Rubik’s Cube

Why Information Grows: The Evolution of Order, From Atoms to Economies

by Cesar Hidalgo  · 1 Jun 2015  · 242pp  · 68,019 words

statistical physics system), getting a series of consecutive moves right is not easy. Think of a Rubik’s cube. A Rubik’s cube illustrates the connection between available paths and entropy perfectly, since you will never be able to solve a Rubik’s cube by chance (even though in your desperation you might try). A Rubik cube has more

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,856,000, or 4.3 × 1019), only one of which is perfectly ordered. Also, a Rubik’s cube is a system in which order is not that far away, since it is always possible to solve a Rubik’s cube in twenty moves or less.10 That sounds like a relatively small number, but finding the

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recently people believed that the number of moves needed to solve the cube was larger than twenty).11 This goes to show that in a Rubik’s cube there are only a few paths that lead to the perfectly ordered solution, and these paths, whether short or long, are rare, as they are

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hidden among the immense number of paths that push the cube away from order. So the growth of entropy is like a Rubik’s cube in the hands of a child. In nature information is rare not only because information-rich states are uncommon but also because they are inaccessible

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identify them? One important characteristic of information-rich states is that these involve both long-range and short-range correlations. In the case of the Rubik’s cube these correlations are conspicuous12: when the cube is perfectly ordered, each color is surrounded by as many neighbors of the same color as it possibly

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can be. Yet correlations are conspicuous not only in man-made objects, like a Rubik’s cube, but also in nature. Consider a strand of DNA, which involves a long sequence of nucleotides (A, C, T, and G). Strands of DNA are

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.* Finally, I will connect the multiplicity-of-states definition of entropy with our ability to process information (that is, compute). As we saw in the Rubik’s cube example, information-rich states are hard to find, not only because they are rare but also because there are few paths leading to them. That

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’s why we equate the ability of someone to solve a Rubik’s cube with a form of intelligence, since those who know how to solve a Rubik’s cube get credit for finding these rare paths (or memorizing the rules to find them). But there are also

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examples simpler than a Rubik’s cube that we can use to illustrate the connection between the multiplicity of states of a system and computation. Consider the game where babies put shapes

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, since even fewer rotations fit. The case of a triangle with unequal sides (in which only one rotation works) is the baby equivalent of a Rubik’s cube, since only a few babies are able to solve that. So as you can see, as babies develop the ability to fit shapes into holes

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is a good minimalistic model of our ability to process information, or compute. This applies to babies putting shapes into holes, or to teenagers solving Rubik’s cubes. We started this chapter by wrecking an imaginary Bugatti to illustrate that physical order, or information, is what is embodied in a product. Yet we

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Complex Familiarity: A Treatise on Matter, Information, Life and Thought (Oxford: Oxford University Press, 2013), 310. 10. Tomas Rokicki et al., “The Diameter of the Rubik’s Cube Group Is Twenty,” SIAM Journal on Discrete Mathematics 27, no. 2 (2013): 1082–1105. 11. The first estimation of the number of moves needed to

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solve a Rubik’s cube was fifty-two, arrived at in July 1981. Then this number gradually decreased, from forty-two in 1990 to twenty-nine in 2000 and twenty

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-two in 2008, eventually reaching the final number of twenty. See “Mathematics of the Rubik’s Cube,” Ruwix, http://ruwix.com/the-rubiks-cube/mathematics-of-the-rubiks-cube-permutation-group. 12. The idea that information involves aperiodicity and a multitude of

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–51, 61, 178 Rocket development, 143 Rolfe, John, 170 Romer, David, 148 Romer, Paul, 148 Route 128 (Boston), contrasted with Silicon Valley, 118–120, 124 Rubik’s cube, 21–22, 23 Ruiz, Israel, 73 Russia, 60 Salter, Arthur, 90 Saltpeter exports, 55, 58 Samsung, 92 Saxenian, AnnaLee, 118–119 Scale economies, 87–88

