# first square of the chessboard / second half of the chessboard

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pages: 72 words: 21,361

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And the inventor could still retain his head. It was as they headed into the second half of the chessboard that at least one of them got into trouble. Kurzweil’s point is that constant doubling, reflecting exponential growth, is deceptive because it is initially unremarkable. Exponential increases initially look a lot like standard linear ones, but they’re not. As time goes by—as we move into the second half of the chessboard—exponential growth confounds our intuition and expectations. It accelerates far past linear growth, yielding Everest-sized piles of rice and computers that can accomplish previously impossible tasks. So where are we in the history of business use of computers? Are we in the second half of the chessboard yet? This is an impossible question to answer precisely, of course, but a reasonable estimate yields an intriguing conclusion.

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.

For information about quantity discounts, email info@raceagainstthemachine.com www.RaceAgainstTheMachine.com Library of Congress Cataloging-in-Publication Data Brynjolfsson, Erik Race against the machine : how the digital revolution is accelerating innovation, driving productivity, and irreversibly transforming employment and the economy. p. cm. eISBN 978-0-9847251-0-6 1. Technological innovations – Economic Aspects. I. McAfee, Andrew. II. Title. eBooks created by www.ebookconversion.com Contents 1. Technology’s Influence on Employment and the Economy 2. Humanity and Technology on the Second Half of the Chessboard 3. Creative Destruction: The Economics of Accelerating Technology and Disappearing Jobs 4. What Is to Be Done? Prescriptions and Recommendations 5. Conclusion: The Digital Frontier 6. Acknowledgments To my parents, Ari and Marguerite Brynjolfsson, who always believed in me. To my father, David McAfee, who showed me that there’s nothing better than a job well done. Chapter 1.

pages: 344 words: 94,332

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

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The inventor requested rice: one grain on the first square, two on the second, four on the third, eight on the fourth, and so on. 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.

In his thought-provoking analysis, Silicon Valley entrepreneur Martin Ford remarks: ‘The threat to overall employment is that as creative destruction unfolds the destruction will fall primarily on labor-intensive businesses in traditional areas like retail and goods preparation while the creation will generate new businesses and industries that simply don’t hire many people.’10 In the words of MIT professors Erik Brynjolfsson and Andrew McAfee, ‘Computers and other digital advances are doing for mental power … what the steam engine and its descendants did for muscle power’.11 The second half of the chessboard In 1965, Intel’s Geoffrey E. Moore conjectured that the processing power of semi-conductors would double roughly every two years and, to date, this has been an extraordinarily accurate prediction. As a consequence of this exponential growth, ‘Second Machine Age’ proponents argue that we are now in the ‘second half of the chessboard’. This is a reference to a fable concerning a king in India who, bored with all his existing pastimes, set a challenge to his kingdom to come up with a better form of entertainment. When presented with an early form of chess, the king was so delighted he offered the inventor anything he wanted.

With the innovations associated with the dramatic increase in low-cost computational power, it is now possible to develop driverless cars. When this happens it will threaten a significant number of jobs in the logistics industry. Diagnosing medical conditions is another routine task which has required knowledge and pattern recognition skills that have to date proved beyond computers. However, yet again, the implications of the second half of the chessboard is that this is no longer the case. Famously IBM’s supercomputer Watson is now performing oncology diagnosis. As computing power increases, so the hollowing out of the labour market accelerates. Instead of being complementary to skilled labour, technological innovations begin to substitute for it. The fact that this is already happening is given credence in one recent economic study which found that the long-running increase in demand for skilled workers started to go into reverse in 2000.13 In a much-quoted study, Oxford academics Carl Frey and Michael Osborne14 calculate that a total of 47 per cent of jobs in the US are vulnerable to these forces in the next few decades – that’s 60 million jobs.

pages: 138 words: 40,787

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.

