Another simplistic way to see it is that it is a ratio of contained information. In higher dimensional spaces, the space is so big that below the unit spheres c

Another simplistic way to see it is that it is a ratio of contained information. In higher dimensional spaces, the space is so big that below the unit spheres contain exponentially less information. It's just something between 0 and 1 exponentized to d where d is the dimension after all (i.e. the number of eigenvectors). d is an exponential scale factor in a sense.