Alex's Adventures in Numberland

by Alex Bellos  · 3 Apr 2011  · 437pp  · 132,041 words

had brought back. The walls of his study were decorated with tribal masks, feathered headdresses and woven baskets. Academic books overloaded the shelves. A lone Rubik’s Cube lay unsolved on a ledge. I asked Pica how the trip had been. ‘Difficult,’ he replied. Pica is a linguist and, perhaps because of this

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the puzzle when he was struck with the idea of reinventing it in three dimensions. The man, Ernö Rubik, came up with his prototype, the Rubik’s Cube, which went on to become the most successful puzzle in history. In his 2002 book The Puzzle Instinct, the semiotician Marcel Danesi wrote that an

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course, to discover a new puzzle craze. There have been only four international puzzle crazes with a mathematical slant: the tangram, the Fifteen puzzle, the Rubik’s Cube and Sudoku. So far, the Cube has been the most lucrative. More than 300 million have been sold since Ernö Rubik came up with the

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. It is the nonpareil of puzzledom and, unsurprisingly, its presence was felt at the 2008 G4G. A talk on the Rubik’s Cube in four dimensions drew huge rounds of applause. The original Rubik’s Cube is a 3 × 3 × 3 array made up of 26 smaller cubes, or cubies. Each horizontal and vertical ‘slice’ can

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cube a stroke of genius, but the way he made the blocks fit together was an outstandingly clever piece of engineering. When you dismantle a Rubik’s Cube there is no separate mechanical device holding it all together – each cubie contains a piece of a central, interlocking sphere. As an object, the cube

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has had iconic, mystical status since at least the ancient Greeks. The brand name was also a dream: catchy, with delicious assonance and consonance. The Rubik’s Cube had an Eastern exoticism too, not from Asia this time but from Cold War Eastern Europe. It sounded a lot like Sputnik, the original showpiece

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cube (0.96secs), the 4 × 4 × 4 cube (40.05secs) and the 5 × 5 × 5 cube (1min 16.21 secs). He can also solve the Rubik’s Cube with his feet – his time of 51.36secs is fourth-best in the world. However, Akkersdijk really must improve his performance at solving the cube

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to stop the stopwatch. The current record of 48.05secs was set by Ville Seppänen of Finland in 2008. Other speedcubing disciplines include solving the Rubik’s Cube on a rollercoaster, under water, with chopsticks, while idling on a unicycle, and during freefall. The most mathematically interesting cube-solving category is how to

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from the same configuration in a smaller number of moves if he had had 60 hours? The question that has most intrigued mathematicians about the Rubik’s Cube is this: what is the smallest number of moves, n, such that every configuration can be solved in n moves or less? As a mark

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, each containing 19.5 billion positions, and found again that 20 moves was sufficient for a solution. In 2008 he proved that every other remaining Rubik’s Cube position is only two moves away from a position in one of his collections, giving an upper bound for God’s number of 22. Rokicki

Genius Makers: The Mavericks Who Brought A. I. To Google, Facebook, and the World

by Cade Metz  · 15 Mar 2021  · 414pp  · 109,622 words

a lot like a human hand, except it was made of metal and hard plastic and wired for electricity. Standing nearby, a woman scrambled a Rubik’s Cube and placed it in the palm of this mechanical hand. The hand then began to move, gently turning the colored tiles with its thumb and

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, they’d spent more than two years working toward this eye-catching feat. In the past, many others had built robots that could solve a Rubik’s Cube. Some devices could solve it in less than a second. But this was a new trick. This was a robotic hand that moved like a

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human hand, not specialized hardware built solely for solving Rubik’s Cubes. Typically, engineers programmed behavior into robots with painstaking precision, spending months defining elaborate rules for each tiny movement. But it would take decades, maybe even

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centuries, for engineers to individually define each piece of behavior a five-fingered hand would need to solve a Rubik’s Cube. Zaremba and his team had built a system that could learn this behavior on its own. They were part of a new community of researchers

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to accommodate so easily in the physical world but machines, so often, cannot. By the fall of 2019, OpenAI’s robotic hand could solve a Rubik’s Cube with two fingers tied together or while wearing a rubber glove or with someone nudging the Cube out of place with the nose of a

