Richard Feynman, both as a man and as a scientist, excited varied reactions: you either loved him or you hated him. As a man, he was either narrow-minded and sexist, or else charming and completely fair in the most unselfconscious way. As a scientist, he was either “a magician” – the most impressive kind of genius – or else he was “not in the first rank of physicists”. This book will not offer much guidance among this range of opinions, since it is mostly about computation, rather than Feynman. However, the snapshots of – and reactions to – that fascinating personality come as a welcome, refreshing stream running through the technical essays that form the bulk of the text.

Feynman is rightly remembered chiefly for his work on quantum electrodynamics, for which he shared the 1965 Nobel Prize for Physics, and for his three-volume Lectures on Physics. The fact that he worked on the basic principles of computation in his later years has often been regarded as a relatively minor afterthought, but it is becoming more and more clear that Feynman was better at picking his subjects than that implies. After all, it is more important in science to recognize the interest of something significant but not fully understood, than it is to fully understand something insignificant. In the study of computation and its limits, which are set by the underlying laws of nature, we have an example of the former. Although Feynman did valuable work in the early exploration of this subject, his most important contribution was to generate interest in it.

This book is a loosely connected collection of technical articles, lectures and anecdotes selected by Anthony Hey, head of computing at Southampton University. It takes us from stimulating contributions by Feynman himself – such as his famous 1959 lecture “There’s Plenty of Room at the Bottom”, which foresaw nanotechnology, and the clear and focused “Simulating Physics With Computers” lecture from 1981 – to 16 papers, by 16 authors, of varying degrees of precision and readability that cover some of the questions thrown up by the subject. These range from fundamental physics, such as the nature of information, to practical issues such as progress in metal-oxide-silicon technology, with room for exploratory ideas and open questions.

Hey has gathered the papers together under five loose headings – “Feynman’s Course on Computation”, “Reducing the Size”, “Quantum Limits”, “Parallel Computation” and “Fundamentals” – but a weakness is that the collection is not very coherent. It is neither a guide nor an introduction to the subject, nor even a “volume 2” to the earlier Feynman Lectures on Computation (Perseus, 1996), which contained transcripts of a lecture course that Feynman gave in the early 1980s. This book instead provides a tour round some of the issues. The standard varies considerably from author to author, but the introductory overview is well written and succeeds in binding the book together. Indeed, it is a pleasure to find historical notes and scientific analysis next door to one another – a welcome reminder that science is a human endeavour.

After the gentle introduction, we plunge straight into a technical paper by John Hopfield. This is an update of his 1982 paper on neural networks, and is an important contribution – but hard work for the reader. I feel it would have benefited from some illustrative examples of what has been learned since 1982. In contrast, the paper by Gerry Sussman and Jack Wisdom, showing (from specialized computer hardware) that the motion of Pluto is chaotic, stands alone very well. It is not only readable and self-contained but also technically precise and impressive – although again I would have enjoyed a few more descriptive comments. It is left to Marvin Minsky to state the implication that there is sufficient instability in the solar system to throw the Earth out into space one day (unless it is first swallowed up by the Sun swelling to red-giant proportions).

Several of the authors mention Feynman’s championing of real understanding in science. Carver Mead, for example, uses the following apt Feynman quotation: “The real glory of science is that we can find a way of thinking such that the law is evident.” Mead contributes two technical chapters. The first discusses a new approach for combining electromagnetism and quantum mechanics that avoids Maxwell’s equations and starts instead from experimental observations on a loop of superconducting wire. Although his approach is interesting, I am not convinced that it would be the most insightful route to take. “Nowhere in natural phenomena, ” proposes Mead about superconductors, “do the basic laws of physics manifest themselves with more crystalline clarity.” Give me a Young’s slit electron interference pattern any day.

The section on “Reducing the Size” opens with Feynman’s “There’s Plenty of Room at the Bottom” lecture, which is a pleasure to see made available for a wide readership, and which sets a standard for all scientific after-dinner speakers. Feynman’s speech was visionary, and Mead carefully surveys what has happened in practice since then (i.e. metal-oxide-silicon technology), and where things are heading. There is also a chapter by the late Rolf Landauer entitled “Information is Inevitably Physical”, in which he gives opinions and historical notes that help to draw attention to several overlooked contributions.

Quantum computers appear in the section entitled “Quantum Limits”, and the subject is well introduced by Feynman himself, as well as by Charles Bennett and Richard Hughes. Bennett is lively as well as precise. “Quantum computing, ” he says, “is like controlled fusion” – in other words, it promises much, but may take many years to achieve. He also argues that quantum information and communication, not quantum computing, is the “wild west, or Internet” of quantum information science. Hughes, meanwhile, gives a clear and steady discussion of both the theory and practice of quantum computing. However, I found the chapter by Paul Benioff much less useful. It aims to say something about “quantum robots”, which are quantum machines with on-board quantum computers, operating in a quantum environment. But his treatment amounts to writing down sums over quantum states and time-steps, with little insight into what is going on.

Several of the chapters discuss cellular automaton computers. These are the type of updated array computations made widely known by Martin Gardner’s article in Scientific American on John Conway’s “Game of Life”. The chapter by Norman Margolus is excellent, clarifying what can and cannot be done, explaining what are the interesting questions, and incorporating good illustrations. The chapter would allow a beginner to understand what is going on and get to more advanced concepts, such as invertible rules and partitioning. It is also thorough and carefully referenced.

In separate chapters, Minsky and Tommaso Toffoli tackle the idea that the natural world might be like a grand cellular automaton. They try to see if reasonable assumptions about microscopic computing cells distributed throughout space could give rise to laws of physics as we know them, including things like quantum dynamics and relativity. However, I do not know why Hey has assigned these two chapters to different sections of the book, as I feel they should both have been in the section on “Fundamentals”. Toffoli makes a better stab at the task, which renders Minsky’s chapter less interesting by comparison. But one is left with the feeling that the theory is not going to work out with the elegance we look for, and that nature will in fact surprise us with something else that we have not thought of. Wojciech Zurek then follows with a good discussion of Maxwell’s demon and “algorithmic entropy”.

Two chapters seem rather empty to me. These are Geoffrey Fox on “Internetics”, which presents experience of large-scale computing dressed in the muddling language of management structures, and John Wheeler on “Information, Physics, Quantum: the Search for Links”, which seems profound but actually is a fine example of the tale of The Emperor’s New Clothes.

One thing that emerged from the book was a rather lovely glimpse or sketch of the quality of the final period of Feynman’s life. This was not well covered in James Gleick’s biography Genius: Richard Feynman and Modern Physics, but sometimes the heart of a person emerges with greater clarity as they approach death. The chapter by Daniel Hillis, “Richard Feynman and the Connection Machine”, is a wonderful essay, beautifully written: mathematics, history and friendship brought together in Feynman-esque clarity with all the poise and care of a poem.