Mathematics of War – 1 – Ecology and Patterns

In a letter sent on 5 July 2009, accepted on 29 October 2009 (so much for work at the speed of light and thought) and published on 17 December 2009 is Nature 462, 911-914, Juan Camilo Bohorquez, Sean Gourley, Alexander Dixon, Michael Spagat and Neil Johnson write that war can be quantified in a box and push forward a short paper, “Common Ecology Quantifies Human Insurgency”, which the bombastic, pun intended, TED is arguably claiming as the handiwork of their TED Fellow Sean Gourley, so much so as immortalizing the collective sweat and toil of 5 people as the Gourley equation (come on people, show some modesty and appreciation)…

Describes dynamical composition of an insurgency. Here, n_s is number of groups with strength s (> 1). The different terms describe processes of group coalescence, and group fragmentation.
I feel for Bohorquez and others because the spotlight seems to be on Gourley who is listed as the second author and we all (well OK, some geeks) know what that means as noticed in time-tested real-life graduate, academia and university life…

Ha ha. Having started communications with a joke as schooled, let us get to the abstract but not before mentioning that this paper is featured as the cover story of Nature beating out the ‘new earth discovery’ and ‘possible cancer cure’ which says as much of our fascination, nay, obsession with killing other people we don’t know, err… war, terrorism and occupation than nothing else. Enough trivia, le abstract…

Many collective human activities, including violence, have been shown to exhibit universal patterns*. The size distributions of casualties both in whole wars from 1816 to 1980 and terrorist attacks have separately been shown to follow approximate power-law distributions. However, the possibility of universal patterns# ranging across wars in the size distribution or timing of within-conflict events has barely been explored. Here we show that the sizes and timing of violent events within different insurgent conflicts exhibit remarkable similarities. We propose a unified model of human insurgency that reproduces these commonalities, and explains conflict-specific variations quantitatively in terms of underlying rules of engagement. Our model treats each insurgent population as an ecology of dynamically evolving, self-organized groups following common decision-making processes. Our model is consistent with several recent hypotheses about modern insurgency, is robust to many generalizations, and establishes a quantitative connection between human insurgency, global terrorism and ecology. Its similarity to financial market models provides a surprising link between violent and non-violent forms of human behaviour.

(*) I would think that the ‘why’ of universal patterns in any collective human activities, peaceful or violent, is fairly obvious to an acute observer, not just surreal zoologists such as Desmond Morris. We humans are a young and naive species. Inspite of our pretensions to be sentient and complex and underneath all the make-believe layers of civilization and smoke and mirrors, we are still nothing but animals with barbaric instincts influencing our thought patterns which are focused after all, on the primal need to feed, greed and breed. Everything, with a capital E considered, brain has not really evolved after an initial mutation burst but has only adapted
(#) Let me spare the suspense and list out the universal pattern across conflicts, purely by observation and my study and understanding of history (however little I seem to recall) without me reading the paper (which is gated) or the editors note or news article(s) or Q’n’A session or TED Talk or commentary or books like Naked Ape or Human Zoo or just about any sort of reference research whatsoever –
1) Humans organize themselves into collectives. It is natural
2) Each collective, duh, collects stuff that makes others jealous
3) Conflict ensues and power and control comes into equation
4) Vanquished seek revenge. Conquerors seek more blood
5) Uneasy peace exists but there is in-fighting and ambition
6) Objects of affection evolve from materials to idealisms
7) People just want to kill others brutally and be famous for it
A) Pattern holds for war and insurgency. Rinse and Repeat
There. We do not have to face an ordeal of the propaganda and rack our brains to read paper or any related materials to make sense of the world as seen through lens of war, or to be more precise, increasingly fluid insurgency that mathematically fits collected data. Wrong. I thought so too but my brain disagreed. It is a nasty piece of work and wanted to have a peek. After all, it is a beautifully written paper and only about 4 pages – most of which is justifying data gathering to the point of being apologetic – and a look-see will not take too much time or too much rewiring of the neurons. Or so, it said. As a principle, I dont argue with my brain. It makes me do unspeakable things and hurts me if I dont do its bidding. So, I complied and boy, was I glad I did? It was a page-turner and a well written piece of inquiry. Well done. I have much to say (continued in later posts where I delve into math, commentary from other places, media coverage and of course, cartoons), but for this piece, I will just cite/para-phrase/quote and expose a model schematic from the letter itself…

The political scientist Spirling and others have correctly warned that finding common statistical distributions (for example, power laws) in sociological data is not the same as understanding their origin. Possible political, ideological, cultural, historical and geographical influences make conflict arguably one the ‘messiest’ of all human activities to analyse. Mindful of these challenges, yet inspired by recent studies of human dynamics, we analyse the size and timing of 54,679 violent events reported within nine diverse insurgent conflicts, placing equal emphasis on both finding and modelling common patterns. Such insurgencies typify the future wars and threats faced by society. To our knowledge, our model provides the first unified explanation of high-frequency, intra-conflict data across human insurgencies. Other explanations of human insurgency are possible, though any competing theory would also need to replicate and/or fit the results. Our model’s specific mechanisms challenge traditional ideas of insurgency based on rigid hierarchies and networks, whereas its striking similarity to multi-agent financial market models hints at a possible link between collective human dynamics in violent and non-violent settings.