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up a dozen robotic arms—six arms against one wall, six against the other. They were simpler than the arm that would later solve the Rubik’s Cube inside OpenAI. The hands on these arms were not quite hands. They were “grippers” that could grab and lift objects between two viselike fingers. That

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could beat the world’s best players at a three-dimensional video game called Dota, and a five-fingered robotic hand that could solve the Rubik’s Cube. With their robotic hand, Wojciech Zaremba and his team used the same algorithmic technique as their counterparts at Google. But they moved the training into

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virtual reality, building a system that learned to solve the Rubik’s Cube through centuries of trial and error in the digital world. Training systems in the physical world, they believed, would be far too expensive and time

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-consuming as the tasks grew more complex. Like the lab’s effort to master Dota, the Rubik’s Cube project would require a massive technological leap. Both projects were also conspicuous stunts, a way for OpenAI to promote itself as it sought to attract

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corporate pressures that he and Musk preached when they unveiled the lab in 2015 did not last even four years. All this was why the Rubik’s Cube project was so important to the lab’s future. It was a way for OpenAI to promote itself. The rub was that this kind of

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master the real world. This was what OpenAI did with its robotic hand, training a virtual re-creation of the hand to solve a virtual Rubik’s Cube before moving this know-how into the real world. If they could build a large enough simulation of what humans encounter in their daily lives

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. But in the real world, no one was keeping score. Researchers had to define success in other ways, and that was far from trivial. A Rubik’s Cube was very real, but it was also a game. The goal was easily defined. And still, it wasn’t a problem that was completely solved

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, 324 leadership and mission changes, 292–95 and Microsoft, 298–99 Napa winery meeting to plan, 163 research plan, 163 Rosewood Hotel meeting, 160–63 Rubik’s Cube demonstration, 276–78, 281, 297–98 secrecy of certain technologies, 294–95 setting attention-seeking goals, 281–82 universal language model, 273 open research concept

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Brain robotics group, 279–81 learning human movement, 279–81 programming behavior and skills, 277 robots using dreaming to generate pictures and spoken words, 200 Rubik’s Cube demonstration, 276–78, 281, 297–98 use of Covariant’s automation technology in a Berlin warehouse, 284–85 Rosenblatt, Frank criticism of backpropagation, 38 death

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, 17 Mark I machine development, 18 Perceptron machine demonstration, 15–19 research efforts, 25–26, 34, 36 rivalry with Marvin Minsky, 21–22, 24–25 Rubik’s Cube demonstration at OpenAI, 276–78, 281, 297–98 Rumelhart, David, 37–39, 97 Sabour, Sara, 208, 305 Salakhutdinov, Russ, 63 Schmidhuber, Jürgen, 59–60, 141

Narrative Economics: How Stories Go Viral and Drive Major Economic Events

by Robert J. Shiller  · 14 Oct 2019  · 611pp  · 130,419 words

2  An Adventure in Consilience  12 3  Contagion, Constellations, and Confluence  18 4  Why Do Some Narratives Go Viral?  31 5  The Laffer Curve and Rubik’s Cube Go Viral  41 6  Diverse Evidence on the Virality of Economic Narratives  53 Part II   The Foundations of Narrative Economics 7  Causality and Constellations  71

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will see in the next chapter, which examines the narrative constellations associated with the famous (or infamous) Laffer curve. Chapter 5 The Laffer Curve and Rubik’s Cube Go Viral One of the toughest challenges in the study of narratives is predicting the all-important contagion rates and recovery rates. Despite all the

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us, long-term memory formation involves many regions of the brain, including visual-image processing regions.18 Rubik’s Cube, Corporate Raiders, and Other Parallel Epidemics Another fad appeared around the same time as the Laffer curve. Rubik’s Cube, invented in 1974 by Ernő Rubik, is a puzzle in the form of a cube-shaped

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best-selling Gödel, Escher, Bach (1980), Hofstadter was a science writer with a gift for uniting science with art and the humanities. His article presented Rubik’s Cube as representing deep scientific principles. He described connections to quantum mechanics and the rules for combining the subatomic particles called quarks. Few people remember these

