29 of what constitutes a reasonably good observable. Our work has shown that extracting the geometric data requires making judicious choices of these observables. Otherwise, one might find pathological distributions whose averages are infinity entering into the problem when N becomes finite, even though when N is very large they seem to be well behaved. Learning how to avoid pathological measurements requires some trial and error and we gave some examples of how to improve this simple class of observables so that they had better behavior. We also studied how large were the fluctuations on the observables we chose and how fast the results approached the large N limit. From the data we could analyze, the corrections to large N are controlled by various powers of 1 /N , and some of them seem to be inconsistent with the naive planar counting lore. Surprisingly, the convergence to large N was slower than expected, and the fact that some observables had pathologically large fluctuations renders a lot of the analysis inconclusive: even with N ≃ 10000, N was not large enough to see a clear pattern emerging from the simulations. From this point of view we have learned a lot about the scale of simulations that would be required to sort out these features with the same procedures in future studies. We should have much larger simulations, with N ≃ 10 $^{6}$. Part of the reason why such large numbers are required should be obvious to anyone that tries to understand higher dimensional geometries of dimension d by adding a discretized grid approximation to the geometry. If we want to double the spatial resolution, we need a factor of 2 d enhancement on the number of cells. As d becomes larger, this is an issue. A value of N ≃ 10 4 is small to refine five dimensional geometries by these standards. Clearly, any future study should require smarter and faster algorithms than what we have used so far. We have used a simple Monte Carlo that runs on a single processor for these simulations. A better algorithm would involve parallel processing, a faster procedure of generating data sets and it might also require some coarse graining improvements to perform calculations with a study of the consequent systematic errors introduced by approximations. Another feature that we discovered is that it is very likely that there are better ways of analyzing the data than what we did. Particularly, features of the data as shown in figure 1 suggest that that the density profile in the various variables is a rich area to explore. If we improve our theoretical understanding of the data this might be exploited to address issues of geometry further. For example, in our analysis the fact that the geometry is a submanifold of R 6 was not crucial. However, it is a robust theoretical feature that should