The Music Of The Primes by Marcus du Sautoy

The Music Of The Primes by Marcus du Sautoy is not a book for the faint-hearted. The author may be a populariser of mathematics, but certainly in this book there is plenty of substance that would maintain the interest of the specialist and also enough technicality to cause the general reader to pause. The book is a brilliant piece of work, however, so all must resist any temptation to skip. The Music Of The Primes is a glittering account, superbly paced, of an unfinished story.

From the very first page it demands to be read, so much so that like me you will probably finish it in two sittings at most. Marcus du Sautoy regularly refers to prime numbers as the atoms of our number system. I have some reservations with this metaphor, but I was willing to live with it. For the uninitiated, a prime number has just two factors, one and itself. It cannot be exactly divided by anything else. The list begins 2, 3, 5, 7, 11, 13 and continues ad infinitum. The sieve of Eratosthenes established that fact a couple of thousand years ago. But, despite many lifetimes of trying, we have never successfully been able to predict whether a particular number would be prime, or conversely, exactly where the next prime number might be. They seem to be distributed randomly throughout our number system, all odd except for that initial 2, the odd-one-out pair that spoils it for every other even. 

 The Music Of The Primes relates how mathematicians have closed in on the mystery of how these numbers occur without, as yet, managing to crack the complete code. Marcus du Sautoy describes some of the great contributions to the understanding of prime numbers. The names Fermat, Gauss and Euler figure regularly. But it is the great name of Riemann that emerges as the lynchpin of this story, his Conjecture being the unsolved problem that currently occupies many a brain, the one million dollars in prize money offered for its solution oiling the machinations. 

Riemann turned the search for prime numbers on its head when he used complex numbers to reposition the problem. Complex numbers, by the way, are at least in part imaginary and, though they don’t exist, no self-supporting bridge would stand up without them. His now famous Conjecture was that evidence of the existence of prime numbers would line up in a predictable way in a four-dimensional space created when one two-dimensional complex number was plotted against another, the latter being the solution to a particular power series called a zeta function equated to zero. His problem was that he couldn’t prove that things lined up in precisely the way he predicted. He had strong hunches that he was right, but, lacking proof, a conjecture is what it remained. And people have been trying to prove it for a century and a half. 

 Prime numbers are now big business, of course. Public-private key encryption now oils the wheels of internet commerce and the security it offers is based on the possession of quite huge, quite astronomically large prime numbers. Find a few new ones and you could make a very good living. If you want to taste the complexity of the task, then spend no more than five minutes finding the two tree-digit factors of 8051. Imagine then the work involved in identifying two 200 digit prime numbers that combine to a Rivest, Shamir and Adelman security key. Reading this superb book will provide further insight. It will also illustrate very well the value of pure research conducted by specialist academics. 

When the accountants complain that programmes have no apparent immediate application, it is worth remembering how advances in human knowledge made over two hundred years ago are only just finding wide application in fields completely unenvisaged by their inventors. Without the knowledge they developed in their apparent vacuum, of course, the modern-day application may never have been conceived. Just imagine where the human race might be two centuries from now if Kurt Gödel’s ideas have become the basis for all mathematics. Read this book and then imagine.

Deterring Democracy by Noam Chomsky

It is almost twenty years since Noam Chomsky published Deterring Democracy. Its contemporary context is an important starting point in the understanding of its position since most of the material seeks to analyse and contextualise United States foreign policy in the post-War years to the early nineties. In 1991 the United States under George Bush was embroiled in the First Gulf War. I must stress the word “first”, since this gives a clue to the book’s eventual prescience.

Also in 1991, a dim and distant past when the new millennium was not yet a talking point, a bi-polar world, whose permanence and assumed conflict provided the framework for all political analysis, was already being transformed. The Soviet Union had already ceased to be, but the years of Yeltsin’s IMF poverty lay ahead, as did those of Putin’s new pragmatic if demagogic prosperity.

Regimes of all political stances came and went in Central and South America. But all of them were classified as good or evil by the Manichean filter of the age. Occasionally, a convenience of political pragmatism offered re-branding, as in the case of Jamaica, where Michael Manley, a leader once undermined as a leftist was reinstated with eternal backing after Edward Seaga’s neo-liberal experiment predictably burnt out. Chomsky’s record of Manley’s second era being that of his violin phase is extremely succinct. He was put up by the left, but played by the right.

