first square of the chessboard

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pages: 72 words: 21,361

Race Against the Machine: How the Digital Revolution Is Accelerating Innovation, Driving Productivity, and Irreversibly Transforming Employment and the Economy by Erik Brynjolfsson

"Robert Solow", Amazon Mechanical Turk, Any sufficiently advanced technology is indistinguishable from magic, autonomous vehicles, business cycle, business process, call centre, combinatorial explosion, corporate governance, creative destruction, crowdsourcing, David Ricardo: comparative advantage, easy for humans, difficult for computers, Erik Brynjolfsson, factory automation, first square of the chessboard, first square of the chessboard / second half of the chessboard, Frank Levy and Richard Murnane: The New Division of Labor, hiring and firing, income inequality, intangible asset, job automation, John Markoff, John Maynard Keynes: technological unemployment, Joseph Schumpeter, Khan Academy, Kickstarter, knowledge worker, Loebner Prize, low skilled workers, minimum wage unemployment, patent troll, pattern recognition, Paul Samuelson, Ray Kurzweil, rising living standards, Robert Gordon, self-driving car, shareholder value, Skype, too big to fail, Turing test, Tyler Cowen: Great Stagnation, Watson beat the top human players on Jeopardy!, wealth creators, winner-take-all economy, zero-sum game

It comes from an ancient story about math made relevant to the present age by the innovator and futurist Ray Kurzweil. In one version of the story, the inventor of the game of chess shows his creation to his country’s ruler. The emperor is so delighted by the game that he allows the inventor to name his own reward. The clever man asks for a quantity of rice to be determined as follows: one grain of rice is placed on the first square of the chessboard, two grains on the second, four on the third, and so on, with each square receiving twice as many grains as the previous. The emperor agrees, thinking that this reward was too small. He eventually sees, however, that the constant doubling results in tremendously large numbers. The inventor winds up with 264-1 grains of rice, or a pile bigger than Mount Everest. In some versions of the story the emperor is so displeased at being outsmarted that he beheads the inventor.


pages: 464 words: 116,945

Seventeen Contradictions and the End of Capitalism by David Harvey

accounting loophole / creative accounting, bitcoin, Branko Milanovic, Bretton Woods, BRICs, British Empire, business climate, California gold rush, call centre, central bank independence, clean water, cloud computing, collapse of Lehman Brothers, colonial rule, creative destruction, Credit Default Swap, David Ricardo: comparative advantage, deindustrialization, demographic dividend, Deng Xiaoping, deskilling, drone strike, end world poverty, falling living standards, fiat currency, first square of the chessboard, first square of the chessboard / second half of the chessboard, Food sovereignty, Frank Gehry, future of work, global reserve currency, Guggenheim Bilbao, Gunnar Myrdal, income inequality, informal economy, invention of the steam engine, invisible hand, Isaac Newton, Jane Jacobs, Jarndyce and Jarndyce, John Maynard Keynes: Economic Possibilities for our Grandchildren, Joseph Schumpeter, Just-in-time delivery, knowledge worker, low skilled workers, Mahatma Gandhi, market clearing, Martin Wolf, means of production, microcredit, new economy, New Urbanism, Occupy movement, peak oil, phenotype, plutocrats, Plutocrats, Ponzi scheme, quantitative easing, rent-seeking, reserve currency, road to serfdom, Robert Gordon, Ronald Reagan, short selling, Silicon Valley, special economic zone, The Wealth of Nations by Adam Smith, Thomas Malthus, Thorstein Veblen, transaction costs, Tyler Cowen: Great Stagnation, wages for housework, Wall-E, women in the workforce, working poor, working-age population

For the first twenty years of a thirty-year mortgage the principal still owed declines very slowly. The decline then accelerates and over the last two or three years the principal diminishes very rapidly. There are a number of classic anecdotes to illustrate this quality of compounding interest and exponential growth. An Indian king wished to reward the inventor of the game of chess. The inventor asked for one grain of rice on the first square of the chessboard and that the amount be doubled from one square to the next until all the squares were covered. The king readily agreed, since it seemed a small price to pay. The trouble was that by the time it came to the twenty-first square more than a million grains were required and after the forty-first square (which required more than a trillion grains) there simply was not enough rice in the world to cover the remaining squares.

