What Issues of Literary Analysis Can Differential Equations Clarify?

Introduction

Mathematical modelling penetrated into literary criticism about half a century ago. Among various attempts to apply mathematics to the analysis of plots in fiction there is one, which appears to be most challenging. One type of plots has attracted mathematicians due to the emphasized dynamics of relations between characters. Such are love stories. Love/seduction plots are to be found in a great number of novels and tales. The difference between such plots in fiction and those in real life has been a key issue in literary theory since Aristotle. The structuring of love plots in fiction corresponds to the specific artistic strategy and philosophy of the writer.

Since the late 1980s, there have been several attempts to attain a scientific rather than scholarly-based objectivism to tackle issues, such as plot dynamics and plot structure. It is noteworthy that scholarship in this field put in the foreground love/seduction plots in fiction. Mathematical modelling of love affairs dates back to S. Strogatz’s article (Strogatz, 1988). His aim was to demonstrate the possibilities of modelling using systems of differential equations. The idea was developed in a set of further investigations and the love affairs or marriage plots in some novels and movies were modelled by means of systems of ordinary differential equations. In particular, love plots in Gone with the Wind (Rinaldi, Della Rossa, Landi, 2013), “Beauty and the Beast” (Rinaldi, Landi, Della Rossa, 2013), Jules et Jim (Dercole, 1999) were considered. The powerful machinery of dynamic systems was applied to research the interpersonal relations. Non-linear terms (Sprott, 2004) as well as stochastic interaction with the environment (Barley, Cherif, 2011) have enriched the picture of the possible dynamics of romantic relationships. A classification of love affair scenarios based on the theory of dynamic systems was proposed (Rinaldi, Della Rossa, Dercole, 2010). In all these studies, the choice of a specific form for the model was based upon the psychological veracity of the model, coefficients, etc. The estimation of the validity of a love scenario was made with reference to ‘common notions’ of love affairs.

In this study, the researchers will compare the models of the love affairs in two short novels (novellas). The first one: Torrents of Spring by the Russian 19th century writer Ivan Turgenev (Turgenev, 1872). The second is Venus in Furs by Leopold von Sacher-Masoch (Von Sacher-Masoch, 1869). The aim is to connect the models with the ideas and methods of literary criticism. It is worth mentioning here that the reconstruction of the love relation between Petrarch and Laura was performed (Jones, 1995). The reconstruction was based on the book of Petrarch’s love poems Il Canzoniere. A detailed stylistic and linguistic analysis (Jones, 1995) preceded the model investigation (Rinaldi, 1998). In this research, the authors cannot avoid taking into account the psychological features of the characters. However, they relate their model to literary theory rather than to psychology.