18 FIG. 1: The distribution of radii of the configuration. The plot on the left shows that r$_{3456}$ can be considered as a function of r$_{12}$ , as expected by the singular nature of the saddle point distribution. It also shows that the radius of the distribution makes sense, except for one outlying point that one can call a statistical fluctuation. The plot on the right bins the number of particles in r$_{12}$ values in increments of a half. One notices a strong peak in the distribution, but it does not happen at the inner edge of the distribution. The sample is taken with N = 1000 , Q = 100, from the final configuration. understand how it would approach the large N limit without extensive modeling. Since we do not have an analytic understanding of these distributions yet, it is very hard to use their prominent features in a meaningful way to obtain a reasonable definition of the geometry. For illustration, should we use the density in six dimensions to define the radius? Or should we use the projection of the density distribution to the 12 plane? The choice would depend on which observable we need to evaluate and how it is realized geometrically in the ten dimensional dual geometry. Notice also that the definitions of the radius that we use in most cases do not suppress the peak very much relative to the inner radius. Because there are so many more particles there, one can expect that the radius measurements we are doing at k = 14 are tracking the peak in the distribution above. The distributions above were plotted after the choice was made of which functions to average. In hindsight, other definitions of the radius might have been better choices. After all, we actually know how the distributions were generated, so there is in principle a lot more information encoded in the eigenvalue distributions. In a certain sense, we are purposefully ignoring this information except for some qualitative understanding. The main reason to do this is to think of the algorithm that generated the geometry as a black box: the passage Radius R12 R3456 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 100 200 300 400