Michio Kaku, Parallel Worlds. Scotland on Sunday, February 20, 2005. Review by Andrew Crumey.

THE scenario is familiar from countless science fiction stories - a parallel world; one that looks superficially like ours, but which differs in crucial details. Novelists have had fun imagining what it would be like if Hitler won the war or John F Kennedy dodged Oswald's bullets. For decades, physicists have been taking such parallel realities seriously, as Michio Kaku explains.

The author will be familiar to anyone who watches science documentaries on television, where he crops up regularly to explain relativity or superstrings (a theory to which he has made important contributions). His style, both on screen and on the page, is chatty and accessible.

Do not, however, embark on this book in expectation of the sort of treatment you might get in a TV special. Documentary makers know the value of using history, popular culture and whizz-bang effects to make science engaging. Parallel Worlds makes some nods towards literary history - even bringing in Keats alongside the more predictable HG Wells and Lewis Carroll - but the emphasis is squarely on hard science. As such, this book may disappoint people drawn to the title by a fondness for Star Trek, or even an interest in Leibniz or Baudrillard. But if it's physics you want, you will not be disappointed.

Kaku offers a lightning tour through the subject, from the comparatively well -trodden territory of Einstein and Schroedinger to the latest ideas about "brane-worlds" and the "multiverse." The style is much like that of a New Scientist or Scientific American article: clear, precise and largely free of unwanted flab.

This leanness makes the book an exhilarating read for anyone sufficiently acquainted with the basic jargon to be able to do the odd bit of skimming. Newbies to the burgeoning popular science literature, however, may feel Kaku's sparse prose is at times too much like intellectual muesli: nutritious but dull.

Even so, it is worth staying the course, as Kaku describes the various ways in which our universe might really be only one among many. There is the multiplicity of quantum mechanics: the fabled "Schroedinger's cat" that can be alive and dead at the same time. There is the multiverse theory proposed by Martin Rees, in which our habitable cosmos is one lucky lottery ticket among a great many dead ones. And there is the possibility that our universe is like a single page of a multi-dimensional book, with collisions between neighbouring 'pages' bringing about big bangs in each.

To add a further Matrix-like twist to all this, there is the idea that the entire universe could be encoded into a space no larger than our solar system: meaning that another solar system somewhere might be the place where the cosmic DVD is playing right now. Our apparent cosmos would merely be its projection.

What Kaku's account lacks in lyricism, it makes up for in sheer content. Nobody who reads this book can be anything less than amazed by the possibilities it presents, even if they might not be seduced by the manner of its telling. For that, you need to turn to the likes of Keats.

Adam Phillips, Going Sane. Scotland on Sunday, February 27, 2005. Review by Andrew Crumey.

TWO years ago, the US court of appeal had to deliberate on the case of Charles Singleton. Convicted of murdering a shopworker and sentenced to death, Singleton was convinced his cell was inhabited by demons, a prison doctor had implanted a device in his ear, and he was in fact God. At issue was whether Singleton could be forcibly given anti-psychotic medication that would render him sane enough to be executed.

He was, and met his end in January 2004, his last words being an incoherent ramble attributable to his paranoid schizophrenia.

As Phillips says at the outset of this book, the idea of being "sane enough to execute" is something that might disturb, but does not baffle. We all have an intuitive sense of behaviour so far from the rational norm that moral culpability no longer applies. What Phillips then sets out to explore is the notion of sanity. What exactly is it? At the end of his frustrating book, I was left none the wiser.

Phillips considers a number of positive qualities we might characterise as being those of a sane person: happiness, contentment, geniality, sociability. Sanity could be equated with goodness, and Phillips devotes much space - far too much - to wrestling with this notion. His own initial example of Charles Singleton is enough to make such discussion irrelevant. A sane person can be evil - Harold Shipman may have been sick or warped, but he was not insane.

Phillips' lengthy and discursive book therefore suffers from a basic missing of its own point.

He considers three types of "insanity": autism, depression and schizophrenia. Most people would judge only the last of these to be a genuine example. Depressed people commonly feel they are going mad, and autistic behaviour can be baffling to onlookers - but the crucial dividing line between the sane and the insane is that the latter have somehow lost their grip of reality.

That, though, is far too simple for Phillips, who never even offers it as a possible definition. Inhabiting the treacherous world that lies between literary criticism and psychoanalysis, Phillips is someone for whom reality can never appear in print without being modestly clothed in inverted commas.

His aphoristic, rhetorical style, lends itself to statements that sound arresting but often mean very little. "If it is mad to hear voices, what is it then sane to hear?" More concerned with the number of occurrences of "sane" in Shakespeare (one) as opposed to "mad" (lots), Phillips never tells us anything really useful about how people like Singleton or Shipman are to be explained and, one hopes, cured or avoided.

Instead, the author offers us an up-market self-help book that concludes with a guide on how we can all be "sane." It reads at times like a Victorian manual on etiquette: the sane person "will prize charm in herself and others." The definition he finally arrives at is that sanity "should refer to whatever resources we have to prevent humiliation".

Phillips is marketed as a kind of Alain De Botton of psychiatry, but that is unfair to both. De Botton writes better and Phillips aims higher.

But since the sane apparently "believe that confusion, acknowledged, is a virtue", I have to admit to sanity, having been thoroughly confused by this book.

Roderick Graham, The Great Infidel. Scotland on Sunday, March 13, 2005. Review by Andrew Crumey.

JAMES Boswell watched the funeral of David Hume from behind a wall. So did many others, fearful that the devil might come to carry off the philosopher's soul. "Ye ken he was an atheist!" one overlooker called out, to which someone else replied, "Aye, but he was honest."

Hume remains a controversial figure in Scottish history, but Roderick Graham's welcome biography - the first full-length work of its kind in half a century - reminds us of his towering achievements and endearing personality.

Hume wrote an autobiography in 1776, not long before his death at the age of 65. It begins: "It is difficult for a man to speak long of himself without vanity: therefore I shall be short." In half a dozen pages, it describes how Hume travelled to France as a young man and wrote the landmark Treatise of Human Nature, which "fell dead born from the press".

Living alternately in Edinburgh and London, Hume found fame with a collection of essays, and a history of England brought even more acclaim, as well as attacks from all sides of the political spectrum. A further spell in France made him the darling of the Parisian salons, and he ended his days quietly in Edinburgh.

Graham fills out the details. We learn, for instance, that the Treatise was not quite as "dead born" as Hume claimed, but was reviewed widely throughout Europe. It did not make a household name of its author; but philosophy books seldom do.

