Mathematics and the Unexpected
9780226199900
Mathematics and the Unexpected
"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist
"In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice
"In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice
Table of Contents
Foreword by Felix E. Browder
Introduction
1. The Music of the Spheres
The Marvel of Kepler’s Laws
Celestial Mechanics
Classical Determinism
2. The Shattered Crystal
The Impossible Calculations
Poincaré’s Contribution
Deterministic but Random
Unstable but Stable
3. The Comeback of Geometry
A Word of Warning
Dissipative Systems
Catastrophes
Theory
A Critique
4. Back to the Beginning
Appendix 1. Prelude and Fugue on a Theme by Poincaré
Appendix 2. The Feigenbaum Bifurcation
Bibliography
Index
Introduction
1. The Music of the Spheres
The Marvel of Kepler’s Laws
Celestial Mechanics
Classical Determinism
2. The Shattered Crystal
The Impossible Calculations
Poincaré’s Contribution
Deterministic but Random
Unstable but Stable
3. The Comeback of Geometry
A Word of Warning
Dissipative Systems
Catastrophes
Theory
A Critique
4. Back to the Beginning
Appendix 1. Prelude and Fugue on a Theme by Poincaré
Appendix 2. The Feigenbaum Bifurcation
Bibliography
Index