Thursday, May 22, 2008

Math in the social sciences

The use of mathematics in economics has expanded greatly in the last century – algebra has come to dominate economic journals, and according to NYU professor Mario Rizzo, "[c]ontemporary economics has become a branch of applied mathematics." Some economists have criticized this formalism, arguing that complicated models are useless if they are only good for describing an economy in an ex-post facto nature. But anyway, in this context, it shouldn't surprise anyone that this sort of mathematical formalism has crept into other fields, such as urban planning. In his monograph Zoned Out: Regulation, Markets, and Choices in Transportation and Metropolitan Land-Use, Jonathan Levine criticizes the mathematical orientation of land use and transportation planners:

An early research approach to the impact of metropolitan form on travel behavior was based on linear programming methods. The analyses defined as their objective some minimization of travel requirements under various land-use configurations to simulate the sensitivity of travel demand to those alternatives. [...] The reader gets the feeling that rather than believing that such central control could actually be exerted, researchers were driven to these questions primarily by their linear programming methodology, and any link from research to policy and practice appears to be somewhat of an afterthought.

I'm not dissing mathematics, but I have to agree that a lot of formalism in social science models is considerably more advanced than the data and assumptions researchers can make. While the social sciences are no doubt based ultimately in the physical sciences – there is no psychology outside of impulses in the brain and the physical ordering of matter (see this xkcd comic) – extending such mathematical methods to scenarios in which you can't possibly hope to quantify enough variables or design a good enough model seems to be a waste of time.

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