Ian Stewart's top 10 popular mathematics books

Ian Stewart is an Emeritus Professor of Mathematics at Warwick University and a Fellow of the Royal Society. He has written over 80 books, mainly popular mathematics, and has won three gold medals for his work on the public understanding of science. In collaboration with Terry Pratchett and Jack Cohen he wrote the Science of Discworld series. His new book, 17 Equations That Changed the World, is published by Profile.

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"'Popular mathematics' may sound like a contradiction in terms. That's what makes the genre so important: we have to change that perception. Mathematics is the Cinderella science: undervalued, underestimated, and misunderstood. Yet it has been one of the main driving forces behind human society for at least three millennia, it powers all of today's technology, and it underpins almost every aspect of our daily lives.
"It's not really surprising that few outside the subject appreciate it, though. School mathematics is so focused on getting the right answer and passing the exam that there is seldom an opportunity to find out what it's all for. The hard core of real mathematics is extremely difficult, and it takes six or seven years to train a research mathematician after they leave school. Popular mathematics provides an entry route for non-specialists. It allows them to appreciate where mathematics came from, who created it, what it's good for, and where it's going, without getting tangled up in the technicalities. It's like listening to music instead of composing it.
"There are many ways to make real mathematics accessible. Its history reveals the subject as a human activity and gives a feel for the broad flow of ideas over the centuries. Biographies of great mathematicians tell us what it's like to work at the frontiers of human knowledge. The great problems, the ones that hit the news media when they are finally solved after centuries of effort, are always fascinating. So are the unsolved ones and the latest hot research areas. The myriad applications of mathematics, from medicine to the iPad, are an almost inexhaustible source of inspiration."

1. The Man Who Knew Infinity by Robert Kanigel

The self-taught Indian genius Srinivasa Ramanujan had a flair for strange and beautiful formulas, so unusual that mathematicians are still coming to grips with their true meaning. He was born into a poor Brahmin family in 1887 and was pursuing original research in his teens. In 1912, he was brought to work at Cambridge. He died of malnutrition and other unknown causes in 1920, leaving a rich legacy that is still not fully understood. There has never been another mathematical life story like it: absolutely riveting.

2. Gödel, Escher, Bach by Douglas Hofstadter

One of the great cult books, a very original take on the logical paradoxes associated with self-reference, such as "this statement is false". Hofstadter combines the mathematical logic of Kurt Gödel, who proved that some questions in arithmetic can never be answered, with the etchings of Maurits Escher and the music of Bach. Frequent dramatic dialogues between Lewis Carroll's characters Achilles and the Tortoise motivate key topics in a highly original manner, along with their friend Crab who invents the tortoise-chomping record player. DNA and computers get extensive treatment too.

3. The Colossal Book of Mathematics by Martin Gardner

In his long-running Mathematical Games column in Scientific American, Gardner – a journalist with no mathematical training – created the field of recreational mathematics. On the surface his columns were about puzzles and games, but they all concealed mathematical principles, some simple, some surprisingly deep. He combined a playful and clear approach to his subject with a well-developed taste for what was mathematically significant. The book consists of numerous selections from his columns, classified according to the mathematical area involved. Learn how to make a hexaflexagon and why playing Brussels sprouts is a waste of time.

4. Euclid in the Rainforest by Joseph Mazur

A thoroughly readable account of the meaning of truth in mathematics, presented through a series of quirky adventures in the Greek Islands, the jungles around the Orinoco River, and elsewhere. Examines tricky concepts like infinity, topology, and probability through tall tales and anecdotes. Three different kinds of truth are examined: formal classical logic, the role of the infinite, and inference by plausible reasoning. The story of the student who believed nothing except his calculator is an object lesson for everyone who thinks mathematics is just 'sums'.

5. Four Colours Suffice by Robin Wilson

In 1852 Francis Guthrie, a young South African mathematician, was attempting to colour the counties in a map of England. Guthrie discovered that he needed only four different colours to ensure that any two adjacent counties had different colours. After some experimentation he convinced himself that the same goes for any map whatsoever. This is the remarkable story of how mathematicians eventually proved he was right, but only with the aid of computers, bringing into question the meaning of "proof". It contains enough detail to be satisfying, but remains accessible and informative throughout.

