The Shape of Space

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“The sky starts at your feet. Think how brave you are to walk around.”
— Anne Herbert

“Space is not only high, it’s low. It’s a bottomless pit.”
— Sun Ra

Buckminster Fuller had an unusual way of talking about stairs. Instead of downstairs and upstairs , he encouraged people to say instairs and outstairs . “They all laugh about it,” he wrote, “But if they try saying in and out for a few days in fun, they find themselves beginning to realize that they are indeed going inward and outward in respect to the center of Earth, which is our Spaceship Earth. And for the first time they begin to feel real reality.” Writing in 1970, at the dawn of extra-planetary space travel, Fuller identified a break in humans’ spatial perception. Standing on Earth, we see the ground plane as flat, but we know the planet is a sphere. To describe motion and existence in a vast universe, where planetary surfaces are the exception, we would need a new language.

To describe motion and existence in a vast universe, where planetary surfaces are the exception, we would need a new language.

For centuries, the space away from the Earth’s surface — “outer” space — has confounded attempts to make sense of it with terrestrial geometric schemes. Human occupation of and movement through space on our home planet has been dominated by the horizon and the apparent flatness of the ground plane. Meanwhile, the open sky has been conceived alternately as an unattainable place of infinite freedom or as a hard dome that limits the world, like a cake lid over a Flat Earth. For Nikolai Fyodorov and the Cosmists, in pre-revolutionary Russia, horizontality was the ultimate barrier. They believed humankind had to become vertical — had to resurrect the dead who lay flat in their graves, even — in order to escape the Earth’s surface and achieve immortality.

Fyodorov’s most famous follower was Konstantin Tsiolkovsky, whose astronautic theory shaped the Russian (and later the Soviet) space program. A drawing in his 1883 manuscript Free Space might be the first depiction of humans in orbital weightlessness. Four figures float in a spherical spaceship, each pointed in a different direction, disoriented. Tsiolkovsky’s ship seems better equipped than its passengers to operate in a fully three-dimensional environment. It has engines at both ends of a primary spine and gyroscopes on the other two axes, so that it can spin round and fire rocket thrust in any direction. This basic design — primary thruster, secondary retro rockets, axial gyros for orientation — has been used by all crewed Russian and American spacecraft to date, including the International Space Station.

In the counter-intuitive mechanics of orbital space, objects are continually falling on a trajectory that misses the spherical ground of the planetary body below. A spacecraft that accelerates forward moves to a “higher” orbit — up, or as Fuller would have it, “out.” Firing retro rockets to decelerate, it moves “in.” But these dynamics only apply to a dimensionless point. With a large, massy, complicated object like a spacecraft, we have to deal with gravity gradients and spin motion. Areas of the ship that are farthest from the planetary center are subject to less gravitational tug, and they move faster than the center of the ship’s mass, so objects there drift outward with respect to Earth. On the side of the ship closest to Earth, objects drift inward.

We can imagine the International Space Station crew living in a very tall building with all the intermediate floors removed.

The International Space Station, which orbits about 250 miles up (or out), is designed to mitigate these tidal complexities. Gyroscopes continuously modify the station’s orientation, or “attitude,” to keep its mostly flat grid of modules parallel to Earth’s mostly flat surface, so that scientific instruments and observation windows look down (or in). Other gyros keep the station pointed forward. And as the station is slowed by the slight drag of the upper atmosphere, an engine periodically fires to keep it from falling in toward Earth.

Space is a place, but to be anywhere in that place is to be in motion. Astronauts on the ISS say “on orbit” instead of “in orbit,” and they use the nautical terms forward , aft , port , and starboard . Fuller’s “in” toward Earth is deck and “out” is overhead. These standard directions are labeled at every module junction, and they determine the uniform orientation of wall-mounted equipment. The ISS has ten main capsules, built in four countries, and their alignment on the same spatial axis helps avoid confusion, mitigate motion sickness, and promote community among the international crew. 5 This architectural scheme also reaffirms a connection to Spaceship Earth. Since the bodies of the crew are in a familiar relationship with the ground plane far below, we can imagine that they are in a very tall building with all the intermediate floors removed.

Cylinders, Toruses, and Spheres

A half century ago, the Princeton physicist Gerard O’Neill proposed a more radical break with the planetary surface. In the fall of 1969, after the Apollo 11 moon landing, he led a seminar of advanced freshman students to consider the spatial needs of an “expanding technological civilization.” 6 The students evaluated different environments in terms of access to energy, materials, and waste disposal, and they concluded that high orbit would be the ideal location for new settlements. Orbital factories could use material from the Moon to make energy satellites, while orbital habitats could accommodate thousands of factory workers, and eventually a population of millions. They would occupy a relatively stable place in space, at the Lagrange Points, areas in high orbit where the gravity between large bodies balances out to create invisible hollows. O’Neill and his students worked out the engineering in rough detail, calculating material stress, light levels, atmospheric compositions, and the spin rate for producing artificial gravity through centrifugal force. They believed large-scale space habitats could be built within 25 years using existing technology.

In the 1970s, Princeton physicist Gerard O’Neill proposed a more radical break with the planetary surface.

In 1975, O’Neill convened a “summer study” at Stanford University to refine and visualize these proposals. With funding from NASA, he brought together engineers, space scientists, and physicists, along with artists, urban planners, and architects, for an “exercise in systems design.” Among this group were the multitalented artist-designers Rick Guidice and Don Davis, whose collective experience included science-fiction film posters and book covers, video game art, advertising, and architectural design, as well as science illustration. Their renderings of O’Neill’s space habitats included thirteen large-scale paintings in watercolor, acrylic, and gouache, showing both interior and exterior views, with an emphasis on the unnatural scale and perspective geometries of these new spaces and forms.

The O’Neill Cylinder, Stanford Torus, and Bernal Sphere, were, as their names suggest, volumetric primitives. The designs answered simple requirements: isolate a controlled interior from an alien and hostile exterior, enclose a large volume within a comparatively small surface, and spin on one axis to create a centrifugal force in lieu of gravity. Instead of the profusion of chambers and capsules that make up the ISS (and its Soviet predecessor, Mir), O’Neill and his colleagues imagined the interior as one large habitable environment.

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