The equations of love

Marten Scheffer in Nature:

Few topics are as disparate as mathematics and love — or are they? Modeling Love Dynamics (World Scientific, 2016) by systems theorist Sergio Rinaldi and others playfully, but convincingly, makes the point that even amorous relationships cannot escape the fundamental laws of dynamical systems. The argument propounded by Rinaldi and colleagues builds on the classical framework of coupled differential equations, which have proven so powerful in describing the essence of relationships in nature such as competition, cooperation and predation. The book’s cover illustration hints at the road ahead: it shows Gustav Klimt’s 1908 painting The Kiss (Lovers). A glance inside reveals that art is an essential part of the analysis of the drama of passion — a drama resulting in large part from the interplay of two strong forces, attraction and repulsion. Simple equations illustrated with elegant diagrams show how, depending on personalities, those forces can result in a transient affair, long-lasting stable equilibrium, or everlasting cycles of attraction and repulsion.

The tales and poems chosen masterfully illustrate a range of mathematical features. The limit cycle, known for driving the oscillating dynamics of many economic or biological systems, is linked, for instance, to one of the greatest love stories in Western culture. That is, the cyclical 21-year platonic relationship between fourteenth-century Italian humanist and poet Francesco Petrarca (Petrarch) and the married Laura (possibly the Provençal noblewoman Laure de Noves), charted in Petrarch’s celebrated collection Il Canzoniere. If three variables are mixed in the differential equations of passion, chaotic dynamics can arise. This is illustrated vividly in Henry-Pierre Roché’s semi-autobiographical 1953 novel Jules et Jim (which inspired François Truffaut’s 1962 film of the same name). Roché documents the love triangle between himself, the brilliant and charming journalist Helen Grund and her shy husband Franz Hessel, his best friend. As with the weather, the course of these dynamics is fundamentally unpredictable in the long run, as the smallest event can put things on a different trajectory. This phenomenon is also known as ‘the butterfly effect’, hinging on the idea that the flap of a butterfly’s wing may eventually lead to a hurricane in a distant place.

More here.