Related papers: The Erdos Paradox
The search of a rational explanation of eclipses pervades the beginnings of philosophical and scientific thought. Within this intellectual frame, the knowledge of the "saros cycle" (a cycle of 18 years, 10 or 11 days and 1/3 of a day that…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
A simple classical probabilistic system (a simple card game) classically exemplifies Aharonov and Vaidman's "Three-Box 'paradox'" [J. Phys. A 24, 2315 (1991)], implying that the Three-Box example is neither quantal nor a paradox and leaving…
We analyze the informal notion of truth and conclude that it can be formalized in essentially two distinct ways: constructively, in terms of provability, or classically, as a hierarchy of concepts which satisfy Tarski's biconditional in…
This survey article collects a few of my favorite open problems of Branko Gr\"{u}nbaum.
This article is the first part of a study of the so-called 'mathematical part' of Plato's Theaetetus (147d-148b). The subject of this 'mathematical part' is the irrationality, one of the most important topics in early Greek mathematics. As…
The thought experiment (called the clock paradox or the twin paradox)proposed by Langevin in 1911 of two observers, one staying on Earth and the other making a trip toward a star with a velocity near the light velocity is very well known…
The classical three-box paradox of Kirkpatrick [J. Phys. A 36 4891 (2003)] is compared to the original quantum Three-Box paradox of Aharonov and Vaidman [J. Phys. A 24 2315 (1991)]. It is argued that the quantum Three-Box experiment is a…
This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputability and randomness.
After pointing out the historical avatar at the origin of a would be twin or clock paradox, we argue that, at least on a local scale, the (re-qualified) paradox is but a necessary consequence of the sole principle of causality.
We show in this note that Gibbs paradox arises not due to application of thermodynamic principles, whether classical or statistical or even quantum mechanical, but due to incorrect application of mathematics to the process of mixing of…
This paper is a comment on quant-ph/0606067 by Ravon and Vaidman, in which they defend the position that the ``three-box paradox'' is indeed paradoxical.
A new tool is introduced, specially tailored for the study of order 2 bases of N. It is called the Erdos-Tuan algebra since it suits well their conjecture.
We give an informal introduction to the authors' work on some conjectures of Kazhdan and Lusztig, building on work of Soergel and de Cataldo-Migliorini. This article is an expanded version of a lecture given by the second author at the…
Paradoxes are interesting puzzles in philosophy and mathematics, and they could be even more fascinating, when turned into proofs and theorems. For example, Liar's paradox can be translated into a propositional tautology, and Barber's…
We present an English translation and discussion of an essay that a Japanese physicist, Torahiko Terada, wrote in 1922. In the essay, he described the waiting-time paradox, also called the bus paradox, which is a known mathematical…
Some reflections on the role in the development of Mathematics of our unconscious perception of the world and just as unconscious organizing pulsions for those perceptions.
Proietti et al. (arXiv:1902.05080) reported on an experiment designed to settle, or at least to throw light upon, the paradox of Wigner's friend. Without questioning the rigor or ingenuity of the experimental protocol, I argue that its…
The paper presents a counterexample to the Hodge conjecture.
Gray (2015) argued that the Fermi paradox (FP) is a misnomer, and it is not a valid paradox. Gray also speculated that the argument was misattributed to Fermi, whose lunchtime remarks did not pertain to the existence of extraterrestrial…