A mathematical model for the dynamics of happiness by Gustavo Carrero, Joel Makin & Peter Malinowski (2022)

The idea of happiness being a rate of change, and in particular, the rate of change of satisfaction, is known to both Psychology and Philosophy. In the context of goal and discrepancy theory, Carver and Scheier suggested that the rate of change of satisfaction, also referred to as the rate of change of progress towards a goal, rather than satisfaction itself, determines the experience of happiness. Here, satisfaction is understood to be determined by the discrepancy or gap between one's present perceived reality and what one aspires or thinks one deserves. As the discrepancy decreases, the satisfaction increases.

advtanmoy 13/08/2023

2022 Jan

Happiness

Positive psychology recognizes happiness as a construct comprising hedonic and eudaimonic well-being dimensions. Integrating these components and a set of theory-led assumptions, we propose a mathematical model, given by a system of nonlinear ordinary differential equations, to describe the dynamics of a person’s happiness over time.

The mathematical model offers insights into the role of emotions for happiness and why we struggle to attain sustainable happiness and tread the hedonic treadmill oscillating around a relative stable level of well-being. The model also indicates that lasting happiness may be achievable by developing constant eudaimonic emotions or human altruistic qualities that overcome the limits of the homeostatic hedonic system; in mathematical terms, this process is expressed as distinct dynamical bifurcations.

This mathematical description is consistent with the idea that eudaimonic well-being is beyond the boundaries of hedonic homeostasis.

Happiness has captured the attention and aspirations of humankind throughout history. The reason seems quite simple; nobody wants to suffer and everyone wants to be happy. Despite this common wish for happiness, and arguably due to its subjective nature, happiness remains a concept difficult to define, measure and predict. Influenced by ancient Greek wisdom, positive psychology recognizes happiness as a construct comprising hedonic and eudaimonic well-being dimensions

Reference

C. Sprott, Dynamical models of happiness, Nonlinear Dyn. Psychol. Life Sci., 9 (2005), 23–36.

A. Campbell, P. E. Converse, W. L. Rodgers, The quality of American life: Perceptions, evaluations, and satisfactions, Russell Sage Foundation, New York, NY, 1976.
A. C. Michalos, Measuring the quality of life, in Values and the Quality of life, Science History Publications, New York, NY, 1976, 24–37.

B. L. Fredrickson, Positivity: Groundbreaking Research Reveals how to Embrace the Hidden Strength of Positive Emotions, Overcome Negativity, and Thrive, Crown Publishers, New York, NY, 2009.

S. Frederick, G. Loewenstein, Hedonic adaptation, in Well-being: The Foundations of Hedonic Psychology, Russell Sage Foundation, New York, NY, (1999), 302–329.

J. D. Meiss, Differential Dynamical Systems, SIAM, Philadenphia, 2007.

S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, Perseus Books, Massachusetts, 1994.

J. J. Gross, Emotion regulation: Conceptual and empirical foundations, in Handbook of Emotion Regulation, The Guilford Press, New York, NY, (2014), 3–20.

O. Nydahl, Happiness, in from buddhism to science and back, Hung, Opole & ITAS, Vélez-Málaga, 2007.