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What is the Shape of the universe?
Alexandra Ionescu
→MFA NCSS 2021
My role in the reader’s understanding of this story is to narrate and incite food for thought about the geometry of our thinking. Some paragraphs are left incomplete, with no in-depth explanations given. I imagined what would happen if I had an extensive amount of knowledge in a particular field and what would happen if I encountered a concept radical to this field of expertise, that would throw me into an existential crisis, force me to shift my mental model, question my assumptions, and become aware of my pre-existing knowledge in order to understand it. The story that you are about to read comes a year and a half and many rewrites after the first assignment I received as a graduate student at RISD: to create a fiction based on an object analysis of an item from the RISD Museum, the Nature Lab, or the Fleet Library. This story is an on-going investigation into non-linearity, creative writing, and analytical thinking—or, a search for the shape of thinking that can capture the way in which associations occur in the human mind.
To begin, I chose Buckminster Fuller's structure Six Part Push Pull Tensegrity (1979) from the RISD Museum. I chose this particular object because this is how I learned about RISD—I had previously watched this video on the topic from the Synergetics + Morphology: Explorations into the Shapes of Nature Symposium held by the Synergetics Collaborative: The Philomorphs Group and the Edna Lawrence Nature Lab in 2007.
At first I imagined an interview between myself and Fuller, but as I was sitting in my room I noticed on my left was a copy of Jorge Luis Borges's Labyrinths, on my right there was a copy of Italo Calvino's Mr. Palomar, and in front of me I was writing about tensegrity, a structural principle in which a form maintains its stability through isolated components that are held in tension in such a way that they do not touch each other. In a flash, my mind blended together these three ways of thinking — Fuller's tensegrity structure, Borges's infinite array of hexagonal galleries that comprise his Library of Babel, and the contemplation of a single ocean wave from the first chapter of Mr. Palomar. The following is a thought experiment, more than a story.
Abstract
A fictional character inspired by the architect and inventor Buckminster Fuller (1895-1983) stumbles upon Jorge Luis Borges's short story “The Library of Babel,'' describing a library made of infinite hexagons, which is believed to contain within itself the whole universe. The fictional Fuller believes that the universe is actually a "tensegrity structure" and questions Borges’s geometrical choice of a hexagon. The answer for the fictional Fuller is found in an unexpected place, and perhaps he already knew the answer to the question “What is the shape of the universe?” long before he had asked it.
The thought experiment
It was the morning of May 23rd in the early 1980s when our character inspired by the mind of Buckminster Fuller read the sentence “more incredible than a celestial flower or the flower of a dream is the flower of the future, the unlikely flower whose atoms now occupy other spaces and have not yet been assembled” in H.G. Wells’s book The Time Machine.1
Coincidentally or not, a few days later, in a random newspaper, my fictional character read that the same book is one of Jorge Luis Borges’s favorite books. Not being familiar with the work of the writer, the detail leads him to visit a library where he requests all the books that Borges wrote. The character is given Labyrinths in which he finds the short story “The Library of Babel” which has nothing to do with flowers, but rather with books placed in an infinite hexagonal close packing of space.
The character, like Buckminster Fuller, is already aware that hexagons in three dimensions, unlike spheres, can be packed without leaving any space in between. The character becomes curious about what a writer of short stories, like Borges, would know about the close packing of space in nature. The hexagonal close packing of space is the most efficient way of filling the maximum amount of identical cells in a limited space and can be found across scales in the natural world.2
The character loves to follow unrelated signs because often they lead him to discoveries. The character is a fervent advocate of the fact that the universe speaks to us through signs, and among his multiple obsessions, this is his priority: to pay attention to the associations that appear in each moment. This is a moment that he will follow. He begins to decipher the signs.