By the time the servants got to the sixty-fourth square, the man had more than eighteen quintillion rice grains (18 x 1018), or more than all the wealth in the land. But his wealth and ability to outsmart the emperor came with a price — he ended up being decapitated. In their recent book, Race Against the Machine,1 Erik Brynjolfsson and Andrew McAfee, referenced the fable of the chess and rice grains to make the point that “exponential increases initially look a lot like linear, but they are not. As time goes by — as we move into the second half of the chessboard — exponential growth confounds our intuition and expectations.” As a result, in the early stages of a project or a new technology, it’s very hard to discern whether or not something will experience exponential growth. As you will find in these next chapters, we believe this is exactly what is going to happen with the rise of the Internet of Things. If that’s the case, the next decade and beyond is not only going to be more amazing from the standpoint of new devices and services coming to our everyday lives, but we will also see a dramatic change in our lives and the way we do business.

pages: 515 words: 126,820

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 Gavin Andresen, June 8, 2015. 71. www3.weforum.org/docs/WEF_GAC15_Technological_Tipping_Points_report_2015.pdf, 7. 72. 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.

In previous epochal transitions, societies took action to implement new understandings, laws, and institutions. These transformations of civilization took time, usually centuries, and were often punctuated by strife or even revolutions. Today the situation is different. Change is happening infinitely faster. More important, Moore’s law indicates that the rate of change is accelerating exponentially. We’re moving to the proverbial “second half of the chessboard” where exponential growth upon exponential growth creates the incomprehensible.73 The upshot is that our regulatory and policy infrastructures are woefully inadequate and adapting too slowly or not at all to the requirements of the digital age. The disruptions of today are moving so fast they are getting beyond the capacity of individuals and institutions to comprehend them, let alone manage their impact.

pages: 323 words: 90,868

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

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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.

Yet on the first square of the second half the king must pay that entire sum again, and then twice that, until he owes a Mount-Everest-sized pile of rice. The tale is meant to illustrate the deceptive nature of exponential growth. Decades of progress can yield meaningfully large improvements that nonetheless fall short of transformative change. But each generation of progress is as significant as the sum of all those that came before. Around the time that the process of advance reaches the first square of the second half of the chessboard, the capacities of cutting-edge technologies become truly breathtaking: machines can suddenly drive cars, or hear and understand human speech, or look at a photograph and describe exactly what they see – advances that looked unattainable just a few years before. Those advances open up dramatic and slightly frightening new economic opportunities. And just as the very first start-ups experimenting with the very first business models based on those technologies venture into the marketplace, the next generation of technological advance lands, and adds as much new power as the industry managed to develop in every previous generation of innovation – including the one before, which brought all that scary new machine capacity.

pages: 339 words: 88,732

The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies by Erik Brynjolfsson, Andrew McAfee

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We present this calculation here because it underscores an important idea: that exponential growth eventually leads to staggeringly big numbers, ones that leave our intuition and experience behind. In other words, things get weird in the second half of the chessboard. And like the emperor, most of us have trouble keeping up. One of the things that sets the second machine age apart is how quickly that second half of the chessboard can arrive. We’re not claiming that no other technology has ever improved exponentially. In fact, after the one-time burst of improvement in the steam engine Watt’s innovations created, additional tinkering led to exponential improvement over the ensuing two hundred years. But the exponents were relatively small, so it only went through about three or four doublings in efficiency during that period.9 It would take a millennium to reach the second half of the chessboard at that rate. In the second machine age, the doublings happen much faster and exponential growth is much more salient.

That’s a reasonable quantity—about one large field’s worth—and the emperor did start to take notice. But the emperor could still remain an emperor. And the inventor could still retain his head. It was as they headed into the second half of the chessboard that at least one of them got into trouble.8 Kurzweil’s great insight is that while numbers do get large in the first half of the chessboard, we still come across them in the real world. Four billion does not necessarily outstrip our intuition. We experience it when harvesting grain, assessing the fortunes of the world’s richest people today, or tallying up national debt levels. In the second half of the chessboard, however—as numbers mount into trillions, quadrillions, and quintillions—we lose all sense of them. We also lose sense of how quickly numbers like these appear as exponential growth continues.

