I read an interesting article today on the New York Times from Steven Strogatz a guest blogger for the Times and also Professor of Applied Mathematics at Cornell University. He basically simplifies the dynamic of Love and Hate in a couple with the help of two "simple" differential equations. Suppose there are Romeo and Juliet. Suppose that their love for each other develops according to the following dynamics:
Romeo's Love (dR/dT)= Theta * Juliet's current love (J)
Juliet's Love (dJ/dT)= -Gamma * Romeo's current love (R)
The article explains vary well what are the assumptions, but let me repeat them in common words: when Romeo is an assh*** Juliet finds him attractive, while Romeo loves Juliet when she cooks for him...
So given this description of their love, how does their love evolve through time? The answer is in the article, but here is the graphical answer:
Note the oscillation are the same by assumptions, just to be politically correct...
They both love each other one quarter of the time, all the rest is spent mumbling and thinking about...but this is just the prediction of a theoretical model. The world is different from that, but the model can be augmented to make it more realistic, as described in the article. But it's striking how the law of maths come appropriate even when talking about love and hate. As Einstein told us, the puzzle remains "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?"