Negative recency, randomization device choice, and reduction of compound lotteries

We report an experiment in which subjects are not indifferent between real-money lotteries implemented with randomization devices that are equivalent under the Reduction Axiom. Instead choice behavior is consistent with subjective distortion of conditional probability, and this persists in treatment conditions that control for (i) computational limitations and (ii) possible confounding by ratio bias. --reduction of compound lotteries,negative recency effect,gambler's fallacy,law of small numbers,randomization devices,instruments and materials,design of experiments,St. Petersburg paradox

Free Will in a Quantum World?

In this paper, I argue that Conway and Kochen’s Free Will Theorem (1,2) to the conclusion that quantum mechanics and relativity entail freedom for the particles, does not change the situation in favor of a libertarian position as they would like. In fact, the theorem more or less implicitly assumes that people are free, and thus it begs the question. Moreover, it does not prove neither that if people are free, so are particles, nor that the property people possess when they are said to be free is the same as the one particles possess when they are claimed to be free. I then analyze the Free State Theorem (2), which generalizes the Free Will Theorem without the assumption that people are free, and I show that it does not prove anything about free will, since the notion of freedom for particles is either inconsistent, or it does not concern our common understanding of freedom. In both cases, the Free Will Theorem and the Free State Theorem do not provide any enlightenment on the constraints physics can pose on free will

Thoughts on the Riemann hypothesis

The simultaneous appearance in May 2003 of four books on the Riemann hypothesis (RH) provoked these reflections. We briefly discuss whether the RH should be added as a new axiom, or whether a proof of the RH might involve the notion of randomness

Deriving Bell's nonlocality from nonlocality at detection

It is argued that Bell's nonlocality is a particular case of nonlocality at detection, which appears already in single-particle interference experiments. The unity of nonlocality and local causality is crucial to provide a consistent description of the world.Comment: 9 pages, 2 figure

A new foundational crisis in mathematics, is it really happening?

The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.Comment: Final versio

Exploring the Local Orthogonality Principle

Nonlocality is arguably one of the most fundamental and counterintuitive aspects of quantum theory. Nonlocal correlations could, however, be even more nonlocal than quantum theory allows, while still complying with basic physical principles such as no-signaling. So why is quantum mechanics not as nonlocal as it could be? Are there other physical or information-theoretic principles which prohibit this? So far, the proposed answers to this question have been only partially successful, partly because they are lacking genuinely multipartite formulations. In Nat. Comm. 4, 2263 (2013) we introduced the principle of Local Orthogonality (LO), an intrinsically multipartite principle which is satisfied by quantum mechanics but is violated by non-physical correlations. Here we further explore the LO principle, presenting new results and explaining some of its subtleties. In particular, we show that the set of no-signaling boxes satisfying LO is closed under wirings, present a classification of all LO inequalities in certain scenarios, show that all extremal tripartite boxes with two binary measurements per party violate LO, and explain the connection between LO inequalities and unextendible product bases.Comment: Typos corrected; data files uploade