Vector A Surprising Story Of Space Time And Mathematical Transformation Pdf
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Vector
Author: Robyn Arianrhod
language: en
Publisher: University of Chicago Press
Release Date: 2024-05-30
"The stars of the latest book by award-winning science writer and mathematician Robyn Arianrhod are unlikely celebrities--vectors and tensors. If you took a high school physics course, the word "vector" might remind you of the mathematics needed to determine forces on an amusement park ride, say; or of cross products, a special kind of multiplication using a bespoke table and a right-hand rule. You might also remember the introductory definition of a vector as a quantity that has magnitude and (this is the key) direction. Velocity--for example, 25 miles per hour northwest--is a vector; speed, such as 25 miles per hour, is not. Put another way, a velocity vector in space contains not one number, but three-a measurement of speed along each of three dimensions. It sounds simple, in hindsight--yet, as Arianrhod shows in this intriguing story, the idea of a single symbol expressing several things at once is a sophisticated one, millennia in the making. Vectors are examples of an even more sophisticated idea, the tensor. And it's not just space that vectors and tensors can represent, but information, too. Which means that whenever you use a search engine, say, or AI bot, computer graphics, or a host of other digital applications, vectors and tensors are there somewhere in the software. As for physics, there's much more to it than velocities and simple forces! Arianrhod shows how the discovery of vectors and tensors enabled physicists and mathematicians to think brand new thoughts-such as Maxwell did when he ushered in the wireless electromagnetic age, and Einstein when he predicted the curving of four-dimensional space-time and the existence of gravitational waves. Quantum theory, too, makes fine use of these ideas. In other words, vectors and tensors have been critical not only to the way we see our universe, but also to the invention of Wi-Fi, GPS, micro-technology, and so much else that we take for granted today. In exploring the history and significance 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. A celebration of an idea, Vector shows the genius required to imagine the world in new dimensions-and how a clever mathematical construct can direct the future of discovery"--
Vector
‘The story I’ll tell here is about the evolution of the way we humans record and make sense of all the data that swirl around us...’ Vector takes readers on an extraordinary 5000-year journey through the human imagination. The stars of this book, vectors and tensors, are unlikely celebrities. Yet mathematician and science writer Robyn Arianrhod shows how they enabled physicists and mathematicians to think in a brand-new way. They inspired James Clerk Maxwell to usher in the wireless electromagnetic age; Albert Einstein to predict the curving of space-time and the existence of gravitational waves; Paul Dirac to create quantum field theory; and Emmy Noether to connect mathematical symmetry and the conservation of energy. Today, you’re likely relying on vectors or tensors each time you pick up your mobile phone, use a GPS, or search online. In Vector, Robyn Arianrhod shows the genius required to reimagine the world — and how a clever mathematical construct can dramatically change discovery’s direction. ‘In Vector, Arianrhod shows, with beautiful ease, that maths is not some foreign world only geeks inhabit. It is the world around us.’ ― Adam Spencer, author of Adam Spencer's Big Book of Numbers: Everything you wanted to know about the numbers 1 to 100 ‘Arianrhod’s Vector, a masterpiece of science exposition, reads as a welcoming cognitive cliffhanger tour of vectors, their generalizations, and their accompanying symbolic tools of mathematical physics, all dovetailing through germane history vignette accounts of astonishing connections and applications.’ ― Joseph Mazur, author of The Clock Mirage: Our Myth of Measured Time ‘A vector is quantity that has magnitude and, crucially, direction. This idea has enabled physicists and mathematicians to imagine and describe the world in new dimensions. The author traces the influence of vectors over the past 5,000 years, and why vectors (and tensors) are still relevant today.’ ― The Bookseller ‘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, editor-in-chief of The Mathematical Intelligencer ‘With a flair for exposition that makes the complex simple, and a gift for storytelling, Arianrhod is without peer in conveying the beauty, and power, of mathematics. William Rowan Hamilton, James Clerk Maxwell, and Albert Einstein come alive in this dramatic tale of a simple idea that changed our world.’ — Amir Alexander, author of Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World ‘Everyone understands what it means to move at some particular speed in some particular direction. But it took a long time to start thinking of such behavior in terms of a single clarifying concept, the vector. Arianrhod’s lively and detailed chronicle explains why vectors and tensors are at the heart of our best ways to think about the universe.’ — Sean Carroll, author of The Biggest Ideas in the Universe '...mathematician Robyn Arianrhod tells the story beautifully...a very human story of how men and women explored and refined pure maths and physics, their friendships and rivalries, frustration and insights. Dr Arianrhod is most effective in describing collaboration across time and nationalities, as well trained minds and curious mavericks picked up the challenge to understand our universe.' — Robyn Douglass, The Daily Telegraph 'Written with wit and impressive scholarship in both history and mathematics.' — Peter Main 'Arianrhod has an encyclopedic knowledge of the history of physics and mathematics, as well as a deep understanding of often very technical subject matter...Arianrhod’s deep research and attention to neglected figures in the history of science, many of them women, is refreshing...Vector is a fascinating read.' — Michael Lucy, Australian Book Review
A Vector Space Approach to Geometry
Author: Melvin Hausner
language: en
Publisher: Courier Corporation
Release Date: 1998-01-01
This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965 edition.