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Wednesday, October 26, 2011

My Book on Symmetry

Some details about my book on symmetry can be seen at


A word about how this book was conceived. I have been working on a comprehensive book on complex systems. I had planned a chapter on symmetry in complex systems in that book. As I was writing that chapter, it became clear that I have material which is far in excess of what can be put in a chapter. So I took a break from writing the book on complexity, and spent almost two years writing the book on symmetry.

I am pleased with the response from fellow scientists. Here is what Prof. A. M. Glazer from the University of Oxford wrote in his Foreword for the book:

'Wherever we look we see a variety of patterns and shapes that show different types of symmetry. Much of this is obvious, such as for instance when we look at the pyramids of Egypt, or crystals in a museum. However, what is not so obvious is just what exactly is symmetry and why is it so prevalent? In this unique and intriguing book, Professor Vinod Wadhawan has set about answering these sorts of questions. He takes us on a journey from very basic descriptions, such as the growth of a crystal, on to more esoteric and complex notions, demonstrating that, in fact, symmetry is even more pervasive than we thought before. Some symmetries are far from obvious, as illustrated by the idea of latent symmetry. This is said to manifest itself when one combines two or more 'equal' objects or systems, each with its own symmetry description, and the resulting composite system exhibits new symmetry elements that were not expected from the original systems. For instance, two identical right-angled isosceles triangles can be joined together to form a square, that has an unanticipated four-fold rotational symmetry. The notion of latent symmetry is relatively new and deserves further consideration.

Not only do we have the symmetry exhibited by living organisms and physical objects, but also by ideas themselves. As such this book has a strong philosophical content that will enable the reader to gain much more insight into the phenomenon than is normally got from a typical university education. Wadhawan shows us how even the concept of randomness is intricately bound up with notions of symmetry. Even the idea of predictability is an example of symmetry in action! And then, having explained what symmetry is, emphasis is placed on what happens when symmetry is broken. In a sense, pure symmetry could even be described as rather boring, since it implies a lack of change or progress. Nonetheless, we still need to understand it. It is when symmetry is broken that fun things start to happen and new ideas, progress and phenomena are created. This book explains how this comes about and why symmetry-breaking is so important.

The book is written with an eye to explaining the fundamental concepts of symmetry, rather than go into complex mathematical proofs and lemmas, which in any case can be found elsewhere for those who like those sorts of things. This means that Wadhawan is able instead to concentrate on the philosophical importance of understanding symmetry, and how it impacts on the world that we observe. Rather like the Second Law of Thermodynamics, symmetry is seen to play a vital role in what holds the universe together. You can see then that this book covers just about everything that we know about symmetry, and possibly that which we do not!'
 Vinod Wadhawan (2nd from the left) as a Nuffield Foundation Fellow at the Clarendon Laboratory, University of Oxford, 1979. Prof. Glazer is 4th from the left in the front row.