How Symmetry Shapes Laws of Physics [video]

Information already has a precise, functional definition in the context of mathematics, machine learning, and AI. It is the number of bits necessary to encode a message, and that is the most essential aspect of coding theory. I would suggest reading the original works of Claude Shannon to become enlightened about how the word 'information' is used in the context of math, electrical engineering, and computer science.

The manifestation of observational asymmetries absolutely must be equivocal to the asymmetry of manifest observation. Therefore, the format of an observation is manifest via the symmetry of a relation under a set of attributes. Thusly, the asymmetry of observations is a point measurably manifested by the difference in attributes. That allows for the derivation of: a union operation over the observations; an intersection operation over the asymmetries; and a manifest closure property. This is how one may define points of 'data' in the sense that is absolutely congruent with the terms database, big data, or data science.

Information Theory and Relational Algebra have some overlap, but they are not completely intertwined. The subjects of Abstract Algebra and Information Geometry are there at the intersection, but they still too terminologically distinct to be taught in tandem. The former subject is still best learned in French; whereas the latter subject is still best learned in Japanese. It is possible for one to teach themselves these subjects by machine translation, if they have a deep understanding for the grammar and history of each language. Deep learning of this sort is a kind of meditative activity, the type of which is only available to the most erudite thinkers.