Taking our empirical findings for event size, and event timings. Our model (described in schematic) provides a quantitative explanation by treating the insurgent population as an ecology of dynamically evolving, decision-making groups, in line with several recent sociological hypotheses. In addition to explaining the ubiquity of approximate power-laws in the event size distribution it explains the conflict-dependent deviations beyond a power-law. Furthermore, the same model framework also explains the common burstiness in the distribution of event timings that we observe across insurgent conflicts. Following our preliminary 2005 results for Iraq and Colombia, we had suggested that other insurgent wars might be clustered around similar findings supporting our hypothesis. By contrast, we find that the Spanish Civil War and the American Civil War – neither of which are considered insurgent – each give distributions where log-normal can not be rejected, and therefore different from conventional wars. This finding provides quantitative support for claims circulating in social science that insurgent wars represent qualitatively different dynamics from traditional wars and can be classified as “open source”, “fourth generation” warfare – for lack of terms.

Insurgent population comprises of N people, weapons, resources, money etc. distributed into groups with diverse strengths at each time-step t. This distribution changes over time as groups join and break-up. Dark shadows indicate strength of numbers and fire-power, and hence severity of casualties that can be inflicted in an event involving that group.
Our model framework incorporates two key features: (1) ongoing group dynamics within the insurgent population (for example, as a result of internal interactions and/or the presence of an opposing entity such as a state army); (2) group decision-making about when to attack based on competition for media attention. Mechanism (1) is consistent with recent work on human group dynamics in everyday environments, and with current views of modern insurgencies as fragmented, transient and evolving. Mechanism (2) is consistent with comments by former US Senior Counter insurgency Adviser David Kilcullen (no kidding, this is the real name and is a combination of ‘kill’ and ‘cull’ – how apt), who noted that when insurgents ambush an American convoy in Iraq, “… they’re not doing that because they want to reduce the number of Humvees we have in Iraq by one. They’re doing it because they want spectacular media footage of a burning Humvee …”

If a group launches an attack during a day with many other attacks, its media coverage will in general be reduced. If, instead, it launches an attack on a quiet day, its media coverage will increase. Each group receives daily some common but limited information (for example, public radio or newspaper announcements about previous attacks, opposition troop movements, a specific religious holiday, even a shift in weather patterns). The actual content is unimportant provided it becomes the primary input for the group’s decision-making process (akin to a financial market). Although the groups are heterogeneous in terms of their strategies, they tend to converge towards similar responses when fed the same information. Our model also includes trapdoors allowing us to interpret the increase in non-randomness over time for Iraq and Colombia when insurgent groups in both wars have become less cautious over time about whether to launch attacks providing more fodder to empirical evidence that groups of humans do indeed use such generic decision-based mechanisms. The data for all the 9 conflicts deviates from its ‘random war’ model (randomizing event occurrences within each epoch): the ‘real war’ exhibits an over-abundance of “light days” (that is, days with few attacks) and of “heavy days” (that is, days with many attacks), but a lack of “medium days” compared with the ‘random war’. By considering subsets of days, we have determined that these features are not just an artefact of a variation in attack volume across days of the week (for example, Fridays). Interestingly, this burstiness has become more pronounced over time for the wars in both Iraq and Colombia, suggesting that they have become less random (ergo, more predictable) as they have evolved.

Just some high-level observations. One, this study shows humans are predictable and therefore, their actions, which is predictable on by and itself. Boy, you know, people don’t like to think that their lives can be tracked so accurately, but, uh, human action isn’t very different than any other data, is it? Two, what this letter really achieves is refute/ratify (not fully clear at this point) the mathematics of a fictional character Charlie Eppes in the CBS TV series Numb3rs Season 2, Episode 16 “Protest” where Charlie blurts that terrorists/insurgents/soldiers/fighters behave on the lines of a social network. They are after all, only human and like all other humans form social networks from bridge clubs and church groups to university staff and federal agencies to jihadi extremists. Mathematically, we can analyze these organizational structures to reveal who the leaders are. Now, these various insurgents or terrorists or freedom-fighters or even, anti-war anarchists (depends on which glasses one wears) are also social networks an analysis of which can reveal which members of groups got along, and which didn’t, and who linked up with people in other groups quantifying relationships. It reveals sub-structures in networks, like cliques, romances, even secret alliances with other groups. Now, using bipartite network analysis, one can identify who the true connectors are and bomb the crap out of them through unmanned predator strikes which will kill more innocent people prompting their loved kith and kin to take up arms against the marauding invaders who had no reason to be there in the first place. Three, there are people who are actually collecting the data which all made the headlines and getting international press right down to the international section in a local newspaper in rural Mongolia whereas the mission to Mars, or its postponement has become a footnote in history. Four, the authors are not really expounding any new theory. They say that current theories being explored by other people are somewhat true or false – it depends on the theory – based on quantitative analysis of public domain data on insurgent attacks. Five, perhaps, they need not have done this research at all. But since they did, they would have been better off explaining their work by just showing “Monty Python’s Life of Brian”, especially ‘Judean People Front’ vs. ‘People Front of Judea’ vs. ‘Judean Popular People Front’ vs. ‘Popular Front of Judea’ scene, “Romans Go Home” graffiti scene and kidnapping planning/execution scene where two groups land at the same time and scuffle that they thought of it first. Just a fun touch. Finally, the irony is if one has to verify if this model and/or the theory behind it holds any water using the scientific method i.e. conduct more experiments to see if it fits to new streams of data, we need more violence, more bombings, more killings and more attacks. The constant quandary of such analyses. To get more data, you need more wars in spirit of curiosity.

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