Fairy tales have transfixed readers for thousands of years, and for many reasons; one of the most compelling is the promise of a magical home. How many architects, young and old, have been inspired by a hero or heroine who must imagine new realms and new spaces — new ways of being in this strange world? Houses in fairy tales are never just houses; they always contain secrets and dreams. This project presents a new path of inquiry, a new line of flight into architecture as a fantastic, literary realm of becoming.
— Kate Bernheimer & Andrew Bernheimer
One Grain of Rice
There are many iterations of a story sometimes called “One Grain of Rice.” The story usually begins with the same visual scene — the image of a grain of rice. The grain then begins to multiply and never stops, though the story does come to a natural end.
The story of the single grain of rice can be traced back to the 13th century, to Persia; as with many tales, there are different names and many retellings, and it would be difficult to say which came first. The retelling brought to me by Bernheimer Architecture was in a children’s book intended for pedagogical use, in math class. In this version, by an author named Demi, there is a king who is hoarding rice “in case of famine.” A young and honest girl retrieves some rice that has fallen from a cart headed toward the king, and brings it to him. In gratitude, the king offers the girl a reward. She makes what strikes him as a modest and reasonable request: a single grain of rice, doubled each day. One tiny grain of rice, two tiny grains of rice, four tiny grains of rice …
I learned from Bernheimer Architecture designer Paul Rasmussen that the story can be traced to narratives about the invention of chess. The creator of chess presents the game to the king, who falls in love with it. The king offers him a gift. The inventor asks for one grain of rice, or, depending on where the story was told, possibly wheat, or maybe another grain entirely, doubled for every square of the chess board. Ultimately, the king is unable to pay the inventor, because the number of grains becomes impossibly large. I found the math online:
With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + . . . and so forth for the 64 squares. The total number of grains equals 18,446,744,073,709,551,615 (eighteen quintillion, four hundred forty-six quadrillion, seven hundred forty-four trillion, seventy-three billion, seven hundred nine million, five hundred fifty-one thousand, six hundred and fifteen) — about 2,000 times annual world production — much more than most expect.
The immediate association for me with the mad math of this story is through an iconic Fabergé shampoo advertisement of the 1980s that haunted my teen years. The television segment featured the grainy, pre-high-resolution face of the young actor Heather Locklear: “When I first tried Fabergé Organic Shampoo with wheatgerm and honey, it was so good that I told two friends about it, and they told two friends, and so on, and so on … try it, and you’ll tell your friends about it, and they’ll tell their friends, and so on, and so on …” The 30-second commercial features goodness and gossip (another word for storytelling). Locklear’s lovely face is framed with the feathered hairstyle some of us only could chase but never achieve; the ad presents us with an avatar of mainstream femininity. And as in many fairy tales, it deploys an intuitive logic that flies past us viewers. As Locklear speaks, the image of her face is replicated over and over on the television screen, as “she tells two friends, and so on, and so on.” As if to say, she is her own friends … the single grain of rice, the source of all stories.
Confession: I got a D in math in tenth grade, the last year that I ever took a math class (I seem to recall that my school let me switch over to Russian after I submitted a verse poem instead of the answers to the algebra final). Thinking closely about actual numbers makes me uneasy. The origin story of “One Grain of Rice” is a kind of verbal equivalent of a Maurits Cornelis Escher drawing, which seems not to end at its borders but to continue beyond the page. (Incidentally, it is said that Escher, too, did poorly in school.) I dislike his artwork but I admire his exploration of infinite terror, not unlike that of Jorge Luis Borges in “The Library of Babel,” another story about the impossible pursuit of mimetic perfection. I’m hardly alone in my unease with the idea of the copy. We can consult Sigmund Freud’s concept of “the uncanny” for further examination of why the very notion of doubles evokes a chilling sensation. In a double, for example, we intuitively imagine ourselves mirrored, replicated, reborn, kind of “not-dead” (even after we die). Why else would twins, mannequins, or dolls be so easily used to scare readers of horror? “The idea of the eternal soul allows us an energetic denial of the power of death,” wrote Freud; but of course, we cannot fail to think of death when we see double.
This story may offer a lesson about doubling in math, but it is not about math. And it isn’t a frightening story; it’s about goodness.
