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Love as a Spring

Few other paradigms in Physics are so easy to translate into ``normal life'' terms as the linear restoring force. As a whimsical example, consider an intimate relationship between two lovers. In this case  x  can represent ``emotional distance'' - a difficult thing to quantify but an easy one to imagine. There is some equilibrium distance  x₀  where at least one of the lovers is most comfortable^11.11 -- this time, just to show how it works, we will not choose  x₀  to be the zero position of  x  but leave it in the equations explicitly. When circumstances (usually work) force a greater emotional distance for a while, the lover experiences a sort of tension that pulls him or her back closer to the beloved. This is a perfect analogy to the linear restoring force:

$$F = - k \, (x - x_0)$$

What few people seem to recognize is that this ``force,'' like any linear restoring force, is symmetric: it works the same in both directions, too far apart and too close. When circumstances permit a return to greater closeness, the lover rushes back to the beloved (figuratively - we are talking about emotional distance  x  here!) and very often ``overshoots'' the equilibrium position  x₀  to get temporarily closer than is comfortable. The natural repulsion that then occurs is no cause for dismay - you can't really have an attraction without it - but some people seem surprised to discover that the attraction that binds them to their beloved does not just keep acting no matter how close they get; they are very upset that  x  cannot just keep getting closer and closer without limit.^11.12 In later chapters I will have much more to say about the oscillatory pattern that gets going [see Fig. 11.4] when the overshoot is allowed to occur without any friction to dissipate the energy stored in the stretched spring [a process known as damping]. But first I really must pick up another essential paradigm that has been begging to be introduced.