Skip to main content

Music by the Numbers - Eli Maor ***

If you wanted to classify this book, you might guess ‘music’ or ‘mathematics’ from the title. Actually, ‘history of science’ is a better fit than either of those. Roughly half the book deals with various ways in which music influenced the development of science. These weren’t always to the good, either. For example, we’re told that Pythagoras – who tried to shoehorn musical and cosmic harmonies into an over-simplified geometric model – ‘impeded the progress of science for the next two millennia’.

There are some surprises, too. Fourier analysis, which might top many people’s list of musically-relevant mathematical techniques, was originally developed in the context of the propagation of heat in solids. On the other hand, the world’s first partial differential equation – courtesy of  d’Alembert in 1746 – really did come out of music theory. Personally I found these insights fascinating, but readers who aren’t sure what Fourier analysis and partial differential equations are might not share my enthusiasm.

On several occasions, Maor makes the point that the interaction between music and science was a strictly one-way affair. Science might be informed by music, but music – at least in the period he’s talking about – wasn’t informed by science. That wasn’t entirely for lack of trying, though – Stravinsky is quoted as saying ‘I once tried to read Rayleigh’s Theory of Sound but was unable mathematically to follow its simplest explanations’.

So what’s the other half of the book about? This is where the author gets much more subjective and idiosyncratic, drawing various parallels between the history of music and the history of science. Beethoven is likened to Newton, musical keys to coordinate systems, Stravinsky’s abrupt changes of rhythm to non-Euclidean geometry and Schoenberg’s 12-tone system to Einstein’s theory of relativity.

It’s this last analogy that gets the longest treatment, in the book’s final two chapters. It’s not quite as subjective as the others, in that it’s backed up by quotations from Schoenberg himself and the famous composer-conductor Pierre Boulez, but they don’t go as far as saying that Schoenberg’s music was directly influenced by relativity. On that issue, even Maor admits ‘there is no hard evidence to suggest such a connection’.

The irony is that just as the book ends, in the middle of the 20th century, composers and music theorists really did start to listen to what scientists and mathematicians had to say. In the preface, Maor makes a brief passing reference to Iannis Xenakis, who took inspiration from things like statistical mechanics, game theory, Markov chains and Brownian motion for his ‘stochastic’ musical compositions – but he never comes back to talk about them in more detail. In parallel, late-20th-century music analysts like Allan Forte drew on the language of set theory and mod-12 arithmetic as a more flexible and powerful alternative to traditional music theory.

Let’s stick with set theory for a moment. Picture a Venn diagram with two partially overlapping sets: readers who are interested in the history of science, and readers who are interested in music theory. Is the book going to appeal to the union of the two sets – which is bigger than either audience on its own – or to the intersection, which probably isn’t many people at all? Sadly I think the answer is the latter. Personally, I enjoyed the book – but I’m in that narrow overlap in the Venn diagram.



Review by Andrew May


Popular posts from this blog

The AI Delusion - Gary Smith *****

This is a very important little book ('little' isn't derogatory - it's just quite short and in a small format) - it gets to the heart of the problem with applying artificial intelligence techniques to large amounts of data and thinking that somehow this will result in wisdom.

Gary Smith as an economics professor who teaches statistics, understands numbers and, despite being a self-confessed computer addict, is well aware of the limitations of computer algorithms and big data. What he makes clear here is that we forget at our peril that computers do not understand the data that they process, and as a result are very susceptible to GIGO - garbage in, garbage out. Yet we are increasingly dependent on computer-made decisions coming out of black box algorithms which mine vast quantities of data to find correlations and use these to make predictions. What's wrong with this? We don't know how the algorithms are making their predictions - and the algorithms don't kn…

Infinity in the Palm of your Hand - Marcus Chown *****

A new Marcus Chown book is always a treat - and this is like a box of chocolates: a collection of bite-sized delights as Chown presents us with 50 science facts that are strange and wonderful.

The title is a quote from William Blake's Auguries of Innocence: 'To see a World in a Grain of Sand, / And a Heaven in a Wild Flower, / Hold Infinity in the palm of your hand, / And Eternity in an hour.' It would seem particularly appropriate if this book were read on a mobile phone (so it would be literally in the palm), which could well be true for ebook users, as the short essays make excellent reading for a commute, or at bedtime. I found them distinctly moreish - making it difficult to put the book down as I read just one more. And perhaps another. Oh, and that next one looks really interesting...

Each of the 50 pieces has a title and a short introductory heading, which mostly give a feel for the topic. The very first of these, however, briefly baffled me: 'You are a third mus…

How to Invent Everything - Ryan North ****

Occasionally you read a book and think 'I wish I'd thought of that.' This was my immediate reaction to Ryan North's How to Invent Everything. The central conceit manages to be both funny and inspiring as a framework for writing an 'everything you ever wanted to know about everything (and particularly science)' book.

What How to Invent Everything claims to be is a manual for users of a time machine (from some point in the future). Specifically it's a manual for dealing with the situation of the time machine going wrong and stranding the user in the past. At first it appears that it's going to tell you how to fix the broken time machine - but then admits this is impossible. Since you're stuck in the past, you might as well make the best of your surroundings, so the aim of the rest of the book is to give you the knowledge you need to build your own civilisation from scratch.

We start with a fun flow chart for working out just how far back in time you are…