Hume never married; his closest attachment was to his sister, with whom he lived. But when he arrived in Paris in 1763, there were many female readers eager to meet le bon David. They were all surprised by his appearance: the French philosopher Denis Diderot initially took the rotund Hume for an overfed priest.

Hume loved food and drink more than he cared for socialising. He was shy but knew how to behave. His geniality had its greatest challenge in his relations with Jean-Jacques Rousseau, who took Hume's glassy stare ("glaikit" is how Graham describes his customary look) to be Satanic.

Graham's book reminds us that the much-vaunted Edinburgh Enlightenment rests almost entirely on Hume's achievement; though he did his greatest work in France. His friend Adam Smith was in Kirkcaldy and Glasgow; Boswell was a young upstart whose Life of Johnson lay in the future.

The Edinburgh literati (Hume among them) admired Augustan poets who are now mostly forgotten, and took pains to remove "Scotticisms" from their speech. Hume described himself as an Englishman, and called the poems of Ossian a hoax because Highlanders could not possibly have come up with sophisticated verse (he was right, if for the wrong reasons).

Denounced as an atheist by the Church of Scotland, and viewed with suspicion by his contemporaries, Hume was always an outsider, and so he has remained. The statue of him outside Edinburgh's Sheriff Court ("truly appalling", Graham calls it) is of a man who remains too singular for comfort, irreducible to cosy legend. He was no Braveheart: his bravery was of the intellectual kind, and we can still learn much from it.

Arthur I Miller, Empire of the Stars. Scotland on Sunday, April 3, 2005. Review by Andrew Crumey.

HAVING previously written a book comparing Einstein with Picasso, Arthur Miller now explores another fascinating example of the crossover between science and art. His subject is the 20th-century Indian astronomer Subrahmanyan Chandrasekhar.

Known as Chandra, he made one of the greatest breakthroughs in the study of dying stars, and ended his days writing essays on Monet's paintings. Chandra's life highlights the fickleness of scientific fame. In 1930, the 19-year-old prodigy set sail from Madras to take up a research studentship at Cambridge. It was on the boat that he had the insight for which he is remembered.

When a star runs out of nuclear fuel it collapses under its own weight, but Chandra realised that for stars above a certain size there might be nothing to stop them squeezing right down to a point.

Chandra's idea flew in the face of conventional wisdom, and Miller brilliantly portrays the clash of egos in which the young researcher found himself enmeshed.

Not only was he up against the physics establishment - and in particular Arthur Eddington, famous for having proved Einstein's relativity during a solar eclipse some years earlier - but Chandra also faced institutionalised racism. In the end, his response to academic politics was to become an expert in it himself.

Thus the man Miller portrays is a complex one. Chandra came to adopt the same withering scorn unleashed on him by Eddington. Embittered by the rejection of his ideas, he went to work in America.

It was only very gradually that his theory of collapsing stars became an accepted part of orthodox science. Today, the neutron stars and black holes he predicted are routinely observed by astronomers.

Chandra was awarded the Nobel Prize in 1983, but when he heard the news - on his 73rd birthday - he felt aggrieved that it was for an idea he had had so long ago, as a teenager. He responded by publishing a detailed list of all the other work he had done since.

All of this makes Miller's book a sad one, as well as one of the finest of its kind. Miller skilfully manages to convey the meat of the science without undue technicality, but also without any dumbing down. And alongside his account of the way astronomy developed, there is the unfolding drama of warring personalities, with Eddington in particular being the 'evil genius' whose aloofness is both chilling and compelling.

In his last years, Chandra wrote a book called Truth and Beauty: Aesthetics and Motivations in Science. He found many similarities between art and science (Monet's haystacks, for instance, suggesting parallels with general relativity), but also one crucial difference. Artists, Chandra noted, often improve over time, doing their greatest work in old age. With scientists this rarely happens. Einstein, Newton and James Clerk Maxwell did no great work after their mid-30s or early 40s.

For Chandra, himself an old man, it was a painful conclusion. The Nobel committee had made the right decision - Chandra had never topped the discovery made when he was 19.

Palle Yourgrau, A World Without Time. Scotland on Sunday, April 17, 2005. Review by Andrew Crumey.

THIS book tells the intriguing story of Albert Einstein's friendship with a reclusive, neurotic man who claimed he could prove that time is an illusion. Even today, Kurt Goedel's findings remain controversial, and Palle Yourgrau - a professor of philosophy - has done much to keep them alive.

Goedel is remembered as one of the greatest mathematicians of the 20th century. As a young man he found the "incompleteness theorem", showing that some mathematical truths are unprovable by normal means. In his native Vienna, Goedel was friendly with leading philosophers, and his interest in abstract metaphysical problems never left him.

In 1929, the owners of a New Jersey department store sold their business to Macy's. This was fortuitous for the sellers - who struck the deal just before the Wall Street Crash - and also for science, since the money was used to found the Princeton Institute for Advanced Study - a centre where the world's greatest researchers could work without needing to do any teaching or administrative work.

Einstein was soon signed up, and as the political situation worsened in 1930s Europe, Kurt Goedel followed him to America. Thus the two met and became friends. As far as Einstein was concerned, Goedel was every bit his intellectual equal, and they spent hours talking together each day.

But while Einstein was recognised in the streets of Princeton even by small children, Goedel was unknown.

A hypochondriac who mistrusted doctors and filled himself with medication, he wrapped himself in thick coats in the height of summer and went through bouts of paranoia, believing there was a plot to poison him. One friend contacted a psychiatrist, wanting to know if Goedel might be a threat to himself or others.

Amid this psychological turmoil, Goedel mastered Einstein's general theory of relativity, and in 1949 he made a startling discovery. According to Einstein's own theory, it ought to be possible to travel into the past.

Goedel found that time travel would be possible if the universe were rotating. Light beams would follow curved paths and it would be possible to beat these light beams to their destinations, enabling travellers to arrive before they departed.

Goedel studied photographs of distant galaxies in search of evidence of a rotating universe, but found none. His model is a theoretical one - yet it troubled Einstein greatly.

But Yourgrau points out a basic error in later interpretations of Goedel's work. What he really found was a possible universe in which you could go round and round in a loop, revisiting your past again and again. There would be no starting point, no before or after - and hence it would be a universe in which time had no meaning.

Goedel is by no means the only person to have taken such a view. Many thinkers - including Plato, Leibniz and Kant - have argued that time is an "ideal" existing within our minds.

For Goedel, though, as for everyone, time ran out. Overcome by his food paranoia, he starved himself to death in 1972.

