Lovers as harmonic oscillators
Steven Strogatz, professor of applied mathematics at Cornell, introduces differential equations to a general audience in “The Wild Side” as a guest columnist in the New York Times. In honor of the season (“In the spring,” wrote Tennyson, “a young man’s fancy lightly turns to thoughts of love”), he presents Romeo and Juliet, whose love for each other as a function of time is expressed by R and J, respectively. Romeo’s behavior, Strogatz writes, is modeled by dR/dt = aJ, in which Romeo’s feelings about Juliet mirror hers about him. Juliet, however, backs off in the face of ardent affection from Romeo; her behavior is modeled by dJ/dt = -bR. Consequently, notes Strogatz, the two behave like harmonic oscillators and experience “a never-ending cycle of love and hate. At least they manage to achieve simultaneous love a quarter of the time.”
Strogatz says he tried to apply such math to an early relationship of his own—without success. It turns out that he was unknowingly involved in an intractable three-body problem.
Commenter “Scott” writes that he advises his engineering students “not to draw on the equations that we use in classes in order to understand social interactions,” because the equations are unlikely to yield useful answers and will waste time that could be more gainfully spent engaging in actual social interactions. As for the three-body problem, he suggests that the “constant tweeting and texting that occurs these days” might help to maintain “some kind of metastable equilibrium in an ages-old problem.”
Strogatz—whose book “The Calculus of Friendship: What a Teacher and a Student Learned about Life While Corresponding about Math” will be published in August—wrote last week about Zipf’s law and has one more column next week, before the return of the regular contributor"The Wild Side," the evolutionary biologist Olivia Judson. I can see that evolutionary biology probably has more interest for general readers than mathematics, but it’s nice to see a mathematician get a turn.