I respect the story’s possible origins with regard to the inventor of chess. Yet I have more fondness for the charming retelling Bernheimer Architecture brought me, the math book where a clever girl asks a greedy king, the hoarder of rice in a famine, for a seemingly modest payment for her good deed: one grain of rice, two grains of rice, four grains of rice. This story may offer a lesson about doubling in math, but it is not about math. And it isn’t a frightening story; it’s about goodness. Its heroine rules over a methodical game in an unequal society and brings forth a glorious outcome for people who are hungry. She is the winner of that impossible croquet game in Alice’s Adventures in Wonderland — she is handed a flamingo and makes her way across the board, step by step, with total panache!
The story also suggests a lovely choreography, which is captured beautifully by Bernheimer Architecture in their abstracted representations of replicated rice grains. The moment I first saw their drawings, I was transported back to 1985, when, as a dance student in college, I learned an iconic work called “Accumulation,” by Trisha Brown. Sometimes, at night, students would gather on the lawn and someone would set up a boom box and play music — Laurie Anderson or the Beastie Boys or Janet Jackson. With my dance friends of all genders — all of us sporting barber shop crew cuts, army jackets, house dresses, Converse high tops — we’d do “Accumulation.” Here, in a passage from Trisha Brown: Dance and Art in Dialogue, the choreographer describes the dance’s structure:
One simple gesture is presented. This gesture is repeated until it is thoroughly integrated into my kinesthetic system. Gesture 2 is then added. Gesture 1 and 2 are repeated until they are assimilated, then Gesture 3 is added. I continue adding gestures until my system can support no further additions. The first 4 gestures occur on the first 4 beats. The subsequent gestures are packed into that one measure.
Until the system can support no further additions: This is such an important phrase at a time when the cosmos seems weary of our human abuses; enough is enough, if you will. The girl in “One Grain of Rice” was saying as much. And as it happens, this also suggests a simple and beautiful answer to the question so many students ask: “How do you know when a story you are writing is finished?”
Three Questions for Bernheimer Architecture from Kate Bernheimer
How did you choose this story?
“One Grain of Rice” resonated with us in this time of pandemic. We were wary of aestheticizing data from the catastrophe as a way of visualizing this tale — there are already strong and articulate data visualizations that capture what is happening, how COVID-19 spreads and transmits. Yet the story is so pertinent in this plague year of 2020, especially as every day, on the front pages of the news or on social media, we are confronted with numbers that otherwise might be incomprehensible, growing in ways we can quantify and graph but that nonetheless, because of their scale, remain all too abstract.
What was the very first step you took as you began to adapt this story about replication into a design?
We began with a single mark.
That mark doubles, doubles again, doubles again. Like the grain of rice.
We began by thinking about the act of drawing, of mark-making. But also with a weird constraint — that a framed image with boundaries is itself contradictory, and thus a limited number of elements on a page describing exponential growth is a contradiction, and a strange one. How does one illustrate a path to the infinite, a spiraling out of control (and the seeming chaos that comes with that)? How do you represent that, either physically or virtually, in analog fashion or digitally? The physical page is limited. The computer seems to create a space that is near-infinite; but it is defined by pixels, vectors, finite coded information, typically held within the discrete boundaries of a screen or captured in a facsimile of page-space.
Where did you go from the idea of a mark, and a pixel — how did you create these super-dimensional images? Somehow it strikes me that the idea of the mark or pixel corresponds to the limitations that architects face — or to put it another way, you have to stop somewhere, don’t you? How does a design, like a story, find an end?
We overlap these pixel-based marks and vectors to create space, to reference each other. This limits their own existence (thanks to their reference to each other) but it also allows them to co-exist due to multiplying and cross-hatching, a repeating, a growth without boundary. But unlike paintings or drawings, which exist in a world of (mostly) flatness (Sol LeWitt and Jasper Johns come to mind), the software and spatial media of Rhino and computer modeling permit us architects to create environments within a near-infinite field. Which means we are faced with a conundrum: how do we expand, grow these marks to create the environmentally infinite of the story when our own urge is to create the finite, the controlled? The story of the single grain of rice contains a chess board, a framed space with rules and boundaries. Our files have very few of those. And so our drawings explicate that character in the story: the framed infinite. Our drawing is a collection of countless marks, nearly innumerable pixels, articulating vectors of growth that speak to the infinite while also exerting a level of chaotic control over the story itself. A bit of a parallel to our current struggles, perhaps.