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investigates the consequences of the information-theoretic result that representations
of numbers in base-e are most
efficient. Since theories on complex system behavior in both natural and
physical systems assume that Nature is optimal, as is done, for example, in the
principle of least action, natural representations must be to the base e. Another way to interpret this fact is
to take e as the information dimension
of the data space. Some implications of this noninteger dimensionality are
investigated. The approximate equivalent to such a space is the Menger sponge
in which the recursion is taken to be random.