When RM sent me this highly entertaining NYTimes column (by Strogatz) on using diff equ's to model love, I had to share it. Of course, in the process of said sharing, came another little gem from the Journal on Applied Math (from the Society for Industrial and Applied Mathematics).
An excerpt from the abstract:
Three ordinary differential equations are proposed to model the dynamics of love between Petrarch, a celebrated Italian poet of the 14th century, and Laura, a beautiful but married lady. The equations are nonlinear but can be studied through the singular perturbation approach if the inspiration of the poet is assumed to have very slow dynamics. In such a case, explicit conditions are found in the appeals of Laura and Petrarch and in their behavioral parameters that guarantee the existence of a globally stable slow-fast limit cycle. ... The result is that the calibrated model shows that the poet's emotions followed for about 20 years a quite regular cyclical pattern ranging from the extremems of ecstasy to despair. All of these findings agree with the recent results of Frederic Jones, who, through a detailed stylistic and linguistic analysis of the poems inspired by Laura, has discovered Petrarch's emotional cycle in a fully independent way.
In summarizing the work of Jones, the authors state that Jones made the assumption of the cyclical nature of Petrarch's emotions, and "on the basis of this conjecture, Jones... put all undated poems in chronological order." But in this case, the authors set up some basic behavioral parameters:
And found the solution to be a limit cycle.
Oh, and more pretty graphs:
The paper is highly entertaining, very readable, and not as verbose as you might otherwise expect. Really, papers in the humanities should read like this. Characterized by precision, humorous, and defended up to the limits of falsifiability. Well worth the effort to read it, for poets and scientists alike, not just the slender intersection of the two.
Rinaldi, Sergio. Laura and Petrarch: An Intriguing Case of Cyclical Love Dynamics. SIAM Journal on Applied Mathematics, Vol. 58, No. 4 (Aug., 1998), pp. 1205-1221
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