The Mathematics of War

A very interesting article in the Economist (subscription required, but recently syndicated in a bunch of other papers, so may be elsewhere on the web),
which opens:

ON JULY 19th, IraqBodyCount, a group of academics who are attempting to monitor the casualties of the conflict in that country, published a report suggesting that almost 25,000 civilians have been killed in it so far. In other words, 34 a day. But that is an average. on some days the total is lower, and some higher — occasionally much higher.


It is this variation around the mean that interests Dr. Neil Johnson of the University of Oxford and Michael Spagat of Royal Holloway College, London. They think it is possible to trace and model the development of wars from the patterns of casualties they throw up.

The groundwork for this sort of study was laid by Lewis Fry Richardson, a British physicist, with a paper on the mathematics of war that was published in 1948….

The outcome was startling: rather than varying wildly or chaotically, the probability of individual wars having particular numbers of casualties followed a mathematical relationship known as a power law….

Terrorist attacks within G7 countries could be distinguished from those inside non-G7 countries by their different indices….

While trying to find a version of this not behind a subscription firewall, I came across
a related story in Nature. Net, net: the war in Iraq is approaching the same pattern as the long-running war in Colombia, though one started as a conventional war and the other a decentralized conflict.

The Economist article claimed that Johnson and Spagat’s paper was published on ArXiv, but I couldn’t find it there. If anyone else has better luck, let me know.

  • Peter Rip

    I think this is it.

  • Chris Anderson


    The powerlaw distribution of casualties in war is descibed, along with many other examples of the ubiquity of powerlaws, in a quite good book called, unsuprisingly, Ubiquity.

  • Thanks, Peter, for the arXiv link. In Physics, not Math, I see. No wonder I couldn’t find it.

  • This is an interesting Flash visualisation of the casualty data:

  • David
  • Tim, I didn’t create a new account to read the article, but I’m curious how they could have written it at all considering how well-known the flaws in the Herold/Slobodo methodology have been. Yet this faction continues to get press which takes them at face value…?

    (Herold was found to have wildly overstated Afghani casualities through his technique of min/max in press reports, particularly considering that Coalition forces rarely ventured raw estimates… what remained were quotes from wild speakers, Baghdad Bob and the like. This media technique was later adopted by a “peace” group for Iraq, with similar fundamental problems but even better media results.)

    If you check the site today you’ll see included totals from market-bombings and the rest of the oppression. Logically, to include such attacks on civilians you’d also include the daily shreddings from Saddam and his sons, which still shows a net benefit to the people of Iraq. Such counter-scoring is what the NoBodyCount Project did for awhile, but that was, literally, years ago.

    The extremely interesting thing here is how some memes persist despite lack of foundation. Herold’s Afghanistan campaign was quickly debunked, so many of us were surprised when the same flawed methodology was adopted for Iraq. But the shocking things is how this campaign still gets press, and how they’ve taken over the search engine results as well. Feels like the Scientologists, to me, it does…. :(

    Summary: GIGO.

    (For the powerlaw angle, yes, things near the mean are more frequent than things far from the mean, almost by definition…?)

  • Logically, to include such attacks on civilians you’d also include the daily shreddings from Saddam and his sons, which still shows a net benefit to the people of Iraq.

    Yes, those who focus on current death toll in Iraqi and even seek to inflate it are revealingly disinterested in the much higher numbers undeniably killed by Saddam. The hundreds of thousands of bodies, many of them children, being dug up by the Finns in mass graves in Iraqi interests neither them nor the so-called “mainstream media.” They are not there assisting with the body count, and they’d rather spin computer estimates of current death tolls from a distant locale. Nor do they care about the opinion the Iraqi people have about the relative merit of being killed by Saddam for simply being in the wrong ethnic group or thinking versus the risk of being killed in a war against terrorism and for democracy and a decent government.

    Personally, I have to admit that I was suprised to see the more radical left in the U.S. and Europe, so eager to keep Saddam in power and so angry to see him unseated. While it is true that to some extent Saddam had the once-revered Stalin as a role model, I did think that the left had some content, however small, in its rationale for supporting bloody dictators. Saddam, after all, does have ties to radical Islam and until recently some on the left were quite eager to warn us that an elderly Jewish rabbi, a Baptist preacher who likes bass fishing, and a Catholic mother who recites “Hail Mary,” all “religious fundamentalists,” had something in common–evil religious repression–with the mudullahs in the Middle East. Now it appears that the Western Left, including many of my neighbors, would be content to see Islamic “fundamentalism” remain in power perhaps forever.

    I had forgotten just quickly the radical left turned from anti-Nazi to pacifism in 1939 after the pact between Stalin and Hitler. I’d also perhaps forgotten that the real goal of the radical left has always being a sort of serfdom where the few rule over the many. The ideological justification is irrelevant, Marxism, nationalism, environmentalism or even Islam serve as well. It’s why Earth Day was selected to be Lenin’s birthday, although the dictator murdered between 2-3 million people. It’s why the Marxist terrorist, Carlos the Jackel, is now a radical Muslim terrorist. Ideology is the rationale for what is really desired, the power to regiment and kill. And of course, there is always the “stupid” factor, which applies to many of my neighbors. There really are people who believe these weird conspiracy theories about 9/11.

    In the end, I suspect Bush and Condi Rice will be as successful at bringing democracy to the Middle East as Reagan was at bring it to Eastern Europe. Their foes are certainly the same people and groups, so that’s a good sign. These people lost once; let’s hope they lose again. Every time they lose, the world becomes a better place.

    That doesn’t mean all will be perfect in the Middle East. Russia itself doesn’t seem to be taking to democracy very well, unlike Poland or the Czech republic. As J. R. R. Tolkien noted, no victory over evil is ever final. There will always be a battle to be fought against both evil and its apologists. In fact, Tolkien toyed with a follow-up to The Lord of the Rings in which Minas Tirith ends up looking remarkable like today’s Paris or Berlin, decadent and dabling half-hearted in evil-at-a-distance. He gave it up as too depressing. Unfortunately, it’s our reality and can’t be dismissed that easily.

    –Mike Perry, Seattle, Untangling Tolkien

  • Mike —

    While I agree that IraqBodyCount may have an axe to grind, I fail to see how turning a post on an interesting mathematical paper that looks at the casualty patterns in wars into a Right/Left debate is appropriate. I was interested in the observation that we can discern features of wars by statistical analysis, not in making a political point about Iraq.

  • Mylasticus

    After reading a bit about the use of mathematics for descriptions of war, I was wondering does anyone know if there are any papers dealing with applying social network theory to terrorist cells?

  • KC

    IIRC, Slashdot covered this quite a while back. I’d love ot see it with more information and updated with the results of the past 4 years…

  • bloody econ working in shitty it

    This is the article, sayz one of those bloody econs:


  • Sonia

    That’s no wonder they use mathematics for description of war. Actually mathematicians are used to apply their sience to any side of our life and it works. At least for them and probably has no sence to ordinary people. I just use morality when thinking about this disaster.

  • Sonia:

    Do you still associaty morality with politics?!