An information geometrical evaluation of Shannon information metrics on a discrete n-dimensional digital manifold

Abstract

The definition and nature of information have perplexed scientists due to its dual nature in measurements. The information is discrete and continuous when evaluated on a metric scale, and the Laplace-Beltrami operator and Gauss-Bonnet Theorem can map one to another. On the other hand, defining the information as a discrete entity on the surface area of an n-dimensional discrete digital manifold provides a unique way of calculating the entropy of a manifold. The software simulation shows that the surface area of the discrete n-dimensional digital manifold is an effectively computable function. Moreover, it also provides the information-geometrical evaluation of Shannon information metrics.