To keep to a satisfactory growth rate right now would mean finding profitable investment opportunities for an extra nearly $2 trillion compared to the ‘mere’ $6 billion that was needed in 1970. By the time 2030 rolls around, when estimates suggest the global economy should be more than $96 trillion, profitable investment opportunities of close to $3 trillion will be needed. Thereafter the numbers become astronomical. It is as if we are on the twenty-first square of the chessboard and cannot get off. It just does not look a feasible growth trajectory, at least from where we sit now. Imagined physically, the enormous expansions in physical infrastructures, in urbanisation, in workforces, in consumption and in production capacities that have occurred since the 1970s until now will have to be dwarfed into insignificance over the coming generation if the compound rate of capital accumulation is to be maintained.


pages: 138 words: 40,787

The Silent Intelligence: The Internet of Things by Daniel Kellmereit, Daniel Obodovski

Airbnb, Amazon Web Services, Any sufficiently advanced technology is indistinguishable from magic, autonomous vehicles, barriers to entry, business intelligence, call centre, Clayton Christensen, cloud computing, commoditize, connected car, crowdsourcing, data acquisition, en.wikipedia.org, Erik Brynjolfsson, first square of the chessboard, first square of the chessboard / second half of the chessboard, Freestyle chess, Google X / Alphabet X, Internet of things, lifelogging, Metcalfe’s law, Network effects, Paul Graham, Ray Kurzweil, RFID, Robert Metcalfe, self-driving car, Silicon Valley, smart cities, smart grid, software as a service, Steve Jobs, web application, Y Combinator, yield management

Below is a well-known story, popularized by Ray Kurzweil and retold as we know it, that illustrates the power of exponential growth. In ancient China a man came to the emperor and demonstrated to him his invention of the game of chess. The emperor was so impressed by the brilliance of the man’s invention that he told the man to name his reward. The man asked for his reward in an amount of rice — that one grain be placed on the first square of the chessboard, two on the second, four on the third, and so on — doubling the number of grains on each subsequent square. Not being a very good mathematician, the emperor at first thought the reward to be too modest and directed his servants to fulfill the man’s request. By the time the rice grains filled the first half of the chessboard, the man had more than four billion rice grains — or about the harvest of one rice field.


pages: 288 words: 85,073

Factfulness: Ten Reasons We're Wrong About the World – and Why Things Are Better Than You Think by Hans Rosling, Ola Rosling, Anna Rosling Rönnlund

animal electricity, clean water, colonial rule, en.wikipedia.org, energy transition, first square of the chessboard, first square of the chessboard / second half of the chessboard, global pandemic, Hans Rosling, illegal immigration, income inequality, income per capita, Intergovernmental Panel on Climate Change (IPCC), jimmy wales, linked data, lone genius, microcredit, purchasing power parity, Stanford marshmallow experiment, Steven Pinker, Thomas L Friedman, Walter Mischel

Each infected person was infecting, on average, two more people before dying. As a result, the number of new cases per day was doubling every three weeks. The graph showed how enormous the outbreak would soon become if each infected person kept infecting two more. Doubling is scary! I had first learned about the effect of doubling at school. In the Indian legend, the Lord Krishna asks for one grain of rice on the first square of the chessboard, then two grains on the second square, four grains on the third square, then eight, and so on, doubling the number of grains each time. By the time he gets to the last of the 64 squares, he is owed 18,446,744,073,709,551,615 grains of rice: enough to cover the whole of India with a layer of rice 30 inches deep. Anything that keeps doubling grows much faster than we first assume. So I knew the situation in West Africa was about to become desperate.


pages: 389 words: 87,758

No Ordinary Disruption: The Four Global Forces Breaking All the Trends by Richard Dobbs, James Manyika

