Author: Sundar Sarukkai
Publisher: Indian Institute of Advanced Study
Year: 2004
Language: English
Pages: 167
ISBN/UPC (if available): 8179860426
Description
The idea of symmetry is one of the most important and pervasive ideas, occurring in disciplines ranging from the sciences to the arts. Symmetry is manifested very widely in the natural world as seen in the intricate shapes, patterns and colours of both inanimate and animate beings. It is a guiding principle in modern physics and is an integral part of many important woks in architecture, sculpture, music, painting and so on.
This book discusses some of the essential themes that will help us understand the philosophical foundation of symmetry in all its manifestations. The philosophical analysis is in two parts: metaphysical and phenomenological. The first draws upon metaphysics and considers the relation between symmetry and categories such as objects, form, properties, laws, invariance and change, thereby exhibiting symmetry as an essential property that inheres in objects and processes. This part also discusses in some detail the metaphysics of groups, which are the mathematical objects that describe symmetry in science.
There is also a significant phenomenological experience of symmetry, which is captured by the use of terms such as balance, unity, simplicity, beauty, boredom and harmony. The phenomenological analysis of symmetry begins with phenomenology of perception, then considers the relation between Gestalt principles of vision and symmetry, and finally addresses the aesthetics of symmetry, which includes a discussion on the relation between beauty and symmetry.
Contents
PREFACE
PART ONE: UNIVERSALITY OF SYMMETRY
Symmetry in Nature
Symmetry of Figures
Symmetry and Science
Broken symmetry and asymmetry
Functions of symmetry in science
Symmetry and Groups
General Symmetry Principles
Symmetry in Art
So What is Symmetry?
PART TWO: METAPHYSICS OF SYMMETRY
OBJECTS
What is an object?
Form and objects
Abstract objects
Shape or symmetry?
Tropes and Symmetry
Quantum Objects
SETS, GROUPS AND CLASSES
Sets and groups: some differences
Classes
Groups and classes
Membership
Singletons and partition of groups
Ontological commitment to groups
CHANGE
Change and symmetry
Centre of mass and oriented form
Mathematical Change
Invariance
PROPERTY
Nature of properties
Role of properties
Symmetry as property
Shape or symmetry? A lesson from physics
Symmetry as first-order property: An analogy from motion
Conservation Laws and Conserved Properties
PART THREE: PHENOMENOLOGY AND AESTHETICS OF SYMMETRY
Phenomenology of Perception
Form and Vision
Symmetry, Form and the Gestalt
Gestalt laws of perception
Groups and the Gestalt
Observing Symmetry
1. Explanation and observation
2. Invariance vs. independence
Symmetry and Aesthetics
Beauty
Nature and Art
Beauty in Science
Beauty as Value
Symmetry and Beauty
References
Index