  We explore the idea of asymptotic silence in causal set theory and find that
causal sets approximated by continuum spacetimes exhibit behaviour akin to
asymptotic silence. We make use of an intrinsic definition of spatial distance
between causal set elements in the discrete analogue of a spatial hypersurface.
Using numerical simulations for causal sets approximated by D=2,3 and 4
dimensional Minkowski spacetime, we show that while the discrete distance
rapidly converges to the continuum distance at a scale roughly an order of
magnitude larger than the discreteness scale, it is significantly larger on
small scales. This allows us to define an effective dimension which exhibits
dimensional reduction in the ultraviolet, while monotonically increasing to the
continuum dimension with increasing continuum distance. We interpret these
findings as manifestations of asymptotic silence in causal set theory.
