Lumen Naturae: Visions of the Abstract in Art and Mathematics

Description

Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art-and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science-the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe-while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dali, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Leger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe. Contents List of Figures 1. Introduction 2. Still Life as a Model of Spacetime 2.1 Time and Transience 2.2 Space and Time A.1 Guide to Still Life and the Artistic Movements A.2 Guide to the Science of Space and Time 3. The Notion of Space in Mathematics through the Lens of Modern Art 3.1 Space as Structure 3.2 Linear Spaces 3.3 Projective Spaces 3.4 Topological Spaces 3.5 Smooth Spaces 3.6 Metric Spaces 3.7 What Kind of Space Is Space? 3.8 Singular Spaces 3.9 Measure Spaces and Fractals 3.10 Aperiodic Order 3.11 Why Do We Need So Many Notions of Space? A.1 Guide to the Art and Artists A.2 Guide to Space and Symmetry in Mathematics A.3 Guide to Linear Spaces A.4 Guide to Projective Geometry A.5 Guide to Topology A.6 Guide to Smooth Geometry A.7 Guide to Metric and Riemannian Geometry A.8 Guide to Algebraic Geometry and Singularities A.9 Guide to Fractal Geometry and Measure Theory A.10 Guide to Mathematical Quasicrystals 4. Entropy and Art: The View beyond Arnheim 4.1 Thermodynamic Entropy 4.2 Entropy and Cosmology 4.3 Entropy and Information 4.4 Quantum Information and Entanglement 4.5 Entropy versus Complexity 4.6 The Problem with Arnheim A.1 Guide to the Art Theory and the Artists A.2 Guide to the Science of Entropy and Information 5. Structures of Randomness 5.1 Traces 5.2 Randomness and the Cosmos 5.3 What Is Randomness? 5.4 Kinds of Randomness 5.5 All the Colors of Noise 5.6 Chaos versus Randomness A.1 Guide to the Artists A.2 Guide to the Theory of Randomness 6. Plentiful Nothingness: The Void in Modern Art and Modern Science 6.1 The Vacuum 6.2 Gravity and the Geometry of Empty Space 6.3 The Void in Quantum Physics 6.4 The Void in Quantum Gravity 6.5 The Void Has Energy 6.6 False Vacua: The Higgs Field 6.7 A Proliferation of Vacua: The Multiverse Landscape A.1 Guide to the Artists and Artistic Movements A.2 Guide to the Void in Modern Science 7. The Geometry and Physics of Numbers 7.1 Kinds of Numbers 7.2 The von Neumann Construction of Natural Numbers 7.3 The Mystery of Prime Numbers 7.4 Primes as Elementary Particles of Arithmetic A.1 Guide to the Artists A.2 Guide to Number Theory and Physics 8. Matter and Forces 8.1 The Standard Model of Particle Physics 8.2 The Geometrization of Physics 8.3 What Is a Good Mathematical Model? 8.4 Abstraction and Representation A.1 Guide to the Artists A.2 Guide to the Geometry of Particle Physics 9. Can You Hear the Shape of the Cosmos? 9.1 The Geometry of the Cosmos 9.2 The Shape of Space 9.3 The Universe Like a Drum A.1 Guide to the Artists A.2 Guide to the History of Cosmology A.3 Guide to the Geometry of the Cosmos 10. The Train and the Cosmos: Visionary Modernity 10.1 Mythopoesis and Modernity 10.2 Futurist Trains 10.3 The Body Electric 10.4 The City and the Stars 10.5 The Modern Destiny of Visionary Modernity A.1 Guide to the Artists and the Artistic and Philosophical Movements A.2 Guide to Anarchism and Modernism A.3 Guide to Trains and Electrification as Symbols of Modernity A.4 Guide to the Mechanical Body in the Avant-Garde A.5 Guide to Cosmism, Automata, and Cybernetics A.6 Guide to Transhumanism and Posthumanism 11. Mathematical Illuminations 11.1 Between Meditation and Scientific Illustration 11.2 Illuminated Mathematical Notebooks 11.3 Some Further Readings A.1 Guide to the Art and the Artists A.2 Guide to Graphical Language in Science A.3 Guide to the Mathematical Results Mentioned in This Chapter A.4 Guide to Further General Readings Acknowledgments Individuals and Institutions Funding Agencies Images Sources Index