The “critical positivity ratio”, advanced by Fredrickson and Losada’s 2005 paper in American Psychologist, is the idea that if the ratio of positive to negative emotions is above a certain value, 2.9013 in fact, then you will ‘flourish’; lower than that, and you will ‘languish':
…these data [N = 188] suggest that at three levels of analysis—for individuals, marriages, and business teams—flourishing is associated with positivity ratios above 2.9. Likewise, for individuals, marriages, or business teams that do not function so well—those that might be identified as languishing—positivity ratios fall below 2.9. The relationship between positivity ratios and flourishing appears robust: It emerges repeatedly despite differences in (a) measures of positivity and negativity, (b) measures of flourishing, (c) time scales, and (d) levels of analysis (Fredrickson and Losada 2005, p. 684).
“Together with other evidence,” Fredrickson and Losada write in their abstract, “these ﬁndings suggest that a set of general mathematical principles may describe the relations between positive affect and human ﬂourishing.”
But, not so fast. In a recent paper, “The Complex Dynamics of Wishful Thinking: The Critical Positivity Ratio,” Nicholas Brown, Alan Sokal, and Harris Friedman demonstrate that the Fredrickson and Losada findings suggest nothing of the kind. The Neuroskeptic has the story here, but Brown et al.’s abstract sums up their point:
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; furthermore, we demonstrate that the purported application of these equations contains numerous fundamental conceptual and mathematical errors. The lack of relevance of these equations and their incorrect application lead us to conclude that Fredrickson and Losada’s claim to have demonstrated the existence of a critical minimum positivity ratio of 2.9013 is entirely unfounded. More generally, we urge future researchers to exercise caution in the use of advanced mathematical tools, such as nonlinear dynamics, and in particular to verify that the elementary conditions for their valid application have been met.