  We initiate the study of Horava-Lifshitz models of gravity in the framework
of spectral geometry. As the first step, we calculate the dimension of
space-time. It is shown, that for the natural choice of a Dirac operator (or
rather corresponding generalized Laplacian), which respects both the foliation
structure and anisotropic scaling, the result of Horava on a spectral dimension
is reproduced for an arbitrary, non-flat space-time. The advantage and further
applications of our approach are discussed.
