TITLE:
Projections between Euclidean Volumes with Information Due to Spontaneous Symmetry Breaking
AUTHORS:
Louis M. Houston
KEYWORDS:
Entropy, Symmetry, Bit, Multi-Dimensional, Cuboid
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.11,
November
22,
2023
ABSTRACT: The goal of our research was to determine a coupling between information theory, geometry and multi-dimensional projections. This was accomplished after preliminary mathematics was presented to determine an alternative method for the illustration of multi-dimensional spaces. That was developed with a unique series that gives structure to integer exponents of power sets. The desired coupling is concisely illustrated in a single figure which includes three cyclic phases that are isomorphic to the three phases of Euclidian, rectangular cuboids. The series enables projections between n- and m-dimensional volumes. The associated figure also illustrates how vertical and/or horizontal symmetry breaking or symmetry emits or absorbs information.