She says she has come to see “sufficient reason to question the particular mathematical framework Losada and I adopted.” She writes that she has “neither the expertise nor the insight” to defend that framework. Still, she says, much of the paper remains valid, even if the ratio must be abandoned or, as she puts it, the researchers must “unthread the now-questionable element of mathematical modeling from this braid.”
Fredrickson points to the failure of the peer-reviewed journals that published Losada in the first place, writing in an e-mail that “what this process shows yet again is that peer review is not fail-safe. It is the best we have, though.” Likewise, Seligman, who cites the ratio multiple times in Flourish and in his presentations on achieving happiness, says that he relied on those peer reviewers and that his understanding of the ratio was “very superficial.”
Sokal, however, argues that the mathematics in the ratio is not that complicated and that basing a theory or a book on an idea just because it’s published in a journal is unwise. “I would say that it’s rather naïve for a researcher in psychology to assume that anything published in an applied-mathematics journal is automatically completely correct—much less that it can be applied in psychology as a ‘black box’ without even bothering to understand what is inside it,” he writes in an e-mail.
The researcher who came up with the ratio to begin with, Marcial Losada, has so far been silent on the controversy. Even Fredrickson has had trouble getting in touch with her co-author and says now that she is “troubled by Losada’s lack of attention to this matter.”
He did respond to e-mail questions from The Chronicle. He writes that he started to read the Brown paper but “lost interest” when he discovered what he says were gross miscalculations. He also points out that his paper has been cited favorably many times and that this is the first negative appraisal. However, Losada, who is chief executive of Losada Line Consulting and has a Ph.D. in psychology from the University of Michigan, doesn’t address the serious questions raised by the paper, which is perhaps understandable considering that he never finished reading it.
American Psychologist asked him to write a response, but he declined. “I didn’t have the time to prepare a proper response,” he writes in an e-mail. “I am not an academic, I am a consultant to business and I am fully booked for the rest of 2013. The demand for training in my model has taken all my available time. My priority is not to publish, but to attend my clients properly.”
Papers turn out to be flawed all the time. But this was a widely cited paper that has remained a powerful talking point in the how-humans-flourish literature for years. And the timing of the Brown paper is not good for social psychology, which is struggling with the problem of results that can’t be replicated, with high-profile researchers—like Diederik Stapel—who turn out to be con artists. Having two big names in the field, Fredrickson and Seligman, admit that they didn’t even understand the ratio they featured in presentations and popular books doesn’t exactly inspire confidence.
Fredrickson says she has no regrets and sees what happened as a consequence of “pushing the boundaries of what the science of emotion can offer.”
Both Sokal and Brown say they are surprised that no one, before now, had taken a more skeptical look at such a revolutionary ratio. “The main claim made by Fredrickson and Losada is so implausible on its face that some red flags ought to have been raised,” Sokal writes in an e-mail. “At this point I can’t resist drawing the analogy with the reaction of the editors of Social Text to a certain strange manuscript that appeared on their desks in the fall of 1995.”
