Physicist Demolishes The Maths Behind A Popular Happiness Theory

A highly cited and discussed 2005 paper from Barbara Fredrickson and Marcial Losada suggested a mathematical ratio between positivity and happiness, arguing that human beings flourish when the ratio of positive to negative statements made in an interaction is about 2.9.

Now a new paper claims that the happiness ratio is complete and utter bunk.

University of East London grad student Nicholas Brown analysed the paper with NYU Physics professor Alan Sokal and University of Florida psychologist Harris Friedman after he noticed some potential errors when reading it for a class.

What’s shocking is the sheer magnitude of the errors the trio uncovered. They put it plainly in the abstract, arguing that the paper’s approach is fundamentally flawed: “We find no theoretical or empirical justification for the use of differential equations drawn from fluid dynamics, a subfield of physics, to describe changes in human emotions over time,” they write.

In short, Brown, Sokal, and Freidman see no evidence that complex physics equations can be applied to human emotion.

The rebuttal examines a few particular errors at length from both the 2005 paper and Losada’s previous work:

  • There are five essential criteria that determine whether you can apply differential equations, used to model changes over time. Brown and Sokal’s paper detail that Losada’s equations, assumptions, and variables meet none of them.
  • Losada’s framework applies the Lorenz equations — which narrowly apply to convection in fluids — to human emotions, with no apparent basis.
  • The empirical data the paper alludes to, because of the way the equations are structured, don’t actually connect to the famous positivity ratio.
  • If the assertions of the paper were true, we’d basically have to revise a large portion of modern psychology and neuroscience.

Here’s one of the most brutal paragraphs of Brown’s paper, which draws an analogy to the pair’s attempt to link the Lorenz equations and emotions:

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 characterised by “smoke and mirrors could be modelled using the physics of airborne particulate combustion residues, combined in some way with classical optics.

Fredrickson recently published a defence in response, distancing herself from the ratio and the maths, which came from co-author Losada, a Chilean consultant and psychologist. She continues to uphold the core positive psychology concepts, which aren’t particularly controversial.

The group’s findings are particularly shocking for a few reasons. Leading psychologists including Daniel Gilbert, Daniel Goleman, and Martin Seligman endorsed Fredrickson’s book, which cites the ratio prominently in the subtitle; Fredrickson is a prominent and long-serving professor at the University of North Carolina; the paper was peer reviewed; and no one who read the paper spoke up for 7 plus years.

The popular Discovery blog Neuroskeptic recently called for the original paper’s retraction. Fredrickson has yet to do so.

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