6. What is Mathematics Really? by Reuben Hersh

The classic text What is Mathematics? by Richard Courant and Herbert Robbins focused on the subject's nuts and bolts. It answered its title question by example. Hersh takes a more philosophical view, based on his experience as a professional mathematician. The common working philosophy of most mathematicians is a kind of vague Platonism: mathematical concepts have some sort of independent existence in some ideal world. Although this is what it feels like to insiders, Hersh argues that mathematics is a collective human construct – like money or the Supreme Court. However, it is a construct constrained by its own internal logic; it's not arbitrary. You choose the concepts that interest you, but you don't get to choose how they behave.

7. Magical Mathematics by Persi Diaconis and Ron Graham

Both authors are top-rank mathematicians with years of stage performances behind them, and their speciality is mathematical magic. They show how mathematics relates to juggling and reveal the secrets behind some amazing card tricks. Here's one. The magician mails a pack of cards to anyone, asking them to shuffle it and choose a card. Then he shuffles the cards again, and mails half of them to the magician—not saying whether the chosen card is included. By return mail, the magician names the selected card. No trickery: it all depends on the mathematics of shuffles.

8. Games of Life by Karl Sigmund

Biologists' understanding of many vital features of the living world, such as sex and survival, depends on the theory of evolution. One of the basic theoretical tools here is the mathematics of game theory, in which several players compete by choosing from a list of possible strategies. The children's game of rock-paper-scissors is a good example. The book illuminates such questions as how genes spread through a population and the evolution of cooperation, by finding the best strategies for games such as cat and mouse, the battle of the sexes, and the prisoner's dilemma. On the borderline between popular science and an academic text, but eminently readable without specialist knowledge.

9. Mathenauts: Tales of Mathematical Wonder edited by Rudy Rucker

A collection of 23 science fiction short stories, each of which centres on mathematics. Two are by Martin Gardner, and many of the great writers of SF are represented: Isaac Asimov, Gregory Benford, Larry Niven, Frederik Pohl. The high point is Norman Kagan's utterly hilarious "The Mathenauts", in which only mathematicians can travel through space, because space is mathematical – and, conversely, anything mathematical can be reality. An isomorphomechanism is essential equipment. Between them, these tales cover most of the undergraduate mathematics syllabus, though not in examinable form.

10. The Mathematical Principles of Natural Philosophy by Isaac Newton

There ought to be a great classic in this top 10, and there is none greater. I've put it last because it's not popularisation in the strict sense. However, it slips in because it communicated to the world one of the very greatest ideas of all time: Nature has laws, and they can be expressed in the language of mathematics. Using nothing more complicated than Euclid's geometry, Newton developed his laws of motion and gravity, applying them to the motion of the planets and strange wobbles in the position of the Moon. He famously said that he "stood on the shoulders of giants", and so he did, but this book set the scientific world alight. As John Maynard Keyes wrote, Newton was a transitional figure of immense stature: "the last of the magicians … the last wonderchild to whom the Magi could do sincere and appropriate homage." No mathematical book has had more impact.

• © 2012 Guardian News and Media Limited or its affiliated companies. All rights reserved.

Learning batting from David Warner

Ed Smith

On Sunday, I fly to Adelaide for the fourth Test between India and Australia. I'm due to arrive just in time for the first ball. I hope the plane isn't late: David Warner might have scored a hundred by lunch.

In smashing 180 off 159 balls in Perth, Warner proved quite a few people wrong - not least those who said that Twenty20 would never produce a Test cricketer. Warner, of course, played T20 for Australia and in the IPL long before making the step-up to Test cricket - well, I suppose it's up to him to judge whether it's a step up. 

We've all heard the arguments against the Warner career path: that T20 ruins technique rather than developing it, that you have to learn to bat properly before you can learn to smash it, walk before you can run etc.

But the naysayers may be wrong. The Warner story reveals deep truths about how players bat at their best. In fact, I think it is time we reconsidered the whole question of what constitutes good technique.

Cricket gets itself in a tangle about the word. In football, technique is short-hand for skill. Pundits explain how Cesc Fabregas' brilliant technique allows him to make the killer pass or eye-catching volley. Technique is not the enemy of flair and self-expression: it is the necessary pre-requisite. "Technique is freedom," argued the ballet dancer Vaslav Nijinsky.

Sadly, the word "technique" in cricket is often used as short-hand for controlled batsmanship, even introspection. It is true that some great technicians are very controlled players (think of Rahul Dravid - though even he plays best technically when he is positive). But it is not compulsory that good technique has to be accompanied by caution or repression. After all, Adam Gilchrist had a wonderful technique: there is no other explanation for how he managed to hit the ball in the middle of the bat quite so consistently.

