Essay Abstract
Everything in the universe is interrelated and interdependent. The laws of physics are same everywhere. The macro and the micro replicate each other. By properly correlating them, we can know about each other. Completeness must be viewed in that context. Incompleteness is the reductionist approach - hence limited in scope. Extending information on part to the whole leads to confusion. Language is the transposition of information to another system/person's CPU/mind by signals/sound using energy. Mathematical equations transpose SCALAR QUANTITATIVE ASPECT of information only. Thus mathematics is a language only for quantitative aspects of Nature. Physics is mostly vector - hence not confined to mathematics only. Equations in math are different from those of physics and imply special conditions for interaction. Exchanging both (as in renormalization or brute-force approach) is like extending limited information to build abstract models without the restrictions imposed on them by rules of the physical world. This leads to incompleteness issues. The validity of a mathematical statement is judged by its logical consistency. The validity of a physical statement is judged by its correspondence to reality. The way math is now being done is incomplete and inconsistent. The problem is with dualism of bivalent logic of propositional calculus or sentential logic that leads to incompleteness based on linearity. Mathematics deals with scalar numbers. Physics is all about interactions, which makes it vector. Scalars and Vectors do not follow the same math rules. This dualism must be sublimated within formal systems by logically consistent reasoning - both mathematical and physical. Napier's logarithms, Hilbert's problems, Gödel's negative solution and Wigner's Unreasonable effectiveness of mathematics - all tend to limit the limits of probability in formal theories. They arise out of improper extension or non-inclusion of sectoral issues with consequential implications in fundamental interactions and other theories in physics.
Author Bio
seeker of truth.