Related papers: Mathematics via Symmetry
This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the…
A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
There is no mysterious link between mathematics and physics, because both of them are human inventions designed to study the world.
This preprint deals with the symmetry of parametrized families of systems and the changes therein as the parameter changes. There are (at least ?) two kinds of symmetry: generic and specific which behave in almost totally opposite ways as…
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to…
This paper proposes a new definition of science based on the distinction between the activity of scientists and the product of that activity: the former is denoted (lower-case) science and the latter (upper-case) Science. These definitions…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…