Information, Representation, and Structure

This paper 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.