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details today, but they do remember that Rubik’s Cube is somehow impressive. Rubik’s Cube was bigger than the Laffer curve on ProQuest News & Newspapers, but smaller than the Laffer curve on Google Ngrams. Both show similar hump

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was a particularly powerful narrative. It had good visual imagery in the form of a scribbled-on napkin, it had authorities behind it just as Rubik’s Cube had Scientific American, and it suggested that politicians who raised taxes were fools. One narrative circulating in the supply-side economics constellation was a widely

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. “Ten years from now, what difference does it make?” replies the clerk. “Well,” says the car-buyer, “the plumber’s coming in the morning.”25 Rubik’s Cube was just a toy, not support for an economic narrative. But Reagan’s lighthearted jokes made for economically powerful entrepreneurial narratives. These new narratives encouraged

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and risk taking, and they brought about profound changes in the legal structure of the world’s advanced economies. These examples, the Laffer curve and Rubik’s Cube, are just two of a vast universe of narratives. We need to understand their organizing force. The storage points for all these narratives is the

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, 1951, p. 13. 22. Display ad, Los Angeles Times, July 29, 1991, p. A4. 23. Salganik et al., 2016. Chapter 5: The Laffer Curve and Rubik’s Cube Go Viral 1. Shiller, 1995. 2. Litman, 1983. 3. Jack Valenti, in a speech “Motion Pictures and Their Impact on Society in the Year 2001

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fair competition and, 132; confidence narratives and, 114 Roper, Elmo, 196–97 Ross, Andrew, 7 Roth, Benjamin, 141 RSA algorithm, 9–10 Rubik, Ernő, 47 Rubik’s Cube, 47, 52 Rumsfeld, Donald, 44 R.U.R.: Rossum’s Universal Robots (Čapek), 181–82, 196 Ryōkan, 150 Sadow, Bernard, 38 Saiz, Albert, 222 Salganik

Artificial Intelligence: A Modern Approach

by Stuart Russell and Peter Norvig  · 14 Jul 2019  · 2,466pp  · 668,761 words

the true depth. This means that the total search cost is O(bd–kh) compared to O(bd) for an uninformed search. Their experiments on Rubik’s Cube and n-puzzle problems show that this formula gives accurate predictions for total search cost for sampled problem instances across a wide range of solution

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). ABSOLVER generated a new heuristic for the 8-puzzle that was better than any preexisting heuristic and found the first useful heuristic for the famous Rubik’s Cube puzzle. If a collection of admissible heuristics h1 ... hm is available for a problem and none of them is clearly better than the others, which

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in 1878). Ratner and Warmuth (1986) showed that the general n × n version of the 15-puzzle belongs to the class of NP-complete problems. Rubik’s Cube was of course invented in 1974 by Ernő Rubik, who also discovered an algorithm for finding good, but not optimal solutions. Korf (1997) found optimal

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efficient algorithm. Agostinelli et al. (2019) used reinforcement learning, deep learning networks, and Monte Carlo tree search to learn a much more efficient solver for Rubik’s cube. It is not guaranteed to find a cost-optimal solution, but does so about 60% of the time, and typical solutions times are less than

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). The relaxation method for linear inequalities. Canadian Journal of Mathematics, 6, 382–392. Agostinelli, F., McAleer, S., Shmakov, A., and Baldi, P. (2019). Solving the Rubik’s Cube with deep reinforcement learning and search. Nature Machine Intelligence, 1, 356–363. Agrawal, P., Nair, A. V., Abbeel, P., Malik, J., and Levine, S. (2017

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. and Zhang, W. (2000). Divide-and- conquer frontier search applied to optimal sequence alignment. In AAAI-00. Korf, R. E. (1997). Finding optimal solutions to Rubik’s Cube using pattern databases. In AAAI-97. Korf, R. E. and Reid, M. (1998). Complexity analysis of admissible heuristic search. In AAAI-98. Koutsoupias, E. and

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Language Processing. Bradford Books. Rock, I. (1984). Perception. W. H. Freeman. Rokicki, T., Kociemba, H., Davidson, M., and Dethridge, J. (2014). The diameter of the Rubik’s Cube group is twenty. SIAM Review, 56, 645–670. Rolf, D. (2006). Improved bound for the PPSZ/Schoning-algorithm for 3–SAT. Journal on Satisfiability, Boolean