David Hall, the company’s founder and CEO, estimates that mass production would allow his product’s price to “drop to the level of a camera, a few hundred dollars.”24 All these examples illustrate the first element of our three-part explanation of why we’re now in the second machine age: steady exponential improvement has brought us into the second half of the chessboard—into a time when what’s come before is no longer a particularly reliable guide to what will happen next. The accumulated doubling of Moore’s Law, and the ample doubling still to come, gives us a world where supercomputer power becomes available to toys in just a few years, where ever-cheaper sensors enable inexpensive solutions to previously intractable problems, and where science fiction keeps becoming reality. Sometimes a difference in degree (in other words, more of the same) becomes a difference in kind (in other words, different than anything else). The story of the second half of the chessboard alerts us that we should be aware that enough exponential progress can take us to astonishing places.

pages: 602 words: 177,874

Thank You for Being Late: An Optimist's Guide to Thriving in the Age of Accelerations by Thomas L. Friedman

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The king agreed, noted Brynjolfsson and McAfee—without realizing that sixty-three instances of doubling yields a fantastically big number: something like eighteen quintillion grains of rice. That is the power of exponential change. When you keep doubling something for fifty years you start to get to some very big numbers, and eventually you start to see some very funky things that you have never seen before. The authors argued that Moore’s law just entered the “second half of the chessboard,” where the doubling has gotten so big and fast we’re starting to see stuff that is fundamentally different in power and capability from anything we have seen before—self-driving cars, computers that can think on their own and beat any human in chess or Jeopardy! or even Go, a 2,500-year-old board game considered vastly more complicated than chess. That is what happens “when the rate of change and the acceleration of the rate of change both increase at the same time,” said McAfee, and “we haven’t seen anything yet!”

That is what happens “when the rate of change and the acceleration of the rate of change both increase at the same time,” said McAfee, and “we haven’t seen anything yet!” So, at one level, my view of the Machine today is built on the shoulders of Brynjolfsson and McAfee’s fundamental insight into how the steady acceleration in Moore’s law has affected technology—but I think the Machine today is even more complicated. That’s because it’s not just pure technological change that has hit the second half of the chessboard. It is also two other giant forces: accelerations in the Market and in Mother Nature. “The Market” is my shorthand for the acceleration of globalization. That is, global flows of commerce, finance, credit, social networks, and connectivity generally are weaving markets, media, central banks, companies, schools, communities, and individuals more tightly together than ever. The resulting flows of information and knowledge are making the world not only interconnected and hyperconnected but interdependent—everyone everywhere is now more vulnerable to the actions of anyone anywhere.

The PS3 fits underneath a television, runs off a normal power socket, and you can buy one for under two hundred [pounds]. Within a decade, a computer able to process 1.8 teraflops went from being something that could only be made by the world’s richest government for purposes at the furthest reaches of computational possibility, to something a teenager could reasonably expect to find under the Christmas tree. Now that Moore’s law has entered the second half of the chessboard, how much farther can it go? A microchip, or chip, as we said, is made up of transistors, which are tiny switches; these switches are connected by tiny copper wires that act like pipes through which electrons flow. The way a chip operates is that you push electrons as fast as possible through many copper wires on a single chip. When you send electrons from one transistor to another, you are sending a signal to turn a given switch on and off and thus perform some kind of computing function or calculation.

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The Innovation Illusion: How So Little Is Created by So Many Working So Hard by Fredrik Erixon, Bjorn Weigel

