Physicist Alan Sokal, who was last seen demolishing postmodernist pretensions, has set his sights on positive psychology. This time his target is the critical positivity ratio, which blogger Neuroskeptic describes as “the idea that if your ratio of positive to negative emotions is over a certain value, 2.9013, then you will ‘flourish’; any lower and you won’t.”

The concept was laid out in an influential 2005 paper, which according to Google Scholar has been cited more than 950 times. Neuroskeptic explains what Sokal and his colleagues, Nicholas Brown and Harris Friedman, found:

[T]he idea of a single ‘critical ratio’ that determines success or failure everywhere and for everyone is absurd in itself. … But even were there a magic ratio, it wouldn’t be 2.9013. The whole analysis in the 2005 paper was based on taking a poorly-described dataset and then making it fit a mathematical model, purely by means of elementary misunderstandings.”

Of *course* it drew on 1960s geophysics:

[Study author Marcial] Losada observed positive and negative emotions change over time, and that we can model this process in the form of a Lorenz system. The Lorenz system is a mathematical function famous for being pretty (e.g. ooh!). There are infinitely many Lorenz systems, based on three set-up ‘parameters’, each of which can be any number. It turns out that Losada set two of those three variables to the values used by a geophysicist in 1962, who picked them purely to make a pretty illustration for his paper about air flow.

If you set up a Lorenz system in exactly this way, and set it running, you can get a number out, 2.9013. This number is meaningful only within this particular system, with those particular parameters. Yet by means of an epic series of assumptions, Losada declared this meaningless quantity to be the Key to Happiness and Success.

Mathematicians David H. Bailey and Jonathan M. Borwein aren’t terribly surprised:

From all indications, the Fredrickson-Losada article is an exercise in “physics envy” — trying very hard to dress work in the social sciences, which, by definition, are not closely connected to very precise physical laws and processes, in the exalted language of mathematics and mathematical physics. It is also the case that the whole area of social psychology has been rocked by recent scandals and by a prevalence of sloppy ‘science’. It has been described by Nobel economist Dan Kahneman as a “train wreck waiting to happen.”

But more generally, the lesson for all who would apply mathematics in this or any other arena of modern science and engineering is clear. Mathematics is a powerful tool, but there is no point in attempting to apply it beyond reasonable boundaries, or with a level of numeric precision far beyond what is justified by the original problem in hand. Mathematical excesses can lead to nonsense.

Watch out, David Brooks.