Descriptions of prevailing issues in Nicaragua, El Salvador and Guatemala figure large, of course. But Chomsky also visits the Dominican Republic, the Philippines and Europe to illustrate his central point. And it is a point that he makes and re-makes, a point that he still makes today. His analysis, simply put, is that an alliance of elite interests involving legislators, the powerful and those who own and control big business drives the US foreign policy agenda. The elite’s sole aim is to preserve and further its own power, influence and prosperity. The fact that it does not always speak with a consistent voice is merely evidence that within the group there remains competition. Indeed, the group is neither particularly stable nor permanent. It is rather a loose alliance of interest, perhaps heavily reliant on birthright, but not determined by it. Notions of freedom, democracy, individual or collective rights and even development are peddled, attached like advertisers’ catchlines to the same product every time it is recommended. To maintain its ascendancy, this ideology that fosters profit via power needs an enemy to provide a shield behind which it can hide its pursuit of self-advancement. The Soviet Union sufficed for most of the second half of the last century, but since then others have had to be identified to fulfil this essential role. It will not require much imagination to identify the current dark threats.

The population at large, meanwhile, has to be sold these ideas. When threat of nuclear war between super-powers loomed large, it was not difficult to fix the framework. How much easier is it now, when the current all-powerful, all-pervading enemy might just be within and among us? This low-intensity, back-burner threat continues to mask the activity that fuels an ever-increasing concentration of power and wealth. The people of the democratic, individualistic West are perfectly willing to stand by as recession bites, banks declare deposits worthless, pension funds dwindle, retirements recede and wages stagnate while those who perhaps cause these strictures luxuriate in ever-increasing, often self-granted rewards.

And, in a truly prescient passage, Chomsky describes this submissive, passive mentality perfectly. “For submissiveness to become a reliable trait,” he writes, “it must be entrenched in every realm. The public are to be observers, not participants, consumers of ideology as well as products. Eduardo Galeano writes that ‘the majority must resign itself to the consumption of fantasy. Illusions of wealth are sold to the poor, illusions of freedom to the oppressed, dreams of victory to the defeated and power to the weak.’ Nothing less will do.” In this context, is it any surprise that the average contemporary consumer knows more of celebrity gossip than political option?

Deterring Democracy is packed – perhaps over-packed – with detailed evidence. Chomsky makes his point repeatedly and forcefully. I was once privileged to co-host the author as chair of a London conference. At first hand I can vouch for the sincerity and passion that underpins these views. I can also vouch for the solidity of the evidence upon which they are based.

Noam Chomsky is not anti-American. It is the exploiters of self-seeking power and self-deferential influence who deserve that label. Noam Chomsky is a man of the people, intensely humanistic and fundamentally democratic. He seems to maintain that if people turn their backs and refuse to acknowledge the obvious, they will have foregone a real opportunity to realise something more sustainable than the current illusion. And, along the way, they will probably have said goodbye to their principles, along with their bank deposits, pensions, retirement and freedom. At least they can talk about their woes on their latest-model mobiles, if, that is, they can still pay the bill. When you read Noam Chomsky’s Deterring Democracy, give its arguments a chance to register. Then see if they ring true.

The Child In Time by Ian McEwan

Stephen Lawes appears to be pretty well-heeled. His successes seem remarkable. He is a successful writer of children’s books. He is acquainted with Charles Darke, who is apparently being groomed for a ministerial position in government. Via this connection, Stephen also sits on a Whitehall committee to examine policy options on childhood, children, education and related issues. He himself also seems to have the prime minister’s ear. He has a wife, Julie, who loves him and beautiful little three-year-old daughter, Kate, whom he worships. But then one day Kate is no longer there. On a trip to the shops with her father, there are events that take her out of her parents’ lives.

In her absence, Stephen continues to worship her, to see her walking along the street, in a school playground, perhaps everywhere he tries to look. Meanwhile life goes on, but for Stephen aspects of it begin to disintegrate. The child has stopped his time. There follows, in Ian McEwan’s novel, The Child In Time, an examination of childhood. 

In various guises, this biologically-fixed but socially-defined state is seen to influence and control the lives of the book’s characters. The fact that children are sexually and physically immature human beings whose characteristics are still developing seems pretty immutable. But what is it that demands they should eat special foods from special menus? Is it essential that the experience of childhood should be always multi-coloured, perhaps as a preparation for the unending greyness of adulthood? 

And why, in the twenty-first century is it deemed that children should not work, when in the nineteenth it was considered desirable, perhaps even essential for everyone’s greater well-being? If we are stressed in our daily lives, how much of our ability to cope, or not cope, stems from our ability to re-invent a child’s curiosity and enthusiasm, not to mention naiveté? And is this state also perhaps a place of protecting retreat? 

