The question of disciplinary boundaries is a perennial, and Brian Weatherson’s CT post on Richard Gott’s Copernican principle provides yet another instance. Gott, an astrophysicist, is interested in the question of whether you can infer the future duration of a process from its present age, and this issue seems to received some discussion in philosophy journals.
It may be beneath the notice of these lofty souls, but statisticians and social scientists have actually spent a fair bit of time worrying about this question of survival analysis (also called duration analysis). For example, my labour economist colleagues at ANU were very interested in the question of how to infer the length of unemployment spells, based on observations of how long currently unemployed people had actually been unemployed. The same question arises in all sorts of contexts (crime and recidivism, working life of equipment, individual life expectancy and so on). Often, the data available is a set of incomplete durations, and you need to work out the implied survival pattern.
Given a suitably large sample (for example, the set of observations of Broadway plays, claimed as a successful application of Gott’s principle) this is a tricky technical problem, and requires some assumptions about entry rates, but raises no fundamental logical difficulties. The problem is to find a distribution that fits the data reasonably well and estimate its parameters. I don’t imagine anyone doing serious work in this field would be much impressed by Gott’s apparent belief that imposing a uniform distribution for each observation is a good way to go.
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