5 theory in these approximations as a proxy for the full dual (quantum) geometry. Naturally, one can argue that this is the same problem of comparing apples to oranges and therefore the results are of limited value. Although this is technically true, a toy model that performs this reorganization of degrees of freedom into some type of geometry is extremely valuable because some of the conclusions might be universal enough that they apply even in the general case. A case in point is the usage of N = 4 SYM at finite temperature as a proxy for finite temperature QCD, and the use of the gravity dual to SYM to make predictions about the viscosity of the quark gluon plasma [28]. Contrary to other approaches of quantum gravity that attempt to build a spacetime from nothing: like those growing spacetime from a point in the no-boundary proposal for the wave function of the universe [29], or the causal set approach to quantum gravity [30]; in this setup there is no unique preferred wave function, and different wave functions correspond to different geometries. Some wave functions might not correspond to a single geometry either: superposition of geometries is possible. These states would be like a Schr¨ odinger cat state: a simple measurement would destroy the superposition. However, when we can barely understand a single geometry at this stage of the research program, studying this feature of superpositions of geometry is not desirable. The setup we are describing is similar to string states as solutions of the string equations of motion in a background spacetime: for each vertex operator of dimension (1 , 1) (this is how we describe quantum states via the operator- state correspondence) one can associate a different motion to the string in the semiclassical setup, and that motion defines a geometric trajectory for the string. Neither of these motions is preferred a priori, except as described by some preparation of an experiment. What we are studying here is the same: how different wave functions in our quenched minisuperspace description correspond to different geometries. Our ultimate goal is to establish a tractable dictionary between geometries and wave functions in this very limited context and to study how the fluctuations inherent to the wave function give fluctuations of geometric data. Our aim is not to be exhaustive, but to instead develop some intuition about emergent geometry with some simple wave functions that are easy to evaluate numerically. It has also been found that by changing the wave function, the geometry of the field theory degrees of freedom admits different topologies in the thermodynamic limit. Numerically this has been observed in [6]. This is also what is expected from the classification of half BPS states in the dual supergravity theory [31], where topology changing transitions are allowed.