The Mathematical Representation of Physical Reality

This book deals with the rise of mathematics in physical sciences, beginning with Galileo and Newton and extending to the present day. The book is divided into two parts. The first part gives a brief history of how mathematics was introduced into physics—despite its "unreasonable effectiveness" as famously pointed out by a distinguished physicist—and the criticisms it received from earlier thinkers. The second part takes a more philosophical approach and is intended to shed some light on that mysterious effectiveness. For this purpose, the author reviews the debate between classical philosophers on the existence of innate ideas that allow us to understand the world and also the philosophically based arguments for and against the use of mathematics in physical sciences. In this context, Schopenhauer’s conceptions of causality and matter are very pertinent, and their validity is revisited in light of modern physics. The final question addressed is whether the effectiveness of mathematics can be explained by its “existence” in an independent platonic realm, as Gödel believed.

The book aims at readers interested in the history and philosophy of physics. It is accessible to those with only a very basic (not professional) knowledge of physics.

Introduction.- 1.Classical Period.- 2.Enlightenment.- 3.Electricity and Magnetism.- 4.Modern Physics: Relativity.- 5.Modern Physics: Quantum Mechanics.- 6.Quantum paradoxes.- 7.Quantum Mechanics and Relativity.- 8.Other (Mathematical) Worlds.- 9.Cosmology.- 10.For Mathematics.- 11.Against Mathematics.- 12.Programs of the Mind.- 13.Geometry a priori.- 14.Causality, Sufficient Reason and Determinism.- 15.Matter and Causality.- 16.Mathematics and Reality.- 17.Conclusions: Pythagoras’Dream.

Shahen Hacyan studied Physics (1965-1968) at the National Autonomous University of Mexico (UNAM) and obtained a Ph.D. in Theoretical Physics in 1972 at the University of Sussex, UK. After returning to Mexico, he took up a position at the Institute of Astronomy, at UNAM. His fields of interest at that time were Relativistic Astrophysics, General Relativity and Cosmology. In 1990, he moved to the Institute of Physics, also at UNAM, and worked on Quantum Field Theory and Quantum Optics, as well as delving into philosophical aspects of Physics. Prof. Hacyan is currently Investigador Titular C (equivalent to Full Professor) at UNAM.

Shahen Hacyan has published more than 90 scientific papers in respected international journals such as Physical Reviews, Astrophysical Journal, Journal of Mathematical Physics. He has also been very active as Popularizer of science in Mexico, having published 11 popular science books, 9 of them with Fondo de Cultura Económica (FCE), the main editorial house in Mexico.

From 1994 to 2009, Prof. Hacyan was in charge of a weekly newspaper column on popular science, Aleph Cero, in one of the main Mexican newspapers, Reforma. There he published more than 600 articles on popular science.

His 11 books on popular science span all of theoretical physics and beyond, addressing Cosmology, Black Holes, Relativity, the Quantum World and the Universe, Interstellar Travels, Quantum Mechanics and Gravitational Waves. In 2004, again with FCE, he also published a book about the philosophy of Physics, Física y Metafísica del Espacio y el Tiempo (Physics and metaphysics of space and time).