January 22, 2022 5:24 pm

The “number of God”, Rubik magic and a better investment than gold: Lego blocks

With over 30 degrees Celsius and oppressive humidity in and around Buenos Aires, the weekend after last Christmas Eve most people opted to rest and recover. This was not the case of some 30 families, many of whom traveled on Saturday December 25 from various provinces to participate on Sunday 26, very early and in the Defensores de la Loma Club (in Lomas del Mirador), of the Rubik’s Cube Christmas Open. The “cubera family” had exhausted the online registration for the tournament the previous week, in just 15 minutes: about 50 fans of this three-dimensional puzzle were left wanting to compete in the different categories, in an instance that validates records internationally.

The enthusiasm has largely to do with the quarantine, in which many kids have perfected this hobby that requires patience and time, as well as algorithmic thinking. Argentina has very good cuberos: Bautista Bonazzola holds the South American record in 3x3x3 (the most popular format), with a 5.5 second mark, and Manuel Gutman He was world champion in Australia 2019 in the same cube size, but blind (you have to memorize the entire resolution sequence and then execute it): he did it in 18.44 seconds. In the event of 26, a possible breaking of the world record in Megaminx (twelve faces) was expected, but the candidate to break it could not attend due to being close contact of someone with Covid.

The magic cube or Rubik It was invented in 1974 by the Hungarian sculptor and professor of architecture Erno Rubik. Although it reached its peak of popularity in the 80s, it has only been since 2003 that the World Cube Association organizes competitions around the world and certifies the records.

Rubik says that the idea came out of nowhere and that the success took him by surprise. He invented it at home, when he was very young, bored, when his parents divorced and his sister went to study medicine in another city. Three years passed between the moment it occurred to him and the moment it was released on the market, because no one thought it had a good chance of selling.

Rubik invented the cube at home, when he was very young, bored, when his parents divorced and his sister went to study medicine in another city. Between the moment it occurred to him and the moment it was released on the market, three years passed

In a book he published in 2020, Cubed: The Puzzle of us all (not yet translated), reviews his memoirs and talks about a Rubik philosophy built around this icon of pop design. “The character of the cube is contradictory, a mixture of simplicity and complexity,” he said in an interview. “The product’s slogan in Japanese is ‘a minute to learn it, a lifetime to perfect it’. You never finish it, there will always be new challenges and discoveries ”.

Before its occurrence, Rubik spent time putting together two-dimensional puzzles. “The puzzles bring out important qualities in each one of us: concentration, curiosity, sense of the game, the desire to discover a solution”, explained in his book. “These are the same qualities that form the basis of all human creativity,” he added.

But the Rubik’s cube hides other infinite secrets. For the mathematician Pablo Groisman, professor of Exact and director of the Data Sciences career at the UBA, “The Rubik’s cube lends itself to doing a lot of super interesting math. It is full of beautiful questions, many still unanswered. Good questions, the kind that serve to learn about relevant issues “.

Groisman has been doing very popular threads on Twitter about mathematics, under the hashtag #TeRegaloUnTeorema, which will become a book in 2022 published by TantaAgua editorial. In his last thread he immersed himself in the ocean of knowledge that hides only behind 3×3 (which, says Groisman, makes for a separate book).

Among other interesting questions, the mathematician wondered in how many movements the cube can be solved. “This number is called God number, and the precise definition says that it is the smallest number N of movements such that, starting from any configuration, it is possible to solve the cube in at most N steps. That number, as we know since July 2010, is 20, after having passed through several higher levels: 52 in 1981, 42 in 1990, 29 in 2000, 22 in 2008 and finally 20, obtained thanks to the fact that Google donated the equivalent of 36 years of CPU to solve the cube from all possible configurations in less than 21 movements, ”says the Exactas professor, who also teaches in China.

A question posed by the mathematician Pablo Groisman is in how many movements can the cube be solved. That number, as we know since July 2010, is 20.

Another question Groisman posed is whether the cube can be solved at random. “This concern is very similar to whether a monkey typing keys at random is ever going to write the complete works of Shakespeare (Borges’ theorem) and whether it is possible to win at Tetris,” he explains.

The French mathematician and politician Emile Borel demonstrated that if an event has a positive probability of occurring – no matter how small it is – if we independently “repeat the experiment” infinitely many times, the event will surely occur. “Infinite times. Infinite times the monkey will type Hamlet, infinite times we will solve the magic cube with random movements ”, says Groisman.

But the key is, as with monkeys and Tetris, in calculating the time necessary for that to happen for the first time, which is of such a great magnitude that several times the lifetime of the universe would not be enough for us to see it. . “Why then is it important to understand how likely things are unlikely. It helps us, among other things, to understand the properties of matter. What things can really happen and what are only speculations, as with the Kepler conjecture ”, adds the mathematician from the UBA and the University of Shanghai.

“In addition to serving us to talk about very relevant issues related to chance, the cube naturally lends itself to talking about group theory, a core area of ​​mathematics Groisman says. This abstraction is precisely what allows dealing with the same ideas and tools to the magic cube, to the matrices, to physical systems such as crystals or the hydrogen atom, to cryptographic problems and all kinds of symmetries that are so essential for the understanding of the universe”.

In his fury, in the 80s, 100 million cubes were sold in three years. A great deal, no doubt, although not as much as buying Lego boxes: According to a study by the Moscow University School of Economics published last month, those who have bought kits of these blocks since 1987 saw their value rise to 11% per year (thanks to the collectibles market and some scarcity): more than gold, stocks or bonds, on average. “Tens of thousands of transactions are carried out each year in the Lego secondary market,” says Moscow academic Victoria Dobrynskaya, one of the study’s authors. Not infinite typing monkeys could have guessed it.


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