2013 Report for America's Infrastructure - American Society of Civil Engineers - 19 March 2013, access to a mobile phone, additive manufacturing, Airbnb, Amazon Mechanical Turk, American Society of Civil Engineers: Report Card, autonomous vehicles, Bakken shale, barriers to entry, business cycle, business intelligence, Carmen Reinhart, central bank independence, cloud computing, corporate governance, creative destruction, crowdsourcing, demographic dividend, deskilling, disintermediation, disruptive innovation, distributed generation, Erik Brynjolfsson, financial innovation, first square of the chessboard, first square of the chessboard / second half of the chessboard, Gini coefficient, global supply chain, global village, hydraulic fracturing, illegal immigration, income inequality, index fund, industrial robot, intangible asset, Intergovernmental Panel on Climate Change (IPCC), Internet of things, inventory management, job automation, Just-in-time delivery, Kenneth Rogoff, Kickstarter, knowledge worker, labor-force participation, low skilled workers, Lyft, M-Pesa, mass immigration, megacity, mobile money, Mohammed Bouazizi, Network effects, new economy, New Urbanism, oil shale / tar sands, oil shock, old age dependency ratio, openstreetmap, peer-to-peer lending, pension reform, private sector deleveraging, purchasing power parity, quantitative easing, recommendation engine, Report Card for America’s Infrastructure, RFID, ride hailing / ride sharing, Second Machine Age, self-driving car, sharing economy, Silicon Valley, Silicon Valley startup, Skype, smart cities, Snapchat, sovereign wealth fund, spinning jenny, stem cell, Steve Jobs, supply-chain management, TaskRabbit, The Great Moderation, trade route, transaction costs, Travis Kalanick, uber lyft, urban sprawl, Watson beat the top human players on Jeopardy!, working-age population, Zipcar

In their bestseller The Second Machine Age, Erik Brynjolfsson and Andrew McAfee of the Massachusetts Institute of Technology dubbed the current era the “second half of the chessboard.” Brynjolfsson and McAfee give a modern twist to an old story about the power of exponential growth. Pleased with the invention of chess, a Chinese emperor offered the inventor his choice of prizes. At the outset, the inventor asked the emperor for a single grain of rice to be placed on the first square of the chessboard, two on the second square, four on the third, and eight on the fourth. The amounts doubled with each move. The first half of the chessboard was fairly uneventful. The inventor received spoons of rice, then bowls, then barrels. One version of the story has the emperor going bankrupt and being replaced by the inventor, as sixty-three doublings would have ultimately totaled eighteen million trillion grains of rice—enough to cover twice the surface area of the earth.


pages: 294 words: 96,661

The Fourth Age: Smart Robots, Conscious Computers, and the Future of Humanity by Byron Reese

agricultural Revolution, AI winter, artificial general intelligence, basic income, Buckminster Fuller, business cycle, business process, Claude Shannon: information theory, clean water, cognitive bias, computer age, crowdsourcing, dark matter, Elon Musk, Eratosthenes, estate planning, financial independence, first square of the chessboard, first square of the chessboard / second half of the chessboard, full employment, Hans Rosling, income inequality, invention of agriculture, invention of movable type, invention of the printing press, invention of writing, Isaac Newton, Islamic Golden Age, James Hargreaves, job automation, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kevin Kelly, lateral thinking, life extension, Louis Pasteur, low skilled workers, manufacturing employment, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Mary Lou Jepsen, Moravec's paradox, On the Revolutions of the Heavenly Spheres, pattern recognition, profit motive, Ray Kurzweil, recommendation engine, Rodney Brooks, Sam Altman, self-driving car, Silicon Valley, Skype, spinning jenny, Stephen Hawking, Steve Wozniak, Steven Pinker, strong AI, technological singularity, telepresence, telepresence robot, The Future of Employment, the scientific method, Turing machine, Turing test, universal basic income, Von Neumann architecture, Wall-E, Watson beat the top human players on Jeopardy!, women in the workforce, working poor, Works Progress Administration, Y Combinator

To understand just how quickly something that repeatedly doubles gets really big, consider the story of the invention of chess. About a thousand years ago, a mathematician in what is today India is said to have brought his creation to the ruler, and showed him how the game was played. The ruler, quite impressed, asked the mathematician what he wanted for a reward. The mathematician responded that he was a humble man and his needs were few. He simply asked that a single grain of rice be placed on the first square of the chessboard. Then two on the second, four on the third, each square doubling along the way. All he wanted was the rice that would be on the sixty-fourth square. So how much rice do you think this is? Given my setup to the story, you know it will be a big number. But just imagine what that much rice would look like. Would it fill a silo? A warehouse? It is actually more rice than has been cultivated in the entire history of humanity.


