Related papers: Physical Constraints of Numbers
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
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…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
I argue that scientific determinism is not supported by facts, but results from the elegance of the mathematical language physicists use, in particular from the so-called real numbers and their infinite series of digits. Classical physics…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more…
The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
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…
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are…
Dirac sought an interpretation of mathematical formalism in terms of physical entities and Einstein insisted that physics should describe "the real states of the real systems". While Bell inequalities put into question the reality of…
Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with…
We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain)…