Patricia Fara, Fatal Attraction. Scotland on Sunday, May 1, 2005. Review by Andrew Crumey.

MAGNETS are used nowadays in alternative therapies - alongside crystals, pyramids and soothing colours. But there was a time when they were mainstream science. In the 18th century you could pay top guinea for a session at the Temple of Health, an exclusive London sex therapy centre where couples resolved their marital problems on a magnetic bed.

Patricia Fara traces the curious field lines of magnetic history in a fascinating little book that forms a companion to her earlier volume on electricity. We learn of Edmund Halley's theory that the Earth contains concentric shells, each one a giant magnet inhabited by people whose illumination would come from glowing gas trapped beneath the planet's surface. And we are told of an unsung hero of British science, Godwin Knight, who was the first director of the British Museum and the first person to mass produce magnets.

Why is Knight almost totally forgotten? Probably, Fara suggests, because he was so unpopular in his lifetime. He had no friends, and when he got tired of people walking past his office on the way to a communal toilet, he had it bricked up and put out of use.

Fara appears to take a somewhat jaded view of scientists, all of whom, in her estimation, were motivated (in the 18th century at least) solely by a desire for self-promotion, fame and wealth. Certainly for the many quacks and charlatans Fara describes, pursuit of knowledge was not the major driving force. She is lenient, though, when it comes to a man remembered as one of the greatest charaltans of his era: Franz Anton Mesmer. His theory of 'animal magnetism' led him to try to manipulate the 'magnetic vapours' emanating from his patients.

He became a sensation in Paris, where his mainly female clientele would lapse into orgasmic convulsions as he gazed into their eyes, waved his hands, and 'mesmerised' them. A team of scientists led by Benjamin Franklin investigated Mesmer's claims and found them bogus. Using blind testing and placebos, they proved the medical benefits were the result of psychological suggestion, not magnetism.

But any benefit is surely good, and Fara maintains that Mesmer's fall from grace (he was hounded out of Paris) was a case of scientific power politics, in which the mainstream closed ranks and expelled an outsider whose discovery - hypnosis - they could not fathom.

This lively book is a reminder that the border between orthodox and alternative medicine has much to do with academic politics and the professionalisation of science.

Emmanuel Carrere, I Am Alive And You Are Dead. Scotland on Sunday, May 29, 2005. Review by Andrew Crumey.

IN SEPTEMBER, 1977, cult novelist Philip K Dick arrived in France as guest of honour at a science fiction convention. He had been through a lot - drugs, personal problems and a long creative silence following the initial flood of books that had made his reputation.

But things had recently begun to look up: Warner Brothers had bought the film rights to one of his novels, which Ridley Scott would turn into Blade Runner. Later film adaptations - Total Recall and Minority Report - would make Dick's paranoid plotlines world famous. He was on the verge of mainstream acceptability.

But Dick had an announcement to make. "Often people claim to remember past lives," he told his audience. "I claim to remember a different, very different, present life." After writing so many science fiction books, Dick had come to believe he was living in one. The world around him was an illusion; he had lost the plot.

Dick's descent into madness is the subject of Emmanuel Carrere's book. Carrere is a novelist with a lifelong interest in Dick's work, but even he finds it hard to make this a sympathetic portrait of a writer who, from the outset, seemed destined for mental disaster.

Dick was born in Chicago in 1928, along with a twin sister who soon died. The heartbroken parents marked the grave with the names of both children. All that was missing was Phil Dick's body, and the date when he would join his sister.

Dick's parents split and he was brought up by his highly strung mother, who got him hooked on his most permanent and incurable addiction - Jungian therapy. "It took only a few sessions," writes Carrere, "for young Phil to begin speaking knowledgeably about 'neuroses', 'complexes' and 'phobias'. He subjected his classmates to various personality tests of his own devising."

By the age of 13 he had written his first novel (it took him 10 days) and founded a literary magazine which lasted one issue. The same hectic rush through life would manifest itself in his relations with women - a pattern of what Carrere calls "serial monogamy" that resulted in five failed marriages. Wife number two was a left-wing activist called Kleo, who attracted the attention of the FBI. One day in 1955, while Dick was alone in the house, two men came to the door whom he initially took for salesmen. Only their total lack of humour made him realise that they were agents. One of them subsequently became a regular visitor, though whether to snoop or simply chat is not clear. Dick was living in paranoid times, reflected in popular science fiction movies such as Invasion Of The Body Snatchers. However, he took these fears to a deeper level.

His moment of epiphany - the warped equivalent of Proust's madeleine - was when he entered the bathroom one night in the dark and reached for the light cord. Then he realised the light had a wall-switch, not a cord. So why had he thought there ought to be one? Was there another Philip K Dick in another universe whose bathroom light worked differently?

Dick went on to write a novel called Time Out Of Joint, whose hero, Ragle Gumm, spends his days doing newspaper puzzles. Twiddling his radio, he tunes into aircraft flying overhead. "You're passing over him now," a voice says. "Yes, you're looking down at Ragle Gumm himself."

Gumm's world is a fake, and everyone knows it except Gumm. A similar idea would later form the basis of the movie The Truman Show; but unlike Truman, Gumm is not on TV. His puzzle solutions are saving the Earth from alien missiles. It is 1998, and he is trapped in a theme-park recreation of 1950s America.

It was Dick's sixth novel - there were to be over 40 in all. The one that brought him fame was The Man In The High Castle, which won the Hugo Award in 1963. It imagines Germany and Japan triumphing in the Second World War, dividing America between them. Then a subversive novel appears which supposes the Allies to have won instead.

Dick's parallel histories reflected his uncertainties about reality. By the 1970s he was living alone, his latest wife having walked out, and his place became open house for "addicts, juvenile delinquents, runaways - in short, a bunch of freaks".

When his house was broken into he called the police, who wondered if he had done it himself. Dick almost believed them, though he later came up with countless other theories involving the CIA, Black Panthers, Watergate conspirators and many more. He described it all in an interview for Rolling Stone which brought him new fame and notoriety.

MEANWHILE, DICK continued to experience unsettling epiphanies. A girl came to the door to make a delivery - she wore a Christian fish pendant. Staring at it, Dick had a revelation. "The Empire never ended." His novels were right - we are all living in a parallel universe. The truth is that Ancient Rome never fell. And while Ragle Gumm was a few decades out of joint, for Dick it was far worse. He was really living in 70AD.

Carrere subtitles his book 'A journey into the mind of Philip K Dick'. It is one heck of a journey. But mental illness is no fun, and Carrere's portrayal of Dick's thought processes becomes wearying to read, as the anguished novelist debates with himself whether Romans, Soviets or aliens might be sending messages into his mind.