., “Job Satisfaction.” 4.Blanchflower and Oswald, “Well-Being, Insecurity, and the Decline of American Job Satisfaction.” 5.Crabtree, “Worldwide, 13% of Employees Are Engaged at Work.” 6.Dreyer and Hindley, “Trade in Information Technology Goods.” 7.The Economist, “Planet of the Phones.” 8.Bogost, “The Secret History of the Robot Car.” 9.The “second half of the chessboard” is an expression by Ray Kurzweil to explain the power of exponential growth. Legend has it that when the inventor of chess presented the game to the emperor of India and was offered to choose a reward, he asked for one grain of rice on the first square, two on the second, four on the third, and so one. The emperor found the request modest but accepted it. It was not until they got to the second half of the chessboard that the emperor realised where it would end. At the sixty-fourth square, the pile of rise equaled the size of Mount Everest. 10.Nietzsche, Thus Spoke Zarathustra, 41. 11.Levy, Love and Sex with Robots. 12.Holley, “Apple Co-founder on Artificial Intelligence.” 13.Romm, “Americans Are More Afraid of Robots Than Death.” 14.Smith and Anderson, “AI, Robotics, and the Future of Jobs.” 15.This section on Stafford Beer and Project Cybersyn builds on Medina, Cybernetic Revolutionaries. 16.Medina, Cybernetic Revolutionaries, 25. 17.Morozov, “The Planning Machine.” 18.Huebner, “A Possible Declining Trend for Worldwide Innovation,” 985. 19.Taleb, Antifragile. 20.Kelly, “The New Socialism.” 21.Mason, Postcapitalism. 22.The Economist, “Caught in the Net.” 23.Gilder, Microcosm. 24.Carswell, The End of Politics and the Birth of iDemocracy. 25.Fukuyama, The End of History, 98–108. 26.Kaminsky, “Iran’s Twitter Revolution.” 27.Nixon, “Lack of Innovation Leaves EU Trailing.” 28.OECD, “Territorial Review: Stockholm, Sweden 2006.” 29.Legrain, European Spring, 367. 30.Gordon, “Secular Stagnation.” 31.Gage, “The Venture Capital Secret.” 32.Marmer et al., “Startup Genome Report Extra,” 10. 33.Schumpeter’s vision of capitalism is explained in Schumpeter, The Theory of Economic Development and, in a different way, in Schumpeter, Capitalism, Socialism, and Democracy. 34.For a discerning analysis of the similarities between Marx and Schumpeter, see Elliott, “Marx and Schumpeter on Capitalism’s Creative Destruction.” 35.Schumpeter, Capitalism, Socialism, and Democracy (1992), 61. 36.To avoid repetition in the book we will use terms like contestable innovation, big innovation, radical innovation, or game-changing innovation to describe the same phenomenon: innovation that contests markets. 37.Mokyr, “Long-Term Economic Growth and the History of Technology,” 4. 38.Broadberry et al., British Economic Growth. 39.Clark, A Farewell to Alms, 1. 40.Phelps, Mass Flourishing. 41.Our version of modern capitalism and its birth draws on several scholars such as Gregory Clark, David Landes, Joel Mokyr, and Edmund Phelps.

If you suffer from rheumatoid arthritis, you can implant SetPoint’s nerve stimulator and download the tablet app to manage it. If you are worried about colon cancer, you no longer have to wait for an appointment with a cancer specialist: you can use PillCam’s digestive tract sensor to screen for it. Electronic devices will soon be able to communicate with each other and perform everyday services in real time, without our command or even knowledge. Data, like money, never sleeps. When it reaches the “second half of the chessboard,”9 to use a phrase from techno-futurists, the exponential growth of computer capacity can disrupt life, technology, and markets far faster than in the past. Experts quarrel about the exact date, but in a few decades they say we will reach the point of technological singularity. That is when artificial intelligence (AI) will outsmart human intelligence. Robots will then not just beat us at chess but recursively improve themselves and constantly develop their own skills in a way that humans can no longer control.

pages: 464 words: 116,945

Seventeen Contradictions and the End of Capitalism by David Harvey

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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: 696 words: 143,736

The Age of Spiritual Machines: When Computers Exceed Human Intelligence by Ray Kurzweil

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That’s a reasonable quantity—about one large field’s worth—and the emperor did start to take notice. But the emperor could still remain an emperor. And the inventor could still retain his head. It was as they headed into the second half of the chessboard that at least one of them got into trouble. So where do we stand now? There have been about thirty-two doublings of speed and capacity since the first operating computers were built in the 1940s. Where we stand right now is that we have finished the first half of the chessboard. And, indeed, people are starting to take notice. Now, as we head into the next century, we are heading into the second half of the chessboard. And this is where things start to get interesting. OKAY, LET ME GET THIS STRAIGHT, MY CONCEPTION AS A FERTILIZED EGG WAS LIKE THE UNIVERSE’S BIG BANG—UH, NO PUN INTENDED—THAT IS, THINGS STARTED OUT HAPPENING VERY FAST, THEN KIND OF SLOWED DOWN, AND NOW THEY’RE REAL SLOW?

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

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.