In fact, good technique has a very straightforward definition: it is the simplest, most efficient way of doing something.

Andre Agassi had near-perfect technique on his groundstrokes. He could hit with exceptional power and consistency. How did he learn this technique? When Agassi was a boy, his father used to get him to hit thousands of tennis balls as hard and as cleanly as possible. "Hit it, Andre!" That was the essence of his coaching. If you learn how to hit the ball hard in the middle of the racket, you have to move your body and feet into the right positions to do so. In the same way, Jack Nicklaus summed up his approach to learning golf: "First, hit it hard. Then we'll worry about getting it in the hole."

I should have remembered Agassi and Nicklaus when I was out of form as a batsman and needed to go back to basics. Not only did I suffer prolonged periods of bad form, I would often get out in similar ways - nicking off to the slips, or getting trapped lbw. There were usually plenty of theories about what I was doing wrong. As one coach memorably put it to me, "If you stop getting caught and lbw, you'll be a top player." Er, yes: it would take great ingenuity to get bowled or run out throughout your career!

Many coaches tried to persuade me to change my shot selection. But that rarely helped. When I was nicking off, it was usually because I was driving badly rather than driving at the wrong ball. And I was a far less good player when I was knocked off my instinct to play positively. I came to realise that good form was a very simple issue, almost binary - like a switch that just needed to be clicked back on.

Here comes the difficult part that used to get me into trouble. I learnt that the best way to click the switch back on, to get back into the groove of playing well, was to practise driving on the up. You've probably guessed why it got me in trouble. Imagine a situation in which I had failed three or four times in a row, each time caught in the slips, and the coach walks into the nets and sees me…practising drives! I'd sense him thinking: "Doesn't he ever learn?"

But I knew what worked for me, and I think there are good reasons why it worked. To play at my best, I needed to get into good positions to attack. Why? Because when I was in position to attack, I was inevitably in a good position also to defend. But when I set out my stall to play a defensive shot - before the ball was even bowled - then I not only attacked badly, I also defended badly. Having the intention of defending caused me to be passive and late in my movements. The shot would almost happen to me, rather than me determining the shot.

	To play at my best, I needed to get into good positions to attack. Why? Because when I was in position to attack, I was inevitably in a good position also to defend

On the other hand, having the intention of attacking was a win-win: I defended and attacked better. I would set myself to play positively, which had the effect of giving me more time at every stage of the shot.

I think many players are the same. The key to their batting - whether it is defence or attack - is the question of intent. That has nothing to do with recklessness, or even scoring rate. Intent merely determines the messages you send to your brain. Imagine batting as a series of dominos that culminates in the ball being struck. The very first domino, the critical one that begins the whole process, is not physical, but mental. We might call it your "mental trigger movement".

I know it sounds ridiculously simplistic - technique from kindergarten - but many players find that the best mental trigger movement is setting themselves to move towards the ball to strike it back in the direction that it comes from. That does not mean you commit to lurching onto the front foot or playing a drive; you still react to whatever is thrown at you. But your intent is positive and pro-active.

Greg Chappell used the science of physiology to examine the connection between intent and good execution. He studied the preliminary movements of the world's greatest players. Though they all had unique styles and methods, their techniques shared one common thread: at the point of delivery, they were all pushing off the back foot, looking to come forward. Chappell argued that this trait gives great players optimal time to judge length. Why? Because a full ball is released from the bowler's hand early, a short ball is released later. So when batsmen set themselves for the full ball, they will inevitably have time to adjust for the short ball.

Here is my heretical conclusion: by encouraging them to have the intention of striking down the ground with a proper backlift and swing of the bat, T20 may help batsmen get into some good technical habits. Admittedly, T20 will not develop the refinements of sophisticated Test match batting, such as soft hands and the ability to concentrate for six or seven hours. But in terms of basic technique, there is a lot to be said for keeping cricket as simple as possible. The foundation is positive intent and a clear head. In short, we could all learn something from Warner.

The counter-argument is that Warner is a freak of nature, and that no one should try copying him just yet. Either way, I can't wait to watch him in Adelaide and judge for myself. 

Huaxi: The socialist village where everyone is wealthy

Imagine a place where everyone is entitled to a free home, a free car and free healthcare. Clifford Coonan travelled to Huaxi to find out the secret of its success.

