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.


Paperback:  

Kindle:  


Review by Andrew May

Comments

Popular posts from this blog

Rockets and Rayguns - Andrew May ****

The Cold War period saw dramatic developments in science and technology, coinciding with the flourishing of the science fiction genre. In Rockets and Rayguns, Andrew May draws on the parallels between reality and fiction, each influencing the other.

Inevitably a major Cold War theme was the threat of nuclear war, and May opens with the bomb. It's fascinating that fiction got there first - nuclear weapons were featured in science fiction when many physicists were still doubting the practicality of using nuclear energy. Of course, it's a lot easier to simply take a concept and dream up a weapon than it is to make it for real - for example, H. G. Wells' prophetic nuclear bombs from his 1914 The World Set Free were nothing like the real thing. And some science fiction devices concepts - notably ray guns and force fields - came to very little in reality. However this doesn't prevent the parallels being of interest.

May gives us a mix of the science - describing how nuclear we…

Galileo Galilei, the Tuscan Artist – Pietro Greco ****

Near the beginning of John Milton’s epic poem Paradise Lost, he refers to a ‘Tuscan artist’ viewing the Moon through an optic glass. He’s talking about Galileo – one of history’s greatest scientists, but not the most obvious person to slap an ‘artist’ label on. Yet Galileo lived at a time – the Renaissance – when it was fashionable to dabble impartially in both the arts and sciences. Look up ‘Renaissance man’ on Wikipedia and you’ll see Galileo’s picture right there underneath Leonardo da Vinci’s. It’s a less well-known side to his life, but it crops up again and again – interspersed among his many scientific achievements – in this excellent new biography by Pietro Greco.

If you’re looking for interesting trivia, you’ll find plenty in this book. Galileo’s father was a musician with scientific leanings, who carried out some of the first experiments on musical acoustics – which Galileo may have assisted with. As a young professor of mathematics, Galileo delivered a couple of lectures on …

The Ultimate Interplanetary Travel Guide - Jim Bell **

Not too long ago, NASA brought out a series of spoof ‘space tourism’ posters for various destinations in the Solar System. For people like me, who have watched NASA depressingly fail to send humans to the other planets for decade after decade, it was just another painful twist of the knife. On the other hand, the posters probably have more appeal for younger and less cynical minds, by presenting familiar astronomical objects in a new and engaging way. There may even be scope for a whole book along these lines – and that’s what Jim Bell has attempted here.

The main thing I learned from it is that my brain is programmed to read either fiction or non-fiction, and can’t handle a 50:50 mix of the two – which is what this book is. It drove me mad –  not least because I could see that the same material, presented as straight non-fiction, could have made a really excellent book. Using the NASA posters as a starting point, he could have enumerated the potential ‘tourist sights’ at each location…