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, 1085 RPM (relational probability model), 643 RRT (rapidly exploring random trees), 954, 985 RRT*, 955 RSA (Rivest, Shamir, and Adelman), 327 Ruan, P, 587, 1113 Rubik’s Cube, 116, 118, 124 Rubin, D., 476, 515, 516, 799, 1093, 1096, 1111 Rubin, J., 1060, 1115 Rubinstein, A., 588, 637, 638, 640, 1085, 1108, 1111

The Pattern Seekers: How Autism Drives Human Invention

by Simon Baron-Cohen  · 14 Aug 2020

two with a delay in social and fine motor development. At age ten, he was given his first Rubik’s Cube, and by age fifteen he had won the World Championship in both the 3x3 Rubik’s Cube and the one-handed events. His average solve time was 6.85 seconds with two hands, and 10

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world. See D. M. Greenberg et al. (2015), “Musical preferences are linked to cognitive styles,” PLoS ONE 10(7), e0131151. 31. On autism and the Rubik’s cube, see S. Baron-Cohen et al. (2009), “Talent in autism: Hyper-systemizing, hyper-attention to detail, and sensory hyper-sensitivity,” Proceedings of the Royal Society

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B 364, 1377–1383. On Max Park, see J. Rapson (2017), “They said autism meant he’d need life-long care—then he got a Rubik’s cube,” For Every Mum, July 29, foreverymom.com/family-parenting/autism-rubiks-cube-max-park/. On June 18, 2014, we hosted an event in Cambridge Union

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called “Autism and the Rubik’s Cube: Creating order from chaos,” with Professor Ernesto Rubik (architect and inventor of the cube); see “Event investigates ‘Autism and the Rubik’s Cube: Creating order from chaos,’” Cambridge Network, June 24, 2014, www.cambridgenetwork.co.uk/news/event

American Kingpin: The Epic Hunt for the Criminal Mastermind Behind the Silk Road

by Nick Bilton  · 15 Mar 2017  · 349pp  · 109,304 words

the pill and, hopefully, talk with them. That day, as Jared’s government-issued Crown Victoria zigzagged through the North Side of Chicago, the small Rubik’s Cube that hung from his key chain swung back and forth in the opposite direction. His car radio was dialed into sports: the Cubs and White

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, Jared, was walking through the halls of the U.S. Attorney’s Office, his giant backpack over his shoulder, which was bulging with laptops, a Rubik’s Cube, and folders with pictures of evidence inside. In his hands he carried a large white mail-room tub filled with thirty or so envelopes of

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he was standing in the Barnes & Noble in Lincolnshire, awkwardly asking about the Mises Institute. In recent weeks he had sat at his desk, a Rubik’s Cube always spinning in his hand, as he read all of the online postings by the Silk Road’s creator, looking for similarities in the author

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54 JARED BECOMES CIRRUS When Jared Der-Yeghiayan was a freshman in high school, his math teacher would walk into class each day with a Rubik’s Cube in hand. Young Jared would watch as the teacher passed the colored square cube around the room, instructing every student to jumble it as much

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as possible. “If I can solve this Rubik’s Cube in under a minute, you all get homework,” the teacher said to the class each day. “If I can’t, you don’t get any

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by a desire to figure out how his teacher could always solve the riddle of the cube. He ran out and picked up his own Rubik’s Cube and spent weeks trying to solve the puzzle. With a lot of tenacity and a smidgen of help from the teacher, he was finally able

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to do the same thing. Over the years, Jared had collected dozens of different Rubik’s Cubes, now scattered all over his home and office. They hung from key chains and fell unexpectedly out of backpacks. To this day Jared had never

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Airport to explore the evidence locker and see the packages and drugs that had been seized the night before. Backpack slung over his shoulder, a Rubik’s Cube inside, he lumbered along the long hallway to the evidence room. He was excited to know that the case he had started working on years

