Related papers: Math{\'e}matiques, musique et cosmologie : A parti…
In a context of increasing scientific specialization and deficiencies in the scientific literacy of the population, there arises a need to broaden the methods of scientific dissemination. This study proposes an approach that combines music…
In this essay a critical review of present conceptual problems in current cosmology is provided from a more philosophical point of view. In essence, a digression on how could philosophy help cosmologists in what is strictly their…
Sujets qui sont plus particulierement abordes dans ce cours: 1. Elements de cosmologie, l'Univers homogene Les principes cosmologiques et leurs verifications observationnelles Histoire thermique de l'Univers Inflation, motivations et…
This is a philosophy-intense physics article, or, if you wish, a physics-intense philosophy article. Also, being a mathematician, I tend to view the physics, in particular the essence of quantum physics, in emphasizing the mathematical…
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.
The collaboration of mathematics in the two musical systems of Pythagorean sounds and of equal sounds is evident and opportune for generating the elements and managing their relationships. The only essential notion for a rational…
This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it…
In this paper, we introduce a mathematical method to extract similarities between paintings and musical tracks. Our approach is based on the digitalization of both paintings and musical tracks by means of finite expansions in terms of…
Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of…
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
This is the material for two lectures given at Ecole Polytechnique in May 2011 for the math teachers of "classes pr\'eparatoires"(parallel to the undergraduate classes in universities). The introduction is a personal overview on Fourier…
This paper attempts to look for a mathematical method of composing music by incorporating Schonbergs idea of tone rows and matrix theory from linear algebra. The elements of a note set S are considered as the integer values for the natural…
The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to undergraduates studying physics or…
This paper considers a new and deeply challenging face of the problem of time in the context of cosmology drawing on the work of Thiemann (2006, 2007). Thiemann argues for a radical response to the cosmic problem of time that requires us 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…
Talk given at the 6th Philosophy-and-Physics-Workshop ``Epistemological Aspects of the Role of Mathematics in Physical Science'', FEST, Heidelberg, Feb. 1993
These notes were written from a series of lectures given in March 2010 at the Universidad Complutense of Madrid and then in Barcelona for the centennial anniversary of the Spanish Mathematical Society (RSME). Our aim is to give an…