And how exactly did we manage to create this space? The Child In Time examines several strands of thought relating to infancy, childhood and dependency via the assumptions and reactions of adults. It is a novel with multiple parallel strands, more of a meditation on a theme than a focused, linear progression. It always plays with its ideas. But not all of them work. 

Charles Darke’s adoption of a second childhood, whether conscious or not, as a means of protecting himself from himself, is compellingly credible. But the presence of licensed beggars in a society not located in any particular time or any declared political ideology simply doesn’t wash. This science-fiction element of the book asks a sound but imagined question about our attitudes toward childhood, but jars with and detracts from the rest of the book’s recognisable landscape. 

 As ever, Ian McEwan mixes concepts of philosophy and sociology with the minutiae of daily life. Stephen Lawes does not seem to be wholly credible, however. His mix of interests and capabilities seems to be a tad too eclectic, too widely and thinly spread for him to come across as convincing in any discipline. At times, he seems even peripheral, dashing from one event to the next merely to witness what the author wanted to illustrate. But these are small criticisms of a magnificent book. Eventually the novel provides an uplifting experience. 

It takes the reader to places where the characters find themselves, places where they also want to be. Then, having reached their goal, much of what went before falls into new perspectives, and the whole process might just be ready to start again, but this time in socially-changed garb. It’s a bit like life, really... See this book on amazon The Child in Time

The Steps Of The Sun by Caroline Harvey, aka Joanna Trollope

I approached The Steps Of The Sun not knowing what to expect. Its author was listed as Joanna Trollope writing as Caroline Harvey. I had previously read nothing in either name. But it struck me that if you wanted a nom de plume, then Non de Plume was not a good choice. I persevered, however, largely because I have also never read a novel set in the Boer War. The Steps Of The Sun presents life amongst a middle-class set whose lives are turned upside down by the conflict. Matthew Paget is a college lad, son of a churchman, and he is seeking something exciting out of life. His passions sometimes take him that step too far. He enlists to fight in South Africa without his family’s backing or even knowledge. Will Marriott, his cousin, is a military type and also thinks that way to boot. He performs his duty when required and is proud to represent his country in battle. Hendon Bashford is the obvious cad. He’s half Boer but considers himself true-blood English. His contribution to the conflict will always be against his own people, which ever side he joins. 

There are women in The Steps Of The Sun. Adelaide is the most interesting. She flirts with pacifism, even meets journalists. But then she assists the war in her own way. Matthew’s sister, Frances, tends to the prissy. And then there’s a Boer girl who is twice excused her fate. First her home is not burned down – at least today – and second, apparently unlike all other Boer women, as we are told, she is not pregnant. There are some interesting aspects to the book. A description of the war’s concentration camps is welcome, as is Adelaide’s conflict of interest. But overall what promised to be an intriguing read tended to gloss over the military, fragment the history and barely visit the country. The Steps Of The Sun was still worth reading, but its high points were quite well buried.

Arabia by Jonathan Raban

At the end of the seventies Jonathan Raban wandered across the Middle East. Arabia was the book he wrote after impressionistic visits to Bahrain, Qatar, Abu Dhabi, Dubai, Yemen, Egypt, Jordan and, briefly, Lebanon. Paradoxically, the book starts and finishes in London, because it was there that questions about Arab identity and culture arose in the author’s mind. 

 In Earls Court the author muses on the question, “Who are the Arabs?” At the time in common prejudice they had a reputation for association with terrorism, being fundamentally religious and having uncountable wealth. So it seems that times have not changed that much… So Jonathan Raban resolved to find out for himself. Unlike most authors of travelogues, however, Jonathan Raban saw his first task as learning the language and, as a result of this laudable approach, Arabia is perhaps more of an achievement than it otherwise might have been. 

In a nutshell, he found Bahrain seedy and Qatar rich but built in a scrap-yard. Abu Dhabi was new and squeaky clean, eager to impress, while Dubai seemed to be populated by business sharks, opportunistic, pragmatic but obsessively driven and eager to excel. All Yemenis appeared to be overactive dwarves on a spending spree. Egypt was big and scruffy, and Jordan was like Switzerland with parties.

You will gather immediately that Arabia is not an in-depth study of Arab culture, society or indeed anything else. Its pages are heavily populated with stories of expatriates, the sort of people who might be eager to talk over a drink in a bar. Though he quotes Thesiger, Jonathan Raban seems to have neither the inclination nor the means to follow the explorer into the desert. This is not a criticism. He also quotes Alice, but does not venture into wonderland. But there again, perhaps he does precisely that, especially in Abu Dhabi. 

