Vector: A Surprising Story of Space, Time, and Mathematical Transformation
Original price was: $58.00.$19.99Current price is: $19.99.
PDF 8,92 MB • Pages: 474
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.
17 reviews for Vector: A Surprising Story of Space, Time, and Mathematical Transformation
You must be logged in to post a review.
Related products
-
Causal Inference in R: Decipher complex relationships with advanced R techniques for data-driven decision-making
Original price was: $44.99.$19.95Current price is: $19.95. -
Using IBM® SPSS® Statistics for Research Methods and Social Science Statistics
Original price was: $83.00.$19.99Current price is: $19.99. -
The Cartoon Guide to Geometry
Original price was: $26.00.$11.95Current price is: $11.95.
James A. Cavender (verified owner) –
All mathematicians and all physicists need this book. It tells how we got here and why it took so long. The human stories of the pioneers are relevant, and we can actually sympathize with them. Notation was a big part of the story. Arabs were doing algebra in the 9th Century and Italians were solving cubics in the 16th, but it was Harriott early in the 17th who gave us equations with = and + signs and numbers represented by single letters. According to Arianrhod, Hamilton’s quaternions were opposed because they represented sets of 4 numbers by a single letter, which seemed to be an error. So the conflict over quaternions prepared people for coordinate-free vectors, which she calls “whole vectors.” After describing the “vector wars,” Arianrhod turns her attention to the tensors of differential geometry and then to relativity theory. It’s a book with problems. Although Arianrhod rightly gives much space to Hamilton, Rodrigues is never mentioned. In 1840, 3 years before the Broome Bridge incident, Rodrigues published quaternions. Read about it in Altmann (1986) Rotations, Quaternions and Double Groups. On page 26 of Altmann you will see the formulas for the quaternions that NASA engineers use. Altmann mentions in passing that Gauss discovered quaternions even before Rodrigues, but didn’t publish. David Hilbert appears as a player in the story of general relativity, but Hilbert Space is never mentioned, which is strange for a book called Vectors. Arianrhod devotes much of the book to trying to explain the math to readers without math knowledge beyond high school. This is futile and annoying. She compares tensors to multiply-indexed data bases.
John Miller (verified owner) –
_Vector_ is possibly the best science book I’ve ever read. It should be required reading for all university students of science, mathematics, engineering, and computer science: it uses vectors, quaternions, and tensors as a unifying subject to connect all of these topics. It’s like a light switch illuminating years of undergraduate classes.
jules whiteman (verified owner) –
This is an fantastic book.
DC Tidy (verified owner) –
A fascinating background to the development of an important branch of maths and the role played by those who created it. You don’t need to understand every bit of the maths to appreciate it
A. Menon (verified owner) –
Despite vector calculus being standard in undergraduate mathematics curriculum the history of it is not. Vector is largely a history book which provides mathematical content when it enriches the story and is really engaging throughout. The book covers the evolution of thinking from Hamilton to Ricci taking a tour through electromagnetism and general relativity, it weaves both the mathematicians and physicists who were part of this evolution together so that one sees how collaborative this field ultimately was in its development.
The book starts with quaternions and the challenges Hamilton faced when trying to extend complex numbers to 3-dimensions. The author then describes the challenges in having these ideas adopted in the early stages in which there was a broad confusion as to their utility and purpose as well as moves on to some of the thinking taking place elsewhere including Grassmann in Germany. The author also spends time on the life of James Clerk Maxwell and his own path to eventually use some of the ideas in framing the laws of electromagnetism. I personally did not realize that i,j,k unit vector conventions came from quaternions. The author then spends time on the vector algebra wars as people focused on the way to set conventions where some parties wanted to follow Hamilton and others Clifford and Gibbs. The deep connections of these objects with physics is inescapable throughout. One of the other highly interesting topics of discussion is on tensor analysis and the utility of differential geometry concepts in physics. The story of how Einstein navigated the mathematical world through the help of his friend Grossman and how Minkowski (a former professor of Einstein) helped from the geometrical content of relativity is given in much detail as well as how the Italian differential geometry who developed tensor calculus developed their ideas is given.
This is quite a lovely book on a standard topic that is underappreciated historically by those who studied it. The transition from electromagnetism to tensor calculus through the historical transitions of physics is just jot how either physics or math is taught which is a shame as one can better understand the content of the theories if one appreciates the history which drove the field evolution. Overall is both entertaining and informative and has something for those interested in both math and physics.
PETER VAN CALSTEREN (verified owner) –
Nor worked through it all yet, but it’s much better than I expected
Chris Nunn (verified owner) –
A lucid account of the development of vector analysis which is fascinating historically and made it all comprehensible, even to a non-mathematician like me!
odlan (verified owner) –
Recebi hoje, 09/12/2024. Livro de capa dura e sobrecapa. Impressão e acabamento de excelente condições.
Antony W. Shaw (verified owner) –
I couldn’t put it down.
jehosafats (verified owner) –
I was at the bookstore the other day, lamenting the current state of popular science writing, until I came across Arianrhod’s spectacular book. What a treasure.
Sergio Salcido (verified owner) –
Connects a lot of concepts in a meaningful way without getting bogged down in the details. Did a really good job of making reader feel the struggle it took to bring the notations and algebra we do routine to light. Succeeds in goal of appreciation for the journey
Philip J. Lillies (verified owner) –
It is written for someone with an undergraduate level of mathematics who wants to be inspired by what lies at the next level.
kevan rudling (verified owner) –
I thoroughly enjoyed the book; it is well-written and informative. I wish such books were part of my maths curriculum; they would have made maths much more comprehensible. One minor criticism: the narrative occasionally veered off into tedious feminist flag-waving, as if the author found it so exceptional that women had any part to play.
I look forward to the time when it is unquestionably accepted that the chicks are a natural part of the process without all this tiresome point-scoring😎.
.
Hawkeye (verified owner) –
It’s a very impressive historical account of maths developments leading to calculus, the concepts of vectors and tensors, matrices and some applications of advanced algebra. Not an easy read for me personally and right now I’m struggling with Hamilton’s rewriting of addition and subtraction rules, but definitely worth the effort.
Capnbill76 (verified owner) –
Comprehensive yet digestible, this book finally answered questions I have been pursuing for along time. I’ve read Wheeler and others, and while they are often definitive, they are (to me) difficult. I recommend this book unreservedly.