Creative account of scientific imagery

The late 19th and early 20th centuries saw artists and scientists exploring new ways of looking at the world. These new perspectives were radically different from those that had informed their previous traditions and were significant departures from the realist representations of the world. The resulting concurrence of developments such as cubism and relativity or the avant-garde and quantum mechanics has led some to ask if any causal link existed between them.

In this book, Arthur Miller examines some of the parallels and contrasts between artistic and scientific representations. For the latter, he focuses only on representations in physics to trace the way scientists make use of pictures and images. Despite the outsider's view of physics as a collection of mathematical formulae that codify immutable laws of nature, insiders look at things quite differently. Pictures play a key role in developing intuition, and "thought-experiments" play the role of mental movies that act out the consequences of adventurous natural scenarios. They are an essential part of the creative process in science. Even at the level of mathematical calculation we find diagrammatic techniques, like those introduced by Richard Feynman into quantum theory, playing a vital part in the performance of lengthy mathematical calculations. Good notation is more than mere notation. It thinks for itself, relieving the calculator of having to think about routine mathematical manipulations: they are taken care of by the symmetry of the notation itself. There is real content to things "looking right".

Miller uses his theme as an excuse to explore many different aspects of human creativity, bringing to life several episodes in the historical development of early modern physics as well as telling some of what we know about the workings of human cognitive abilities. This approach necessarily leads to a focus on the working practices of particular scientists to see whether their creative activities are distinctive in ways that are not shared by creative artists in other fields. Albert Einstein and Henri Poincare end up as the principal guinea-pigs.

Much has already been written about Einstein in this respect, and there is little to add. The most interesting aspect of his creativity is the transformation of his style between 1905 and 1915, a change from reliance on simple physically motivated thought experiments to extensive mathematical formalisms. This conversion was brought about by the extraordinary success of the formalisms of tensor calculus he learned from Marcel Grossmann, and used with such power and elegance in the formulation of the general theory of relativity.

Poincare is more introspective, far less has been written about him, and Miller's book provides some fascinating insights into his mode of working. Poincare wrote more than most other scientists and did so in a highly disciplined and reflective fashion. He also wrote about science as well as doing it. Many popularisers of mathematics or students of human creativity like to retell the story that Poincare told of the sequence of events that led him to develop the theory of Fuchsian equations: successive periods of attention, detached reflection, followed by sudden inspiration and leisurely completion of his solution to a problem. No account of mathematical creativity seems to be able to do without this little story. But Miller points out that there is much more to the study of Poincare's creative processes than this little anecdote. Poincare is probably the only world-class mathematical physicist who has taken part in a detailed and systematic psychological study of his working habits. This study was performed by the French psychologist Edouard Toulouse and published in French in 1910 under the title Henri Poincare. Unfortunately, it has never appeared in English and is largely unknown to mathematicians. Miller provides one of the few commentaries on this professional psychological study of Poincare's creative activities and is worth reading for this alone.

Insights of Genius is one of very few books to make a serious attempt to place scientific imagery into a wider context alongside creative activities in the visual and linguistic arts. It provides a lucid and fluently written beginning to a huge subject.

John D Barrow is professor of astronomy, University of Sussex.