A friend of ours is shy and thinks a lot. His girlfriend used to tease him about how it was impossible to predict which side of him, the shy or the thoughtful one, would open his mouth when they met. She found that quirk more interesting than consistency, and her acceptance was, he thought, what made his shy life tolerable. They wouldn’t have met if they hadn’t both been good, contemplative students, but they wouldn’t have attracted one another so much if they hadn’t both been so shy. They each had two faces.
Inspired by our friend (our younger selves!), we want to understand what makes objects come together or repel each other. Textbooks emphasize the easiest case—how objects attract and repel one another when their orientation doesn’t matter. For example, gravity causes masses to attract and electrostatics causes like charges to repel, but those forces depend on separation, not...
