Related papers: Did Hypatia Know about Negative Numbers?
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
A problem of Glasner, now known as Glasner's problem, asks whether every minimally almost periodic, monothetic, Polish groups is extremely amenable. The purpose of this short note is to observe that a positive answer is obtained under the…
This article introduces and translates letters from T.J. stieltjes (1856-1894) to C. Hermite (1822-1891) regarding Stieltjes' published notes claiming to have solved B. Riemann's conjecture "it is very probable that all the roots [of the…
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 report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
Over the last million years, human language has emerged and evolved as a fundamental instrument of social communication and semiotic representation. People use language in part to convey emotional information, leading to the central and…
There are important problems in physics related to the concept of probability. One of these problems is related to negative probabilities used in physics from 1930s. In spite of many demonstrations of usefulness of negative probabilities,…
This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…
A mathematical interpretation of the usual definition of entropy (for a discrete probability distribution or a trace 1 positive operator) is given. This formulation makes some properties of entropy immediate.
Wojcik's hypothesis has been mentioned on page 32 of the text S.Piekarski, "Galilean-Invariant Formulation of the Fluid Mechanics", IFTR REPORTS, 7/2007. Here we discuss it in more detail. Our main is to show that the form of the…
The apparently trifling unexpected hanging paradox has generated an enormous philosophical literature. We introduce the mathematician to this literature, paying special attention to aspects that involve nontrivial mathematics. This xxx…
I was asked to give a brief review of the black hole-string correspondence as a warm-up for a longer SITP-group discussion of a recent paper by Chen, Maldacena, and Witten. Here are my notes in written form.
Some physical aspects of negative mass are examined. Several unusual properties, such as the ability of negative mass to penetrate any armor, are analyzed. Other surprising effects include the bizarre system of negative mass chasing…
We present some questions and suggestion on the second part of the Hilbert 16th problem
In this short note, we answer two questions of Chen and Ruzsa negatively and answer a problem of Ma and Chen affirmatively.
Hurewicz found connections between some topological notions and the combinatorial cardinals b and d. Reclaw gave topological meaning to the definition of the cardinal p. We extend the picture with a topological interpretation of the…
We discuss the (twisted) weak positivity theorem. We also treat some applications.
In a recent interesting Letter [Phys. Rev. Lett. 108, 140401 (2012)] I. Bialynicki-Birula and his coauthor have derived the uncertainty relation for the photons in three dimensions. However, some of their arguments are problematical, and…
We comment on S. Carlip's recent Letter "Hiding the Cosmological Constant" [Phys. Rev. Lett. 123, 131302].