An Appreciation of Piet Hein: The Man Who Wrote 10,000 Grooks

“One of these days I will get around to explaining why this dead Danish guy is such an inspiring 21st-century figure, but in the meantime, just take it on faith” – Bruce Sterling

In a sort of reverse internal earthquake that happened to me recently, I realized that the Soma Cube, a childhood obsession that I passed on to my children, the board game Hex, a mid-life obsession that I also passed on to my children, and grooks, brilliant little poems that I should really get my kids interested in, were all the product of one man, a mathematician / poet / furniture designer / playwright / national treasure (in Denmark) / ladies man / philosopher / game designer named Piet Hein (1905-1996). In the depth and breadth of his thinking only his fellow polymaths Leonardo da Vinci or Buckminster Fuller compare – but they get far better press. Compare Google searches: Leo turns up 11,000 pages, Bucky is close with 9,500 pages, but Piet (pronounced ‘Pete’) only rates 2,000 pages, and many of these, probably most, have to do with other Piet Heins, as it is rather a common name in some parts of the world. There are no biographies of the man, precious few magazine articles, and only perfunctory mentions in encyclopedias. He is the greatest mind you never heard of. Why?

He chose his mother tongue unwisely. Danish, which even Hein characterized as a guttural disease, has only 5 million or so speakers. It is a linguistic jail for a poet-philosopher. Though he could not be better known in Denmark—where a clever speaker is defined as a man who can go 30 minutes without quoting Piet Hein—Hein only flirted with real fame in the rest of the world. His closest approach came in 1964 when he invented the super-ellipse, a mathematically valid curve that was his response to the problem of Sergel’s Square in Stockholm. A traffic loop was needed in the roughly rectangular city center. A circle would not work, an ellipse wasted space in the corners, a rectangle would not allow fast traffic flow—what to do? Hein described his thinking about the problem in an essay that perfectly captures his blend of poetry, philosophy and science:

A Super Ellipse

“Man is the animal that draws lines which he himself then stumbles over. In the whole pattern of civilization there have been two tendencies, one toward straight lines and rectangular patterns and one toward circular lines. There are reasons, mechanical and psychological, for both tendencies. Things made with straight lines fit well together and save space. And we can move easily—physically or mentally—around things made with round lines. But we are in a straitjacket, having to accept one or the other, when often some intermediate form would be better. To draw something freehand—such as the patchwork traffic circle they tried in Stockholm—will not do. It isn’t fixed, isn’t definite like a circle or square. You don’t know what it is. It isn’t esthetically satisfying. The super-ellipse solved the problem. It is neither round nor rectangular, but in between. Yet it is fixed, it is definite—it has a unity.” Put simply, Piet Hein took nothing for granted, not even rectangles. The super-ellipse went on to a career in furniture and industrial design, and currently stars as the body of Big Mike, the Viridian movement mascot.

The Seven Components of a Soma Cube

The Soma Cube and Hex were both billed as children’s games, though they are really—or are also—sophisticated expressions of topological beauty. Of the Cube (marketed by Parker Brothers) Hein wrote, “It is a beautiful freak of nature that the seven simplest irregular combinations of cubes can form a cube again. Variety growing out of unity returns to unity. It is the world’s smallest philosophical system.” It is said that he invented the Cube while daydreaming during one of Neils Bohr’s lectures. Three small cubes can be combined irregularly in only one way, a bracket shape, and four cubes can be combined irregularly in six different ways. These seven polycubes can be combined—there are 240 possibilities—to form a 3×3x3 cube, and many other shapes besides. As a boy, I found it utterly absorbing. A few years ago I made one for myself and my kids; it is still a fascinating sculptural plaything. No home with young minds forming should be or need be without this simple, beautiful puzzle. We tend to haul it out whenever someone visits our home for the first time; we half-seriously suggest that we don’t care to associate with anyone not able to form the cube. As a puzzle, the Soma Cube seems to adapt itself to the puzzler—we’ve never absolutely stumped anyone, and yet no one has ever found it trivial. In other words, we haven’t lost any friends over it… yet.

