  We investigate the behavior of small subsets of causal sets that approximate
Minkowski space in three, four, and five dimensions, and show that their
effective dimension decreases smoothly at small distances. The details of the
short distance behavior depend on a choice of dimensional estimator, but for a
reasonable version of the Myrheim-Meyer dimension, the minimum dimension is $d
\approx 2$, reproducing results that have been seen in other approaches to
quantum gravity.
