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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.
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.
The Silent Intelligence: The Internet of Things by Daniel Kellmereit, Daniel Obodovski
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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.
The 100-Year Life: Living and Working in an Age of Longevity by Lynda Gratton, Andrew Scott
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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.
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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.
Blockchain Revolution: How the Technology Behind Bitcoin Is Changing Money, Business, and the World by Don Tapscott, Alex Tapscott
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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.
Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies by Geoffrey West
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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.