Hemeroteca de la sección ‘Leyes’

Quantum Observables and Ockham’s Razor

Por • 16 feb, 2021 • Category: Leyes

For the paradigm of the quantum double-slit experiment (DSE), we apply Ockham’s Razor to interpret quantum observations and to evaluate terminology often associated with wave-particle duality. One finds that the Correspondence Principle (CP), combined with classical wave DSEs, e.g., Young [1804], is sufficient to predict the observed quantum particle and wave phenomena. The empirical approach of Ockham infers that observed individual quanta are whole particles only; an individual quantum has no observed wavelike character. The observed, so-called wave nature of quanta emerges only in the limit of large numbers of particle observation events. That is, the «measurement problem» is no problem at all; «particle» and «wave» derive from separate and different aspects of the observations.

Geodesic stars in random geometry

Por • 3 feb, 2021 • Category: Leyes

A point of a metric space is called a geodesic star with m arms if it is the endpoint of m disjoint geodesics. For every m∈{1,2,3,4}, we prove that the set of all geodesic stars with m arms in the Brownian sphere has dimension 5−m. This complements recent results of Miller and Qian, who proved that this dimension is smaller than or equal to 5−m.

«It is like egg»: Paul Lorenzen and the collapse of proofs of consistency

Por • 30 ene, 2021 • Category: Leyes

Paul Lorenzen, mathematician and philosopher of the 20th century, mentions October 1947 as the date of a crisis in his mathematical and philosophical investigations. An autograph dated 15 October 1947 documents this crisis. This article proposes a traduction and a commentary of it and sketches the circumstances of its writing on the base of his correspondence with Paul Bernays. A lettter from Lorenzen to Carl Friedrich Gethmann dated 14 January 1988 carves out the story of this crisis by showing how he soaks up the indications of his correspondents and transmutes them into an absolutely original research.

On consistency and existence in mathematics

Por • 21 ene, 2021 • Category: Leyes

This paper engages the question Does the consistency of a set of axioms entail the existence of a model in which they are satisfied? within the frame of the Frege-Hilbert controversy. The question is related historically to the formulation, proof, and reception of Gödel’s Completeness Theorem.

A history of truth-values

Por • 13 ene, 2021 • Category: Leyes

The whole story The compound word “truth-value”, sometimes written “truth value”, is a bit monstrous and ambiguous. It is the name of a central concept of modern logic, but has not yet invaded everyday language. An ordinary man will say: it is true that Paris is the capital of France, rather than: the truth-value of “Paris is the capital of France” is true. And a mathematician also will say: it is true that 2+3=5, rather than the truth-value of “2+3=5” is true. We don’t even find “truth-values” in postmodern or new age discussions side by side with “quantum leap”, “imaginary number”, “betacognition”. It seems that “truth-value” is exclusively used by logicians, philosophers of logic and analytic philosophers.

The Power of Inconsistency in Anti-Realist Realisms about Quantum Mechanics (Or: Lessons on How to Capture and Defeat Smoky Dragons)

Por • 6 ene, 2021 • Category: Leyes

In this work we argue that the power and effectiveness of the Bohrian approach to quantum mechanics is grounded on an inconsistent form of anti-realist realism which is responsible not only for the uncritical tolerance — in physics — towards the «standard» account of the theory of quanta, but also — in philosophy — of the alarming reproduction of quantum narratives. Niels Bohr’s creative methodology can be exposed through the analysis of what John Archibald Wheeler called «the great smoky dragon».

The Ordinal Interpretation of the Integers and Its Use in Number Theory

Por • 29 dic, 2020 • Category: Leyes

The author recently published a paper which claimed that an ordinal interpretation of numbers had limited applicability for cryptography. A further examination of this subject, in particular to what extent an ordinal interpretation is useful for recurrence sequences, is needed. Hilbert favored an interpretation of the natural numbers that placed their ordinal properties prior to their cardinal properties [1] [2]. The author examines ordinal uses of the integers in number theory in order to discuss the possibilities and limitations of this approach.

Fundamental Concepts of Quantum Theories

Por • 22 dic, 2020 • Category: Leyes

Abstract The foundations of the mathematical structure of quantum theories of a massive particle are the basis of this analysis. It proves the coherence of the particle-wave duality of quantum theories and the principle of complementarity as well. Furthermore, the noncommutativity of Hermitian operators proves that quantum theories are inherently indeterministic. This feature does not deny the fact that the classical limit of quantum theories agrees with classical physics. It is also shown that the foundations of the mathematical structure of quantum theories impose constraints on any specific quantum theory.

Race is on for quantum computing killer apps

Por • 18 dic, 2020 • Category: Leyes

Coming back to the Chinese results, to what extent do you consider that they have actually demonstrated “quantum supremacy” over classical computers? algorithms are a moving target. What are their limits? This is one of the greatest unsolved problems. That is part of what makes quantum supremacy so tricky. If the Chinese experiment achieved quantum supremacy at all, then it would be beyond that limit. Even the biggest supercomputer on Earth would not have nearly enough disk space to write down the whole distribution.

Sobre los Fundamentos de las Matemática

Por • 12 dic, 2020 • Category: Leyes

El consejo de redacción de Teorema ha querido anunciar y preparar la presente edición de la traducción castellana de ciertos textos de Lesniewski (cuya traducción francesa inédita yo había hecho con anterioridad) publicando una entrevista en la que respondí a varias preguntas referentes a la lógica en Polonia, la obra lógica de Lesniewski y mis propias contribuciones a la lógica