Clifford Coonan

Tuesday, 17 January 2012

The sort of oxen you expect to see in Chinese villages tend to be pulling carts or tilling fields, not a beasts made of a ton of gold. This precious cow is located on the 60th floor of a 328m-tall skyscraper in Huaxi, China's richest village, and building that juts out of the eastern landscape like a giant tripod topped by a golden ball.

Huaxi is a "model socialist village", according to local officials, and was founded by local Communist Party secretary Wu Renbao in 1961. His foresight was to transform a poor farming community into a super wealthy community, built on its clever adaptations of modern agribusiness methods, then its diversification into steel mills, its logistics firms, and its textile businesses.

The commune listed on the stock exchange in 1998 and is now a major corporation in its own right. Its subsidiary companies, built into something that resembles a modern-day conglomerate, exports to more than 40 countries around the world. Huaxi is where Chinese people come to learn how to get rich. At a time when the rest of the world, and indeed much of China, is trying to absorb an economic slowdown, Huaxi is like a parallel universe.

"This cow cost 300 million yuan (£31m), but now it's worth 500 million yuan," says our guide, Tina Yao, as she steers us from floor to floor in the Zengdi Kongzhong New Village Tower, which is taller than anything in London. "Zengdi" translates as "increase the land" and the skyscraper cost three billion yuan (£310m).

Other floors have giant animals of solid silver. Fearsomely bejewelled chandeliers hang over your head in banquet halls that hold thousands of people. You approach these glittering sites walking on gold-leaf marble, passing aquariums with sharks and stingrays.

Far below, you see the villas and theluxury cars. Every villager gets a share of the corporation's profits and is entitled to a car, a house, free healthcare and free cooking oil.

The village feels a little like Dubai. It is not big on charm – the replicas of the Arc de Triomphe and the Sydney Opera House – are of questionable taste, but where it is widely different is in how well it is able to meet its people's needs. Mr Wu is keen that Huaxi should showcase China's achievements and now some two million visitors come to Huaxi every year to gaze upon its splendour.

The original founding families, who are known as "stakeholders", number around 1,600 and the average household income is around £100,000 a year, once all the bonuses, pensions and wages are factored in. White BMWs are ubiquitous and the murals, instead of depicting socialist realist muscled workers in overalls, have pictures of happy families living in wealthy villas.

This is where Huaxi stands apart from so many other villages in China. While the rest of the country suffers from a yawning wealth gap between the rich cities of the eastern seaboard and southern coasts and the rural hamlets, Huaxi took the initiative, driven by Mr Wu's pragmatism, and headed its own way. It behaved like a city, even importing migrant labour.

"We only ever wanted what was good for our people," is a dictum of Mr Wu, who is now 86 years old and retired. His son has taken over as party secretary, but the father still gives lectures on socialism every day. He avoids allying himself too closely with either capitalism or communism, though his pragmatism has strong elements of the Chinese Communist Party about it.

No one doubts the wisdom of Mr Wu, and looking at the village's wealth, why would they? He broke up the collective system of farming and encouraged people to grow their own crops.

Below the stakeholders in the hierarchy come the residents from neighbouring villages that have been absorbed into Huaxi, and then tens of thousands of migrant workers who perform most of the rest of the work.

Work and wealth are the crowning ideologies. No one takes weekend breaks, and the streets tend to be deserted of residents because they are all off working. The hard work has clearly paid off and the money raised has helped the villagers diversify into other industry.

One of those areas is tourism – wealth tourism – and some of the locals help to meet and greet the two million tourists that come every year to see the village.

A new reason to come is to see the skyscraper, which is impressive, although as there is nothing even remotely as tall in the surrounding countryside, it looks strangely incongruous.

The reason it is so tall is a useful insight into the mindset of the people here. It is, as Mr Wu said in a recent interview, because the people Huaxi can compete with anyone in the country. "Beijing's tallest building is the 328m-tall World Trade Centre. Huaxi wants to maintain the same height with the Central Committee of the Communist Party," he said.

The village's total square area is a little less than one square kilometre, and there are barrack-style dormitories, factories, and pagoda style-buildings for local residents. The skyscraper houses the Longxi International Hotel, which has 2,000 beds and will employ 3,000 people eager to learn how to become wealthy, Huaxi-style.

