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.
Funding
Federico and Elvia Faggin Foundation, San Francisco
History
Email Address of Submitting Author
subhash.kak@okstate.eduORCID of Submitting Author
https://orcid.org/0000-0001-5426-9759Submitting Author's Institution
Oklahoma State University, StillwaterSubmitting Author's Country
- United States of America