Week 4. God, Ernõ and the Magic Cube

Between 1972 and 1976, four patents around the world were filed for mechanical puzzles that featured cubes with 2x2x2 or 3x3x3 dimensions. These puzzles were assembled in a variety of ways, including some with simple magnets and some with complex concealed pivot mechanisms, but they were all a variation on the interlocking puzzle that dates to the 3rd century BC. The most famous of these, the Rubik’s Cube — named after patent-filer number 3, Ernõ Rubik — is the best selling toy of all time, in part for its ingenuity, in part for its simplicity, and in part because it can appease weekend dabblers and competitive enthusiasts alike.

The genius of the cube is its apparent plainness — rotate the various layers to align the multicolored cubes with their like-colored mates — and its practical complexity. Not only is it incredibly hard (if not impossible for those like me) to solve without guidance, but there are in fact 43,252,003,274,489,856,000 ways to scramble the cube — which isn’t quite up there with the possible positions on a chess board (~10^50), but it’s nonetheless 43 quintillion, a word we don’t often hear. Which is to say that there are trillions upon trillions of ways the cube might look when you begin to solve it.

The funny thing about math, though, is that even the most absurdly impossible feat is merely a challenge for the right human brain.

Not long after Ernõ Rubik’s “Magic Cube” found its way from behind the Iron Curtain (Rubik is Hungarian and the cube’s first name was “Buvos Kocka”) via Tom Kremer and the Ideal Toy Company in 1980, people began figuring out general solutions. These early solutions often required less than 100 moves and in 1982 David Singmaster and Alexander Frey hypothesized that every possible permutation could be solved by a number of moves in the “low twenties.” In 2007, a pair of computer scientists refined that number to a hard and fast 26. In 2008, Tomas Rokicki lowered it to 22. And in 2010, Rokicki and a few others working with Google lowered it for the last time to a nice and round 20 moves. This number — 20 — is the God’s Number for the Rubik’s Cube.

God’s Number, is hard to achieve for most dabblers, but for the competitive solvers, it’s not far from the norm. The world record for fewest moves to solve, 19, is shared by three people (contestants are given an hour to study the cube and then write down their solutions). The record for the average number solves in a competition is 24.00.

The list of astounding Rubik’s related records goes on — the fastest blindfold solve is 17.87 seconds, the most cubes solved while blindfolded is 41 out of 41, fastest solve is 4.59 seconds — but there’s something neat in our ability to come so close to God — or at least to a theoretical perception of God. God’s Number comes from the idea that God, if given a cube, could always solve it in 20 moves. That we can come so close — 19 moves on three separate occasions — but not quite achieve the perfection at the heart of the number (20 moves, each and every time) says something marvelous about our capacity: that we can identify perfection and nip at its heels. And it says something about both what we can build — the cube; the computer that solved it; the mere possibility, for it would not exist without us and our habitual tinkering — and what we can do with these contrived constraints and ingenious inventions. Buried even deeper is an appraisal of our own self-worth, that God would busy herself with a toy a tinkerer built to better understand three-dimensional mathematics.

All of that, of course, is only true if you’re willing to take the arbitrary moniker a mathematician bestowed to a pretty number seriously. If you don’t, the cube is just the cube: a test of acumen, problem solving and patience.


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