Related papers: Dialogues about geometry and light
In offered work short historical excursus to the classical theory of light is presented: Grimaldi, Fermat, Newton, Huygens, Young, Fresnel, Fraunhofer, and Gauss. The ray analog of wave model of light and Huygens-Fresnel's elementary waves…
In classical mechanics matter and fields are completely separated. Matter interacts with fields. For particle physicists this is not the case. Both matter and fields are represented by particles. Fundamental interactions are mediated by…
The dark matter and dark energy problem, that is now dominating the research in cosmology, makes the question of the origin of mass-energy content of the universe more urgent than ever. There are two philosophies regarding this question:…
We discuss the nature of reality in the ontological context of Penrose's math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter…
In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
There is no mysterious link between mathematics and physics, because both of them are human inventions designed to study the world.
In 1710, George Berkeley, philospher and scientist, discovered that the directions in which we see (sightlines) are tilted 45 degrees towards the past from the directions in which we look. Looking north from the 3-d present we see to the…
The current standard model of cosmology assumes that the majority of matter in the Universe is made of dark matter, and that the latter is fundamentally different from ordinary matter. Dark matter can in principle explain the rotation of…
We aim to bring a new perspective about some aspects of the current research in Cosmology. We start with a brief introduction about the main developments of the field in the last century; then we introduce an analogy that shall elucidate…
The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern…
Deflection of light by gravity was predicted by General Relativity and observationaly confirmed in 1919. In the following decades various aspects of the gravitational lens effect were explored theoretically, among them the possibility of…
The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant…
When joined the unified gauge picture of fundamental interactions, the gravitation theory leads to geometry of a space-time which is far from simplicity of pseudo-Riemannian geometry of Einstein's General Relativity. This is geometry of the…
A family of sequences produced by a non-homogeneous linear recurrence formula derived from the geometry of circles inscribed in lenses is introduced and studied. Mysterious ``underground'' sequences underlying them are discovered in this…
Understanding geometry relies heavily on vision. In this work, we evaluate whether state-of-the-art vision language models (VLMs) can understand simple geometric concepts. We use a paradigm from cognitive science that isolates visual…
We consider the mathematical theory of geographical maps, with an emphasis on the eighteenth century works of Euler, Lagrange and Delisle. This period is characterized by the frequent use of maps that are no more obtained by the…
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about…
Modern mathematics is known for its rigorous proofs and tight analysis. Math is the paradigm of objectivity for most. We identify the source of that objectivity as our knowledge of the physical world given through our senses. We show in…
New techniques to evaluate the clock effect using light are described. These are based on the flatness of the cylindrical surface containing the world lines of the rays constrained to move on circular trajectories about a spinning mass. The…