Mathematical modeling is more than fitting equations.

Abstract

Comments on the comments made by Brown et al. (see record 2013-24609-001). The article by Brown et al. regarding the Fredrickson and Losada (see record 2005-11834-001) article discussed the use of differential equations in science and repeated our earlier observation (Luoma, Hämäläinen, & Saarinen, 2008) that there is lack of justification for the use of the Lorenz equations in the latter article. In this comment we want to point out that Brown et al. presented a very narrow view on mathematical modeling in behavioral research. We describe how the conceptual use of mathematical models is essential in many fields.

Student teams’ development over time: tracing the relationship between the quality of communication and teams’ performance

“…In future work, due to our initial results on the communication quality that call for more sensitivity of the parameters used, together with the recent criticisms of the mathematical basis of the patterns of team dynamics based on Losada's parameters (Brown, Sokal, & Friedman, 2013; see also Hämäläinen, Luoma, & Saarinen, 2014), we will reexamine the results utilizing Monte Carlo sensitivity analysis (e.g., Lorén, Johannesson, & de Maré, 2009). The analysis will estimate, for example, the most sensitive Losada's initial parameters, which make the normalized communication values too uniform or saturated in the context of new learning teams.…”

Positive psychology and romantic scientism.

“…Along similar lines, Hämäläinen, Luoma, and Saarinen (2014, this issue) chided us for saying that Fredrickson and Losada’s (2005) article “contains numerous fundamental conceptual and mathematical errors” (Brown et al, 2013, p. 801). Hämäläinen et al conceded our main point, namely, the complete lack of justification for the use of the Lorenz equations in modeling the time evolution of human emotions; but they also asserted, incorrectly, that Fredrickson and Losada’s article contains “no clear mathematical errors” (Hämäläinen et al, 2014, p. 633).…”

“…Along similar lines, Hämäläinen, Luoma, and Saarinen (2014, this issue) chided us for saying that Fredrickson and Losada’s (2005) article “contains numerous fundamental conceptual and mathematical errors” (Brown et al, 2013, p. 801). Hämäläinen et al conceded our main point, namely, the complete lack of justification for the use of the Lorenz equations in modeling the time evolution of human emotions; but they also asserted, incorrectly, that Fredrickson and Losada’s article contains “no clear mathematical errors” (Hämäläinen et al, 2014, p. 633). Among the purely mathematical errors clearly noted in our article are Fredrickson and Losada’s assertion that the r = 22 data (alleged to be characteristic of “medium-performance teams”) end up in a limit cycle (Brown et al, 2013, p. 808), and their implicit claims concerning the absence of chaotic attraction at large values of r (Brown et al, 2013, p. 812).…”

“…Where we unequivocally take issue with Hämäläinen et al (2014) is in their assertion that physicists derive their models "by fitting equations to empirical data" (p. 633). In fact, the vast majority of models in contemporary physics, including virtually all those in which the mechanical functioning of a system is described by differential equations, are derivable from first principles by applying well-verified theories to a specific problem and then making plausible simplifications or approximations.…”

“…In the remainder of their comment, Hämäläinen et al (2014) ventured into even more hazardous epistemological territory. They acknowledged that “in the behavioral sciences .…”