During the decipherment of signs, as he was walking the hallways of the library, the concept of a celestial flower reminded him of a flower he once read about, the Snake Gourd flower (Trichosanthes cucumerina). During the daytime, its petals are closed. During the nighttime its petals are open, always occupying a different place in space, always following different pathways of unfoldment, always the same flower, in a different configuration. Our character saw in the flower’s diurnal and nocturnal curling and uncurling the infinite possibilities in which space can configure itself. He also saw the space that has not yet been assembled. Something about the flower reminded him of a tensegrity structure, which he believed was the shape of the universe,3 not a hexagonal pattern.
Did he associate the cyclical curling and uncurling of the fringed, long lace-like tendrils of the Snake Gourd flower with the continuous outward pushing and inward pulling of tensegrity?
Did he imagine that if observers would trace the flower’s outline, they would see a hexagon?
In the moment of perception, what was the unconscious association?4
Across time, various seekers have given the Universe different shapes through their measurements.5 Each seeker’s phenomenological world assigned a certain structure to the already existing structure of nature. What is meant here by “universe” is the cosmos itself—all existing matter and energy including its accelerated expansion. The shape is a concept, a category, a mental construct. This is a story about spatial thinking, the geometry of our thoughts, the shapes we assign to the external world in order to make sense of it.
Sitting in the library with the book opened in his hands, my fictional character started the decipherment process by extracting Borges’s precise statements from his story, an emphasis on the word “precise” because the change of one word can alter one’s perception of the Library.
As my character was walking in the hallways of the library, he spotted Italo Calvino’s Mr. Palomar. He opened the book to the first chapter, “Reading a Wave,” and read about the reflective process of a fictional character trying to understand the composition of a wave:
And in my day-dreaming of how the fictional character would go about finding the answer to this challenge, and as I was pretending to be organizing some drawer full of documents, I found the following notes that Fuller wrote:
In that specific drawer, I also found:
Many questions emerge:
The shape of the universe is the maintenance of pattern12 followed by the moments when its symmetry breaks.
Fig. 1: The search for a shape (projection of a collage printed on a negative).
Courtesy of the author.
Fig. 2: The search for a shape II (projection of a 3D printed model by August Lehrecke). Courtesy of the author.
![]()
Fig. 3: Snake Gourd flower (Trichosanthes cucumerina).
Fig. 4: Snapshots of a Snake Gourd flower (Trichosanthes cucumerina)
in diurnal and nocturnal curling and uncurling.
1 I found this quote in the book Visions and Re-Visions: (Re)Constructing Science Fiction by Robert M. Philmus (Liverpool University Press, 2005), but originally the quote is from H.G. Wells's book The Time Machine (1895). In the essay “Jorge Luis Borges and the Labyrinths of Time,” Philmus mentions that The Time Machine was one of the first books Borges read, and described it as a book that “will be incorporated into the general memory of species.”
2 For more information on this topic, see Philip Ball's article "Why Nature Prefers Hexagons" (2016) and watch the PBS video "Why Nature Loves Hexagons" (2017).
3 Buckminster Fuller talking about tensegrity at the planetary scale: “I saw that the Earth does not touch the Moon, that the electron is remote from the nucleus as Earth is from the Moon with their respective diameters. Nothing in the universe touches anything else.”
4 "The Geometry of Thought: A Conversation with Barbara Tversky” was very influential for me writing this story, in particular Dr. Tversky’s own reflective process about how the human mind creates associations and how our mental structures influence the way in which we perceive the world.
5 For more information on the topic, see Quanta Magazine’s two articles: "What Is the Geometry of the Universe?" (2020) and "What Shape Is the Universe? A New Study Suggest We've Got It All Wrong" (2019)."
6 “The Library of Babel,” Labyrinths: Selected Stories & Other Writings. Jorge Luis Borges, Donald A. Yates (ed.). New Directions, 2007, pp. 51–67.
7 Mr. Palomar. Italo Calvino. Mariner Books, 1986, pp. 3–9.
8 Synergetics: Explorations in the Geometry of Thinking. R. Buckminster Fuller. Macmillan Pub Co, 1983, p. 84.
9 Fuller, Buckminster R. “Conceptuality of Fundamental Structures.” Structure in Art and in Science. Gyorgy Kepes, G. Braziller, 1965.
