Here is a picture of a set of 120 sided dice. Each die has 120 eigenvalues. It is easy to see that as the number of eigenvalues increases, the probability of any eigenvalue gets smaller. In the limit where the number of eigenvalues is ##\infty## the probability of any one eigenvalue approaches zero and the shape becomes a sphere. I suppose that in 120 dimensional space, each die would be represented by a single point. The vector describing that point would have 120 components. Each component would represent the probability that the die would be found in that particular eigenstate.