Related papers: Did Hypatia Know about Negative Numbers?
The values of $\alpha_s$ determined from low- and high-energy measurements are in irreconcilable contradiction with each other. The current status of the problem is critically reviewed. Consequences of the $\alpha_s$ contradiction, in…
Reconciliation of frequentist and Bayesian approaches to elementary treatment of data in nuclear and particle physics is attempted. Unique procedure to express the significance of a small count in presence of background is henceforth…
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
This is an English translation of Euler's 1750 paper "De numeris amicabilibus" (E152), the most substantial of his three works with this name. In it, he expounds at great length the ad hoc methods he has developed to search for pairs of…
We give some comments on W.M. Schmidt's theorem on Diophantine approximations with positive integers and our recent results on the topic.
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
Prime numbers or primes are man's eternal treasures that have been cherished for several millennia, until today. As their academic ancestors in ancient Mesopotamia, many mathematicians are still trying hard to see primes better. I shall…
In October 2017 the Italian National Institute of Statistics (ISTAT), Italy's body for official statistics, has published the book of fairy tales Le streghe di Bayes (The witches of Bayes) written by ISTAT staff members with the commendable…
There has been a growing interest, both in physics and psychology, in understanding contextuality in experimentally observed quantities. Different approaches have been proposed to deal with contextual systems, and a promising one is…
What is known as "Hilbert's hotel" is a story of an imaginary hotel with infinitely many rooms that illustrates the bizarre consequences of assuming an actual infinity of objects or events. Since the 1970s it has been used in a variety of…
The {\it Sierpi\'nski fractal} or {\it Sierpi\'nski gasket} $\Sigma$ is a familiar object studied by specialists in dynamical systems and probability. In this paper, we consider a graph $S_n$ derived from the first $n$ iterations of the…
We are pleased to see that Jeckelmann has made many changes to the original version of his comment on our paper as a result of our response. Here is a copy of this powerful response that reveals problems in his previous results. However,…
The expression for entropy sometimes appears mysterious - as it often is asserted without justification. This short manuscript contains a discussion of the underlying assumptions behind entropy as well as simple derivation of this…
It is commonplace, in the literature, to find that the Bekenstein-Hawking entropy has been endowed with having an explicit statistical interpretation. In the following essay, we discuss why such a viewpoint warrants a certain degree of…
This is the English version of the paper: "Complejidad de los n\'umeros naturales", Gaceta de la Real Sociedad Matem\'atica Espa\~nola 3 (2000) 230--250. In this paper, several conjectures about the complexity of natural numbers are…
We revisit the negative energy solutions of the Dirac equation, which become relevant at very high energies and study several symmetries which follow therefrom. The consequences are briefly examined.
Much recent progress has been made concerning the probable existence of Odd Perfect Numbers, forming part of what has come to be known as Sylvester's Web Of Conditions. This paper proves some results concerning certain properties of the…
The Sleeping Beauty problem is a puzzle in probability theory that has gained much attention since Elga's discussion of it [Elga, Adam, Analysis 60 (2), p.143-147 (2000)]. Sleeping Beauty is put asleep, and a coin is tossed. If the outcome…
The nature of Dark Energy is still very much a mystery, and the combination of a variety of experimental tests, sensitive to different potential Dark Energy properties, will help elucidate its origins. This white paper briefly surveys the…
The zombie menace has so far been studied only qualitatively or through the use of mathematical models without empirical content. We propose to use a new tool in survey research to allow zombies to be studied indirectly without risk to the…