Las matemáticas de la guerra

Para aquellos que gusten de las matemáticas y la estadística, y además tengan interés en su aplicación para la resolución de problemas, les resultarán muy interesantes los artículos de The Economist: ‘Cry havoc! And let slip the maths of war‘ y ‘Tanks in the Cloud‘.

El primero resume un artículo de Neil Johnson, aún sin publicar y en proceso de revisión por la revista Nature, que propone una fórmula para predecir el patrón de ataques terroristas:

The formula in question (Tn = T1n-b) is one of a familiar type, known as a progress curve, that describes how productivity improves in a range of human activities from manufacturing to cancer surgery. Tn is the number of days between the nth attack and its successor. (T1 is therefore the number of days between the first and second attacks.) The other element of the equation, b, turns out to be directly related to T1. It is calculated from the relationship between the logarithms of the attack number, n, and the attack interval, Tn. The upshot is that knowing T1 should be enough to predict the future course of a local insurgency. Conversely, changing b would change both T1 and Tn, and thus change that future course.


El segundo hace una analogía del problema del tanque alemán (la utilización de un estimador insesgado con varianza mínima en la segunda guerrra mundial para calcular el número aproximado de tanques nuevos producidos en Alemania) con el problema de estimación de máquinas virtuales del negocio de computación en la nube de Amazon:

Amazon, for instance, only reveals that it now stores more than 200 billion digital “objects” and has to fulfil nearly 200,000 requests for them per second—impressive numbers but not very useful ones (an object can be a small file or an entire movie). Rackspace says it operates nearly 64,000 servers globally, but notes that only some are used for IaaS.This reluctance to share information has inspired analysts and bloggers to find out more, in particular about Amazon. During the second world war, the allies were worried that a new German tank could keep them from invading Europe. Intelligence reports about the number of tanks were contradictory. So statisticians were called in to help.

They assumed that the Germans, a notoriously methodical lot, had numbered their tanks in the order they were produced. Based on this assumption, they used the serial numbers of captured tanks to estimate the total. The number they came up with, 256 a month, was low enough for the allies to go ahead with their plans and turned out to be spot-on. German records showed it to be 255.

Con éste método estadístico, un bloguero y Cloudkick, una compañía, han estimado el número de computadores virtuales de Amazon:

Mr Rosen decrypted the serial numbers of Amazon’s “virtual machines”, the unit of measurement for buying computing power from the firm. Alex Polvi, the founder of Cloudkick, then used these serial numbers to calculate the total number of virtual computers plugged in every day. This number is approaching 90,000 for Amazon’s data centres on America’s East Coast alone



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