Dick at this time had another wife and another baby, whom he secretly baptised with milk, trying not to be seen by any Ancient Roman surveillance cameras.

He found himself able to speak Greek, and miraculously diagnosed his baby as needing an operation - all of which was enough to convince him he was not mad, but divinely chosen. He poured his thoughts into 8,000 pages of manuscript. Carrere never explains Dick's apparently supernatural abilities, but the key issue is whether any of the supposed miracles took place.

Witnesses to his Greek outbursts were, it seems, as stoned as he was; and Carrere cites no source for his information on the baby. The absence of footnotes or sources is irritating. Quotations from other works are made without any attribution, and Carrere mentions the existence of other Dick biographies without owning up to how much he has lifted from them. It is a fascinating story, but fact and fiction blur in it, just as they did for Dick.

What is certain is that he finally gave up on this world after a stroke from which he never woke up. His baby sister's grave was dug open, he was laid beside her, and the inscription was completed with the year 1982. Had he lived just a little longer, the movies would have made him a millionaire.

Jane Gregory, Fred Hoyle's Universe. Scotland on Sunday, June 5, 2005. Review by Andrew Crumey.

IN 1950, British radio listeners voted for their broadcaster of the year. The winner was not Tommy Handley or Wilfred Pickles, but an astronomer called Fred Hoyle. As one newspaper commented, Hoyle was receiving "the sort of effusions that are usually devoted to variety stars".

Hoyle found fame thanks to a series of radio talks in which he explained space in down-to-earth terms. He had a voice to match: his Yorkshire accent was in marked contrast to the usual plummy announcers, and listeners warmed to it. But Hoyle used his series as a platform for his own unorthodox views.

The big bang model was gaining favour, yet still lacked real proof. Hoyle proposed an alternative "steady state" model, with new matter constantly being created in an ever-expanding universe which had no beginning. Hoyle supposedly came up with the idea after seeing the horror movie Dead of Night, in which the story ends by looping back to its beginning.

Hoyle's model won support among some British cosmologists, but never really caught on elsewhere. As such, it became a particularly British view of the universe, with Hoyle's media fame giving the steady state model equal billing alongside the big bang. When the Festival of Britain opened in 1951, it featured a Discovery Dome in which visitors could learn about the cosmos, with an accompanying text largely drawn from Hoyle's bestselling book based on his radio series.

Hoyle's fame was not only due to his homely accent. In his talks, he raised the question of whether the universe had a creator. He was an outspoken atheist, and for him the 'big bang' (a term that he coined himself) implied a throwback to religious belief. Hoyle's controversial views were what really caught public attention. Jane Gregory quotes Malcolm Muggeridge in the Daily Telegraph at the time, saying Hoyle showed the "intellectual arrogance which is likely to characterise the contemporary scientist".

Gregory's biography is fascinating for the light it sheds on Hoyle's public profile in the 1950s and 1960s. He became a bestselling science fiction novelist, and scripted a TV series, A For Andromeda, which launched the career of Julie Christie.

Then the tide turned. Gregory graphically describes a scientific meeting in which Hoyle was interrupted by a young man at the back of the room, calling out: "You're wrong!" It was Stephen Hawking.

Hoyle later said he would have ripped the upstart apart if it wasn't for his medical condition. But Hoyle's steady state theory was crumbling.

The media found a new star, Hoyle's nemesis Martin Ryle - "nominated by a panel of actresses as one of the seven most romantic men in the world", says Gregory. The big bang won, or as one headline put it: "The Bible was right".

Hoyle's later years were a sad decline, increasingly caught up in academic in -fighting and research bureaucracy. His views became even wilder. He once suggested Aids came from space and was caught by walking barefoot. He died in 2001 aged 86: a genius and a maverick whose wrong ideas, sadly, are more widely remembered than his many correct ones.

Lisa Randall, Warped Passages. Scotland on Sunday, July 3, 2005. Review by Andrew Crumey.

THIS is an intelligent book about a very complicated subject. Randall, a leading American theoretical physicist, believes that the three dimensions of space we see around us are not the whole story. There are other, higher dimensions, which may explain why gravity is so much weaker than magnetism - making it possible, for example, for us to stick things on fridge doors.

She refers to these higher dimensions as "passages", and her explanation of them takes us through chapters such as 'Entryway Passages', 'Restricted Passages', 'Voluminous Passages' and even a 'Profound Passage' - all of which is apt to raise a snigger from any Julian Clary fans.

But laughs are in short supply here: the tone is earnest, lightened only occasionally by very dry wit. This book is not for softies. To be honest, it is hard work. Fridge doors may not sound like cutting-edge science, but the gap between gravity and other forces - the "hierarchy problem" - is a major concern for theorists, who have found many ways of potentially cracking it.

Randall takes us through "grand unified theories", which attempt to connect particles in a single model, but which have the snag of predicting that every atom in the universe will ultimately evaporate. She leads us on to superstring theory and "brane worlds", which picture particles as tiny vibrating filaments and the universe itself as a giant wobbly sheet.

Finally, she stakes out her own theory in detail. Imagine our universe being two-dimensional instead of three. Right next to our flat world is another flat world. Forces such as electricity and magnetism - the forces that make things solid and visible to us - are trapped on the flat sheets, but gravity can leak between them.

This would make gravity appear weaker than it really is - unable to pull a magnet off a fridge door. Other researchers have explored this, but Randall's twist is to make gravity weaken even further on its flight between the sheets. It means the universe might have different numbers of dimensions in different regions. Our three could be a local aberration.

The downside is the number of variations that are possible on the underlying theme. Faced with such a succession of subtly differing theories, the reader can easily be confused by the abundance.

The most appreciative audience for this book will be Randall's academic colleagues. Each chapter is laid out with the clarity of a well-delivered conference presentation: there is even a bullet-point summary of key features at the end of each. All that is missing is the equations.

But there are occasions when words are just as hard to understand: not even someone of Randall's intellect and talent can turn these very abstract ideas into reader-friendly form.

Nevertheless, there is a sizeable public appetite for challenging books such as this. Two decades after Stephen Hawking transformed the popular science market, we continue to see new books which are, if anything, even tougher going than his famously demanding one.

I enjoyed Warped Passages, but was left with a sense that theorists are still a long way from the final answer.

If you had asked Aristotle or Ptolemy to explain how planets move, you would have got a lecture on epicycles and equants. This book felt a little bit like that.

Stephen Walker, Shockwave. Scotland on Sunday, July 31, 2005. Review by Andrew Crumey.

