Strings in a compactified extra dimension can create lower-dimensional particles in two ways: by winding around the extra dimension, and by moving around the circle. It turns out that these are mathematically equivalent. Strings wound around a larger extra dimension, illustrated on the left, give rise to exactly the same set of particles as strings moving around a smaller extra dimension, shown on the right. This equivalence between large and small extends to the full string theory, and is an example of how string theories give rise to different short-distance physics than do particle theories, which is a critical feature of the theory of quantum gravity. (Unit: 4)