Showing posts with label Newton. Show all posts
Showing posts with label Newton. Show all posts
Thursday, 18 November 2021
Sunday, 29 August 2021
Tuesday, 28 May 2013
Globalisation isn't just about profits. It's about taxes too
Big corporates are gaming one nation's taxpayers against another's: we need a global deal to make them pay their way
Why should German taxpayers help bail out a country whose business model is based on avoidance and a race to the bottom? Illustration by Daniel Pudles
The world looked on agog as Tim Cook, the head of Apple, said his company had paid all the taxes owed – seeming to say that it paid all the taxes it should have paid. There is, of course, a big difference between the two. It's no surprise that a company with the resources and ingenuity of Apple would do what it could to avoid paying as much tax as it could within the law. While the supreme court, in its Citizens United case seems to have said that corporations are people, with all the rights attendant thereto, this legal fiction didn't endow corporations with a sense of moral responsibility; and they have the Plastic Man capacity to be everywhere and nowhere at the same time – to be everywhere when it comes to selling their products, and nowhere when it comes to reporting the profits derived from those sales.
Apple, like Google, has benefited enormously from what the US and other western governments provide: highly educated workers trained in universities that are supported both directly by government and indirectly (through generous charitable deductions). The basic research on which their products rest was paid for by taxpayer-supported developments – the internet, without which they couldn't exist. Their prosperity depends in part on our legal system – including strong enforcement of intellectual property rights; they asked (and got) government to force countries around the world to adopt our standards, in some cases, at great costs to the lives and development of those in emerging markets and developing countries. Yes, they brought genius and organisational skills, for which they justly receive kudos. But while Newton was at least modest enough to note that he stood on the shoulders of giants, these titans of industry have no compunction about being free riders, taking generously from the benefits afforded by our system, but not willing to contribute commensurately. Without public support, the wellspring from which future innovation and growth will come will dry up – not to say what will happen to our increasingly divided society.
It is not even true that higher corporate tax rates would necessarily significantly decrease investment. As Apple has shown, it can finance anything it wants to with debt – including paying dividends, another ploy to avoid paying their fair share of taxes. But interest payments are tax deductible – which means that to the extent that investment is debt-financed, the cost of capital and returns are both changed commensurately, with no adverse effect on investment. And with the low rate of taxation on capital gains, returns on equity are treated even more favorably. Still more benefits accrue from other details of the tax code, such as accelerated depreciation and the tax treatment of research and development expenditures.
It is time the international community faced the reality: we have an unmanageable, unfair, distortionary global tax regime. It is a tax system that is pivotal in creating the increasing inequality that marks most advanced countries today – with America standing out in the forefront and the UK not far behind. It is the starving of the public sector which has been pivotal in America no longer being the land of opportunity – with a child's life prospects more dependent on the income and education of its parents than in other advanced countries.
Globalisation has made us increasingly interdependent. These international corporations are the big beneficiaries of globalisation – it is not, for instance, the average American worker and those in many other countries, who, partly under the pressure from globalisation, has seen his income fully adjusted for inflation, including the lowering of prices that globalisation has brought about, fall year after year, to the point where a fulltime male worker in the US has an income lower than four decades ago. Our multinationals have learned how to exploit globalisation in every sense of the term – including exploiting the tax loopholes that allow them to evade their global social responsibilities.
The US could not have a functioning corporate income tax system if we had elected to have a transfer price system (where firms "make up" the prices of goods and services that one part buys from another, allowing profits to be booked to one state or another). As it is, Apple is evidently able to move profits around to avoid Californian state taxes. The US has developed a formulaic system, where global profits are allocated on the basis of employment, sales and capital goods. But there is plenty of room to further fine-tune the system in response to the easier ability to shift profits around when a major source of the real "value-added" is intellectual property.
Some have suggested that while the sources of production (value added) are difficult to identify, the destination is less so (though with reshipping, this may not be so clear); they suggest a destination-based system. But such a system would not necessarily be fair – providing no revenues to the countries that have borne the costs of production. But a destination system would clearly be better than the current one.
Even if the US were not rewarded for its global publicly supported scientific contributions and the intellectual property built on them, at least the country would be rewarded for its unbridled consumerism, which provides incentives for such innovation. It would be good if there could be an international agreement on the taxation of corporate profits. In the absence of such an agreement, any country that threatened to impose fair corporate taxes would be punished – production (and jobs) would be taken elsewhere. In some cases, countries can call their bluff. Others may feel the risk is too high. But what cannot be escaped are customers.
The US by itself could go a long way to moving reform along: any firm selling goods there could be obliged to pay a tax on its global profits, at say a rate of 30%, based on a consolidated balance sheet, but with a deduction for corporate profits taxes paid in other jurisdictions (up to some limit). In other words, the US would set itself up as enforcing a global minimum tax regime. Some might opt out of selling in the US, but I doubt that many would.
The problem of multinational corporate tax avoidance is deeper, and requires more profound reform, including dealing with tax havens that shelter money for tax-evaders and facilitate money-laundering. Google and Apple hire the most talented lawyers, who know how to avoid taxes staying within the law. But there should be no room in our system for countries that are complicitous in tax avoidance. Why should taxpayers in Germany help bail out citizens in a country whose business model was based on tax avoidance and a race to the bottom – and why should citizens in any country allow their companies to take advantage of these predatory countries?
To say that Apple or Google simply took advantage of the current system is to let them off the hook too easily: the system didn't just come into being on its own. It was shaped from the start by lobbyists from large multinationals. Companies like General Electric lobbied for, and got, provisions that enabled them to avoid even more taxes. They lobbied for, and got, amnesty provisions that allowed them to bring their money back to the US at a special low rate, on the promise that the money would be invested in the country; and then they figured out how to comply with the letter of the law, while avoiding the spirit and intention. If Apple and Google stand for the opportunities afforded by globalisation, their attitudes towards tax avoidance have made them emblematic of what can, and is, going wrong with that system.
Wednesday, 18 January 2012
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.
Buy 17 Equations That Changed the World from the Guardian bookshop
"'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."
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.
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.
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.
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'.
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.
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.
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.
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.
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.
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.
- Seventeen Equations that Changed the World
- by Ian Stewart
-
- Buy it from the Guardian bookshop
- Tell us what you think: Star-rate and review this book
"'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.
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