  We study the dimensional aspect of the geometry of quantum spaces.
Introducing a physically motivated notion of the scaling dimension, we study in
detail the model based on a fuzzy torus. We show that for a natural choice of a
deformed Laplace operator, this model demonstrates quite non-trivial behaviour:
the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with
the similar property, the so-called Horava-Lifshitz model, our construction
does not have any preferred direction. The dimension flow is rather achieved by
a rearrangement of the degrees of freedom. In this respect the number of
dimensions is deceptive. Some physical consequences are discussed.