IT was a sunny morning in Hiroshima on August 6, 1945. Had it not been, the atomic bomb would instead have landed on Kokura, both cities having been put on the target list because they were still largely untouched by air raids. The bomb makers wanted to know what their new weapon was capable of. For that they needed a pristine target and a clear view.

Stephen Walker's book describes events leading up to the flash that killed approximately 80,000 people in an instant, and claimed an equal number of lives through injuries and radiation sickness over the months and years. Having interviewed many Americans and Japanese who saw the Manhattan Project from both ends, Walker presents the story through individual lives. This quest for the human touch gets the book off to a shaky start, as the preparations for the bomb test in New Mexico are narrated in a style that sits uncomfortably close to that of a blockbuster thriller. As we progress, however, Walker is content to let the terrible story speak for itself.

Technical details are not Walker's concern: there is little of the science behind the bomb, or of the logistics of the Manhattan Project. Politics, too, are something of a sideline. The real focus is on the flying crew who took the bomb to Hiroshima, and a handful of the citizens who felt its force.

The young airmen were kept in the dark until the last moment; everyone at the airbase on Tinian Island assumed the modified B-29 aircraft were meant to carry newer, larger but otherwise conventional bombs. Only their chief officer, Colonel Paul Tibbets, knew the secret. He piloted the plane which he named after his mother, Enola Gay. He took with him 12 cyanide capsules - one for every man on the plane - in case they were shot down and captured.

Their departure from Tinian was a media circus: the Manhattan Project's commander, Leslie Groves, wanted every moment caught on film, aware the bombing was an exercise in terror, propaganda and geopolitics, not military strategy. The bomb's effects were monitored with equal precision.

The horrors of Hiroshima are well known and well documented; Walker's account adds little but offers a timely and harrowing reminder of them. Though Walker is British, the book appears to be aimed mainly at an American readership; there is virtually no mention of Britain's part in the project. Nor is Nagasaki discussed, other than in an epilogue. But within its restricted scope, Shockwave ably succeeds in creating a dramatised documentary of the moment that changed history.

John Gribbin, The Fellowship. Scotland on Sunday, August 14, 2005. Review by Andrew Crumey.

THE philosopher Thomas Kuhn argued that human ideas periodically undergo "paradigm shifts" of the kind exemplified by Copernicus, Darwin or Einstein. Yet this heroic, revolutionary view of history is "a complete nonsense" according to John Gribbin, who says in The Fellowship that "science really proceeds incrementally, building step by step on what has gone before." That is an odd statement to make, though, given that this book is subtitled "the story of a revolution".

Gribbin's theme is the intellectual revolution which may or may not have taken place in England in the 17th century, when scientists such as Robert Hooke, William Harvey and Isaac Newton transformed the way people thought about the universe. The social glue for this change was the Royal Society, which provides the unifying theme of Gribbin's book. By looking at the individual scientists who founded the fellowship, we get a picture of how the modern age was born.

Despite his swipe at Kuhn, Gribbin evidently has a lot of sympathy for the revolutionary view, which does more than give him a subtitle. He sees the 17th century as a time when the ancient dogmas of Aristotle were finally thrown out in favour of the modern experimental approach to science. That is a conventional and widely held viewpoint, and there is much evidence to support it, but it would have been nice to see more of the alternative view Gribbin hints at: a story of incremental change.

Gribbin's real aim, it seems, is to give due acknowledgement to some of science's less well known heroes, all of whom have wilted in Newton's enormous shadow. Robert Hooke found the law of gravity before Newton - but was unable to show how it predicted planetary orbits. Christopher Wren, who was an astronomy professor before becoming an architect, had similar insights. Wren and Hooke placed a bet on who could solve the orbit problem first, but it was Newton who won, thanks to the intervention of another unsung hero, Edmond Halley.

Gribbin does a fine job of reminding us how brilliant all of these men were. But in discussing their theories, he focuses only on those that turned out to be right. We repeatedly read about other ideas that need not be discussed further because they were "simply wrong." That is a pity, because the greatness of a scientist or artist is measurable in failure just as much as in lucky bullseyes.

Not only that, but the numerous wrong theories of Newton, Halley and others demonstrate that ancient ways of thinking were by no means dead. Newton, for instance, sought to equate spectral colours with the notes of a musical scale, and happily fudged the data when it disagreed with his theory's Platonic beauty.

In the end, it is not entirely clear if Gribbin is arguing that there really was no revolution, or else there was one but not of the kind Thomas Kuhn advocated.

That aside, The Fellowship is an enjoyable and richly researched account of remarkable achievements. Its only real flaw is that it is so evidently written with the benefit of four centuries' worth of hindsight.

Dava Sobel, The Planets. Scotland on Sunday, September 4, 2005. Review by Andrew Crumey.

TEN years ago, an unassuming little book was published about a largely forgotten episode in 18th-century technological history. It was called Longitude and it became an international bestseller, making Dava Sobel the most bankable name in popular science writing.

Countless imitations followed, until Bill Bryson's A Short History Of Nearly Everything made micro-histories of obscure subjects old hat. Instead we got a crop of books promising us the whole of creation in a single, beach-friendly volume.

Now we have Sobel's response: The Planets. Just as unpretentious in tone as Longitude, it nevertheless offers us a fashionably big story. Will it replicate her earlier success? Though I have my reservations, I hope it does.

The concept sounds a winner, with chapters called 'Genesis (the Sun)'; 'Mythology (Mercury)'; 'Beauty (Venus)'; 'Geography (Earth)'; 'Lunacy (the Moon)'; 'Sci-Fi (Mars)', and so on. This is a book about space, but also about the way humans have responded to it. Just think, for example, what there might be in the Mars chapter: everything from Gustav Holst to Orson Welles. Maybe Venus will give us Botticelli or the Velvet Underground?

Well, no, actually. Apart from Holst, none of the above gets a mention. The Planets is not an exercise in cultural studies; instead it is just what it claims to be: a guide to the rocky, gassy, icy spheres of all those classroom wall charts and Nasa photographs. The 'beauty', 'sci-fi', 'Genesis' stuff is only a thematic thread - and even Sobel seems at times unsure what to do with it.

The chapter on Jupiter is called 'Astrology' and begins by describing the horoscope Galileo made for himself. Galileo also discovered the moons of Jupiter, so the chapter mixes facts about the planet with asides about astrology. Galileo, we are told, was born with the Moon in the ninth house, suggesting foreign travel.

Sobel says: "Although Galileo never left Italy, it could be argued that his telescope carried him on the farthest possible journeys." Alternatively, it could be argued that the chart made a dud prediction, and astrology is entertaining hokum that has as much to do with the real Jupiter as chocolate bars do with Mars.