10 When researching on tensegrity, I read about the conflict between Buckminster Fuller and sculptor Kenneth Snelson. Snelson was experimenting with mobile structures, when he found the structural principle of tensegrity. When he was a second-year art student, he spent the summer at Black Mountain College in North Carolina. It is where he met Buckminster Fuller after he was assigned the task of helping Fuller prepare for his lectures. Buckminster Fuller coined the term “tensegrity” by combining “tension” and “integrity” despite the fact that Kenneth Snelson named his first prototype a “floating compression structure.” See this interview with Kenneth Snelson and a letter he wrote about this subject here.
11 I learned about “The Philomorphs” by going through the boxes of archives of the Arthur Loeb Design Science Collection found in RISD's Nature Lab while conducting research for this piece. Spending time in the collection, I learned that the book Space Structures: Their Harmony and Counterpoint (1976) by Arthur Loeb is dedicated to the philomorphs. In the forward of the book, there is an in depth explanation: “The author and I, respectively a mathematician and a metallurgist, have often met as members of a group of people who call themselves the Philomorphs: biologists, artists, crystallographers, architects, sociologists and others-brought together by a common interest in the underlying patterns of interaction between things.” The philomorphs were a group in the 1960s who met in informal contexts in Cambridge to discuss art, science, nature, and design. Loeb was a former colleague of Buckminster Fuller.
12 “The molecules and cells that form our tissues are continually removed and replaced; it is the maintenance of pattern and architecture, I reasoned, that we call life.” Ingber, Donald E. “The Architecture of Life.” Scientific American. January 1998.
To begin, I chose Buckminster Fuller's structure Six Part Push Pull Tensegrity (1979) from the RISD Museum. I chose this particular object because this is how I learned about RISD—I had previously watched this video on the topic from the Synergetics + Morphology: Explorations into the Shapes of Nature Symposium held by the Synergetics Collaborative: The Philomorphs Group and the Edna Lawrence Nature Lab in 2007.
At first I imagined an interview between myself and Fuller, but as I was sitting in my room I noticed on my left was a copy of Jorge Luis Borges's Labyrinths, on my right there was a copy of Italo Calvino's Mr. Palomar, and in front of me I was writing about tensegrity, a structural principle in which a form maintains its stability through isolated components that are held in tension in such a way that they do not touch each other. In a flash, my mind blended together these three ways of thinking — Fuller's tensegrity structure, Borges's infinite array of hexagonal galleries that comprise his Library of Babel, and the contemplation of a single ocean wave from the first chapter of Mr. Palomar. The following is a thought experiment, more than a story.
Abstract
A fictional character inspired by the architect and inventor Buckminster Fuller (1895-1983) stumbles upon Jorge Luis Borges's short story “The Library of Babel,'' describing a library made of infinite hexagons, which is believed to contain within itself the whole universe. The fictional Fuller believes that the universe is actually a "tensegrity structure" and questions Borges’s geometrical choice of a hexagon. The answer for the fictional Fuller is found in an unexpected place, and perhaps he already knew the answer to the question “What is the shape of the universe?” long before he had asked it.
The thought experiment
It was the morning of May 23rd in the early 1980s when our character inspired by the mind of Buckminster Fuller read the sentence “more incredible than a celestial flower or the flower of a dream is the flower of the future, the unlikely flower whose atoms now occupy other spaces and have not yet been assembled” in H.G. Wells’s book The Time Machine.1
Coincidentally or not, a few days later, in a random newspaper, my fictional character read that the same book is one of Jorge Luis Borges’s favorite books. Not being familiar with the work of the writer, the detail leads him to visit a library where he requests all the books that Borges wrote. The character is given Labyrinths in which he finds the short story “The Library of Babel” which has nothing to do with flowers, but rather with books placed in an infinite hexagonal close packing of space.
