by Bright and early on the first Saturday in January, Tomas Rokicki and a few hundred other enthusiasts gathered in a huge lecture hall in the Moscone Center in downtown San Francisco. A major math conference was taking place and Rokicki, a retired computer programmer based in Palo Alto, California, helped organize a special two-day session on “serious recreational mathematics” celebrating the 50th anniversary of the Rubik’s Cube. Erno Rubik, the inventor of the Cube, led the show at 8 am, via video conference from the south of Spain.
Rubik, a Hungarian architect, designer, sculptor and retired professor, participated in a question-and-answer session with Rokicki and his co-organizers, Erik Demaine, a computer scientist at the Massachusetts Institute of Technology, and Robert Hearn, a retired computer scientist, from Portola. Glen, California.
Rokicki asked Rubik about the first time he solved the Cube: “Did you solve corners first?”
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These days, new cubes learn on YouTube, watching tutorials at 1.5x speed. Rokicki recommends instead the old-fashioned strategy: Set out on a single path and find a solution, even if it takes weeks or months. (It took computer scientist Donald Knuth less than 12 hours, starting at his dining table in the evening and working straight through to the morning.) Cornering is a common method the first time, since as soon as the corners are rounded, the edges can be slotted in. relative ease. Rubik said he made corners first, indeed. Rubik, who is known to have a philosophical approach to cubology and life in general, said: “My method was understanding.”
‘Cubitus Magikia’
Rubik dates the Cube to the spring of 1974. While preparing a course on descriptive geometry and tinkering with the five Platonic solids, he was particularly taken by the cube. But, as he wrote in his 2020 memoir, “Cubed, The Puzzle of Us All,” for a long time “it never once occurred to me that I was creating a puzzle.”
By the time of his 30th birthday, in July 1974, he had created the structure, realized its awesome potential and — after toying with it intermittently for a few months — solved the Cube for the first time. He submitted a patent application in January 1975, and by the end of 1977 the “Magic Cube” had debuted in toy stores in Hungary. Travelers packed it “in their luggage, next to other Hungarian delicacies such as sausages and Tokaji wine,” he said.
One enthusiastic exporter and ambassador was David Singmaster, a mathematician who wrote the book “Notes on Rubik’s ‘Magic Cube.'” In it he outlined notation for the faces — Up (U), Down (D), Right ( T), Left (L), Front (F), Back (B) — provide a way to navigate the Cube and reference its pieces, positions and rotations. It also provided a step-by-step solution guide. And he reported a hazard: Dame Kathleen Ollerenshaw, a British politician and recreational mathematician, had developed a case of “‘cubic thumb’, a type of tendinitis that requires minor but delicate surgery to relieve.”
CubeLovers was among the first internet mailing lists – an MIT student sent the inaugural message in July 1980: “I don’t know what we’ll be talking about, but another mailing list can’t hurt (too much).” In March 1981, when the Rubik’s Cube was renamed and hit American toy stores, cognitive scientist Douglas Hofstadter diagnosed the disorder as “cubitis magikia” – “a severe mental disorder accompanied by with him, which can only be alleviated for a long time. contact with a colorful cube,” he wrote in his column for Scientific American. He said: “Symptoms often last for months. Very contagious.”
By November 1982, the mania had died down—“Rubik’s Cube: A Craze Ends,” declared a New York Times headline. But it was resurrected in the 1990s by the World Wide Web. In 2023, Spin Master, the toy company that now owns the brand, sold 7.4 million units worldwide, including both the classic Cube and related complex puzzles. Ben Varadi, co-founder of Spin Master, noted that Rubik has “95% brand awareness” – that almost everyone has heard of it. Rubik’s lore also shows that 1 in 7 people on Earth have played with the Cube. “It gives me hope about the world,” Rubik told his audience in San Francisco. “It brings people together.”
Complexity From Simplicity
After the session with Rubik, Rokicki gave a talk on mathematical aspects of the Cube. It started with the fact that it scrambles into about 43 billion colorful combinations. “A fairly large number,” he said, perhaps more than every grain of sand in the world.
Part of the puzzle’s appeal is the complexity that arises from its simplicity. The Cube is made up of 20 smaller “cubes” (eight corners and 12 edges centered between the corners) and six face-center pieces attached to the core. The core mechanism is anchored by a 3D cross, around which the edge tabs and corner cubes are interlocked in an ingenious geometric way that allows the structure to rotate.
The cubes represent 54 colorful elements, nine of which are white, red, blue, orange, yellow and green. In its solved state, the six faces of the Cube are configured so that all nine faces are the same color. Turning the puzzle over scrambles the colors – in total, there are exactly 43,252,003,274,489,856,000 possible positions in which the elements can be permuted.
