Romeo and Juliet by the Numbers

In order to quantify a person’s opinion of another, we would need to know which factors influence their opinion. Specifically, we might want to know how a person’s affections may change based on grudges: how strongly they value their own opinion of another person; and vanity: how they value the other person’s opinion of them. Let’s name these two people after Shakespeare’s “star-crossed lovers”, Romeo and Juliet. Using a system of linear differential equations and two parameters, we model Romeo and Juliet’s affection for each other and graph how their feelings for each other change over time. Interestingly, though perhaps unsurprisingly, in almost all cases the magnitude of both people’s affections shoot off to infinity, which is bound to end in a dramatic explosion with tragic consequences. These models might also be helpful in understanding how different groups interact with each other and expand under social pressures.