  Within the causal dynamical triangulations approach to the quantization of
gravity, striking evidence has emerged for the dynamical reduction of spacetime
dimension on sufficiently small scales. Specifically, the spectral dimension
decreases from the topological value of 4 towards a value near 2 as the scale
being probed decreases. The physical scales over which this dimensional
reduction occurs have not previously been ascertained. We present and implement
a method to determine these scales in units of either the Planck length or the
quantum spacetime geometry's effective de Sitter length. We find that dynamical
reduction of the spectral dimension occurs over physical scales of the order of
10 Planck lengths, which, for the numerical simulation considered below,
corresponds to the order of 1/10 de Sitter lengths.
