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Titlebook: Undecidability, Uncomputability, and Unpredictability; Anthony Aguirre,Zeeya Merali,David Sloan Book 2021 The Editor(s) (if applicable) an

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發(fā)表于 2025-3-21 19:18:30 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Undecidability, Uncomputability, and Unpredictability
編輯Anthony Aguirre,Zeeya Merali,David Sloan
視頻videohttp://file.papertrans.cn/942/941242/941242.mp4
概述Published in cooperation with the renowned physics "think-tank" Foundational Questions Institute, FQXi.Presents specially reworked versions of the prize-winning essays from among more than 200 submiss
叢書(shū)名稱(chēng)The Frontiers Collection
圖書(shū)封面Titlebook: Undecidability, Uncomputability, and Unpredictability; Anthony Aguirre,Zeeya Merali,David Sloan Book 2021 The Editor(s) (if applicable) an
描述.For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. G?del’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world?. .This book, based on the winning essays from?the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions
出版日期Book 2021
關(guān)鍵詞award-winning essays; FQXi essays; Randomness in physical theory; what is computability?; predictability
版次1
doihttps://doi.org/10.1007/978-3-030-70354-7
isbn_softcover978-3-030-70356-1
isbn_ebook978-3-030-70354-7Series ISSN 1612-3018 Series E-ISSN 2197-6619
issn_series 1612-3018
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Indeterminism, Causality and Information: Has Physics Ever Been Deterministic?,solute certainty, independently of any interpretations. It also tells that it was quantum mechanics that introduced fundamental indeterminacy into physics. We show that there exist alternative stories to be told in which classical mechanics, too, can be interpreted as a fundamentally indeterministic
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,A G?delian Hunch from Quantum Theory,res an over-determination—if the sentence is true then it is false, if it is false then it is true—the “Liar” leads to undecidability, the impossibility to decide whether the sentence is true or false.
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Epistemic Horizons: This Sentence Is ,it was shown that Lawvere’s theorem, which forms the categorical backdrop to phenomena such as G?delian incompleteness, Turing undecidability, Russell’s paradox and others, applied to a measurement context, yields bounds on the maximum knowledge that can be obtained about a system, which produces ma
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Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes,, whether or not a given formula is deemed a theorem in some axiomatic system is not a matter of certainty, but is instead governed by a probability distribution. We then show that this framework gives a compelling account of several aspects of mathematical practice. These include: 1) the way in whi
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