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

Beyond Belief - Helen Pearson *****

Apparently it comes as a surprise to many that medicine was not particularly scientific until the end of the twentieth century (to be honest, it's no surprise to me - we had a GP who used homeopathy in the 90s). Instead it was based on anecdotal guidance - the kind of thing that appeared to work. Evidence-based medicine has since improved the field, trying where possible to base decisions on evidence, ideally based on randomised controlled trials. The first part of Helen Pearson's book covers this well - though I think it's by far the least interesting part of what we discover. Instead what's truly fascinating is the rest of it, looking at a wide range of other fields where evidence was rarely properly used and that are only now starting to dip a toe in the water. These include social policy, policing, conservation, business and education. The main part of the book gives us examples of how bad these areas have been in terms of basing decisions on what's always been ...
Post a Comment
Read more

The Infinite Book – John D. Barrow ****

Authors are often asked to review books on a topic they’ve written on themselves. The reasoning is sensible – they ought to know something about the subject – but there’s always that uneasy suspicion that there’s going to be a bit of bias creeping in. So I think it’s only fair to admit up front that I have written a book on infinity (of which more later). Infinity is a wonderful subject, because it’s intimately mind-bending (if the combination sounds paradoxical, that’s what infinity is all about) and gives you the chance to pull in all sorts of different concepts and assocations along the way, something Barrow does with great gusto. There’s a surprisingly large amount of coverage here for God, and for the universe, and the book jumps around from Aristotle to Hilbert’s Infinite Hotel (explained at great length), from the paradoxes of infinite sets to the paradoxes of time travel. Overall it’s an enjoyable journey that gives plenty of opportunity to be amazed and surprised. The...
Post a Comment
Read more

Adventures of a Computational Explorer - Stephen Wolfram ***

Stephen Wolfram, the man behind the scientist's mathematical tool of choice, Mathematica, plus a whole host of other software products, including the uncanny Wolfram Alpha knowledge engine, is undoubtedly a genius of the first order. In this book, we get an uncensored excursion into the mind of genius - which is, without doubt, a fascinating prospect. The book consists of a collection of essays and speeches that Wolfram has produced over the last ten to fifteen years, covering an eclectic range of topics. Like all such collections, the result is something that lacks the coherence of a book with a narrative that runs through it, inevitably introducing a degree of repetition and a mix of interesting and not-so-interesting topics - but there's likely to be something to catch the attention anyone who is into computing or mathematics. One of the most interesting pieces is the opening one, where Wolfram describes being a consultant on the SF movie Arrival. He seems to hav...
Post a Comment
Read more