  We examine critically the claims made by Fredrickson and Losada (2005)
concerning the construct known as the "positivity ratio". 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.
