Advanced Topics in Information Dynamics
This work is sequel to the book "A Treatise in Information Geometry" submitted to vixra in late 2009. The aim of this dissertation is to continue the development of fractal geometry initiated in the former volume. This culminates in the construction of first order self referential geometry, which is a special form of 8 tensor construction on a differential manifold with nice properties. The associated information theory has many powerful and interesting consequences. Additionally within this treatise, various themes in modern mathematics are surveyed Galois theory, Category theory, K theory, and Sieve theory, and various connections between these structures and information theory investigated. In particular it is demonstrated that the exotic geometric analogues of these constructions save for Category theory, which is foundational form special cases of the self referential calculus.