Screen LibraryThinking about G odel and turing : essays on complexity, 1970-2007 /
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
World Scientific,
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| Publisher Address: | Singapore ; Hackensack, N.J. : |
| Publication Dates: | 2007. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/6536#t=toc |
| Carrier Form: | 1 online resource (xix,347pages) |
| Bibliography: | Includes bibliographical references. |
| ISBN: |
9812708979 (electronic bk.) 9789812708977 (electronic bk.) |
| CLC: | O141 |
| Contents: | On the difficulty of computations -- Information-theoretic computational complexity -- Randomness and mathematical proof -- G del's theorem and information -- Randomness in arithmetic -- Randomness in arithmetic and the decline & fall of reductionism in pure mathematics -- A century of controversy over the foundations of mathematics -- A century of controversy over the foundations of mathematics -- Metamathematics and the foundations of mathematics -- Paradoxes of randomness -- Two philosophical applications of algorithmic information theory -- On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility -- Leibniz, information, math & physics -- Leibniz, randomness & the halting probability -- Complexity & Leibniz -- The limits of reason -- How real are real numbers? -- Epistemology as information theory: From Leibniz to [symbol] -- Is incompleteness a serious problem? -- Speculations on biology, information & complexity -- How much information can there be in a real number? -- The halting probability [symbol]: irreducible complexity in pure mathematics -- The halting probability [symbol]: concentrated creativity. |