Intriguingly, in the central village park, there are the statutes of five of the true icons of Communism in China, some more controversial than others. The panoply includes the former mayor of Beijing, Liu Shaoqi, who was purged in the period of ideological frenzy that was the Cultural Revolution and whom many believed Mao had murdered. He has never really been rehabilitated and remains outside the pantheon of true revolutionary heroes.

But then Mr Wu himself suffered during the Cultural Revolution. He set up factories but the Red Guards paraded him in the village as a "capitalist roader" and locked him up, much in the same way as Liu Shaoqi. Like Deng Xiaoping, who also suffered during the Cultural Revolution, Mr Wu bided his time and soon was back on his capitalist track after Mao died in 1976, except that these ideas became formulated as socialism with Chinese characteristics.

All over the village are megaphones blasting out the village anthem, which tells of how communist skies shine down Huaxi, a village of everyday miracles. "I have heard about Huaxi for many years. I have wanted to see it for many years," said one octogenarian visitor from Chengzhou.

Two men, both of them employed in security and not stakeholders in the village, say they love what is going on in Huaxi, but they admit they are a bit jealous of the shareholders who get a stake in the village's profits every year.

Certainly, there is a lot of bluster in the way Huaxi markets itself. The divisions between the stakeholders and the migrants on the streets are large. But no one in China doubts its importance as a model for the success of the nation. And deny at your peril the wisdom of Mr Wu and of the wider Chinese psyche: The song from the public address system says it proud: "Socialism is best."

Don't blame the ratings agencies for the eurozone turmoil

Europe and the eurozone are strangling themselves with a toxic mixture of austerity and a structurally flawed financial system

• 
• • Ha-Joon Chang
  • guardian.co.uk, Sunday 15 January 2012 21.16 GMT

Standard & Poor's has decided to downgrade France's top-notch credit rating. Photograph: Philippe Huguen/AFP/Getty Images

 

Even the most rational Europeans must now feel that Friday the 13th is an unlucky day after all. On that day last week, the Greek debt restructuring negotiation broke down, with many bondholders refusing to join the voluntary 50% "haircut" – that is, debt write-off – scheme, agreed last summer. While the negotiation may resume, this has dramatically increased the chance of disorderly Greek default.

Later in the day, Standard & Poor's, one of the big three credit ratings agencies, downgraded nine of the 17 eurozone economies. As a result, Portugal pulled off the hat-trick of getting a "junk" rating by all of the big three, while France was deprived of its coveted AAA rating. With Germany left as the only AAA-rated large economy backing the eurozone rescue fund (the Dutch economy, the second biggest AAA economy left, is much smaller than the French economy) the eurozone crisis looks that much more difficult to handle.

The eurozone countries criticise S&P, and other ratings agencies, for unjustly downgrading their economies. France is particularly upset that it was downgraded while Britain has kept its AAA status, hinting at an Anglo-American conspiracy against France. But this does not wash, as one of the big three, Fitch, is 80% owned by a French company.

Nevertheless, France has some grounds to be aggrieved, as it is doing better on many economic indicators, including budget deficit, than Britain. And given the incompetence and cynicism of the big three exposed by the 1997 Asian financial crisis and more dramatically by the 2008 global financial crisis, there are good grounds for doubting their judgments.

However, the eurozone countries need to realise that its Friday-the-13th misfortune was in no small part their own doing.

First of all, the downgrading owes a lot to the austerity-driven downward adjustments that the core eurozone countries, especially Germany, have imposed upon the periphery economies. As the ratings agencies themselves have often – albeit inconsistently – pointed out, austerity reduces economic growth, which then diminishes the growth of tax revenue, making the budget deficit problem more intractable. The resulting financial turmoil drags even the healthier economies down, which is what we have just seen.

Even the breakdown in the Greek debt negotiation is partly due to past eurozone policy action. In the euro crisis talks last autumn, France took the lead in shooting down the German proposal that the holders of sovereign debts be forced to accept haircuts in a crisis. Having thus delegitimised the very idea of compulsory debt restructuring, the eurozone countries should not be surprised that many holders of Greek government papers are refusing to join a voluntary one.

On top of that, the eurozone countries need to understand why the ratings agencies keep returning to haunt them. Last autumn's EU proposal to strengthen regulation on the ratings industry shows that the eurozone policymakers think the main problem with the ratings industry is lack of competition and transparency. However, the undue influence of the agencies owes a lot more to the very nature of the financial system that the European (and other) policymakers have let evolve in the last couple of decades.

