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Record Nr. |
UNINA9910966444503321 |
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Autore |
Ungar Abraham A |
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Titolo |
Beyond the Einstein addition law and its gyroscopic Thomas precession : the theory of gyrogroups and gyrovector spaces / / by Abraham A. Ungar |
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Pubbl/distr/stampa |
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Dordrecht ; ; Boston, : Kluwer Academic Publishers, c2001 |
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ISBN |
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1-280-20689-6 |
9786610206896 |
0-306-47134-5 |
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Edizione |
[1st ed. 2002.] |
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Descrizione fisica |
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1 online resource (462 p.) |
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Collana |
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Fundamental theories of physics ; ; v. 117 |
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Disciplina |
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Soggetti |
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Special relativity (Physics) |
Geometry, Hyperbolic |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 381-401) and indexes. |
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Nota di contenuto |
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Thomas Precession: The Missing Link -- Gyrogroups: Modeled on Einstein’S Addition -- The Einstein Gyrovector Space -- Hyperbolic Geometry of Gyrovector Spaces -- The Ungar Gyrovector Space -- The MÖbius Gyrovector Space -- Gyrogeometry -- Gyrooprations — the SL(2, c) Approach -- The Cocycle Form -- The Lorentz Group and its Abstraction -- The Lorentz Transformation Link -- Other Lorentz Groups. |
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Sommario/riassunto |
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Evidence that Einstein's addition is regulated by the Thomas precession has come to light, turning the notorious Thomas precession, previously considered the ugly duckling of special relativity theory, into the beautiful swan of gyrogroup and gyrovector space theory, where it has been extended by abstraction into an automorphism generator, called the Thomas gyration. The Thomas gyration, in turn, allows the introduction of vectors into hyperbolic geometry, where they are called gyrovectors, in such a way that Einstein's velocity additions turns out to be a gyrovector addition. Einstein's addition thus becomes a gyrocommutative, gyroassociative gyrogroup operation in the same way that ordinary vector addition is a commutative, associative group operation. Some gyrogroups of gyrovectors admit scalar multiplication, |
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giving rise to gyrovector spaces in the same way that some groups of vectors that admit scalar multiplication give rise to vector spaces. Furthermore, gyrovector spaces form the setting for hyperbolic geometry in the same way that vector spaces form the setting for Euclidean geometry. In particular, the gyrovector space with gyrovector addition given by Einstein's (Möbius') addition forms the setting for the Beltrami (Poincaré) ball model of hyperbolic geometry. The gyrogroup-theoretic techniques developed in this book for use in relativity physics and in hyperbolic geometry allow one to solve old and new important problems in relativity physics. A case in point is Einstein's 1905 view of the Lorentz length contraction, which was contradicted in 1959 by Penrose, Terrell and others. The application of gyrogroup-theoretic techniques clearly tilt the balance in favor of Einstein. |
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2. |
Record Nr. |
UNINA9910484663303321 |
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Autore |
Jensen Pablo |
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Titolo |
Your Life in Numbers: Modeling Society Through Data / / by Pablo Jensen |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Copernicus, , 2021 |
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ISBN |
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Edizione |
[1st ed. 2021.] |
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Descrizione fisica |
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1 online resource (VII, 114 p. 16 illus., 10 illus. in color.) |
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Disciplina |
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Soggetti |
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System theory |
Social sciences |
Humanities |
Computer simulation |
Science - Philosophy |
Social sciences - Philosophy |
Sociology - Methodology |
Complex Systems |
Humanities and Social Sciences |
Computer Modelling |
Philosophy of Science |
Social Philosophy |
Sociological Methods |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Introduction -- Three Simple Models -- What can be Learnt from Simple Models? -- Reality Check for Simple Models -- A Physical Simple Model -- What are Simple Models Worth for? -- Complex Models to Understand Complex Social Situations -- Modelling Epidemics -- Why Weather/Climate Forecasts can be Trusted -- We are not Social Atoms -- Social Data are Soaked by Social Complexity -- Machines that Learn How to Model -- Starting from Data to Hunt Causes -- A Moral Thermometer? -- Where do Indicators Lead us?. Which Numbers for the Future? -- Conclusion -- Acknowledgements -- Annexes. |
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Sommario/riassunto |
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More than 300 years ago, Isaac Newton created a mathematical model of the solar system that predicted the existence of a yet unknown planet: Neptune. Today, driven by the digital revolution, modern scientists are creating complex models of society itself to shed light on topics as far-ranging as epidemic outbreaks and economic growth. But how do these scientists gather and interpret their data? How accurate are their models? Can we trust the numbers? With a rare background in physics, economics and sociology, the author is able to present an insider’s view of the strengths, weaknesses and dangers of transforming our lives into numbers. After reading this book, you’ll understand how different numerical models work and how they are used in practice. The author begins by exploring several simple, easy-to-understand models that form the basis for more complex simulations. What follows is an exploration of the myriad ways that models have come to describe and define our world, from epidemiology and climate change to urban planning and the world chess championship. Highly engaging and nontechnical, this book will appeal to any readers interested in understanding the links between data and society and how our lives are being increasingly captured in numbers. |
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