It Must be Beautiful: Great Equations of Modern Science edited by Graham Farmelo, Granta Books, ISBN 1 86207 479 8, £20.
In this lively volume of semipopular essays, 12 leading scientists, historians of science and science writers discuss "beautiful" equations of 20th-century science. Some of the essays are elegant and revealing discourses centring on the equations themselves; others are equally interesting but more historical in nature, sometimes verging on the biographical. Almost all are accessible to a broad audience with a little scientific background.
Roger Penrose and Frank Wilczek thoughtfully discuss the meaning of Einstein's equations of general relativity and Dirac's equation respectively. Steven Weinberg, in his extended afterword, also discusses the Dirac equation, and both Wilczek and Weinberg focus on how the equation has survived despite our significantly altered understanding of its meaning since Dirac's time.
The meaning of the possibly less well known, but certainly beautiful, equations of Yang-Mills theory (as well as such topics as the Higgs mechanism) are also nicely introduced by Christine Sutton. Igor Aleksander provides a rewarding piece on Claude Shannon's great work founding information theory, and John Maynard-Smith discusses some fascinating aspects of the theory of evolution (including his own use of the theory of games in evolution theory, to which this essay provides a good introduction), while Robert May introduces the deceivingly simple logistic equation with its chaotic solutions.
The essays from Graham Farmelo, Peter Galison, Aisling Irwin and Arthur Miller are also stimulating. Since they tended to be less centred on the equations, they leave room for dispute. For example, Arthur Miller makes a remark near the end of "Erotica, aesthetics and Schrodinger's wave equation" (Schrodinger's erotic life is endlessly fascinating to historians) that "the Heisenberg-Schroedinger dispute...was fundamentally one of aesthetic choice" and he points out that physicists use Schrodinger's formalism rather than Heisenberg's matrix mechanics for aesthetic reasons. But Born's great work on the probability interpretation showed that Schrodinger's interpretation of the wavefunction was incorrect, giving, for example, no understanding of the interference terms in a sum of wavefunctions. Furthermore, surely the reason Schrodinger's wavefunction (given the correct interpretation) is so popular is because it is easier to use than matrix mechanics, and because it stimulates visualization in the reader, which ultimately leads to suggestions for applications.
Surprisingly, the contents include an essay on Drake's equation. This is the formula for the number of technological civilizations in our galaxy, depending on such things as the rate of star formation, the likelihood of intelligent life evolving and, least knowable of all, the typical lifespan of a technological civilization. This sums up this collection nicely - you can expect to be entertained and informed in equal measure, often by surprise, and hopefully its success will lead to a second volume.
John March-Russell, CERN.
Great Physicists: the Life and Times of Leading Physicists from Galileo to Hawking by William H Cropper, OUP, ISBN 0 19 513748 5, £24.95.
Physics is the study and formulation by physicists of how nature works. Without physicists, nature would still work but there would be nothing to describe it. Few, even among the physics community, know much about physicists, other than some hype about cult figures like Einstein, Feynman and Hawking.
Only a handful of geniuses, active at a time when their talents can bear fruit, can achieve the milestone discoveries or reveal the new insights that make science history. Here, William Cropper provides biographical snapshots of 30 famous physicists (in 29 chapters - Erwin Schrödinger and Louis de Broglie share a bed), extending through time from Galileo to Hawking, who was born on 8 January 1942, exactly 300 years after Galileo's death. Hawking himself has remarked on this coincidence, and the fact that these dates provide the parameters of this study reflects the book as a whole.
The portraits are drawn from standard biographies, and those who are acquainted with these works will find nothing new. As Cropper explains in his preface, "No claim is made that this is a comprehensive or scholarly study...Read these chapters casually and for entertainment, and learn the lesson that science is a human endeavour."