Thirty years later, a casual visitor to the places Jonathan Raban frequented might have similar impressions, except the places and the associated reactions would all be much bigger. Bahrain’s planned causeway was built and at weekends there are even more Saudis doing what Saudis do at weekends. Abu Dhabi is vastly more splendid, and Dubai is still trying to be the tallest, biggest, the best in something measurable and sellable.

Jordan may well be significantly poorer than the country Jonathan Raban found. It seems he may have found it difficult to escape the swish diplomatic and international resident areas, and he never made it to Wadi Rum or Petra, so didn’t even have a tourist experience to relate. I have never been to Yemen or Egypt, so I cannot comment on them. One thing that always comes across in Jonathan Raban’s work is a willingness to engage with people, very often over a whisky! And, though Arabia might only make a very light scratch across the surface of its subject, its focus on individual vignettes makes it a highly entertaining and engaging read. The region is no doubt still host to many others like them. 

The book is also mildly informative. And, on a weekend where debates rage on the proposed construction of a mosque in New York, it is interesting to reflect how little attitudes towards the book’s subject seem to have changed.

Solar by Ian McEwan

Usually – if such a word can be applied to rare events – Nobel Laureates are recognised towards the end of a lifetime’s achievement. The true significance of work has to be established before it can be recognised. Michael Beard, modifier of Einstein’s photovoltaics, producer of the Beard-Einstein Conflation, or should that have been the Einstein-Beard Conflation, seemed to receive his ultimate recognition a tad early in life. Surely it would have been the proposed grand application of his work that swayed the judges rather than the mere realisation of theory. So if there is to be a criticism of Ian McEwan’s novel, Solar, it is precisely this. 

But then Michael Beard always was a precocious winner, after coming first in a beautiful baby award. So there. This is my only criticism of Solar. I thought that Ian McEwan would never write anything to challenge the intensity, complexity, ease of expression and irony of Saturday. But Solar achieves all of this and much more.

In his professional life, Michael Beard is a scientist, a physicist with an interest in light. Energy becomes his focus and, via his photovoltaic conflation, he begins to address energy production for a warming planet. Or does he? Does he receive rather than initiate? And does he acknowledge? Both meticulous and precise in his professional guise, Michael Beard is a sybaritic, lecherous slob in the private domain. 

We meet him first upon his fifth wife, Patrice. With her he has at last found happiness – at least when they are together. Periods apart find him pursuing anything available before or after a half a bottle of Scotch. Unknown to him, Patrice is doing precisely the same, but remaining sober. From Michael Beard’s conventionally misogynist standpoint, this seems unfair and he calls foul. Aldous is just the sort of bloke that – all things being equal (which of course they are not!) – Michael Beard would both ignore and avoid. He’s big, hefty, wears sandals and a pony tail. 

His apparently laid back approach to life is surely anathema to Michael Beard’s internally perceived order. After all, didn’t a youthful Beard sport a jacket and tie with pens in the top pocket right through the 1960s? How times change, he might reflect, on pushing aside a pile of unwashed dishes mixed with general detritus in his London flat. But besides threatening, Aldous is also brilliant. He is a young post-doc recruited to assist Michael’s research. 

And then there’s Tarpin, a builder decidedly not of the same social class as the venerable academic. Things come together at the end of the book’s first part. Suffice it to say that Michael Beard’s involuntary circumcision at the hands of frost while taking a leak somewhere near Spitzbergen might just have been Mother Nature getting her own back, her feminist equaliser before the stronger opposition has even scored. Unfortunately for Michael Beard, however, his tendency to spread himself too thinly provokes the termination of his Government-sponsored energy research. The director, Braby, sacks him, an act that injures pride. Michael internalises the rejection not as a failure but as an opportunity, given his multiple avenues of interest. How can it offend him? He’s won a Nobel Prize. Can’t he do precisely what he wants, even beyond criticism? 

 Beard is confronted with alternative views of both life and the universe. Everything follows. Later he is apparently committed to just one woman, Melissa, but without marriage, mutually-agreed. But he is constantly pulled elsewhere. His logical-positivist assumptions are questioned, both at home and abroad. People can lie, deconstruct, reconstruct. So can he. The only consistency in his personal life is its inconsistency, constantly inconsistent. But his professional assumptions are questioned by social constructivism, by phenomenological attack on the universality he assumes. The consequence is an irrational but wholly real reconstruction of a reality he thought he had both defined and described. His method of coping is enigmatic and inventive, but its public expression is totally uncontrolled, misconceived. 

