Mário Bacelar Valente

Universidad Pablo de Olavide

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Co-Authors

Helena Moreira

University of Coimbra

Kenneth N.F. Shaw

Children's Hospital of Los Angeles

Helena Moreira

Vetenskap I Skolan

Sharon M. Valente

Hospital de Clínicas "José de San Martín"

Maria Cimmino

Parthenope University of Naples

MARY E. COTTON

University of California, Los Angeles

Giuseppe Galasso

University of Naples Federico II

Maurizio Ceccarelli

Convegno internazionale di studi

Stephen D. Cederbaum

University of California, Los Angeles

Cooperative Institutions

University of California, Los Angeles

University of Southern California

UCLA Health

Children's Hospital of Los Angeles

Kaiser Permanente

UCLA Medical Center

Sapienza University of Rome

Hospital de Clínicas "José de San Martín"

University of Buenos Aires

VA Greater Los Angeles Healthcare System

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On the Relationship Between Geometric Objects and Figures in Euclidean Geometry

Lecture notes in computer science (2021)

Mário Bacelar Valente

Representation

Non-Euclidean geometry

Synthetic geometry

Analytic geometry

Ordered geometry

Solid geometry

Transformation geometry

Geometric Modeling

Idealization

Geometric analysis

Absolute geometry

10.1007/978-3-030-86062-2_7

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Do All Languages Share the Same Conceptual Structure?

Cognitive Semantics (2022)

Mário Bacelar Valente

Abstract In this work, we consider the views of three exponents of major areas of linguistics – Levelt (psycholinguistics), Jackendoff (theoretical linguistics), and Gil (field linguistics) – regarding the issue of the universality or not of the conceptual structure of languages. In Levelt’s view, during language production, the conceptual structure of the preverbal message is language-specific. In Jackendoff’s theoretical approach to language – his parallel architecture – there is a universal conceptual structure shared by all languages, in contradiction to Levelt’s view. In Gil’s work on Riau Indonesian, he proposes a conceptual structure that is quite different from that of English, adopted by Jackendoff as universal. We find no reason to disagree with Gil’s view. In this way, we take Gil’s work as vindicating Levelt’s view that during language production preverbal messages are encoded with different conceptual structures for different languages.

Contradiction

10.1163/23526416-08020001

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The Feynman Diagrams and Virtual Quanta

Mário Bacelar Valente

The received view in philosophical studies of quantum field theory is that the Feynman diagrams are simply calculational tools. Alongside with this view we have the one that takes the virtual quanta to be also simply formal tools. This received view was developed and consolidated in philosophy of physics works by Mario Bunge, Paul Teller, Michael Redhead, Robert Weingard, Brigitte Falkenburg, and others. In this paper I will present an alternative to the received view.

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Ancient Greek Mathematical Proofs and Metareasoning

Mário Bacelar Valente

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we go through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness.

Argument (complex analysis)

10.1007/978-3-031-46193-4_2

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Einstein's physical geometry at play: inertial motion, the boostability assumption, the Lorentz transformations, and the so-called conventionality of the one-way speed of light

arXiv (Cornell University) (2013)

Mário Bacelar Valente

In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a non-conventional view on Euclidean geometry (as the geometry associated to inertial motion and inertial reference frames) and on the uniform time. Also, by taking into account the implications of the view of geometry as a physical geometry, it is presented a critical reassessment of the so-called boostability assumption (implicit according to Einstein in the formulation of the theory) and also of 'alternative' derivations of the Lorentz transformations that do not take into account the so-called 'light postulate'. Finally it is addressed the issue of the eventual conventionality of the one-way speed of light or, what is the same, the conventionality of simultaneity (within the same inertial reference frame). It turns out that it is possible to see the (possible) conventionality of distant simultaneity as a case of conventionality of geometry (in Einstein's reinterpretation of Poincaré's views). By taking into account synchronization procedures that do not make reference to light propagation (which is necessary in the derivation of the Lorentz transformations without the 'light postulate'), it can be shown that the synchronization of distant clocks does not need any conventional element. This implies that the whole of chronogeometry (and because of this the physical part of the theory) does not have any conventional element in it, and it is a physical chronogeometry.

Frame of reference

Simultaneity

10.48550/arxiv.1306.1361

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The Dirac equation, the concept of quanta, and the description of interactions in quantum electrodynamics

Mário Bacelar Valente

In this article the Dirac equation is used as a guideline to the historical emergence of the concept of quanta, associated with the quantum field. In Pascual Jordan’s approach, electrons as quanta result from the quantization of a classical field described by the Dirac equation. With this quantization procedure – also used for the electromagnetic field – the concept of quanta becomes a central piece in quantum electrodynamics. This does not seem to avoid the apparent impossibility of using the concept of quanta when interacting fields are considered together as a closed system. In this article it is defended that the type of analysis that leads to so drastic conclusions is avoidable if we look beyond the mathematical structure of the theory and take into account the physical ideas inscribed in this mathematical structure. In this case we see that in quantum electrodynamics we are not considering a closed system of interacting fields, what we have is a description of the interactions between distinct fields. In this situation the concept of quanta is central, the Fock space being the natural mathematical structure that permits maintaining the concept of quanta when considering the interaction between the fields.

Classical electromagnetism

Impossibility

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Equilíbrio químico: O sistema 2 NO2 (g) N2O4 (g) revisitado, numa perspectiva prática de sala de aula

Boletim da Sociedade Portuguesa de Química (2007)

Mário Bacelar Valente Helena Moreira

10.52590/m3.p631.a30001379

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A Síntese Industrial do Amoníaco: calculadoras gráficas na resolução de problemas numéricos em equilíbrio químico

Boletim da Sociedade Portuguesa de Química (2009)

Mário Bacelar Valente Helena Moreira Joana Noronha Sá

equações de ordem 4, o que está, em princípio, fora do alcance matemático dos alunos do ensino secundário.

10.52590/m3.p642.a30001475

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Geometry of motion: some elements of its historicaldevelopment

Mário Bacelar Valente

in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first conceived by ancient Greek mathematicians.

Galileo (satellite navigation)

Presentation (obstetrics)

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Geometrical objects and figures in practical, pure, and applied geometry

Zenodo (CERN European Organization for Nuclear Research) (2020)

Mário Bacelar Valente

10.5281/zenodo.4625086

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