Does the world embody beautiful ideas? This is the question that Nobel prizewinning theoretical physicist Frank Wilczek poses here. Or, more precisely, can nature be described by a set of mathematical principles that can themselves be considered beautiful?

I will admit to initial irritation at the apparent preciousness of the question: who is Wilczek to tell his readers what they should find beautiful, a subjective judgement if ever there was one? However, that is not really the purpose of this book. Instead, the author describes why and in what way he?finds his subject beautiful, and sets out to convince others of the same. Further, he illuminates the deeply satisfying joy that scientists feel when pieces click into place and a richer understanding of nature is revealed.

A Beautiful Question begins by setting the historical scene, from Pythagoras through the Platonic solids, Johannes Kepler and Isaac Newton, and alighting on James Clerk Maxwell and modern physics. It is not linear, however: Salvador Dal¨ª and Filippo Brunelleschi get mentions in the chapters on the Platonic solids, and Zeno of Elea pops up in a discussion on Newton.

Wilczek is also rather whimsical: symmetry becomes ¡°change without change¡±; he refers to earthly angels and celestial spectacle; and he shamefacedly describes the ¡°method of exhaustion¡± intended to thwart critics, a model that is so complicated that anyone checking it (including its creators) becomes exhausted before detecting any errors. The book is described as a meditation and so it is ¨C an extended, contemplative essay that sometimes meanders.

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It is, therefore, far removed from an arid academic exploration of physics. Indeed, it contains one of the most lyrical descriptions of Maxwell¡¯s equations ¨C hardly the most promising of subjects ¨C that it has been my privilege to read. It is also filled with lavish illustrations. But it requires perseverance and a degree of tolerance, as well as patience and thought.

Wilczek, unlike other theoretical physicists who are devoted to ¡°beautiful theories¡± that must be true simply because they are beautiful, cautions against this view. Kepler¡¯s model of the solar system as a series of interlocking platonic solids was undoubtedly beautiful, both in physical manifestation and satisfying symmetry, but it was also comprehensively wrong. Wilczek does not require beautiful theories to be true; he requires them to be useful. A beautiful theory as yet unsupported by evidence becomes a thought experiment, allowing us to explore the deep nature of the universe without data to get in the way. If conflicting data come along, the theory must be discarded no matter how beautiful; nonetheless, it may shed light.

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Admittedly, the book comes a little unstuck in the description of the Standard Model, which Wilczek rechristens the Core Theory. We are introduced to a host of fundamental particles, fields and forces: charm, top, strange, bottom, bosons, muons and the rest. They are described so concisely that it is difficult to keep everything straight. There are a number of ¡°asides to the expert¡± and apologies that abstract notions are too difficult to describe with brevity. To be honest, you can skip through this section. Suffice it to say that Wilczek does not much like the Core Theory, despite its precision and power, precisely because it is not beautiful enough: it is an awkward beast, and we get the sense that there must be something fundamental and more beautiful underlying it.

And so we come to supersymmetry. If you have skipped through the chapter outlining the Core, I urge you to return to the book for the final two chapters. There is enough detail here to give a glimpse of the current frontiers of theoretical physics without being overwhelming. Wilczek outlines one possibility that may unify the four basic forces so that they do not just appear, fully evolved, from nothing and for no apparent reason. Supersymmetry may not be the right answer, but it does make testable predictions and these are on the way to being tested. We are given a sense of the deep satisfaction associated with tying everything up and clearing away the loose ends ¨C and what is ¡°beauty¡± but a deep personal satisfaction? Wilczek in the end makes it clear: by unweaving the rainbow, we add to its beauty rather than detract from it.

Cait MacPhee is professor of biological physics, University of Edinburgh.

A Beautiful Question: Finding Nature¡¯s Deep Design
By Frank Wilczek
Allen Lane, 448pp, ?25.00
ISBN 9781846147012 and 7029 (e-book)
Published 16 July 2015

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