The first section covers the giant figures of Galileo and Newton, who centuries later still tower over the subject. Subsequent sections deal with thermodynamics (from Carnot to Nernst); 19th-century electromagnetism (Faraday and Maxwell); statistical mechanics (Boltzmann alone); relativity (Einstein supreme); quantum mechanics; nuclear physics (Curie, Rutherford, Meitner, and Fermi); particle physics (Dirac, Feynman and Gell-Mann); and astronomy, astrophysics and cosmology (Hubble, Chandrasekhar and Hawking). Most of the book, therefore, deals with 20th-century figures.
The cast of characters is Cropper's choice and spans the whole spectrum of personality and destiny: tragic figures like Boltzmann, victims of fate like Meitner and Planck, ascetics like Dirac, the flamboyant Feynman, intellectual aristocrats like Gell-Mann and simple geniuses like Rutherford.
The book's subjects include two women (Curie and Meitner) but are mainly confined to Europe and North America. The exceptions are Chandrasekhar, born in India, who spent his research career in Europe and the US; and Rutherford, born in New Zealand, who spent his research career in England and Canada. There are no Russians, which is a pity, considering the wealth of contributions to physics made by scientists in that country and who have been well represented by Nobel awards.
Each biographical snapshot is prefaced by a useful summary, before a fuller account and an appraisal of the science (including some assimilable equations). Each is also labelled by a thumbnail portrait illustration, but otherwise there are no photographs of events (other than a bubble chamber). There is a separate chronology of the main events of the period covered, but there is no systematic indication of exact dates of birth and death, such as in Asimov's work.
However, Cropper has done physics a great service by compiling this book, which compresses between two covers valuable material that would otherwise need a small library.
Gordon Fraser, CERN.
Les neutrinos vont-ils au paradis? [Do Neutrinos Go to Heaven?] by François Vannucci. Published in French by EDPSciences, ISBN 2 86883 559 7, 18.
François Vannucci presented me with his manuscript as his first detective story. I am not surprised that his literary debut takes this form. Vannucci's early career at CERN was followed by a stint at the Stanford linear accelerator. He has been lucky enough to have worked on experiments led by great figures of science in research leading to key discoveries.
That Vannucci is bent wholly on the pursuit of rare game comes as no surprise, and neutrinos with their mysteries were an ideal hunting ground. The nature of the prey lent flavour to the chase. As the secrets of each particle discovered were revealed, they shed new light on the structure of matter at the smallest scale, and on the micro-instants that followed the Big Bang.
Research went on in powerful groups, sometimes numbering several hundred, with ever-more burgeoning budgets. The sociology of this special world had little in common with the atmosphere prevailing in the small university labs of yesteryear. The groups were often led by outstanding physicists whose laurels had often been won as a result of remarkable discoveries - frequently the combined fruit of a great theoretical background and an encyclopaedic knowledge of engineering methods.
But humans being humans, with a genetic baggage built up through scores of millennia of the struggle for life, high-energy physics has included in its ranks the same numbers of men of intelligence, geniuses, madmen, the generous, the envious, the selfish, the disinterested, the brutes, the power-hungry, the poets, the mystics and the cynics as any other group of humanity swept up in any adventure on an equivalent scale. Vannucci introduces us to the way in which the never-ending human comedy is played out at any elementary particle research centre. He brings us into a little world of Parisian physicists headed by a boss with boundless ambition and a fascination for neutrinos. This individual suffers from the shortcomings often found in such people - he is the monster whom no boss would admit to being, yet many ranking physicists will find he has features that smack of their own bosses.
In this book, the research ends in a fiasco that is both material and social. The writer draws a ferocious and desperate fictional portrait of the lives of this team, worn out by failure and disappointed by a leader who had nonetheless fascinated them. Some are still neurotically attached to their boss despite the blind alley that he has led them into. He hangs himself, and we anxiously follow the narrator's efforts to escape the spell that he has cast.
I hope Vannucci's new-found narrative gift will persuade him to inform the public of other secrets from the world of the physicist.
Georges Charpak.