So then what was this? A butterfly graph, the calling card of chaos theory mathematics, purporting to show the tipping point upon which individuals and groups “flourish” or “languish.” Not a metaphor, no poetic allusion, but an exact ratio: 2.9013 positive to 1 negative emotions. Cultivate a “positivity ratio” of greater than 2.9-to-1 and sail smoothly through life; fall below it, and sink like a stone.

The theory was well credentialed. Now cited in academic journals over 350 times, it was first put forth in a 2005 paper by Barbara Fredrickson, a luminary of the positive psychology movement, and Marcial Losada, a Chilean management consultant, and published in the American Psychologist, the flagship peer-reviewed journal of the largest organization of psychologists in the U.S.
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It seemed a case of numbers fudging. In a valid fluid dynamics problem, the numbers plugged into the equation must correlate to the properties of the fluid being studied. But in attempting to draw an equivalence between the physical flow of liquids and the emotional “flow” of human beings, Losada had simply lifted the numbers that Lorenz used in 1963 to explain his method in the abstract, numbers used merely for illustrative purposes. Losada’s results, along with the pretty butterfly graphs Brown had been shown in class, were essentially meaningless.
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The three men brought different skills to the plate. Brown was the outsider, the instigator, who, knowing no better, dared to question the theory in the first place. Friedman provided psychological expertise and played a diplomatic role, helping guide the paper towards publication. Sokal was the finisher, the infamous debunker with the know-how needed to dismantle the theory in hard, mathematic language.

http://narrative.ly/pieces-of-mind/nick-brown-smelled-bull/

The Magic Ratio That Wasn’t

The 2009 book Positivity: Top-Notch Research Reveals the 3 to 1 Ratio That Will Change Your Life, by Barbara Fredrickson, was praised by the heavyweights of psychology. Daniel Gilbert said it provided a “scientifically sound prescription for joy.” Daniel Goleman extolled its “surefire methods for transforming our lives.” Martin E.P. Seligman, often called the father of positive psychology, raved that “this book, like Barb, is the ‘real thing.’”
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One passage they single out for ridicule comes from a 1999 paper by Losada, the findings of which provide the basis for the 2005 paper he wrote with Fredrickson. In that passage, Losada explains how human interaction is a lot like fluid viscosity. People, he writes, “could be characterized as being stuck in a viscous atmosphere highly resistant to flow.” The authors of “Wishful Thinking” offer their opinion of this metaphorical approach in a few sentences worth quoting in full:

One could describe a team’s interactions as “sparky” and confidently predict that their emotions would be subject to the same laws that govern the dielectric breakdown of air under the influence of an electric field. Alternatively, the interactions of a team of researchers whose journal articles are characterized by “smoke and mirrors” could be modeled using the physics of airborne particulate combustion residues, combined in some way with classical optics.

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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.”

http://chronicle.com/blogs/percolator/the-magic-ratio-that-wasnt/33279