The common statistical thread between psychiatric diagnosis and grad school rankings.

A mathematician's guide to the news.
Jan. 5 2011 6:32 AM

The Mathematics of Narcissism

The common statistical thread between psychiatric diagnosis and grad school rankings.

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The NRC, on the other hand, might have done better to toss the idea of rankings entirely, and just clustered the departments into natural groupings. The statistician Leland Wilkinson ran a quick and dirty clustering on the NRC data for math departments. He found that the departments broke up into five clusters: 10 elite departments, a big group of 59 upper-tier departments, 47 lower-tier departments, and two smaller clusters whose meaning, if any, isn't clear to me. This is much coarser information than a full ranking—but it has the advantage of not depending on politically contentious choices as to which criteria matter most.

In the end, dimension reduction and clustering are going to have to coexist. We rely on continuous metrics to describe baseball players, but at the same time we form mental clusters around prototypes like the plodding slugger and the crafty slap hitter. We cluster our music collections into genres and our politicians into parties, but it can be just as illustrative to map bands and senators in two dimensions using continuous coordinates. So narcissists, and the therapists who treat them, can breathe easy—the notion of the narcissist was alive before the diagnosis broke into the DSM in 1980, and it will persist after the diagnosis is gone.

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Jordan Ellenberg is a professor of mathematics at the University of Wisconsin. His book How Not To Be Wrong is forthcoming. He blogs at Quomodocumque.