pages: 323 words: 90,868

The Wealth of Humans: Work, Power, and Status in the Twenty-First Century by Ryan Avent

"Robert Solow", 3D printing, Airbnb, American energy revolution, assortative mating, autonomous vehicles, Bakken shale, barriers to entry, basic income, Bernie Sanders, BRICs, business cycle, call centre, Capital in the Twenty-First Century by Thomas Piketty, Clayton Christensen, cloud computing, collective bargaining, computer age, creative destruction, dark matter, David Ricardo: comparative advantage, deindustrialization, dematerialisation, Deng Xiaoping, deskilling, disruptive innovation, Dissolution of the Soviet Union, Donald Trump, Downton Abbey, Edward Glaeser, Erik Brynjolfsson, eurozone crisis, everywhere but in the productivity statistics, falling living standards, first square of the chessboard, first square of the chessboard / second half of the chessboard, Ford paid five dollars a day, Francis Fukuyama: the end of history, future of work, gig economy, global supply chain, global value chain, hydraulic fracturing, income inequality, indoor plumbing, industrial robot, intangible asset, interchangeable parts, Internet of things, inventory management, invisible hand, James Watt: steam engine, Jeff Bezos, John Maynard Keynes: Economic Possibilities for our Grandchildren, Joseph-Marie Jacquard, knowledge economy, low skilled workers, lump of labour, Lyft, manufacturing employment, Marc Andreessen, mass immigration, means of production, new economy, performance metric, pets.com, post-work, price mechanism, quantitative easing, Ray Kurzweil, rent-seeking, reshoring, rising living standards, Robert Gordon, Ronald Coase, savings glut, Second Machine Age, secular stagnation, self-driving car, sharing economy, Silicon Valley, single-payer health, software is eating the world, supply-chain management, supply-chain management software, TaskRabbit, The Future of Employment, The Nature of the Firm, The Rise and Fall of American Growth, The Spirit Level, The Wealth of Nations by Adam Smith, trade liberalization, transaction costs, Tyler Cowen: Great Stagnation, Uber and Lyft, Uber for X, uber lyft, very high income, working-age population

In an influential 2012 book, Race Against the Machine, two MIT scholars of technology and business, Erik Brynjolfsson and Andrew McAfee, argue that people aren’t very good at assessing the pace of exponential technological progress (for example, the repeated doubling in microchip power described by Moore’s law).11 They borrow a parable popularized by the futurist Ray Kurzweil.12 In the legend, a wise man invents the game of chess and presents it to his king. Pleased, the king allows the man to name his reward. The wise man responds that he wishes only modest compensation, following a simple rule. He would have one grain of rice on the first square of the chessboard, two on the second, four on the third, and so on, doubling each time for each of the sixty-four squares. The king chuckles at the apparent measliness of these amounts and says yes. It soon becomes clear that he has made quite a big mistake. After two rows the king owes nearly 33,000 grains of rice and is not chuckling quite so much. By the last square of the first half of the chessboard the amount involved is enormous, totalling more than 2 billion grains, or nearly 100,000 kg, of rice – but it is not yet absurd.


pages: 344 words: 94,332

The 100-Year Life: Living and Working in an Age of Longevity by Lynda Gratton, Andrew Scott

3D printing, Airbnb, assortative mating, carbon footprint, Clayton Christensen, collapse of Lehman Brothers, creative destruction, crowdsourcing, delayed gratification, disruptive innovation, diversification, Downton Abbey, Erik Brynjolfsson, falling living standards, financial independence, first square of the chessboard, first square of the chessboard / second half of the chessboard, future of work, gender pay gap, gig economy, Google Glasses, indoor plumbing, information retrieval, intangible asset, Isaac Newton, job satisfaction, longitudinal study, low skilled workers, Lyft, Nelson Mandela, Network effects, New Economic Geography, old age dependency ratio, pattern recognition, pension reform, Peter Thiel, Ray Kurzweil, Richard Florida, Richard Thaler, Second Machine Age, sharing economy, side project, Silicon Valley, smart cities, Stanford marshmallow experiment, Stephen Hawking, Steve Jobs, The Future of Employment, uber lyft, women in the workforce, young professional

