“What is a Thing?”: Topos Theory in the Foundations of Physics
A. Döring,C. J. Isham +1 more
TLDR
In this article, the authors summarise the first steps in developing a fundamentally new way of constructing theories of physics and provide a new answer to Heidegger's timeless question "What is a thing?"Abstract:
The goal of this article is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. In doing so we provide a new answer to Heidegger’s timeless question “What is a thing?”.read more
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Journal ArticleDOI
A Topos for Algebraic Quantum Theory
TL;DR: In this article, the authors show how a noncommutative C*-algebra of observables A induces a topos T (A) in which the amalgamation of all of its commutative subalgebras comprises a single commutive C*algebra A. In this setting, states on A become probability measures (more precisely, valuations) on �, and self-adjoint elements of A define continuous functions fromto Scott's interval domain.
Posted Content
Categories for the practising physicist
Bob Coecke,Eric Paquette +1 more
TL;DR: In this article, the authors survey some particular topics in category theory in a somewhat unconventional manner, focusing on monoidal categories, mostly symmetric ones, for which they propose a physical interpretation.
Book ChapterDOI
Categories for the Practising Physicist
Bob Coecke,Eric Paquette +1 more
TL;DR: In this paper, the authors survey some particular topics in category theory in a somewhat unconventional manner, focusing on monoidal categories, mostly symmetric ones, for which they propose a physical interpretation, and discuss posetal categories, how group representations are in fact categorical constructs, and what strictification and coherence of monoidal category is all about.
OtherDOI
Agent-Based Modeling: The Right Mathematics for the Social Sciences?
Paul L. Borrill,Leigh Tesfatsion +1 more
TL;DR: This study provides a basic introduction to agent-based modeling (ABM) as a powerful blend of classical and constructive mathematics, with a primary focus on its applicability for social science research.
Journal ArticleDOI
Adaptation through chromosomal inversions in Anopheles.
TL;DR: An extensive literature review of the different adaptive traits associated with chromosomal inversions in the genus Anopheles, including insecticide resistance and behavioral changes, is provided.
References
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Book
Categories for the Working Mathematician
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
Journal ArticleDOI
On the Problem of Hidden Variables in Quantum Mechanics
TL;DR: The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered in this article, and it is shown that their essential axioms are unreasonable.
Journal ArticleDOI
The Logic of Quantum Mechanics
TL;DR: In this article, it was shown that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and in particular one can never predict both the position and the momentum of S, (Heisenberg's Uncertainty Principle) and most pairs of observations are incompatible, and cannot be made on S simultaneously.
Book ChapterDOI
The Problem of Hidden Variables in Quantum Mechanics
Simon Kochen,E. P. Specker +1 more
TL;DR: The problem of hidden variables in quantum theory has been a controversial and obscure subject for decades as mentioned in this paper, and there are many proofs of the non-existence of such variables, most notably von Neumann's proof, and various attempts to introduce hidden variables such as de Broglie [4] and Bohm [1] and [2].
Book
Introduction to higher order categorical logic
Joachim Lambek,Philip J. Scott +1 more
TL;DR: In this article, Cartesian closed categories and Calculus are used to represent Numerical functions in various categories and to describe the relation between categories. But they do not specify the topology of the categories.
Related Papers (5)
Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalized Valuations
C. J. Isham,Jeremy Butterfield +1 more