Skip to main content

Vector - Robyn Arianrhod ****

This is a remarkable book for the right audience (more on that in a moment), but one that's hard to classify. It's part history of science/maths, part popular maths and even has a smidgen of textbook about it, as it has more full-on mathematical content that a typical title for the general public usually has.

What Robyn Arianrhod does in painstaking detail is to record the development of the concept of vectors, vector calculus and their big cousin tensors. These are mathematical tools that would become crucial for physics, not to mention more recently, for example, in the more exotic aspects of computing.

Let's get the audience thing out of the way. Early on in the book we get a sentence beginning ‘You likely first learned integral calculus by…’ The assumption is very much that the reader already knows the basics of maths at least to A-level (level to start an undergraduate degree in a 'hard' science or maths) and has no problem with practical use of calculus. Although the historical aspects do bring in, for example, the concept of vectors through early and basic forms, we are soon soaring into mathematics that will be outside of the experience of many readers.

For me, when I used the operators of vector calculus in physics at university it seemed as if they had sprung from nowhere - I would have loved a book like this to put them into context. And I think someone like me at the time - a physics undergraduate with an interest in the history as well as the physics itself - would be an ideal audience. As Charles Seife notes on the back of the book, there is plenty of history of science/popular science on the development of physics from Newton to Einstein, but little that really fills in how the necessary mathematics was developed in parallel. While it's true the early days of calculus have been widely covered, there has been far less on the aspects that Arianrhod gives us, making this a classic find for the right readership.

There are some niggles that take it down from a potential five stars. It's very slow paced, sometimes getting a little bogged down in the detail of the historical development of the mathematical tools. (When I read Arianrhod's Seduced by Logic, I had a very similar problem with too much detail.) And the print is poor - it's both small and light weight, making it almost impossible, for example, to distinguish bold and normal fonts on the page, something that is used as a convention in this branch of mathematics.

Clearly not for everyone. But if you fit into the book's target audience, it's a must-have for your shelves.

Hardback:   
Kindle:  
Using these links earns us commission at no cost to you
These articles will always be free - but if you'd like to support my online work, consider buying a virtual coffee:
Review by Brian Clegg - See all Brian's online articles or subscribe to a weekly email free here
Labels:

Comments

Post a Comment

Popular posts from this blog

The Antigravity Enigma - Andrew May ****

Antigravity - the ability to overcome the pull of gravity - has been a fantasy for thousands of years and subject to more scientific (if impractical) fictional representation since H. G. Wells came up with cavorite in The First Men in the Moon . But is it plausible scientifically?  Andrew May does a good job of pulling together three ways of looking at our love affair with antigravity (and the related concept of cancelling inertia) - in science fiction, in physics and in pseudoscience and crankery. As May points out, science fiction is an important starting point as the concept was deployed there well before we had a good enough understanding of gravity to make any sensible scientific stabs at the idea (even though, for instance, Michael Faraday did unsuccessfully experiment with a possible interaction between gravity and electromagnetism). We then get onto the science itself, noting the potential impact on any ideas of antigravity that come from the move from a Newtonian view of a...
Post a Comment
Read more

The World as We Know It - Peter Dear ***

History professor Peter Dear gives us a detailed and reasoned coverage of the development of science as a concept from its origins as natural philosophy, covering the years from the eighteenth to the twentieth century. inclusive If that sounds a little dry, frankly, it is. But if you don't mind a very academic approach, it is certainly interesting. Obviously a major theme running through is the move from largely gentleman natural philosophers (with both implications of that word 'gentleman') to professional academic scientists. What started with clubs for relatively well off men with an interest, when universities did not stray far beyond what was included in mathematics (astronomy, for instance), would become a very different beast. The main scientific subjects that Dear covers are physics and biology - we get, for instance, a lot on the gradual move away from a purely mechanical views of physics - the reason Newton's 'action at a distance' gravity caused such ...
Post a Comment
Read more

God: the Science, the Evidence - Michel-Yves Bolloré and Olivier Bonnassies ***

This is, to say the least, an oddity, but a fascinating one. A translation of a French bestseller, it aims to put forward an examination of the scientific evidence for the existence of a deity… and various other things, as this is a very oddly structured book (more on that in a moment). In The God Delusion , Richard Dawkins suggested that we should treat the existence of God as a scientific claim, which is exactly what the authors do reasonably well in the main part of the book. They argue that three pieces of scientific evidence in particular are supportive of the existence of a (generic) creator of the universe. These are that the universe had a beginning, the fine tuning of natural constants and the unlikeliness of life.  To support their evidence, Bolloré and Bonnassies give a reasonable introduction to thermodynamics and cosmology. They suggest that the expected heat death of the universe implies a beginning (for good thermodynamic reasons), and rightly give the impression tha...
Post a Comment
Read more