First, over this period they have installed a financial regulatory structure that is highly dependent on the credit ratings agencies. So we measure the capital bases of financial institutions, which determine their abilities to lend, by weighting the assets they own by their respective credit ratings. We also demand that certain financial institutions (eg pension funds, insurance companies) cannot own assets with below a certain minimum credit rating. All well intentioned, but it is no big surprise that such regulatory structure makes the ratings agencies highly influential.

The Americans have actually cottoned on this problem and made the regulatory system less dependent on credit ratings in the Dodd-Frank Act, but the European regulators have failed to do the same. It is no good complaining that ratings agencies are too powerful while keeping in place all those regulations that make them so.

Most fundamentally, and this is what the Americans as well as the Europeans fail to see, the increasingly long-distance and complex nature of our financial system has increased our dependence on ratings agencies.

In the old days, few bothered to engage a credit ratings agency because they dealt with what they knew. Banks lent to companies that they knew or to local households, whose behaviours they could easily understand, even if they did not know them individually. Most people bought financial products from companies and governments of their own countries in their own currencies. However, with greater deregulation of finance, people are increasingly buying and selling financial products issued by companies and countries that they do not really understand. To make it worse, those products are often complex, composite ones created through financial engineering. As a result, we have become increasingly dependent on someone else – that is, the ratings agencies – to tell us how risky our financial actions are.

This means that, unless we simplify the system and structurally reduce the need for the ratings agencies, our dependence on them will persist – if somewhat reduced – even if we make financial regulation less dependent on credit ratings.

The eurozone, and more broadly Europe, is slowly strangling itself with a toxic mixture of austerity and a structurally flawed financial system. Without a radical rethink on the issues of budget deficit, sovereign bankruptcy and financial reform, the continent is doomed to a prolonged period of turmoil and stagnation.

• © 2012 Guardian News and Media Limited or its affiliated companies. All rights reserved.

Indian students rank 2nd last in global test

15 Jan, 2012, 02.37AM IST, Hemali Chhapia,TNN

MUMBAI: Across the world, India is seen as an education powerhouse - based largely on the reputation of a few islands of academic excellence such as the IITs. But scratch the glossy surface of our education system and the picture turns seriously bleak.

Fifteen-year-old Indians who were put, for the first time, on a global stage stood second to last, only beating Kyrgyzstan when tested on their reading, math and science abilities.

India ranked second last among the 73 countries that participated in the Programme for International Student Assessment (PISA), conducted annually to evaluate education systems worldwide by the OECD (Organisation for Economic Co-operation and Development) Secretariat. The survey is based on two-hour tests that half a million students are put through.

China's Shanghai province, which participated in PISA for the first time, scored the highest in reading. It also topped the charts in mathematics and science.

"More than one-quarter of Shanghai's 15 year olds demonstrated advanced mathematical thinking skills to solve complex problems, compared to an OECD average of just 3%," noted the analysis.

The states of Tamil Nadu and Himachal Pradesh, showpieces for education and development, were selected by the central government to participate in PISA, but their test results were damning.

15-yr-old Indians 200 points behind global topper

Tamil Nadu and Himachal, showpieces of India's education and development, fared miserably at the Programme for International Student Asssment, conducted by the Organisation for Economic Co-operation and Development Secretariat.

An analysis of the performance of the two states showed:

In math, considered India's strong point, they finished second and third to last, beating only Kyrgyzstan

When the Indian students were asked to read English text, again Tamil Nadu and Himachal Pradesh were better than only Kyrgyzstan. Girls were better than boys

The science results were the worst. Himachal Pradesh stood last, this time behind Kyrgyzstan. Tamil Nadu was slightly better and finished third from the bottom

The average 15-year-old Indian is over 200 points behind the global topper. Comparing scores, experts estimate that an Indian eighth grader is at the level of a South Korean third grader in math abilities or a second-year student from Shanghai when it comes to reading skills.

The report said: "In Himachal, 11% of students are estimated to have a proficiency in reading literacy that is at or above the baseline level needed to participate effectively and productively in life. It follows that 89% of students in Himachal are estimated to be below that baseline level."

Clearly, India will have to ramp up its efforts and get serious about what goes on in its schools. "Better educational outcomes are a strong predictor for future economic growth," OECD secretary-general Angel Gurria told The Times of India.

"While national income and educational achievement are still related, PISA shows that two countries with similar levels of prosperity can produce very different results. This shows that an image of a world divided neatly into rich and well-educated countries and poor and badly-educated countries is now out of date."

