book called The Statistics of Deadly Quarrels. Because he was interested in how long you had to wait for a war that would claim a specified number of victims, he defined an index, M, the magnitude of a war, a measure of the number of immediate deaths it causes. A war of magnitude M = 3 might be merely a skirmish, killing only a thousand people (103). M = 5 or M = 6 denote more serious wars, where a hundred thousand (105) or a million (106) people are killed. World Wars I and II had larger magnitudes. He found that the more people killed in a war, the less likely it was to occur, and the longer before you would witness it, just as violent storms occur less frequently than cloudbursts. From his data we can construct a graph which shows how long on the average during the past century and a half you would have to wait to witness the war of magnitude M.
Richardson proposed that if you continue the curve to very small values of M, all the way to M = 0, it roughly predicts the worldwide incidence of murder; somewhere in the world someone is murdered every five minutes. Individual killings and wars on the largest scale are, he said, two ends of a continuum, an unbroken curve. It follows, not only in a trivial sense but also I believe in a very deep psychological sense, that war is murder writ large. When our well-being is threatened, when our illusions about ourselves are challenged, we tend - some of us at least - to fly into murderous rages. And when the same provocations are applied to nation states, they, too, sometimes fly into murderous rages, egged on often enough by those seeking personal power or profit. But as the technology of murder improves and the penalties of war increase, a great many people must be made to fly into murderous rages simultaneously for a major war to be mustered. Because the organs of mass communication are often in the hands of the state, this can commonly be arranged. (Nuclear war is the exception. It can be triggered by a very small number of people.)
And so we return to Richardson. In his diagram a solid line is the waiting time for a war of magnitude M - that is, the average time we would have to wait to witness a war that kills 10M people (where M represents the number of zeroes after the one in our usual exponential arithmetic). Also shown, as a vertical bar at the right of the diagram, is the world population in recent years, which reached one billion people (M = 9) around 1835 and is now about 4.5 billion people (M = 9.7). When the Richardson curve crosses the vertical bar we have specified the waiting time to Doomsday: how many years until the population of the Earth is destroyed in some great war. With Richardson's curve and the simplest extrapolation for the future growth of the human population, the two curves do not intersect until the thirtieth century or so, and Doomsday is deferred.
But World War II was of magnitude 7.7: some fifty million military personnel and noncombatants were killed. The technology of death advanced ominously. Nuclear weapons were used for the first time. There is little indication that the motivations and propensities for warfare have diminished since, and both conventional and nuclear weaponry has become far more deadly. Thus, the top of the Richardson curve is shifting downward by an unknown amount. If its new position is somewhere in the shaded region of the figure, we may have only another few decades until Doomsday. A more detailed comparison of the incidence of wars before and after 1945 might help to clarify this question. It is of more than passing concern.
I would start by redoing the curve drawn through the point (1 death - 5 minutes) by Carl Sagan (or is that chart by Richardson himself?). This point is drawn differently from the other ones and it doesn't seem to be part of the data set, and the rest of the points appear to be on a straight line:
Here's the plot (including the spurious data point about single deaths every 5 minutes which is not included in the linear fit):
The parameters of the fit are
Where the intercept corresponds to 6 days (the recurrence time of a single death) and the exponent of approximately .5 means that multiplying the number of deaths by 100 multiplies the recurrence time by 10.
Now, to consider this as a fraction of world population, we note that the population at the time of WWII was of the order of 2 billion (whose log10 is 9.30 - cf. WWI clocking in at 7.68) and rescale accordingly. The exponent is still 0.4963 or 1/2 but the intercept (the recurrence time of a war wiping out 100% of the world population) is 2.8262 or 670 years. This means that a recurrence time of 67 years (of the order of a human lifetime) corresponds to 1% of the population of the world being wiped out. Today, this would mean 70 million people. This is mostly a function of Richardson assigning WWI and WWII recurrence times of about 100 years because his sample started in 1820, which barely left out the Napoleonic Wars. In any case, looking at the data from Wikipedia's List of wars and anthropogenic disasters by death toll we find at the top of the list the An Lushan Revolution in the 8th century with estimates of at least 14% (1/7) of world population, which according to our fit would have a recurrence time of no less than 255 years. Still, it seems like too little time given it took place 1200+ years ago.
Now for my obscure point about "complex systems have lulls". The point is that systems in which recurrence times satisfy power laws (straight lines in log-log plots of frequency vs. size as with Richardson) lead to situations in which long periods of relative quiescence are punctuated by large events which appear to come out of nowhere or, rather, appear to be fundamentally distinct from run-of-the-mill events. Something similar happens with earthquakes and the Gutenberg-Richter law. Here's an example of punctuation in War cycles:
In this chart, we see Pax Britannica between the Napoleonic Wars and WWI, punctuated by the wars around 1870 - notably the Franco-German war, the unification of Germany and Italy, and so on. We also see the period of relative peace resulting from the Peace of Westphalia at the end of the 30 Years' War, lasting until the period of the American Revolutionary War, French Revolutionary Wars, and Napoleonic Wars, and punctuated by the War of Spanish Succession in the 1710s.
In terms of our fit to Richardson's data, a recurrence time of 1 year corresponds to 15 thousand deaths. So if we're "used" to seeing violent conflicts with a death toll of thousands of people each year, obviously a 70-Megadeath event is bound to seem shocking. But as we argued above that would be expected once in a lifetime at current population levels. Even an event of the order of 1.5 million deaths every decade would seem out of scale with the 15 thousand deaths per year we'd be "used to" (would the recent Congo Wars, also called the African World Wars, be representative of these 10-year events?). And yet, again even a 1.5M war every decade would not prepare us psychologically for a 70M war every 70 years. It would look like a 70-year "lull", and that is what's to be expected from Richardson's statistics. Anyway, recurrence times are just average quantities, and even though a "big one" might be "due about now" (70 years after WWII), it doesn't mean it "has" to happen. An average recurrence time of 70 years is compatible with a couple hundred years of "world peace punctuated by small scale conflict". In that connection, "Pax Americana" is just the nature of things - between two "big" wars the typical event will be orders of magnitude smaller.