In other words, just as computing power doubles every two years, so the number of grains of rice doubled with the move from each square. In the fable, the king soon realized that he didn’t have enough grains of rice to meet the challenge, running out before the thirtieth square (before the second half of the chessboard). To meet the inventor’s demand the king would have to provide a mountain of rice larger than Mount Everest – nearly 18.5 quintillion grains. On the first square of the chessboard there is one grain of rice, and by the 33rd square the number is 4.3 billion. The parallel with Moore’s Law is obvious. Back in 1981, Bill Gates said 640K of computer memory should be enough for anyone; thirty years later not only do computers have huge processing power, but also the increase that will happen in the next two years is enormous compared to cumulative past progress. The increase in processing power going from the 32nd chess square to the 35th is worth four times the cumulative sum of processing power across the first 32 squares.


pages: 317 words: 101,074

The Road Ahead by Bill Gates, Nathan Myhrvold, Peter Rinearson

Albert Einstein, Apple's 1984 Super Bowl advert, Berlin Wall, Bill Gates: Altair 8800, Bob Noyce, Bonfire of the Vanities, business process, California gold rush, Claude Shannon: information theory, computer age, Donald Knuth, first square of the chessboard, first square of the chessboard / second half of the chessboard, glass ceiling, global village, informal economy, invention of movable type, invention of the printing press, invention of writing, John von Neumann, knowledge worker, medical malpractice, Mitch Kapor, new economy, packet switching, popular electronics, Richard Feynman, Ronald Reagan, speech recognition, Steve Ballmer, Steve Jobs, Steven Pinker, Ted Nelson, telemarketer, the scientific method, The Wealth of Nations by Adam Smith, transaction costs, Turing machine, Turing test, Von Neumann architecture

No experience in our everyday life prepares us for the implications of a number that doubles a great number of times—exponential improvements. One way to understand it is with a fable. King Shirham of India was so pleased when one of his ministers invented the game of chess that he asked the man to name any reward. "Your Majesty," said the minister, "I ask that you give me one grain of wheat for the first square of the chessboard, two grains for the second square, four grains for the third, and so on, doubling the number of grains each time until all sixty-four squares are accounted for." The king was moved by the modesty of the request and called for a bag of wheat. The king asked that the promised grains be counted out onto the chessboard. On the first square of the first row was placed one small grain. On the second square were two specks of wheat.


pages: 515 words: 126,820

Blockchain Revolution: How the Technology Behind Bitcoin Is Changing Money, Business, and the World by Don Tapscott, Alex Tapscott

Airbnb, altcoin, asset-backed security, autonomous vehicles, barriers to entry, bitcoin, blockchain, Blythe Masters, Bretton Woods, business process, buy and hold, Capital in the Twenty-First Century by Thomas Piketty, carbon footprint, clean water, cloud computing, cognitive dissonance, commoditize, corporate governance, corporate social responsibility, creative destruction, Credit Default Swap, crowdsourcing, cryptocurrency, disintermediation, disruptive innovation, distributed ledger, Donald Trump, double entry bookkeeping, Edward Snowden, Elon Musk, Erik Brynjolfsson, Ethereum, ethereum blockchain, failed state, fiat currency, financial innovation, Firefox, first square of the chessboard, first square of the chessboard / second half of the chessboard, future of work, Galaxy Zoo, George Gilder, glass ceiling, Google bus, Hernando de Soto, income inequality, informal economy, information asymmetry, intangible asset, interest rate swap, Internet of things, Jeff Bezos, jimmy wales, Kickstarter, knowledge worker, Kodak vs Instagram, Lean Startup, litecoin, Lyft, M-Pesa, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, means of production, microcredit, mobile money, money market fund, Network effects, new economy, Oculus Rift, off grid, pattern recognition, peer-to-peer, peer-to-peer lending, peer-to-peer model, performance metric, Peter Thiel, planetary scale, Ponzi scheme, prediction markets, price mechanism, Productivity paradox, QR code, quantitative easing, ransomware, Ray Kurzweil, renewable energy credits, rent-seeking, ride hailing / ride sharing, Ronald Coase, Ronald Reagan, Satoshi Nakamoto, Second Machine Age, seigniorage, self-driving car, sharing economy, Silicon Valley, Skype, smart contracts, smart grid, social graph, social intelligence, social software, standardized shipping container, Stephen Hawking, Steve Jobs, Steve Wozniak, Stewart Brand, supply-chain management, TaskRabbit, The Fortune at the Bottom of the Pyramid, The Nature of the Firm, The Wisdom of Crowds, transaction costs, Turing complete, Turing test, Uber and Lyft, uber lyft, unbanked and underbanked, underbanked, unorthodox policies, wealth creators, X Prize, Y2K, Zipcar

