  In this Letter, we propose a new scenario emerging from the conjectured
presence of a minimal length $\ell$ in the spacetime fabric, on the one side,
and the existence of a new scale invariant, continuous mass spectrum, of
un-particles on the other side. We introduce the concept of \textit{un-spectral
dimension} $\mathbb{D}_U$ of a $d$-dimensional, euclidean (quantum) spacetime,
as the spectral dimension measured by an "un-particle" probe. We find a general
expression for the un-spectral dimension $\mathbb{D}_U$ labelling different
spacetime phases: a semi-classical phase, where ordinary spectral dimension
gets contribution from the scaling dimension $d_U$ of the un-particle probe ; a
critical "Planckian phase", where four-dimensional spacetime can be effectively
considered two-dimensional when $d_U=1$; a "Trans-Planckian phase", which is
accessible to un-particle probes only, where spacetime as we currently
understand it looses its physical meaning.
