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E-raamat: Lumen Naturae: Visions of the Abstract in Art and Mathematics

(California Institute of Technology)
  • Formaat: 392 pages
  • Sari: The MIT Press
  • Ilmumisaeg: 22-May-2020
  • Kirjastus: MIT Press
  • Keel: eng
  • ISBN-13: 9780262358316
  • Formaat - PDF+DRM
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  • Formaat: 392 pages
  • Sari: The MIT Press
  • Ilmumisaeg: 22-May-2020
  • Kirjastus: MIT Press
  • Keel: eng
  • ISBN-13: 9780262358316

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"This book is about how certain ideas related to the concept of space in mathematics and physics have been expressed, whether intentionally or unintentionally, in contemporary and abstract art. It discusses the notion of space, and related abstract notions such as randomness, entropy, the geometry of numbers, the shape of the cosmos, and how such notions were envisioned and elaborated in both scientific developments and across the history of modern and contemporary art, especially abstract art. The author, a mathematical physicist, presents a series of mathematical and scientific concepts and themes and describe their counterparts in the work of (mostly) contemporary artists. Readers with a more advanced scientific background will find precise mathematical terminology, while the material is organized so that people can also read through the text by ignoring the more technical aspects and still follow easily the plain language explanation of ideas and concepts. Scientifically minded readers will recognizefamiliar concepts, such as entropy, randomness, and topology, as playing an important role in the language of abstract art. Artists, art historians, and art enthusiasts who are curious about the ideas underlying modern developments in mathematics and theoretical physics will see the connections to the work of contemporary artists"--



Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos.
List of Figures
xi
1 Introduction
1(6)
2 Still Life As A Model Of Spacetime
7(34)
2.1 Time and Transience
8(12)
2.2 Space and Time
20(14)
A.1 Guide to Still Life and the Artistic Movements
34(3)
A.2 Guide to the Science of Space and Time
37(4)
3 The Notion Of Space In Mathematics Through The Lens Of Modern Art
41(66)
3.1 Space as Structure
41(5)
3.2 Linear Spaces
46(5)
3.3 Projective Spaces
51(11)
3.4 Topological Spaces
62(16)
3.5 Smooth Spaces
78(4)
3.6 Metric Spaces
82(4)
3.7 What Kind of Space Is Space?
86(2)
3.8 Singular Spaces
88(1)
3.9 Measure Spaces and Fractals
89(6)
3.10 Aperiodic Order
95(3)
3.11 Why Do We Need So Many Notions of Space?
98(1)
A.1 Guide to the Art and Artists
99(1)
A.2 Guide to Space and Symmetry in Mathematics
100(1)
A.3 Guide to Linear Spaces
101(1)
A.4 Guide to Projective Geometry
101(1)
A.5 Guide to Topology
101(2)
A.6 Guide to Smooth Geometry
103(1)
A.7 Guide to Metric and Riemannian Geometry
104(1)
A.8 Guide to Algebraic Geometry and Singularities
104(1)
A.9 Guide to Fractal Geometry and Measure Theory
104(1)
A.10 Guide to Mathematical Quasicrystals
105(2)
4 Entropy And Art: The View Beyond Arnheim
107(30)
4.1 Thermodynamic Entropy
107(9)
4.2 Entropy and Cosmology
116(3)
4.3 Entropy and Information
119(5)
4.4 Quantum Information and Entanglement
124(4)
4.5 Entropy versus Complexity
128(2)
4.6 The Problem with Arnheim
130(2)
A.1 Guide to the Art Theory and the Artists
132(2)
A.2 Guide to the Science of Entropy and Information
134(3)
5 Structures Of Randomness
137(28)
5.1 Traces
138(3)
5.2 Randomness and the Cosmos
141(2)
5.3 What Is Randomness?
143(8)
5.4 Kinds of Randomness
151(3)
5.5 All the Colors of Noise
154(2)
5.6 Chaos versus Randomness
156(5)
A.1 Guide to the Artists
161(2)
A.2 Guide to the Theory of Randomness
163(2)
6 Plentiful Nothingness: The Void In Modern Art And Modern Science
165(38)
6.1 The Vacuum
165(4)
6.2 Gravity and the Geometry of Empty Space
169(9)
6.3 The Void in Quantum Physics
178(5)
6.4 The Void in Quantum Gravity
183(3)
6.5 The Void Has Energy
186(3)
6.6 False Vacua: The Higgs Field
189(2)
6.7 A Proliferation of Vacua: The Multiverse Landscape
191(7)
A.1 Guide to the Artists and Artistic Movements
198(2)
A.2 Guide to the Void in Modern Science
200(3)
7 The Geometry And Physics Of Numbers
203(24)
7.1 Kinds of Numbers
203(2)
7.2 The von Neumann Construction of Natural Numbers
205(2)
7.3 The Mystery of Prime Numbers
207(8)
7.4 Primes as Elementary Particles of Arithmetic
215(8)
A.1 Guide to the Artists
223(1)
A.2 Guide to Number Theory and Physics
224(3)
8 Matter And Forces
227(20)
8.1 The Standard Model of Particle Physics
227(5)
8.2 The Geometrization of Physics
232(7)
8.3 What Is a Good Mathematical Model?
239(2)
8.4 Abstraction and Representation
241(2)
A.1 Guide to the Artists
243(1)
A.2 Guide to the Geometry of Particle Physics
244(3)
9 Can You Hear The Shape Of The Cosmos?
247(20)
9.1 The Geometry of the Cosmos
247(10)
9.2 The Shape of Space
257(4)
9.3 The Universe Like a Drum
261(3)
A.1 Guide to the Artists
264(1)
A.2 Guide to the History of Cosmology
264(1)
A.3 Guide to the Geometry of the Cosmos
264(3)
10 The Train And The Cosmos: Visionary Modernity
267(50)
10.1 Mythopoesis and Modernity
267(1)
10.2 Futurist Trains
268(9)
10.3 The Body Electric
277(17)
10.4 The City and the Stars
294(15)
10.5 The Modern Destiny of Visionary Modernity
309(2)
A.1 Guide to the Artists and the Artistic and Philosophical Movements
311(2)
A.2 Guide to Anarchism and Modernism
313(1)
A.3 Guide to Trains and Electrification as Symbols of Modernity
314(1)
A.4 Guide to the Mechanical Body in the Avant-Garde
314(1)
A.5 Guide to Cosmism, Automata, and Cybernetics
315(1)
A.6 Guide to Transhumanism and Posthumanism
316(1)
11 Mathematical Illuminations
317(20)
11.1 Between Meditation and Scientific Illustration
317(10)
11.2 Illuminated Mathematical Notebooks
327(6)
11.3 Some Further Readings
333(1)
A.1 Guide to the Art and the Artists
334(1)
A.2 Guide to Graphical Language in Science
335(1)
A.3 Guide to the Mathematical Results Mentioned in This
Chapter
335(1)
A.4 Guide to Further General Readings
336(1)
Acknowledgments 337(1)
Individuals and Institutions 337(1)
Funding Agencies 338(1)
Images Sources 338(17)
Index 355