The same chapter shows Sobel's occasional shakiness with regard to basic science. Jupiter, she notes, has roughly 1,000 times Earth's volume, but only about 11 times its diameter. She considers this remarkable, and explains it by the way the planets formed. Actually it is an elementary consequence of the mathematical formula for the volume of any sphere.

ON THE WHOLE, though, Sobel is admirable for the simplicity and accuracy of her planetary voyage, which takes us from the baking heat of Mercury to the frozen regions of Pluto and beyond. She says that she has had a "planet fetish" since the age of eight, and her enthusiasm shows. She begins the book with a homely recollection of her childhood attempt to model the solar system as a collection of marbles and ping-pong balls, their order committed to memory from the first letters of the sentence "My very educated mother just served us nine pies".

It is only at the very end, in the acknowledgments, that we learn what prompted the book's writing. Sobel's agent wanted to know the difference between the solar system and the Milky Way. That says a lot about the state of knowledge in the American publishing industry, and it also indicates the low baseline Sobel is aiming at - though if you don't know your galaxy from Uranus, I doubt you'll really have the patience for a lecture about orbital resonances in the rings of Saturn.

Even so, the subject is still fascinating, and Sobel's complete lack of pedantry is most endearing. She would make a wonderful planetarium guide. I do feel, though, that buried in this commendably simple offering there is an altogether different book struggling to get out: the one hinted at in those rather misleading chapter titles.

Sobel strives here for a kind of nature writing that is very typically American, and could harshly be summed up on this side of the Atlantic as purple prose. For example, her Moon chapter begins by describing a friend who managed to get hold of a tiny sample of Moon dust - and swallowed it.

"In a reverie I saw the Moon dust caress Carolyn's lips like a lover's kiss… Crystalline and alien, it illuminated her body's dark recesses like pixie powder, thrumming the senseless tune of a wind chime through her veins..."

Sobel admits that, in reality, the inert speck passed right through Carolyn's body and disappeared down the toilet. Yet there are many other moments in The Planets when you feel the level-headed Sobel has been at the pixie powder. "Even the brightest Moonlight induces pallor in each face it illuminates, and creates shadows like oubliettes, where all who enter disappear." Only after looking up "oubliettes" in a dictionary was I able to work out that all she means is that shadows are dark.

Clearly, alongside Sobel's cosy pie-serving persona there lurks a thwarted prose-poet of Melvillean proportions. That, for me, is the real pleasure of The Planets: you never know if you are about to get a breakdown of atmospheric gases or an iambic hexameter.

We see this Jekyll and Hyde effect when she discusses a Martian meteorite whose microscopic worm-like structures, initially seen as evidence of fossil life, may really have been chance illusions. "The processing had caused textural changes that inexplicably copied the outline of familiar life forms - the way a windblown mesa on Mars may perchance assume the contours of a human face," she writes.

Try saying the second half of that sentence in your best Shakespearean voice and you will see how Sobel perchance assumes the contours of a style very different from what you expect in a discussion of geology. During such flights of lyricism, she sometimes comes a cropper. "On Moonless nights when Venus is nigh, her strong light throws soft, unexpected shadows on to pale walls or patches of ground. The faint silhouette of a Venus shadow, which evades detection by the colour-sensitive inquiry of a direct gaze, often answers to sidelong glances that favour the black-and-white acuity of peripheral vision."

The problem with this rather lovely passage is that its least lovely word - the cod-poetic "nigh" - is simply wrong. When Venus is closest she is lost in the Sun's glare. It is when Venus is brightest that we can hunt for her shadows (I have often tried and always failed). And since Venus is a point source, her shadows lack the penumbral edges of the Sun's - they are hard, not soft; nor are they unexpected. As for the benefits of peripheral vision, these have little to do with colour.

I could quibble with many other passages in the book, but that is only nitpicking. The Planets is a highly informative book as well as a loveably odd one. It educates and entertains, and for all its minor flaws, deserves every success.

AC Grayling, Descartes. Scotland on Sunday, September 25, 2005. Review by Andrew Crumey.

RENE Descartes penned the most famous phrase in the history of philosophy: "I think, therefore I am." But he was also a scientist and mathematician, a solider and a traveller. According to AC Grayling's fascinating biography of the enigmatic Frenchman, we can add yet another item to the CV. Descartes, claims Grayling, was a spy.

Descartes was born in 1596, and he lived through the turbulent years of the Counter-Reformation and the Thirty Years War. As a young man he signed up for military service under the Prince of Orange in the Netherlands, which would eventually become his home during the greatest years of his life as a philosopher.

But first he needed to have his moment of epiphany, and it came while he was on campaign, spending the night (he later wrote) in a stuffy, stove-heated room. In his sweaty, insomniac state, he asked himself whether there was anything of which we could be truly certain, and decided there was only one: the fact of our own existence. Anything else was open to doubt.

Descartes' sceptical philosophy put him on a collision course with theological dogma, but Grayling notes several oddities in the man's life. He travelled through hostile war zones which the French regarded as enemy territory. He somehow acquired enough money to live in comparative comfort. In Paris he was rumoured to belong to a secret society, the Rosicrucians. He had a meeting with a top-level French cleric, after which he moved permanently to the Netherlands, where he was left in peace.

For Grayling, this all amounts to compelling evidence that Descartes was a spy in the pay of the French court, assigned to reconnoitre hotbeds of potential opposition. The Rosicrucians were suspect, and so Descartes may have infiltrated their ranks.

The Rosicrucians themselves were more rumour than fact. Paris was awash with lurid tales about their secret practices, but nobody quite knew who they were or what they stood for. Some people put notices in newspapers saying they wanted to join, and asking to whom they should apply. Others claimed membership simply to draw attention to themselves. It was the mother of all conspiracy theories, and its ripples carried over into freemasonry and beyond.

Grayling is a professor of philosophy and author of many books on the subject, both popular and academic. This does not stop him resorting to the most basic kind of deduction: "smoke requires fire", as he puts it. The evidence for Descartes's life as a spy is, he admits, entirely circumstantial. But it makes for a most intriguing read.

Simon Winchester, A Crack In The Edge Of The World. Scotland on Sunday, October 2, 2005. Review by Andrew Crumey.

DISASTERS aren't what they used to be. In former, simpler times they were the stuff of movies, the premise being that no matter what happened, a bunch of hardy survivors would hold together until rescue came. Recent events in the United States, and before that the tsunami of Boxing Day 2004, reminded us otherwise. When it comes to humans against nature, there is no contest.

