Four distinct lines of evidence suggest that high ratios of positive to negative affect would distinguish individuals who flourish from those who do not. First, studies show that mild positive affect characterizes the modal human experience (

Diener & Diener, 1996). This

*positivity offset* equips individuals with the adaptive bias to approach and explore novel objects, people, or situations (

Cacioppo, Gardner, & Berntson, 1999). Second, several recent research reviews have concurred that “bad is stronger than good” (e.g.,

Baumeister, Bratslavsky, Finkenauer, & Vohs, 2001;

Rozin & Royzman, 2001). The implication is that to overcome the toxicity of negative affect and to promote flourishing, experiences of positivity may need to outnumber experiences of negativity, perhaps at ratios appreciably higher than those typically represented in the modal positivity offset. Third, on the basis of a mathematical model of consciousness rooted in Boolean algebra, the reformulated balanced states of mind model (

Schwartz, 1997) suggests that optimal mental health is associated with high ratios of positive to negative affect. According to this model, normal functioning is characterized by ratios near 2.5,

^{1} whereas optimal functioning is characterized by ratios near 4.3 (

Schwartz et al., 2002). Fourth, summarizing two decades of observational research on marriages,

Gottman (1994) concluded that unless a couple is able to maintain a high ratio of positive to negative affect (~5), it is highly likely that their marriage will end.

Consistent with this earlier evidence, our suggestion that individuals or groups must meet or surpass a specific positivity ratio to flourish derives from a nonlinear dynamics model empirically validated by

Losada (1999), who studied the interpersonal dynamics of business teams. From behind one-way mirrors, trained coders observed 60 management teams crafting their annual strategic plans and rated every speech act. Utterances were coded as

*positive* if speakers showed support, encouragement, or appreciation, and they were coded as

*negative* if speakers showed disapproval, sarcasm, or cynicism. They were coded as

*inquiry* if they offered questions aimed at exploring a position and as

*advocacy* if they offered arguments in favor of the speaker’s viewpoint. They were coded as

*self* if they referred to the person speaking, the group present, or the company, and they were coded as

*other* if they referenced a person or group who was neither present nor part of the company.

Later,

Losada (1999) identified 15 flourishing teams, defined as showing uniformly high performance across three indicators: profitability, customer satisfaction, and evaluations by superiors, peers, and subordinates. Other teams had mixed (

*n* = 26) or uniformly low performance (

*n* = 19). Observation of the structural characteristics (i.e., amplitude, frequency, and phase) of the time series of the empirical data for these three performance categories led Losada to write a set of coupled differential equations to match each of the structural characteristics of the empirical time series. presents these equations. Model-generated time series were subsequently matched to the empirical time series by the inverse Fourier transform of the cross-spectral density function, also known as the

*cross-correlation function*. Goodness of fit between the mathematical model and the empirical data was indicated by the statistical probability of the cross-correlation function at

*p* < .01.

| **Table 1**Coupled Differential Equations Developed by Losada (1999) to Describe the Differential Performance of Low-, Medium-, and High-Performance Teams |

plots the model-generated dynamical structures descriptive of

Losada’s (1999) three types of business teams in phase space. Readers may recognize here the famous butterfly-shaped chaotic attractor of the Lorenz system, first introduced in 1963 to represent the complex dynamics underlying weather forecasting. The Lorenz system is credited with expanding horizons in many areas of science because the mathematical structure of the original Lorenz system has been found to apply more generally (

Hirsch, Smale, & Devaney, 2004;

Lorenz, 1993).

The large, dark-gray structure presents the model trajectory derived from the empirical time series of the flourishing, high-performance teams. It reflects the highest positivity ratio (observed ratio = 5.6) and the broadest range of inquiry and advocacy. It is also the most generative and flexible. Mathematically, its trajectory in phase space never duplicates itself, representing maximal degrees of freedom and behavioral flexibility. In the terms of physics and mathematics, this is a chaotic attractor.

The midsized, light-gray structure presents the model trajectory derived from the empirical time series of the medium-performance teams. Although it begins with a structure that mirrors the model for flourishing teams—albeit with a lower positivity ratio (observed ratio = 1.8) and narrower range of inquiry and advocacy—its behavioral flexibility is insufficient for resilience. The lowest loop in the left wing of this structure reflects a moment of extreme adversity. After this point (proceeding clockwise) the dynamic model calcifies into a limit cycle inside the right wing. The model suggests that following extreme negativity, these teams lose behavioral flexibility and their ability to question; moreover, they languish in an endless loop centered on self-absorbed advocacy.

