Legacy of Galileo (Father of Relativity): Philosophical Transaction of Relativity of Space-Time Symmetry. Relevance to Physical and Biological Frame of Reference

In Greek philosophy, symmetry was closely tied to the concepts of harmony, beauty, and unity of Nature. Modern physics reveals that the integrity of the Universe is intimately linked to concepts of symmetry and relativity. In philosophy, the idea that a single set of laws and principles governs all forms of existence is called monism. In physics, this conjecture was first articulated by Galileo as the relativity principle (RP). Thus, it is fair to say that Galileo is the father of relativity. The historical perspective unveils that the most generalized manifestation of RP is the unity of the Universe. All subsequent evolutions of RP were unfolding of this foundational idea. The evolution of the RP was closely tied to the refinement of the mathematical formulation of space-time geometry and symmetry. Euclidean geometry was gradually displaced from the status of absolute to the role of an initial approximation of physical space determinants. At present, it becomes evident that perceptual indistinguishability of uniform motion, articulated by Galileo, is a consequence of fundamental determinants of existence - space-time symmetry and relativity (STSR). Remarkable, but the nature of elementary (smallest) constituents, the evolution of the largest scales of the Universe, and human behavior follow the same fundamental physical principles. The review is written in a language comprehensible to physicists, mathematicians, biologists, and philosophers (students and teachers). Prerequisite: The biologists should be familiar with the fundamental aspects of geometry, and physicist with the origin and evolution of life.