  If gravity is asymptotically safe, operators will exhibit anomalous scaling
at the ultraviolet fixed point in a way that makes the theory effectively
two-dimensional. A number of independent lines of evidence, based on different
approaches to quantization, indicate a similar short-distance dimensional
reduction. I will review the evidence for this behavior, emphasizing the
physical question of what one means by `dimension' in a quantum spacetime, and
will discuss possible mechanisms that could explain the universality of this
phenomenon.