The small, white structure presents the model trajectory derived from the empirical time series of the low-performance teams. It reflects the lowest positivity ratio (observed ratio = 0.4) and never shows the complex and generative dynamics of the model derived from high-performance teams but, instead, is stuck in self-absorbed advocacy from the start. But worse than being stuck in an endless loop, its dynamics show the properties of a fixed-point attractor, suggesting that low-performance teams eventually lose behavioral flexibility altogether.

The nonlinear dynamic model that emerged from

Losada’s (1999) empirical analysis of business teams translates the tenets of the broaden-and-build theory into mathematics. As predicted by the theory, the mathematical model shows that higher levels of positivity are linked with (a) broader behavioral repertoires, (b) greater flexibility and resilience to adversity, (c) more social resources, and (d) optimal functioning (

Losada, 1999;

Losada & Heaphy, 2004).

Subsequent work on the model (

Losada & Heaphy, 2004) revealed that the positivity ratio relates directly to the control parameter by the equation

*P*/

*N* = (

*c* −

*Y*_{0} − 1) b

^{−1}, where

*P*/

*N* is the ratio of positivity to negativity;

*c* is connectivity, the control parameter (see );

*Y*_{0} is 16, the value of the transient before the attractor settles; and b

^{−1} is the inverse of the Lorenz constant, equal to 0.375. So, if positivity ratios are known, one can predict whether the complex dynamics of flourishing will be evident. Past mathematical work on Lorenz systems by

Sparrow (1982) and others (

Frøyland & Alfsen, 1984;

Michielin & Phillipson, 1997) has established that when

*r*, the control parameter in the Lorenz model, reaches 24.7368, the trajectory in phase space shows a chaotic attractor.

Losada (1999) established the equivalence between his control parameter,

*c*, and the Lorenzian control parameter,

*r*. Using the above equation, it is known that the positivity ratio equivalent to

*r* = 24.7368 is 2.9013.

Mathematically, then, a positivity ratio of about 2.9 bifurcates the complex dynamics of flourishing from the limit cycle of languishing. We call this dividing line the *Losada line*. From a psychological standpoint, this ratio may seem absurdly precise. Yet we underscore that this bifurcation point is a mathematically derived theoretical ideal. Empirical observations made at various levels of measurement precision can test this prediction.

Evidence corroborating the idea that this positivity ratio separates flourishing from languishing can be drawn from

Gottman (1994). He and his colleagues observed 73 couples discussing an area of conflict in their relationship. Researchers measured positivity and negativity using two coding schemes: one focused on positive and negative speech acts and another focused on observable positive and negative emotions. Gottman reported that among marriages that last and that both partners find to be satisfying (

*n* = 37)—what might be called flourishing marriages—mean positivity ratios were 5.1 for speech acts and 4.7 for observed emotions. By contrast, among marriages identified as being on cascades toward dissolution—languishing marriages at best—mean positivity ratios were 0.9 for speech acts and 0.7 for observed emotions (

Gottman, 1994).

Further evidence corroborating the significance of the 2.9 positivity ratio can be extracted from

Schwartz et al. (2002). They tracked the outcomes of 66 men undergoing treatment for depression and measured positivity ratios before and after treatment. Before treatment, positivity ratios were very low at 0.5. Schwartz and colleagues reported that among patients who showed optimal remission, indexed by both self-report and clinical ratings (

*n* = 15), mean posttreatment positivity ratios were 4.3. Among those who showed typical remission by the same criteria (

*n* = 23), mean posttreatment positivity ratios were 2.3. By contrast, among patients who showed no remission whatsoever, mean posttreatment positivity ratios were 0.7 (

Schwartz et al., 2002).

Learning that positivity ratios for flourishing marriages and optimal remission from depression surpassed the Losada line inspired us to test the hypothesis that positivity ratios at or above 2.9 also characterize nonpatient samples in flourishing mental health. Although this hypothesis derives from Losada’s nonlinear dynamics model, testing it does not require time-series data or knowledge of temporal dynamics. Rather, we computed aggregate positivity ratios by tallying daily reports of emotional experience over a month, and we compared those ratios for people identified as flourishing or not.