  We analyse the connections between the Wheeler DeWitt approach for two
dimensional quantum gravity and holography, focusing mainly in the case of
Liouville theory coupled to $c=1$ matter. Our motivation is to understand
whether some form of averaging is essential for the boundary theory, if we wish
to describe the bulk quantum gravity path integral of this two dimensional
example. The analysis hence, is in a spirit similar to the recent studies of
Jackiw-Teitelboim (JT)-gravity. Macroscopic loop operators define the
asymptotic region on which the holographic boundary dual resides. Matrix
quantum mechanics (MQM) and the associated double scaled fermionic field theory
on the contrary, is providing an explicit "unitary in superspace" description
of the complete dynamics of such two dimensional universes with matter,
including the effects of topology change. If we try to associate a Hilbert
space to a single boundary dual, it seems that it cannot contain all the
information present in the non-perturbative bulk quantum gravity path integral
and MQM.