Hex has the interesting distinction of having been invented by two different distinguished mathematicians. Hein was first, in 1942, and John Nash (who later won a Nobel Prize for his work in game theory) independently re-invented it in 1948 while at Princeton. Hex is played on a grid of hexes, such as one might find on a tiled bathroom floor. Two players place black and white stones alternately, whoever connects opposite sides first wins. The game cannot be drawn, since the only way to prevent your opponent from connecting is to connect yourself. And it is far from trivial; though Nash was able to prove that the first player always has a winning strategy, neither he nor anyone else has been able to show what that strategy is. On a grid of 8×8, hex’s complexity approaches chess, on a 13×13 grid, as commonly played, it is astronomically higher.

Dandelions in seed were meaningful to Hein all his life. In his homes and books and journals they were more or less pervasive, appearing in photographs, pictures and in his poems. Of them, he wrote: “I think it’s good not to value things just because they are difficult to get, costly. If the dandelion were not so willing and generous and fertile, I’m sure it would be the most highly valued and appreciated flower in the world because it is so beautiful, so optimistic, so simple, so radiating.” The same is true of grooks, the name he made up for the short, rhyming, gnomic poems that he created so generously. There are 10,000 of them. They contain his whole philosophy, in manageable chunks. They have been compared to Biblical proverbs. Hein, not a modest man, felt that the grooks would be his legacy. He learned English and several other languages so that he could translate them himself. Whether you realize it or not, you’ve heard a grook, or even recited one. They’re everywhere, like dandelions.

Problems
Problems worthy of attack,
prove their worth by hitting back.”

A Maxim for Vikings
Here is a fact that should help you fight a bit longer:
Things that don’t actually kill you outright make you stronger.

Ars Brevis
There is one art, no more, no less:
to do all things with artlessness.

The Road to Wisdom
The road to wisdom?- Well, it’s plain and simple to express:
Err and err and err again
but less and less and less.

Dream Interpretation
Everything’s either concave or –vex,
so whatever you dream will be something with sex.

Grooks began as Hein’s response to Germany’s occupation of Denmark. At the time, he was the president of the Anti-Nazi Union; “Not the best thing to be on April 9, 1940.” the date of the invasion, “I had to go underground.” Under the pseudonym Kumbel (gravestone) he began to publish the Grooks as an oblique way of encouraging his countrymen. He thought there would be just four or five of them; later, when they numbered in the 1,000s, he used to say that he should have named them with more care.

Hein is due, overdue, for his fifteen minutes and it will be a fine thing for the 21st century if the minutes stretch out indefinitely. If it happens, it won’t be for his games, scientific achievements or even the grooks; it will be for his philosophy. In the ‘40s, he began to write of the two cultures, “cultism” and “technocy”, “The first term having not-unintended echoes of ‘occultism’ and the second having certain qualities in common with ‘idiocy’”. So in the 40s he began to describe one of the great divides of our day; the divide, not between the ‘haves’ and the ‘have nots’, but between the ‘knows’ and the ‘know nots’. His solution was art: “Of course I see the necessity for specialization. Nobody more strongly believes in the need to specialize than the person who has trespassed from one field to the other. I do not dispute the need for specialization, but I don’t think the way we do it is the right way. The specialist must know more of the total human activity. It is not just a question of listening politely to a few lectures from people in other fields, or of a few cross-technical conferences. We have to cut over the whole attitude of our civilization. After all, what is art? There is no way of defining art except from the inside. Art is the creative process and it goes through all fields. Einstein’s theory of relativity – now that is a work of art! Einstein was more of an artist in physics than on his violin. Art is this: art is the solution of a problem which cannot be expressed explicitly until it is solved.”

Sadly, Piet Hein is out of print in English. Sadly, because I feel I’m ready for his mind now, trained by days with the Soma Cube and Hex, and exposure to Grooks. It is easy to say that art is the solution to the world’s problems, far more difficult to live it. Hein lived it. “The man who is only a poet,” he used to say, “is not even that.” and, “Whether I am writing a poem or solving some technical problem, I think the same.”

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