Interview with Constance Choi, April 10, 2015. 73. The digital revolution has moved on to “the second half of the chessboard”—a clever phrase coined by the American inventor and author Ray Kurzweil. He tells a story of the emperor of China being so delighted with the game of chess that he offered the game’s inventor any reward he desired. The inventor asked for rice. “I would like one grain of rice on the first square of the chessboard, two grains of rice on the second square, four grains of rice on the third square, and so on, all the way to the last square,” he said. Thinking this would add up to a couple bags of rice, the emperor happily agreed. He was misguided. While small at the outset, the amount of rice escalates to more than two billion grains halfway through the chessboard. The final square would require nine billion billion grains of rice—enough to cover all of Earth. 74.


pages: 578 words: 168,350

Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies by Geoffrey West

Alfred Russel Wallace, Anton Chekhov, Benoit Mandelbrot, Black Swan, British Empire, butterfly effect, carbon footprint, Cesare Marchetti: Marchetti’s constant, clean water, complexity theory, computer age, conceptual framework, continuous integration, corporate social responsibility, correlation does not imply causation, creative destruction, dark matter, Deng Xiaoping, double helix, Edward Glaeser, endogenous growth, Ernest Rutherford, first square of the chessboard, first square of the chessboard / second half of the chessboard, Frank Gehry, Geoffrey West, Santa Fe Institute, Guggenheim Bilbao, housing crisis, Index librorum prohibitorum, invention of agriculture, invention of the telephone, Isaac Newton, Jane Jacobs, Jeff Bezos, Johann Wolfgang von Goethe, John von Neumann, Kenneth Arrow, laissez-faire capitalism, life extension, Mahatma Gandhi, mandelbrot fractal, Marchetti’s constant, Masdar, megacity, Murano, Venice glass, Murray Gell-Mann, New Urbanism, Peter Thiel, profit motive, publish or perish, Ray Kurzweil, Richard Feynman, Richard Florida, Silicon Valley, smart cities, Stephen Hawking, Steve Jobs, Stewart Brand, technological singularity, The Coming Technological Singularity, The Death and Life of Great American Cities, the scientific method, too big to fail, transaction costs, urban planning, urban renewal, Vernor Vinge, Vilfredo Pareto, Von Neumann architecture, Whole Earth Catalog, Whole Earth Review, wikimedia commons, working poor

Here’s a version of the story: When the inventor of chess showed the game to the king, the ruler was so taken by it that he asked the inventor to name his reward for creating such a marvelous and challenging game. The man, who was mathematically inclined, asked the king for what seemed to be an extremely modest reward in the form of grains of rice. However, these were to be apportioned in the following manner: he would receive 1 grain of rice on the first square of the chessboard, 2 grains on the second, 4 on the third, 8 on the fourth, 16 on the fifth, and so on, doubling the amount for each progressive square. The king, though somewhat offended by such an apparently measly response to his very generous offer, reluctantly accepted the inventor’s request and ordered the treasurer to count out the grains of rice as prescribed by the inventor. However, when the treasurer had not completed the assignment by the end of the week, the king called him to task and asked him the reason for his extreme tardiness.