British psychology student Nick Brown and two co-authors have just published an astonishing demolition of a top-ranked paper in the field of positive psychology: The Complex Dynamics of Wishful Thinking One of the authors of the critique is Alan Sokal, the physicist who, in 1996, famously wrote a parody of then-fashionable postmodernist theorizing and had it published as a serious paper in a cultural studies journal, thus sparking years of controversy.

It might happen again. The target this time is the 'critical positivity ratio' - 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 'critical positivity ratio' is a popular idea. Fredrickson and Losada's 2005 paper on it has been cited a massive 964 times on Google Scholar, just for starters. And yet - that paper is complete rubbish. As are Losada's previous papers on the issue. I criticize a lot of papers mysef, but this one really takes the biscuit. It's an open and shut case. As Brown et al write, the idea of a single 'critical ratio' that determines success or failure everywhere and for everyone is absurd in itself:

The idea that any aspect of human behavior or experience should be universally and reproducibly constant to ﬁve signiﬁcant digits would, if proven, constitute a unique moment in the history of the social sciences.

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. 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 infintely 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 paramaters. Yet by means of an epic series of assumptions, Losada declared this meaningless quantity to be the Key to Happiness and Success. There's loads more detail in the Brown et al paper, and it's surprisingly readable for something so depressingly stupid. As Brown et al say:

One can only marvel at the astonishing coincidence that human emotions should turn out to be governed by exactly the same [Lorenz] equations that were derived as a deliberately simpliﬁed model of convection in ﬂuids, and whose solutions happen to have visually appealing properties. An alternative explanation - and, frankly, the one that appears most plausible to us - is that the entire process of “derivation” of the Lorenz equations has been contrived to demonstrate an imagined ﬁt between some rather limited empirical data and the scientiﬁcally impressive world of nonlinear dynamics.

But why has it taken eight years for someone to point this out, given the size of the claim combined with the paucity of the evidence?

[The 2.9013 critical positivity ratio] would, if veriﬁed, surely require much of contemporary psychology and neuroscience to be rewritten; purely on that basis we are surprised that, apparently, no researchers have critically questioned this claim, or the reasoning on which it was based, until now.

The Emperor's New Clothes analogy is horribly overused, and but in this case, it seems apt - or at least, I hope so. The alternative is worse: that no-one spoke out simply because no-one in the field of positive psychology could see anything wrong with it. On that note, it would obviously be wrong to dismiss all of positive psychology research just because of one bad paper. However, positive psychologists do have a case to answer, for letting this get 964 citations. For example, the guru of the field, Martin Seligman, quoted the Losada 2.9 ratio in a talk, although he did warn that it should not be taken as universally valid. Everyone who cited this either did so without understanding it, or didn't bother to check.

Brown, NJL, Sokal, AD, & Friedman, HL (2013). The Complex Dynamics of Wishful Thinking: The Critical Positivity Ratio American Psychologist DOI: 10.1037/a0032850