The character, like Buckminster Fuller, is already aware that hexagons in three dimensions, unlike spheres, can be packed without leaving any space in between. The character becomes curious about what a writer of short stories, like Borges, would know about the close packing of space in nature. The hexagonal close packing of space is the most efficient way of filling the maximum amount of identical cells in a limited space and can be found across scales in the natural world.2
The character loves to follow unrelated signs because often they lead him to discoveries. The character is a fervent advocate of the fact that the universe speaks to us through signs, and among his multiple obsessions, this is his priority: to pay attention to the associations that appear in each moment. This is a moment that he will follow. He begins to decipher the signs.
During the decipherment of signs, as he was walking the hallways of the library, the concept of a celestial flower reminded him of a flower he once read about, the Snake Gourd flower (Trichosanthes cucumerina). During the daytime, its petals are closed. During the nighttime its petals are open, always occupying a different place in space, always following different pathways of unfoldment, always the same flower, in a different configuration. Our character saw in the flower’s diurnal and nocturnal curling and uncurling the infinite possibilities in which space can configure itself. He also saw the space that has not yet been assembled. Something about the flower reminded him of a tensegrity structure, which he believed was the shape of the universe,3 not a hexagonal pattern.
Did he associate the cyclical curling and uncurling of the fringed, long lace-like tendrils of the Snake Gourd flower with the continuous outward pushing and inward pulling of tensegrity?
Did he imagine that if observers would trace the flower’s outline, they would see a hexagon?
In the moment of perception, what was the unconscious association?4
Across time, various seekers have given the Universe different shapes through their measurements.5 Each seeker’s phenomenological world assigned a certain structure to the already existing structure of nature. What is meant here by “universe” is the cosmos itself—all existing matter and energy including its accelerated expansion. The shape is a concept, a category, a mental construct. This is a story about spatial thinking, the geometry of our thoughts, the shapes we assign to the external world in order to make sense of it.
Sitting in the library with the book opened in his hands, my fictional character started the decipherment process by extracting Borges’s precise statements from his story, an emphasis on the word “precise” because the change of one word can alter one’s perception of the Library.
“The Universe (which others call the Library) is composed of an indefinite, perhaps infinite number of hexagonal galleries.”
“The library is a sphere whose exact center is any hexagon and whose circumference is unattainable.”
“From any hexagon, one can see the floors above and below — one after another, endlessly.”6
As my character was walking in the hallways of the library, he spotted Italo Calvino’s Mr. Palomar. He opened the book to the first chapter, “Reading a Wave,” and read about the reflective process of a fictional character trying to understand the composition of a wave:
“You cannot observe a wave without bearing in mind the complex features that concur in shaping it and the other, equally complex ones that the wave itself originates. These aspects vary constantly, so each wave is different from another wave, even if not immediately adjacent or successive; in other words, there are some forms and sequences that are repeated, though irregularly distributed in space and time.”7
And in my day-dreaming of how the fictional character would go about finding the answer to this challenge, and as I was pretending to be organizing some drawer full of documents, I found the following notes that Fuller wrote:
“Universe does not have a shape. Do not waste your time, as man has been doing for ages, trying to think of a unit shape outside which there must be something or within which, at the center, there must be a smaller something.”
“All the words in the dictionary do not make one sentence; all the words cannot be simultaneously considered, yet each of these words is valid as a tool of communication; and some words combine in a structure of meaning.”8
[...]
“Do not waste your time looking for a singular unit shape. Shapes are just tools for communication.”9
In that specific drawer, I also found:
A photograph of Saturn’s hexagon, the compound eye of a dragonfly, soap bubbles, and honeycombs
A photograph of snapshots of different oceans’ waves breaking
A photograph of snapshots of a Snake Gourd flower (Trichosanthes pilosa) diurnal and nocturnal, curling and uncurling
A diagram of the anatomy of an ocean wave
A set of sketches of the proposed shapes of the universe
And a photograph of Kenneth Snelson's Needle Tower10
Many questions emerge:
What is the function of the library, should the shape need to follow?
Why would a library be a tensegrity structure and not a hexagonal array?
Can we define what the “universe” means in order to give it a shape?In the end, I believe that my fictional character should contact one of the philomorphs, a group of people who were constantly trying to understand the structure of things.11
The shape of the universe is the maintenance of pattern12 followed by the moments when its symmetry breaks.