In case of scientific literacy levels in TN, students were estimated to have a mean score that was below the means of all OECD countries, but better than Himachal. Experts are unsure if selecting these two states was a good idea.

Shaheen Mistry, CEO of Teach For India programme, said, "I am glad that now there is data that lets people know how far we still have to go."

If everyone did a Worrall Thompson, maybe Tesco wouldn't be too big to fail

Tesco's poor results have led it to review its practices. The self-service tills used by Wozza may be a good place to start

• 
• • Marina Hyde
  • guardian.co.uk, Friday 13 January 2012 21.00 GMT
  • larger | smaller

Illustration by Otto

Sad news for Tesco, which this week discovered an unexpected item in its bagging area. The rogue element has since been identified as "awful Christmas sales and a profits warning", and the company's chief executive Philip Clarke now appears to be having problems removing this item before continuing with Tesco's hitherto unstoppable rise. I do hope he has to wait a long time for assistance.

Britain ceased to be a nation of shopkeepers some time ago, as the local independent stores had the life bled out of them by the supermarket giants. But we're a nation of shoppers, and perhaps this two fingers to the daddy of them all is our retail version of the Arab spring. Watching the suddenly humble Clarke promising to address product quality, customer service and "longstanding business issues" rather put one in mind of a besieged dictator. "Wait!" is the despot's reaction to increasingly volatile protests. "I am literally just about to introduce a raft of democratic reforms!"

It will take rather more than Clarke's needy mea culpa to reverse the perception that Tesco stands for everything that is monolithic, mercilessly expansionist, and machine driven. Tesco is a place that people more principled than myself probably manage to avoid entirely, but into which most of us feel compelled to go fairly frequently because it's nearby, or because it has effectively shut down any alternatives.

For a long time, criticism of it was crushed by that pat little assertion that it was "what the people wanted". Tesco executives and their defenders appeared to be graduates of the Richard Desmond school of debate, which is to paint anyone who questions your methods as snobs or enemies of enterprise. They acted as if everyone criticising Tesco must have the luxury of shopping at Waitrose or M&S, when this week's evidence has revealed that they might just as easily get their goods at Aldi or Lidl.

Thus the unthinkable has happened. And now that Tesco appears to be not so much what the people want, what precisely does it have going for it?

Its expansion has certainly told us little we did not already know about this septic isle, merely throwing into even sharper relief the iniquities of such institutions as council planning departments. Countless ordinary citizens have tales of their applications to make minuscule home improvements being rejected, while mock Tudor Tesco superstores are waved through with as many clock towers and metal-effect weather vanes as their architects care to spike them with. Since the 90s, 200 have been plonked down like spaceships, pulling customers off high streets with their seemingly irresistible tractor beams. Yet we now discover that these behemoths are among the "less potent" parts of Tesco's enterprise. Whether scarcely 15 years of rapacious profits was worth leaving a blight of potential white elephants scattered across the countryside, only time will show.

But it is in the area of employment, and its effect on customer service, that the Tesco modus operandi has been most pernicious. There are few sights in modern retail more pathetic, in the true sense of that word, than that of the lone, low-paid human charged with overriding technical glitches in the banks of self-service tills that have already claimed the jobs of countless check-out assistants, knowing that they will soon enough claim theirs. (Eighteen months ago, Tesco began trialling a stall with no manned checkouts at all, merely the single overseer.) Given the Japanese government is investing heavily in technology that could provide robot care for the elderly, it seems a likely bet that Tesco hopes one day to have its shelves robotically stacked, and even the automated till supervisors replaced by customer service droids. A similar process of dehumanisation has been afoot in car plants, but few of us have the occasion to pass through those very often. Nowhere is the rise of the machine at the expense of human employment more evident than in supermarkets such as Tesco. It is an everyday dystopia.

What is to be done? Oddly enough, perhaps one mad answer lies in the other Tesco-related story of the week. Just possibly – and obviously entirely unwittingly – shoplifting chef Antony Worrall Thompson has suggested an act of civil disobedience. If a critical mass of shoppers were to decide to do a Wozza for moral reasons, then the robotic scanners would become less economically viable than human checkout workers. Pilfering from Tesco would become a political act. However, if your preference is for grandiose schemes that won't involve accepting a police caution before embarking on psychiatric treatment, perhaps we could get up a campaign for a sort of Tesco Tobin tax, in which some tiny percentage of every penny spent in one of their out-of-town stores would be dedicated to reviving Britain's denuded high streets.

