Related papers: Why Mathematics Works So Well
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
The fundamental physical theories that interpret and explain behaviour of matter in nature are dependent on several unobservables and insensibles in their construction. While a rigorous natural philosophy cannot take them for granted, there…
We all are fascinated by the phenomena of intelligent behavior, as generated both by our own brains and by the brains of other animals. As physicists we would like to understand if there are some general principles that govern the structure…
Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…
The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
We acuminate the idea of a final theory of physics in order to analyze its logical implications and consequences. It is argued that the rationale of a final theory is the principle of sufficient reason. This implies that a final theory of…
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…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
One source of beauty in mathematics is totally unexpected connections between two fundamentally different objects. For instance, is it not surprising that the time period of a real simple pendulum is linked with a function arising out of…
This article supports the epistemological claim that sound human reasoning about ultimate knowledge is either foundational or circularly justified. In particular, questions which naturally arise in theology, philosophy, and related…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a…
Existential fixed point logic (EFPL) is a natural fit for some applications, and the purpose of this talk is to attract attention to EFPL. The logic is also interesting in its own right as it has attractive properties. One of those…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
Here I briefly discuss why supersymmetry is considered a leading candidate of physics beyond the standard model. I also highlight the salient features of different supersymmetry breaking models. A few other symmetries, broken or intact,…