An interesting article by Andrew Anthony in the Guardian talks about an assault on the “mathematics of happiness”:
“Not many psychologists are very good at maths,” says Brown. “Not many psychologists are even good at the maths and statistics you have to do as a psychologist. Typically you’ll have a couple of people in the department who understand it. Most psychologists are not capable of organising a quantitative study. A lot of people can get a PhD in psychology without having those things at their fingertips. And that’s the stuff you’re meant to know. Losada’s maths were of the kind you’re not meant to encounter in psychology. The maths you need to understand the Losada system is hard but the maths you need to understand that this cannot possibly be true is relatively straightforward.”
Brown had studied maths to A-level and then took a degree in engineering and computer science at Cambridge. “But I actually gave up the engineering because the maths was too hard,” he says, laughing at the irony. “So I’m really not that good at maths. I can read simple calculus but I can’t solve differential equations. But then neither could Losada!”
He went back over Losada’s equations and he noticed that if he put in the numbers Fredrickson and Losada had then you could arrive at the appropriate figures. But he realised that it only worked on its own terms. “When you look at the equation, it doesn’t contain any data. It’s completely self-referential.”
You might even call it the “hockey stick model” of psychology.
Following much negotiation, Brown, Sokal and Friedman had their paper accepted by American Psychologist and it was published online last July under the only slightly less provocative title of The Complex Dynamics of Wishful Thinking [PDF]. Referring to the bizarrely precise tipping point ratio of 2.9013 that Fredrickson and Losada trumpeted applied to all humans regardless of age, gender, race or culture, the authors — in fact Brown, in this sentence — wrote: “The idea that any aspect of human behaviour 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.”
The paper mounted a devastating case against the maths employed by Fredrickson and Losada, who were offered the chance to respond in the same online issue of American Psychologist. Losada declined and has thus far failed to defend his input in any public forum. But Fredrickson did write a reply, which, putting a positive spin on things, she titled Updated Thinking on Positivity Ratios [PDF].
She effectively accepted that Losada’s maths was wrong and admitted that she never really understood it anyway. But she refused to accept that the rest of the research was flawed. Indeed she claimed that, if anything, the empirical evidence was even stronger in support of her case. Fredrickson subsequently removed the critical chapter that outlines Losada’s input from further editions of Positivity. She has avoided speaking to much of the press but in an email exchange with me, she maintained that “on empirical grounds, yes, tipping points are highly probable” in relation to positive emotions and flourishing.
“She’s kind of hoping the Cheshire cat has disappeared but the grin is still there,” says Brown, who is dismissive of Fredrickson’s efforts at damage limitation. “She’s trying to throw Losada over the side without admitting that she got conned. All she can really show is that higher numbers are better than lower ones. What you do in science is you make a statement of what you think will happen and then run the experiment and see if it matches it. What you don’t do is pick up a bunch of data and start reading tea leaves. Because you can always find something. If you don’t have much data you shouldn’t go round theorising. Something orange is going to happen to you today, says the astrology chart. Sure enough, you’ll notice if an orange bicycle goes by you.”