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In search of continuity: thoughts of an epistemic empiricist
Ian T. Durham,Lawrence B. Brod +1 more
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In this paper, the authors argue that both classical and quantum physics include limits that prevent us from definitively answering the question "Is the universe digital or analog?" They argue that classical physics is itself really nothing more than a convenient approximation.Abstract:
Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics does so is rather unexpected. In fact, I argue that classical physics is itself really nothing more than a convenient approximation. Either way, it turns out that our knowledge of the universe is discrete and so it is extraordinarily difficult, perhaps even impossible, to determine the underlying continuity of the universe itself.read more
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Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics
TL;DR: In this article, the authors examine Connes' criticisms of Robinson's infinitesimals starting in 1995 and conclude that Connes views a theory as being virtual if it is not definable in a suitable model of ZFC.
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Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics
TL;DR: In this paper, the authors examine Connes' criticisms of Robinson's infinitesimals starting in 1995 and reach an opposite conclusion: all definable sets of reals are Lebesgue measurable, suggesting that Connes views a theory as being virtual if it is not definable in a suitable model of ZFC.
决定物理学发展的六大思想——《Six Ideas That Shaped Physics》赏析
TL;DR: The Six Ideas That Shaped Physics (6-6): as discussed by the authors ) is a collection of six ideas that shaped physics that include physics, astronomy, biology, and computer science.
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Boundaries of Scientific Thought
TL;DR: The scientific revolution, as understood to be the rise of modern science, began in the late Renaissance and took firm hold during the Enlightenment as discussed by the authors, and the scientific revolution became a global phenomenon.
References
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Non-standard analysis
TL;DR: The history of the calculus can be traced back to the Calculus of Differential and Integral Calculus (DIC) as discussed by the authors, which is a generalization of the integral calculus.
Book
Global Lorentzian Geometry
TL;DR: In this paper, the Riemannian themes in Lorentzian geometry connections and curvature of curvature are discussed and the splitting problem in global geodesic geometry is discussed.
Book ChapterDOI
Was sind und was sollen die Zahlen
TL;DR: In this paper, the author verstehe unter einem Ding jeden Gegenstand unseres Denkens, and verstehen den Denkens unter den Dingen sprechen.
Book ChapterDOI
Non-Standard Analysis
TL;DR: Robinson as discussed by the authors showed that non-standard models of arithmetic can be applied to a theory so far removed from it as the infinitesimal calculus, i.e., a non-archimedian approach to the calculus with infinitely small and infinitely large numbers.