A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions--sparking both controversy and discovery.
The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word "vector" might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough--and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn't have such a deep understanding of our world.
Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it's not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional "spaces," and why you're likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone.
In exploring the evolution of vectors and tensors--and introducing the fascinating people who gave them to us--Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world--and how a clever mathematical construct can dramatically change discovery's direction.
Table of Contents:
Prologue
1. The Liberation of Algebra
2. The Arrival of Calculus
3. Ideas for Vectors
4. Understanding Space (and Storage)
5. A Surprising New Player and a Very Slow Reception
6. Tait and Maxwell: Hatching the Electromagnetic Vector Field
7. The Slow Journey from Quaternions to Vectors
8. Vector Analysis at Last--and a "War" over Quaternions
9. From Space to Space-Time: A New Twist for Vectors
10. Curving Spaces and Invariant Distances: On the Way to Tensors
11. Inventing Tensors--and Why They Matter
12. Everything Comes Together: Tensors and the General Theory of Relativity
13. What Happened Next
Epilogue
Timeline
Acknowledgments
Notes
Index
"There have been lots of books about the evolution of modern physics: from Newton to Maxwell to Einstein and on to quantum theory. But seldom does an author pay attention to the mathematical revolutions that made those physical theories possible. Only as the mathematical toolkit expanded from simple scalars to include such tools and ideas as quaternions and vectors and tensors could physicists and mathematicians find the language to describe an increasingly bewildering universe. Arianrhod does a remarkable job telling the story of the mathematical revolution under the hood, the engine that drove the physics revolutions of the nineteenth and twentieth centuries; the result is a book well worth your time."--Charles Seife, author of "Zero: The Biography of a Dangerous Idea"
"'If all mathematics disappeared, ' physicist Richard Feynman opined, 'it would set physics back precisely one week.' To which mathematician Mark Kac retorted, 'Precisely the week in which God created the world.' Arianrhod persuades us that vectors and tensors are among those creations. Students and teachers should read this excellent book together."--Marjorie Senechal, Smith College, editor-in-chief of "The Mathematical Intelligencer"
"I recommend this book to all those interested in the historic development of scientific ideas."--Ilhan M. Izmirli "Mathematical Reviews"
Robyn Arianrhod is a science writer and a mathematician affiliated with Monash University's School of Mathematics, where she researches general relativity and history of science. She is the author of the critically acclaimed books Einstein's Heroes: Imagining the World through the Language of Mathematics; Seduced by Logic: Émilie du Châtelet, Mary Somerville and the Newtonian Revolution; and Thomas Harriot: A Life in Science.