That, of course, is about as likely to happen as one of Tesco's machines accepting you've placed your 25g packet of parsley in the bagging area. Alas, Britain's biggest retailer is such a massive part of our economy that it presumably won't be long before someone is explaining that it is too big to fail, in keeping with the vogue for the most rampant capitalists becoming socialists in their many hours of need.

Nothing wrong in killing; you just shouldn't urinate on the corpses.

Robert Fisk: This is not about 'bad apples'. This is the horror of war

How many other abuses took place off camera? How many Hadithas? How many My Lais?

Robert Fisk

Friday, 13 January 2012

So now it's snapshots of US Marines pissing on the Afghan dead. Better, I suppose, than the US soldiers pictured beside the innocent Afghan teenager they fragged back in March of last year. Or the female guard posing with the dead Iraqi prisoner at Abu Ghraib. Not to mention Haditha or the murder videos taken by US troops in the field – the grenading of an old shepherd by an Iraqi highway comes to mind – or My Lai or the massacre of refugees by US forces in Korea or the murder of Malayan villagers by British troops. Or the Bloody Sunday massacre of 14 Catholics by British troops in Derry in 1972. And please note, I have not even mentioned the name of Baha Mousa.

The US Marines' response to the pissing pictures was oh so typical. These men were not abiding by the "core values" of the Marines, we were informed. Same old story. A "rogue" unit, a few "bad apples", rotten eggs. Maybe.

But if there is one game of pissing on the dead, how many others happened without pictures? How many other shepherds got fragged in Iraq? How many other Hadithas have there been? There were plenty of other My Lais.

As laptop filmography gets better, so it all comes slopping out, the rapes and slaughter – and yes, by the Taliban the stoning of young women for supposed sexual misconduct in Afghanistan; by al-Qa'ida, executions and throat-cuttings in Iraq.

And no – the Americans are not the Nazis, the Brits are not the French Paras of 1960 Algeria (but surely we're not comparing the French paras to the Nazis). The Canadians handed prisoners over to Afghan thugs for brutal questioning but the Canadians are not like Saddam's secret police – and, I suppose, the Taliban are not Stalin's NKVD or Putin's KGB (before he became a statesman). And you can't compare – surely – the Soviet invaders of Afghanistan in 1979 with Genghis Khan.

So let's take a little guessing game. A British Sunday paper reveals shocking revelations of torture and cigarette burning, of physical brutality where prisoners must be hospitalised for a week, of possible electric torture. The French in Algeria? Saddam's mukhabarat? Nope. It's The Sunday Times Insight Team's report of 7 May 1972; the victims, of course, IRA suspects in Belfast. A "rogue" unit? A "few bad apples"? I doubt it.

When the Gloucestershire Regiment went on a rampage near Divis flats, smashing every window in the street the day before they were due to leave Belfast, the line was changed. They had been under "enormous strain" – but weren't these the "Glorious Gloucesters" of Imjin River fame? And the killer Paras of Derry – weren't these the same Paras of Arnhem Bridge?

And so we go on. Yes, British troops murdered SS prisoners after Normandy – just as the Red Army did in the Second World War and the Americans. And all this gets a bit dull, doesn't it?

Dresden was worse than the Blitz – but who started it? Hiroshima was worse than Pearl Harbour (ditto). The Canadians bayoneted German prisoners in the First World War – but the Germans really did committed atrocities in Belgium in 1914. And what about Waterloo? What did we do with the heaps of French dead? Why, we honoured them by shipping their corpses off to Lincolnshire and using them as manure on the fields of East Anglia.

If war were not about the total failure of the human spirit, there would be something grotesquely funny about the American reaction to the pissing pictures.

For note, it was not the killing of these men that worried the Marine Corps in the US – it was the pissing. Nothing wrong in killing amid the "core values" of the Marine Corps; you just shouldn't urinate on the corpses. And even more to the point: YOU MUSTN'T DO IT ON CAMERA! Too late. It comes to this. Armies are horrible creatures and soldiers do wicked things but when we accept all these lies about "bad apples" and the exceptionalism of crime in war – "there may have been some excesses" is the usual dictator-speak – we are accepting war and going along with the dishonesty of it and we are making it more possible and easier and the killings and rapes more excusable and more frequent.
And how should armies react? With one word: guilty.