Related papers: The Erdos Paradox
A pedagogical account of entropy and its history.
This paper discusses the dual interpretation of the Jeffreys--Lindley's paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to…
A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the violation of Bell's inequality is explained by maintaining realism, inductive…
Some mathematical properties of the Erd\"os number and its formal equivalents are shown. An informetric equivalent is presented: the Rousseau number. This contribution honors Ronald Rousseau for his 73th birthday.
Paul Halmos' work in dilation theory began with a question and its answer: Which operators on a Hilbert space can be extended to normal operators on a larger Hilbert space? The answer is interesting and subtle. The idea of representing…
This is a philosophy paper rather than mathematical physics work. I will publish it in some other place.
On the seminal paper written by Einstein, Podolsky and Rosen [1], a critique to the completeness of quantum mechanics was posed. Part of the critique consisted in the following argument: if quantum mechanics is complete, then, two physical…
We throw a brief glance at Galois' life, on the occasion of his 200th anniversary (written in German).
A short essay on the life and mathematical heritage of Coble. A substantially edited version will be part of the series of biographical memoirs of past members of the National Academy of Sciences. Version 2: minor changes. Version 3. Typo…
This is the second of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. One of the many…
The "twin paradox" of special relativity offers the possibility to make interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the…
The Fermi Paradox is the apparent contradiction between the high probability extraterrestrial civilizations' existence and the lack of contact with such civilizations. In general, solutions to Fermi's paradox come down to either estimation…
The fact that the author of an excellent textbook on electromagnetism could be duped by "hidden momentum" vividly illustrates the problematic nature of its use.
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we…
In this paper, I aim to articulate and investigate the philosophical implications and inherent symbolism surrounding the mathematical properties of Ouroboros spaces and their respective functions. Initially, I provide a brief historical…
This is the third of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. This time, rather…
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
We debate, departing from 2-3 readings of a single sentence in Proclus' Commentary to Plato's Republic, the plausibility of a rigorous (inductive) arithmetical derivation of an infinite sequence of pairs of side and diameter numbers by…
The paradoxical aspect of integration of a social group has been highlighted by Peter Blau (Exchange and Power in Social Life, Wiley and Sons, 1964). During the integration process, the group members simultaneously compete for social status…
According to Paul Erd\H{o}s [Some notes on Tur\'an's mathematical work, J. Approx. Theory 29 (1980), page 4] it was Paul Tur\'an who "created the area of extremal problems in graph theory". However, without a doubt, Paul Erd\H{o}s…