Monday, January 28, 2008

Category Theory vs. General Systems Theory

After moving to northern Alabama this winter (and seeing the job openings in Huntsville), I took an Systems Engineering Overview course through the University of Alabama at Huntsville Continuing Education. One of the things I learned is that I am not particularly interested in becoming a Systems Engineer (I am a technical guy and a computer scientist; project management is not fascinating). The other is that the definition of a system according to General Systems Theory (the nominal, theoretical roots of systems engineering),
"A system is here defined as a set of objects together with relationships between the objects and between their attributes related to each other and to their environment so as to form a whole."
is almost the same as that of a category in mathematical category
theory,
a collection of mathematical entities and the relationships which exist between those entities

The difference is that in category theory the objects have no internal attributes or structure and that if an environment is necessary, it is represented as one or more additional objects.

If anyone has a tame professor of mathematics handy, I am sure there are several dissertations in this observation. (I cannot help much; I am still waiting for "Category Theory for the Slobbering Moron". But give me a footnote if you can.)

Why People Turn to Bombs

The 14 December 2007 issue of Science contains a review ("Why People Turn to Bombs") by Ethan Bueno de Mesquita of What Makes a Terrorist: Economics and the Roots of Terrorism by Alan B. Krueger (ISBN 9780691134383). The reviewer writes that Krueger suggests two root causes of terrorism: "First..., the absence of political freedom is positively correlated with terror attacks....Second, democracies are more often the victims of terrorism than autocracies...[because] democratic leaders are more responsive than autocratic leaders to public opinion...."

Am I wrong in thinking that these two root causes are contradictory? The "absence of political freedom" would seem to indicate a government *not* "responsive...to public opinion", and vice versa. While I suspect that the two statements can be made compatible in some fashion (perhaps the countries with a lack of political freedom are exporting their terrorists to those with democratic leaders, or perhaps Krueger is concerned with countries with a combination of democratic leaders and an absence of political freedom; a false democracy), I think this issue is fundamental in the question of whether Krueger's work is worthwhile.

The reviewer, however, focuses on potential methodological problems and takes issue with Krueger's policy implications. (I have significantly less of a problem with Krueger's described policy conclusions: "The importance of guaranteeing civil liberties has been underemphasized as a means of prosecuting the war on terrorism and the war in Iraq," and terrorism "only matters in a big way if we let it matter." On the other hand, I do agree with the reviewer that it is plausible that there is a significant relationship between poverty and terrorist recruitment, and that Krueger's analysis may have avoided this relationship.)