The San Francisco earthquake of 1906 is legendary. A movie made about it 30 years later, starring Clark Gable, cemented the image of a hedonistic town flattened by heavenly wrath. Special effect scenes showing the ground opening up beneath people's feet aimed to recreate what seemed beyond imagining.

In retrospect, though, the disaster appears almost quaint. The death toll in San Francisco was somewhere between 700 and 3,000, caused mostly by fires that broke out after gas mains ruptured. The body count, terrible though it was, has been trumped considerably since then. The quake was one of the largest ever recorded, but while natural disasters haven't grown in the ensuing hundred years, human populations have. We live in a world that is increasingly urbanised, and therefore increasingly vulnerable.

As Simon Winchester's fascinating book shows, San Francisco served as an unheeded warning of things to come. Founded by Spanish settlers in 1776, the town still had a population of only 200 more than half a century later. But when it became a US territory after the Mexican War, it "grew at an exuberant, almost irrational rate".

The spur to growth was the 1848 gold rush, quickly creating a town filled with people who either had money to spend or were desperate to get hold of it. New words emerged to describe the new metropolis: "hoodlum" possibly came from "huddle 'em" - the signal for mobs to descend on hapless victims, many of them inhabitants of 'Chinatown', of which San Francisco's was the first. Other words coined at the time have since dropped from currency: a 'French restaurant' meant "a two-storey building where meals were sold on the first floor and girls on the second." The city boasted a Hotel Nymphomania with 150 cubicles offering sexual services on an industrialised scale.

What the gold-prospecting, whoring San Franciscans overlooked was that they had built their city right on top of the San Andreas fault. As with the coastlines of Louisiana or Sumatra, beautiful places are not necessarily safe ones; and the more people who crowd into a danger zone, the greater the ultimate cost will be.

Winchester's previous book was Krakatoa - he evidently has a fondness for earth-churning disasters - but while the protracted pyrotechnics of the volcano leant themselves to lengthy and vivid description, the 90 seconds of the San Francisco earthquake - which took place in the early hours of an April morning when most people were still in bed - require a different approach.

This book meanders through geology, history and travelogue, with the disaster serving as a leitmotif that frequently sinks from view altogether, as Winchester's leisurely narrative takes him off on some new tangent. Not all readers will have the patience for this approach, but those willing to surrender themselves to the author's relaxed tone will find this an enjoyable, if slightly overfilled book. And when he sticks to earthquakes, there is much that makes the mind boggle.

Those who were awake in San Francisco at 5.12am on April 18 1906 saw a sight that can hardly be imagined. The epicentre was a mile off-shore, and created a surge of water that flooded the streets. Even more terrifying was the shockwave that rippled the ground itself, throwing whole buildings off their foundations, and roared down the faultline at 7,000 miles an hour. A policeman "was appalled to see huge cracks opening up on the pavement… closing and reopening as the shockwaves shook everything to pieces." He then saw a stampede of wild cattle, set loose from the docks in the pandemonium, and began shooting at them - but was unable to kill them all before a man was gored to death.

ENRICO CARUSO WAS staying in San Francisco following a performance there. He was found "in a near-hysterical state, claiming that the quake was a punishment sent to him directly, and announcing that his voice had been irreparably damaged" - proof that prima donnas need not be female.

The most dramatic shifting of the liquefying ground - leaving cracks 20ft wide - happened at a town called Olema, 40 miles north of the city, whose stores nowadays sell caps and shirts proudly, if wrongly, proclaiming it to have been the epicentre.

Another town on the faultline, Parkfield, continues to have the highest level of seismic activity, and is cashing in on its status as the likely scene of the next major quake. "The town's cafe… sports a water tower painted with the slogan 'Be Here When It Happens', and the hotel tries to tempt passers-by with 'Sleep Here When It Happens'. On the menu is a steak called the Big One - as well as a rather more modest version called the Magnitude Six. The desserts are called Aftershocks."

Such humour will one day seem fatally misguided. The flooding of New Orleans was predicted long before it took place, and the same will be true of the next big shudder of the San Andreas Fault, whose sides are steadily slipping, storing huge amounts of energy in the geological equivalent of a gigantic elastic band. Eventually it will snap, and the only question is when. Scientists estimate a 60% chance of it occurring some time in the next 25 years.

San Franciscans reassure themselves that their buildings are earthquake proof, but in the light of recent events, their faith in human ingenuity is surely mistaken. And unlike hurricanes or tsunamis, earthquakes are the one type of natural disaster that strike without any warning whatsoever. Some geologists have claimed to have found statistical patterns in their occurrence, but betting on the next one is like trying to predict horse races or the stock exchange. The only difference is the stakes are significantly higher.

San Francisco was on its way to becoming California's most important city when the 1906 quake struck. Businesses learned the lesson and moved to Los Angeles, which is vulnerable too, though not as much.

It remains to be seen what will become of New Orleans, but Winchester's fine book is a timely reminder that there are some events, predictable or otherwise, for which we can never adequately prepare. When nature decides to show us who's boss, we just have to hunker down and hope for the best.

Mick O'Hare (ed.), Does Anything Eat Wasps? Scotland on Sunday, November 13, 2005. Review by Andrew Crumey.

HOW fat would you need to be so as to be bullet-proof? That was one among thousands of questions submitted to New Scientist magazine, and this book offers a selection of the most entertaining and informative, together with answers supplied by readers. A 30cm thickness of all-round body fat, it seems, would probably be enough to provide you with natural armour, though since you'd also end up weighing half a ton, it would not be a very useful asset.

Some of the questions are familiar science-teasers, such as "what is our expanding universe expanding into?" or "why is the sea blue?" Most, though, stem from simple everyday observations that have aroused people's curiosity.

One reader wrote asking why lemon juice makes tea go lighter in colour. Another wanted to know why it stops sliced apples going brown. The answer in both cases comes from the acidity of the juice - you can evidently do a lot of science with a lemon. As for the one in the title about whether anything eats wasps (the questioner suggesting "very stupid birds" as the only creature likely to try it), it turns out that wasps are a veritable delicacy of the natural world. Many people wrote to describe how they had seen wasps being gobbled by badgers, buzzards, other insects and even a hungry crab. One correspondent added himself to the list of predators, reporting that wasp larvae are very tasty when fried in butter.

Culinary matters are a recurring feature, from the pointless but intriguing (such as the fastest way to pour all the wine out of a bottle), to the genuinely useful. In the latter category is a piece about green potatoes, offering dire warnings against eating them. Cutting off the green bits does nothing to remove the potentially lethal toxins inside - you should throw the whole spud in the bin. The same kind of poison is found in tobacco - so don't go eating cigarettes or you'll die even sooner than you would from smoking them.

