Related papers: Dialogues about geometry and light
What is light and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: Geometrical optics, wave optics and quantum optics are increasingly sophisticated…
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
Quantum optics and classical optics have coexisted for nearly a century as two distinct, self-consistent descriptions of light. What influences there were between the two domains all tended to go in one direction, as concepts from classical…
This is the first expression of my thoughts and my experiments with Nature about the mathematical description of the Universe. The theories about our surrounding Nature became popular from our ancient civilizations and may be from the…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
We present some episodes from the history of interactions between geometry and physics over the past century.
Development of optometry in western countries was studied on a viewpoint of the history of science. It was revealed that optometry had been formed on the basis of optics, a branch of physics, to which biomedical study was added. Optometry…
These are the lecture notes for a course that I am teaching at Zhiyuan College of Shanghai Jiao Tong University (available at https://www.youtube.com/derekkorg), though the first draft was created for a previous course I taught at the…
Standard pedagogy introduces optics as though it were a consequence of Maxwell's equations, and only grudgingly admits, usually in a rushed aside, that light has a particulate character that can somehow be reconciled with the wave picture.…
Glasses constitute a widespread form of solid matter, and glass production has been an important human technology for more than 3000 years. Despite that long history, new ways to understand the fundamental physics of glasses continue to…
In this article, I discuss the relationship of mathematics to the physical world, and to other spheres of human knowledge. In particular, I argue that Mathematics is created by human beings, and the number $\pi$ can not be said to have…
While purely philosophical in the early times, and still very speculative at the beginning of the twentieth century, Cosmology has gradually entered into the realm of experimental science over the past eighty years. It has raised some…
The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…
In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…
The space-time of modern physics is tailored on light. We rigorously construct the basic entities needed by kinematics: geometry of the physical space and time, using as tool electromagnetic waves, and particularly light-rays. After such a…
We show how the birth of perspective painting in the Italian Renaissance led to a new way of interpreting space that resulted in the creation of projective geometry. Unlike other works on this subject, we explicitly show how the craft of…
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early…
We discuss how developments in physics often imply in the need that spacetime acquires an increasingly richer and complex structure. General Relativity was the first theory to show us the way to connect space and time with the physical…
Linear Geometry studies geometric properties which can be expressed via the notion of a line. All information about lines is encoded in a ternary relation called a line relation. A set endowed with a line relation is called a liner. So,…