Fig. 1: The search for a shape (projection of a collage printed on a negative).
Courtesy of the author.
Fig. 2: The search for a shape II (projection of a 3D printed model by August Lehrecke). Courtesy of the author.
Fig. 3: Snake Gourd flower (Trichosanthes cucumerina). Fig. 4: Snapshots of a Snake Gourd flower (Trichosanthes cucumerina)
in diurnal and nocturnal curling and uncurling.
1 I found this quote in the book Visions and Re-Visions: (Re)Constructing Science Fiction by Robert M. Philmus (Liverpool University Press, 2005), but originally the quote is from H.G. Wells's book The Time Machine (1895). In the essay “Jorge Luis Borges and the Labyrinths of Time,” Philmus mentions that The Time Machine was one of the first books Borges read, and described it as a book that “will be incorporated into the general memory of species.”
2 For more information on this topic, see Philip Ball's article "Why Nature Prefers Hexagons" (2016) and watch the PBS video "Why Nature Loves Hexagons" (2017).
3 Buckminster Fuller talking about tensegrity at the planetary scale: “I saw that the Earth does not touch the Moon, that the electron is remote from the nucleus as Earth is from the Moon with their respective diameters. Nothing in the universe touches anything else.”
4 "The Geometry of Thought: A Conversation with Barbara Tversky” was very influential for me writing this story, in particular Dr. Tversky’s own reflective process about how the human mind creates associations and how our mental structures influence the way in which we perceive the world.
5 For more information on the topic, see Quanta Magazine’s two articles: "What Is the Geometry of the Universe?" (2020) and "What Shape Is the Universe? A New Study Suggest We've Got It All Wrong" (2019)."
6 “The Library of Babel,” Labyrinths: Selected Stories & Other Writings. Jorge Luis Borges, Donald A. Yates (ed.). New Directions, 2007, pp. 51–67.
7 Mr. Palomar. Italo Calvino. Mariner Books, 1986, pp. 3–9.
8 Synergetics: Explorations in the Geometry of Thinking. R. Buckminster Fuller. Macmillan Pub Co, 1983, p. 84.
9 Fuller, Buckminster R. “Conceptuality of Fundamental Structures.” Structure in Art and in Science. Gyorgy Kepes, G. Braziller, 1965.
10 When researching on tensegrity, I read about the conflict between Buckminster Fuller and sculptor Kenneth Snelson. Snelson was experimenting with mobile structures, when he found the structural principle of tensegrity. When he was a second-year art student, he spent the summer at Black Mountain College in North Carolina. It is where he met Buckminster Fuller after he was assigned the task of helping Fuller prepare for his lectures. Buckminster Fuller coined the term “tensegrity” by combining “tension” and “integrity” despite the fact that Kenneth Snelson named his first prototype a “floating compression structure.” See this interview with Kenneth Snelson and a letter he wrote about this subject here.
11 I learned about “The Philomorphs” by going through the boxes of archives of the Arthur Loeb Design Science Collection found in RISD's Nature Lab while conducting research for this piece. Spending time in the collection, I learned that the book Space Structures: Their Harmony and Counterpoint (1976) by Arthur Loeb is dedicated to the philomorphs. In the forward of the book, there is an in depth explanation: “The author and I, respectively a mathematician and a metallurgist, have often met as members of a group of people who call themselves the Philomorphs: biologists, artists, crystallographers, architects, sociologists and others-brought together by a common interest in the underlying patterns of interaction between things.” The philomorphs were a group in the 1960s who met in informal contexts in Cambridge to discuss art, science, nature, and design. Loeb was a former colleague of Buckminster Fuller.
12 “The molecules and cells that form our tissues are continually removed and replaced; it is the maintenance of pattern and architecture, I reasoned, that we call life.” Ingber, Donald E. “The Architecture of Life.” Scientific American. January 1998.
Alexandra Ionescu is interested to know what you think the answer to the questions