Mathematics of Warfare

ERPZ have always been rather social science oriented, doing analysis mostly on social/economic/political matters and lots of writing in just plain language (ie. no greek symbols or mathematical operators). Nevertheless, economics is fundamentally somewhat about logic and it attempts to connect the maths and science of our society with reality. Sean Gourley, a physicist is doing the same sort of analysis in his research on the mathematics of war, which he presented on

Gourley's Equation
Gourley's Equation

The most interesting idea presented in the talk is that even within the chaos of conflict, there are universal principles and relationships between the myriad of different variables in the field (in this case, fatality and frequency of attacks). More importantly, the use of alpha as a measure of fragmentation of insurgency is an interesting result and hopefully can be exploited as a means to achieve peace more quickly during a conflict.

This research paper that eventually resulted from his collaboration with the various experts of different fields was recently published on Nature magazine. TED Blogs features a Q&A with Gourley about the research. It’s great that scientists and mathematicians are using their tools to learn more about complex reality and uncover patterns previously hidden from us; the applications of these mathematics, however, remains to be discovered. As science is often the neutral party, it is important to note also that the same tools can be used by the opposing parties. Strategic thinking, remains an important means of conducting these affairs.


This is an article draft penned some time in 2008 reflecting the style and content of my earlier writings driven by my intellectual passion for education and pursuit of knowledge.

Social Scientists are plagued with this particular divide that is non-existent in the word of Arts and Science. Well, there are cases of particularly weird arts-science mix of beings like Euler, who, as one of the greatest Mathematician, devoted substantial time trying to introduce mathematical notations for music and in essence, mix everything music and mathematics up. It’s as if vector geometry and complex number’s correspondence, but this time, things just get a little more complicated as more of our senses becomes involved in the concoction. But Euler is really rare, and he cleaned almost the entire realm of mathematics of quirky symbols that everyone everywhere would not agree upon and introduced the whole idea of ‘functions’ and it’s notations, without which, we may not be even able to learn programming language because of the sheer complexity of the machine codes kind of ideas.

Pardon me for the introduction that seem to have absolutely no link with the title itself, but in all, I was attempting to demonstrate that there are poetic social scientist who sees humans as being somewhat divine and miraculous and studies the non-mechanical, the purpose-fixed aspects of humans, stuff like aggregate ontology (if there’s even such thing) or philosophies that involves questioning of functions, fundamental reason. For me, I prefer to look into the observable patterns, and the parallels between science and humans themselves, and how laws that govern nature often has its twin doing similar things for the humans. These laws, when stripped to its barest level, is as good as a gravitation acceleration constant – absolutely meaningless. I therefore, must propose this idea of segmenting the human world into 2 layers – 1) Before Reason – the layer void of reason, like molecular interactions, the existence, and many questions that philosophers can debate for another millennium and fail to obtain answers for, all the laws that govern things before human participation, and 2) After Reason – the layer of purpose, where we can explain things after making some assumptions and ignoring the previous layer. For example, when we ask why he went to the post office, we are satisfied with the answer that ‘He went there to get some stamps for his friend’. In that sense, we ignore all the layers beneath, like why his friend need stamps, why is he the one getting it, and if his friend can’t get it, why, and if his friend is attending some functions, why is he doing so and this goes on up to a point like, ‘why is he in this world’, and even further, why his great-great-great-great-great-great-great-great-grandparents exist’. This asymptotic line of reason is the transition to the previous layer, where there’s absolutely no point of explaining things, and not possible anyway.

That was a preamble to thinking about things, and I have chosen to express the above concepts in a more mathematical, and scientific way so that it aids understanding. In any case, I have selected certain laws that are throwing their weight around the scientific realm to explain social sciences, and here, I shall be elucidating the effect of intervention of nature’s equilibria.