NB. I was sent this book as a review copy.

From Princeton University Press

This is a beautiful book, it is a thought-provoking books and it is an informative book.  It really is the intersection of mathematics, nature and art, and explores the three themes via the language of Catastrophe Theory, the theory by René Thom which aims to classify the possible folds in the solution space of natural systems and their two dimensional projections.

The book starts by introducing the alphabet of curves from the image of the human body, its curves and crevasses, its osculations and puckerings and from this alphabet it branches out to study the universe of catastrophes in the natural world.

As a fan/devotee/obsessive of atmospheric optics, the fold catastrophe which occurs in the production of the rainbow was bound to appeal to me. As Rene Descartes said in 1673:

A single ray of light has a pathetic repertoire, limited to bending and bouncing (into water, glass or air, and from mirrors). But when rays are put together into a family – sunlight, for example – the possibilities get dramatically richer. This is because a family of rays has the holistic property, not inherent in any individual ray, that it can be focused so as to concentrate on caustic lines and surfaces. Caustics are the brightest places in an optical field. They are the singularities of geometrical optics. The most familiar caustic is the rainbow, a grossly distorted image of the Sun in the form of a giant arc in the skyspace of directions, formed by the angular focusing of sunlight that has been twice refracted and once reflected in raindrops.

Had Descartes had the vocabulary of Rene Thom, he would most certainly have waxed lyrical on the catastrophic nature of the rainbow. In fact, I have a feeling that the theory of catastrophes may have been on the tip of Descarte’s tongue. McRobie talks in detail about the rainbow as a prelude to discussing the enhancement in the family of catastrophes when extra symmetry is introduced in the phenomenon of gravitational lensing.

The world of catastrophe optics is introduced via Michael Berry‘s study of caustics, which by a strange coincidence was the person who first introduced me to the Green Flash – something which I have been rather obsessed by ever since.

A recent photo of mine of a green rim on the sun at sunset in Die Kelders:

The descriptions in the book straddle the swallowtail between poetry, mathematics and the natural world, and, while having a personal feel and a self-confessed naivety about certain topics, remains ever-enthralling.

The last part of the book which deals with the natural world is that of Thom’s personal desire to explain biological morphogenisis using catastrophe theory – something which the biological community has somewhat shunned, and McRobie does not attempt to push this agenda any more than suggesting some potential experiments which may show somewhat unambiguously the utility of this language for describing certain biological processes.

Having introduced the necessary vocabulary through the human body, the rainbow, gravitational lensing, caustics and the analysis of structural stability, McRobie returns to the world of art and looks at a number of artists who rather explicitly have used this language in their work, the likes of Kapoor, Hockney, Gabo and Dali being some of the most obvious.

The penultimate chapter is a closer inspection of Thom’s life and his relationship with art and philosophy. As such it take a dive into linguistics and the poststructuralists, with a somewhat skeptical eye of the true understanding with which philosophers ported his mathematical ideas into their theories – though perhaps not as skeptical as the likes of Sokal.

Finally, he discusses the personal and ideological relationship between Thom and Dali and expounds on quite how influential Thom was on Dali’s later year, Dali having been extremely explicit in his use of Catasrophe theory in much of his work after discovering this new language of the universe.

The book is truly a beautiful object, having poetic descriptions interspersing photography, illustration and artworks and, on bringing the book to a dinner last night, I had engineers, artists, anthropologists and astronomers pouring over its content and vowing to get a copy for themselves. The mathematics is not overwhelming as most of it is of a visual nature and thus even without the understanding of what the manifolds may mean in terms of phase-space, the ideas still hold together well.

If I were to give the book one, rather important, criticism it is that the views exposed are a very Eurocentric take on both art and mathematics, and the illustrations are highly skewed towards the female nude, which, while having indeed been a major part of world art, give a somewhat unnecessarily biased ideology of beauty. The Eurocentric nature of the examples could, I think have been easily remedied by obvious examples of art from India, Australia, China or Mali to think of a few obvious, if not perfect possibilities.

Overall, if I had an appropriate coffee table, this would be absolutely put on display there in the hope and expectation that it would enthrall guests from just about any field.