The most inventive question came from a six-year-old wanting to know if there was any way you could surf on molten lava (dangerous sports fanatics will need a bucket of water and an erupting volcano if they want to try the proposed solution). And from the point of view of contributing to science, the prize goes to a questioner who enjoyed pouring cream on Tia Maria. She noticed strange, delicate patterns appearing in the cream and wanted to know their cause. The result was a research project in a Spanish university which found 'solutal convection' to be the answer.

This book is endlessly fascinating and an absolute treat. Ideal for dipping and browsing, it is also crammed with so much odd information and so many answers to questions you never knew you had, that once you start reading it you may well want to go straight on to the end in one sitting (as I did).

A word of warning, though. If you are squeamish, don't read the section on whether guillotined people remain briefly conscious afterwards. A hundred years ago, a French doctor found the answer to be yes - and the description of how he did it gave me nightmares.

David S Katz, The Occult Tradition. Scotland on Sunday, December 4, 2005. Review by Andrew Crumey.

DAN Brown's sequel to The Da Vinci Code, it is rumoured, will be about a masonic conspiracy in Washington DC. It would certainly fit the pattern of his previous books. In Angels And Demons, his first thriller featuring code-breaking scholar Robert Langdon, a sinister secret society called the Illuminati figured prominently.

Then, in The Da Vinci Code, we had - among other things - the Knights Templar, who have long been a favourite topic with historical conspiracy theorists.

To see where the next book could be coming from, we only need to look at that funny picture on the back of every US dollar bill, showing a truncated pyramid with a disembodied eye floating above it. The American founding fathers' fondness for masonic symbolism has long been a source of puzzlement and speculation.

Walk into any bookshop and you will find a plentiful supply of books about Atlantis, pyramids, lost ancient wisdom and secret societies. Brown's ability to turn this esoteric pop culture into readable thrillers has made him a millionaire and spawned countless imitators. But where did it all come from? David Katz's fascinating book offers a few answers.

Right from the start, Katz - an Israeli professor of literature and history - makes his position clear. There are, he says, lots of "trashy" and "parasitic" books on this subject, and his is not one of them. Instead, his book "traces the growth and meandering path of the occult tradition over the past five hundred years and shows how the esoteric world view fits together".

That is a big ambition, and this is not a particularly big book. Moreover, the time period it has to cover is not really 500 years, but is instead more than 2,000. Yet although Katz's book is necessarily incomplete in what it can cover, it lives up to its goals remarkably well. Anyone wanting to understand the deep historical connections between the numerous strands of modern esoterica would do well to read it.

THE STORY BEGINS with Plato. The Greek philosopher believed our world to be a shadow of the true reality, so for Plato's later followers - the neo-Platonists and Gnostics of the early Christian period - wisdom was to be found by looking beneath the surface appearance of things. Truth was 'occult', meaning hidden, and it became the business of philosophers and alchemists to seek it by mystic means.

Katz fast-forwards to the Renaissance, when many people believed in the existence of a lost, ancient Egyptian book, the Corpus Hermeticum, offering the key to astrology, alchemy and magic. In 1463, a Balkan monk showed up in Florence with the fabled book, which he had found in a Byzantine archive. It turned out to be less spectacular - and a lot less old - than initially hoped, but this did nothing to shake the belief that the ancients knew far more about the secrets of the universe than later generations, and had left their wisdom in code.

Isaac Newton was a firm believer in this hidden code theory. As Katz explains, Newton thought that the lost Temple Of Solomon, described in the Bible, was a scale model of the universe, built by people who knew all about gravity and planetary orbits. Brown's next opus - whose title has been announced as The Solomon Key - will presumably regurgitate such information, as the hero tries to solve a mysterious murder.

Seventeenth and 18th-century interest in Hermeticism spawned numerous clubs and societies, some more secretive than others. Many people tried to join the Rosicrucians, but nobody could find out where they were. Even when the society's creator announced it was all a hoax, some reckoned he was lying so as to hide the sinister truth.

Freemasons claimed to be the modern heirs of the builders of Solomon's Temple, and the Knights Templar, and one of their early leaders in France was Andrew Ramsay, an exiled Jacobite whom Katz considers "a key figure in the development of esoteric lore". Ramsay gave Hermeticism a new twist by saying it all started not in Egypt, but in China.

The Order of Illuminati began as a student society in 1776 and was soon accused of infiltrating Masonic lodges. "By the time the French Revolution began in 1789," writes Katz, "not only was there a myth of conspiratorial secret societies, but a reality as well, as life imitated art."

The remainder of Katz's absorbing book illustrates this well. Through Swedenborgianism, spiritualism, Mormonism and other belief systems, he shows how people have continued to be inspired by the notion that life is fundamentally mystical, interconnected and inexplicable. Equally, certain people are attracted by organisations offering elaborate rituals, ancient tradition, and ascending levels of rank. Some find what they are looking for in the Boy Scouts, others need something a little edgier. Symbolism, sprinkled in art and architecture (or on dollar bills), adds to the sense of significance.

Katz is under no illusion about the fakes and charlatans who have used esoteric lore as a way of profiting from a credulous public, but what is fascinating about his study is the way it makes historical sense of patterns of belief which - whether you share them or not - have a certain coherence over time.

Thus, for example, the enigmatic Madame Blavatsky, founder of the Theosophical Society, made an "impressive attempt to synthesise... a single esoteric philosophy tinged with an aura of Indian wisdom". Blavatsky claimed to have seen a book of magic in a Himalayan monastery whose wisdom she relayed. Detractors soon identified the various modern books she had cribbed for her alleged mystical vision, but the Theosophical Society she founded became a respectable political movement in India, playing an important role in the independence movement. In the end it did not matter whether Blavatsky's ideas made sense.

Many would say much the same about Brown's novels. His secret masters of the world may be a myth, but imagining they exist can make for an enjoyable reading experience. Like Blavatsky, Brown can pick his themes from the mass of esoteric literature already extant, and his success has led to a renewed surge of the sort of "parasitic" book Katz despises.

The Occult Tradition is of a different order, demonstrating how ideas can lodge themselves in public consciousness and stay there for hundreds or even thousands of years, regardless of whether they ever had any basis in fact. The book's only flaw is that it is too short to cover such a vast field in adequate depth; but for people seeking a sane, authoritative and entertaining guide to the intriguing world of fringe beliefs, this is an excellent starting point.