The Psychopath Inside: A Neuroscientist's Personal Journey Into the Dark Side of the Brain

by James Fallon  · 30 Oct 2013

study. But for the sake of simplicity, especially when teaching or writing a paper, I like to organize the brain into a 3×3×3 “Rubik’s Cube” pattern. This twenty-seven-part brain is as simple as I’m willing to go and still be able to sleep at night without violating

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to see if someone has taken one of your french fries when you weren’t looking. FIGURE 3B: Brain hemispheres. The next slicing of the Rubik’s Cube brain is from front, or anterior, to back, or posterior. The most posterior region of the cortex is dedicated to the visual sensory system, as

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1938, when Henry was sixteen and his brother was fourteen, the elder brother kept his pronounced Frankish accent while Walter sounded very American. In the Rubik’s Cube middle sector of the hemisphere, there are the somatic and motor areas that map the skin senses in the back half of this middle piece

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, which appears to be the typical average peak time of human insight, cognition, and understanding in many realms of life. The central cube in the Rubik’s Cube brain consists of the subcortical structures that lie deep in the cortex, and these include the basal ganglia, the thalamus, and the brain stem. The

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ventral morality systems to inhibit me. FIGURE 6E: My PET scan. • • • In early 2013, I came to understand another aspect of my brain. In the Rubik’s Cube model, I discussed the different brain circuits thought to form the anatomical basis of behaviors, from attention to memory, language, emotion, and morality. While no

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conflict between drives and social context, and makes a decision. FIGURE 6F: Dualities perceived by the dorsal prefrontal cortex. A second dualistic circuit, in our Rubik’s Cube brain and the figure just given, involves one part that monitors the outer sensory-motor world that connects us to our external environment. This circuit

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, 153, 200–201, 219–20 risk taking, 218–19 RNA, 76, 89, 94–95 Rockefeller, Nelson, 30 Rodrigues, Sarina, 84, 145 Roth, Eli, 126–29 “Rubik’s Cube” brain model, 49–57, 122–26 Sagman, Doron, 181 Saks, Elyn, 182 Saxe, Rebecca, 148 schizophrenia, 3, 10, 33, 73, 74–76, 78, 85, 86

Permanent Record

by Edward Snowden  · 16 Sep 2019  · 324pp  · 106,699 words

, I’d always take a few—one for myself, and the others to salt across my friends’ workstations. I kept my copy propped against the Rubik’s Cube on my desk, and for a time made a habit of reading it over lunch, trying not to drip grease on “We the People” from

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11 mm for the micro, basically the size of your pinkie fingernail—eminently concealable. You can fit one inside the pried-off square of a Rubik’s Cube, then stick the square back on, and nobody will notice. In other attempts I carried a card in my sock, or, at my most paranoid

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the Tunnel. I’d usually try to banter with the guards, and this was where my Rubik’s Cube came in most handy. I was known to the guards and to everybody else at the Tunnel as the Rubik’s Cube guy, because I was always working the cube as I walked down the halls. I

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of increasingly difficult challenges, is the belief that they can be won. Nowhere is this more clear to me than in the case of the Rubik’s Cube, which satisfies a universal fantasy: that if you just work hard enough and twist yourself through all of the possibilities, everything in the world that

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to a certain quiet alcove by the hotel restaurant, furnished with an alligator-skin-looking pleather couch, and wait around for a guy holding a Rubik’s Cube. The funny thing was that I’d originally been wary of using that bit of tradecraft, but the cube was the only thing I’d

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I was out of the fire. Once we were airborne, I loosened my grip from my thighs and felt an urge to take my lucky Rubik’s Cube out of my bag. But I knew I couldn’t, because nothing would make me more conspicuous. Instead, I sat back, pulled my hat down

Hacking Vim 7.2

by Kim Schulz  · 29 Apr 2010  · 236pp  · 67,823 words

195 196 198 199 Appendix A: Vim Can Do Everything 201 Appendix B: Vim Configuration Alternatives 215 Index 223 Vim games Game of Life Nibbles Rubik's cube Tic-Tac-Toe Mines Sokoban Tetris Programmers IDE Mail program Chat with Vim Using Vim as a Twitter client Tips for keeping your vimrc file

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