The Undecidable Charge Gap and the Oil Drop Experiment

Decision problems in physics have been an active field of research for quite a few decades resulting in some interesting findings in recent years. However, such research investigations are based on a priori knowledge of theoretical computer science and the technical jargon of set theory. Here, I discuss a particular, but a significant, instance of how decision problems in physics can be realized without such specific prerequisites. I expose a hitherto unnoticed contradiction, that can be posed as a decision problem, concerning the oil drop experiment and thereby resolve it by refining the notion of ``existence'' in physics. This consequently leads to the undecidability of the charge spectral gap through the notion of ``undecidable charges" which is in tandem with the completeness condition of a theory as was stated by Einstein, Podolsky and Rosen in their seminal work. Decision problems can now be realized in connection to basic physics, in general, rather than quantum physics, in particular, as per some recent claims.Comment: 14 pages, 1 figur

Abstract verification and debugging of constraint logic programs

The technique of Abstract Interpretation [13] has allowed the development of sophisticated program analyses which are provably correct and practical. The semantic approximations produced by such analyses have been traditionally applied to optimization during program compilation. However, recently, novel and promising applications of semantic approximations have been proposed in the more general context of program verification and debugging [3],[10],[7]

Innovation management from fractal infinite paths integral point of view

While a mastery of management innovation is crucial for the future of the economy, to date, there is no theory able to base with objectivity the management of creativity and entrepreneurship. This absence is not due to the lack of methods but to ignorance of mathematical foundations which justify the paradigmatic transgression. These foundations exist nevertheless. It can be mentioned the fractal geometry and the role played by the singularities and correlations over long distances. In the set theory, let us mention Cohen's forcing methods and its engineering consequences through CK theory. In the categories theory, we can mention the principles of Kan extension herein applied by the mean of holomorphic analysis and the analytical extensions. All these methods are based on the recognition of the incompleteness of any structure axiomatically closed (Goedel). At the junction between the physics and the economy, the goal of the present work is to show that the lack of recognition of the role of singularities in this science must be searched in mental biases and the paradigms that affect our concept of equilibrium. We show that this concept must be generalized. If the criticism of the concept of equilibrium in economics is already known, it does not lead, quite as much, to a theory of innovation. We would like to address the issue of creativity by backing the reasoning by the questioning of the concept of equilibrium, using an analogy coming from the physics in fractal structures. The idea is to consider the equilibrium as some steady state limit of a fractional dynamics. The fractional dynamics is a dynamics controlled by non integer fractional equation. These equations will be considered in the Fourier space and by the means of their hyperbolic geodesics. Due to the intrinsic incompleteness of the fractality and of its cardinality, the thickening of the infinite will be used to show that there is no even physical balance but only pseudo-equilibria. The practical use of this observation leads to the design of a dynamic model of creativity, named DQPl (Dual Quality Planning), giving a topologic content to the innovation process. New principles of management of innovation emerge in naturally

A Note on Gödel, Priest and Naïve Proof

In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the connection between Gödel’s theorem and naïve proof so understood, both from a classical and a dialetheic perspective

Implications of Foundational Crisis in Mathematics: A Case Study in Interdisciplinary Legal Research

As a result of a sequence of so-called foundational crises, mathematicians have come to realize that foundational inquiries are difficult and perhaps never ending. Accounts of the last of these crises have appeared with increasing frequency in the legal literature, and one piece of this Article examines these invocations with a critical eye. The other piece introduces a framework for thinking about law as a discipline. On the one hand, the disciplinary framework helps explain how esoteric mathematical topics made their way into the legal literature. On the other hand, the mathematics can be used to examine some aspects of interdisciplinary legal research

Independence of the Continuum Hypothesis: an Intuitive Introduction

The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the main workhorse of set theory; and it has broad implications on mathematical foundations and on the role of syntax versus semantics. Despite its broad impact, it is not broadly taught. A main reason is the lack of accessible expositions for nonspecialists, because the mathematical structures and techniques employed in the proof are unfamiliar outside of set theory. This manuscript aims to take a step in addressing this gap by providing an exposition at a level accessible to advanced undergraduate mathematicians and theoretical computer scientists, while covering all the technically challenging parts of the proof.Comment: - Edited the example in the Reflection definition. - Changed fonts for rank() and nr() - Changed fonts for CH to \mathrm{CH} - Corrected a few spurious typo

CP debugging tools: Clarification of functionalities and selection of the tools

Abstract is not available

What Socrates Began: An Examination of Intellect Vol. 1

Walter E. Russell Endowed Chair in Philosophy and Education Symposium 1988https://digitalcommons.usm.maine.edu/facbooks/1237/thumbnail.jp

Mathematical Structure of the Emergent Event

Exploration of a hypothetical model of the structure of the Emergent Event. Key Words: Emergent Event, Foundational Mathematical Categories, Emergent Meta-system, Orthogonal Centering Dialectic, Hegel, Sartre, Badiou, Derrida, Deleuze, Philosophy of Scienc