 Michael’s research points to a breakthrough in energy production. He can split water using sunlight and catalysts that promote artificial photosynthesis. He can truly harness the sun. Perhaps it vies for the centre of his universe. The results can burn carbon-free to power the world. His new daughter calls him a saviour. But his business brain shares his scientific nodes. He has patents. He hires Hammer to deal with detail, a task he accomplishes supremely until just before the scheduled switch on of the prototype in the New Mexico desert. 

The rest is history. Solar presents a multiplicity of themes. But I think its main plank is an age-old conundrum. In an address presenting the Nobel Prize to Beard, a professor refers to Feynman’s illustration of the elegance of Beard’s Conflation. Tangled, knotted strings that dancers further complicate can, under the right conditions, with the right foresight, fall to a simple untangled simplicity with a single tug. Thus Beard had taken a knotted intellectual theory and let it fall free of its complications. In his private life, however, Beard truly found complication. What was simple he knotted by quirk, by over-indulgence, by ill-discipline and by visceral opportunity. 

If the beautiful but independently-minded Melissa was temporarily unavailable across an ocean that provided the vacuum, then the fiftyish, flabby Darlene, a waitress in a New Mexico diner, provided the pressure. But she took her temporary role seriously, an attitude that Michael Beard never expected. No matter how complicated our lives become, no matter how intertwined, no matter how independently we present identity, career, research or discovery, ultimately they all reduce to a simple cocktail of body fluids, desires – usually only partly fulfilled - and ultimately a resort to self-preservation, a fundamental state that can be obscured by our relentless pursuit of receding detail. 

Thus Ian McEwan presents a contrast between potentially enduring rationality that seeks out permanence and base, immediate desire driven by instincts we cannot even recognise, let alone control. At the last, it is illusory permanence that presents the true delusion. And what about constancy and the enduringly rational? Ask me tomorrow. See this book on amazon Solar

Tree by F Sionil José

Having just re-read Ngugi’s A Grain Of Wheat, I decided to visit Frankie Sionil José’s novel Tree. Ngugi described a struggle for freedom that succeeded. The perspective he chose was that of poor people caught up in events. Francisco Sionil José, on the other hand, describes the aftermath of a national struggle that failed, and from the point of view of the middle classes who may even have benefited from the USA’s initially opportunist snatch of victory from the nationalists. 

In the Philippines, the struggle was against Spain, and it was won. But then Spain collapsed and the USA intervened and a new war had to be won. From the point of view of Filipinos, perhaps it was lost. Four hundred years in a convent followed by fifty in Hollywood is how Filipinos often sum up their history. 

In its own way, Francisco Sionil José attempts a description of that history via his sequence of Rosales novels. Tree covers the period from the 1930s to the 1950s, and follows the growth of its main character from a child to a freshman medical student. It describes the Philippines from Commonwealth to independence. Crucially, when the latter arrives, it is hardly celebrated. The social order has long since been cemented and our family in Rosales are on the landowners’ side. Independence brings the Huk rebellion and a dangerous challenge to their status. 

 Tree is a novel that is not strong on plot. It is almost possible to read its chapters as a series of short stories, portraits of the people and events that filled its narrator’s life. In concept, the Rosales novels have something – only something, I stress! – in common with Anthony Powell’s Dance To The Music Of Time. They bear witness, but only rarely interpret. In the centre of Rosales, a small town in Pangasinan, north of Manila, is a large, old and rambling balete tree. It seems to be indestructible. Even when an American soldier with an excavator runs into it, the tree survives. The excavator is ruined – the hardware, not the person – and hangs around until locals cut it up for scrap. Now there’s a comment on the USA’s legacy in the Philippines. Spain’s colonial legacy survives in the form of vocabulary, names of dishes and of people. 

What’s in a name? The answer is a culture – a landowner versus a peasant, a Catholic versus an Aglipayan, not to mention a new-fangled follower of Iglesia Ni Kristo. Tree, essentially, is an impressionistic picture of a small society. There are hints at conflict, suggestions of the unrealised, usually centred on lack of rights to land, to produce, to opportunity. In microcosm, Tree suggests what the Philippines might have been, but never achieved. Crucially, had it done so, its main character would probably never have the chance of entering medical school. It is also important to note that beneath the balete tree nothing grows. Now most tropical earth stays blank when it is denied light. In Tree, F. Sionil José uses this image to suggest that, left to its own device, maybe the Philippines might have prospered – but then maybe not. After all, the tree was indigenous. 

Tree is a novel replete with cultural experience mixed with personal reference. Its lack of linear plot has to be accepted and not criticised. It’s just not that kind of book. And, as with most things Filipino, there’s much more going on under the surface, despite the fact that under the tree there’s nothing but bare earth. View this book on amazon Tree