All the while, the essential form of the puzzle — its cubicity — remains unchanged. This aspect represents group theory, the mathematical study of symmetry: A so-called symmetry group of a geometric object is a collection, or group, of transformations that can be applied to the object but still leave the structure preserved. A square has eight symmetries: It can be rotated or reflected four ways each and still be a square. A regular cube has 48 symmetries. The Rubik’s Cube has about 43 quintillion.
These symmetries are “amazing properties,” Rokicki said, “that really bring out the beauty of the Cube.”
In much the same vein, the hobby math meeting included talks on how to build an origami computer; the controlled art of juggling (as opposed to “joggling,” chasing a ball uncontrollably); and numerical problems in knitting.
Barry Cipra, a mathematician and math writer, invented a wooden tray puzzle he called the bricklayer’s challenge. The arrangement: four rows of six brick-like blocks of different lengths. The goal: Arrange the bricks so that none of their vertical joints are aligned between adjacent horizontal rows.
As Cipra spoke, some members of the audience rushed to the stage (who had been sent away) and went to work trying to find one of the 2,184 solutions to the puzzle. Among this keen subset were Bram Cohen, a programmer (and inventor of BitTorrent, a file-sharing protocol) who devised Rubik-like puzzles, such as the Maltese Gear Cube (in collaboration with Oskar van Deventer); and Rivka Lipkovitz, high school senior and speed cuber (official personal record in competition, 14.71 seconds; personal at home, 10.75).
Cubic contacts
There are many ways to solve the Cube. During his lecture, Rokicki posed a specific number: What is the minimum number of moves needed to solve even the most scrambled positions?
Rokicki tried to calculate this quantity, called God’s number, in 1999. In 2010 he found the answer: 20. He got help from many talented people, especially Herbert Kociemba, a German hobbyist cuber and programmer known for its named algorithm. The feat also benefited from a lot of computing time donated by Google, and another algorithm that took advantage of the symmetries of the Cube, reducing the number of necessary calculations by a factor of 48, and subsequently reducing the required computing power.
Rokicki’s current obsession is identifying all of God’s number positions — they are “extremely rare, extremely hard to find,” he told the audience. As he spoke, three computers in his home spun the task – their combined 336 gigabytes dig up about 100,000 area-20 posts a day. To date, Rokicki has a database of about 100 million. “They are mathematical gems,” he said.
The Cube is also a good challenge for machine learning systems and robots.
And Maria Mannone, an Italian theoretical physicist and composer, invented the “CubeHarmonic,” a musical instrument, developed with Japanese collaborators. “It’s a Rubik’s Cube where every face has a musical chord, every facet has a note,” she explained in an email. “While scratching the cube, we make a bunch of musical chords.”
Parisian street artist Invader creates “Rubikcubist” works, figurative canvases configured as a mosaic with hundreds of cubes. Invader’s version of “Les Demoiselles d’Avignon,” Picasso’s first cubist painting, used 1,848 cubes to reproduce the same size as the original.
Lauren Rose, a mathematician at Bard College in New York, uses the Cube as a teaching tool in courses for math majors (who delve into algebra) and non-STEM majors (they learn how to solve the puzzle, explore patterns , count configurations, and design and build mosaics). “There is so much depth to this puzzle,” Rose said at the conference in San Francisco. She believes part of the reason the Cube has endured is that it is “so accessible and so fun.”
“It’s a good way to get people to want to learn math,” she said.
By now, all the Platonic solids have been transformed into complicated versions of a puzzle. And riffing on the original, there’s the 4-by-4-by-4 Rubik’s Revenge, the 5-by-5-by-5 Professor’s Cube and going up to the 7-by-7-by -7, the largest. a cube used in World Cube Association competitions. The 21-by-21-by-21 is the largest cube generally available in the supermarket ($1,499.99). The 256-by-256-by-256 exists only in the virtual realm, where a team of six solved it with 633,494 moves in a cumulative time of about 96 hours.
During the question and answer session, Rokicki asked Rubik about the hollow Non-Empty Cube, with Japanese inventor Katsuhiko Okamoto, who created many versions of the original. Somehow, the central cubes and the mechanics inside that hold Rubik’s iconic invention together are missing. On this subject, Rubik got philosophical again. “Perfection is an ideal touch,” he said. He understood the curiosity-driven explorations, putting something, putting something away. He preferred the classic combination of cubes and colors. “I also love the sound of the Cube, the movement,” he said.
Rubik later said that he was less keen on puzzles designed to be only answers. He said, “I love the vague matter of life and the universe as it is.”
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