Geometry of Meaning: the Sphere

Have you ever stared down at a spreadsheet of numbers, or up at a canopy of distinct leaves, and had a fleeting realization that a pattern had fallen into place, assuredly and satisfying like a German car door closing? Math aligns with geometry which aligns with your particular, individual point of view on this bubbling universe, and an organized pattern that apparently has no center or origin quickly reveals itself.

A certain recurring pattern has been winking and blinking at me from the periphery. It’s art and math and experiential and doesn’t look like it should work as a real construction.

I first noticed it in a set piece on a streaming show called Devs on FX/Hulu: our plucky, confused heroine encounters the walls of a building-sized AI computer, a computer that runs such sublime simulations as to force all the characters to question their free will. See her against the gold, scalloped walls:

Scene from inside the AI: Devs on FX/Hulu

Scene from inside the AI: Devs on FX/Hulu

Six-sided spherical scoops. Regularly irregular; rationally irrational. A form that represents unknown maths and terrifying, deterministic futures. The show is written and directed by Alex Garland, who made another sublime movie about computational consciousness in Ex Machina.

Scene from Devs, on FX/Hulu

Scene from Devs, on FX/Hulu

I see the pattern again days later in a work by Olafur Eliasson, one of my favorite environmental artists slash designers. It is a wall called “Atmospheric wave wall” and it uses similar five-sided spherical shapes to re-produce the experience of looking at the windy surface of a lake. Perhaps it shows us the surface at all scales: our experiential one, and all cascadingly smaller nano scales, down to the vibrating thing that is only energy or will, below and within the pieces of all the named particles.

“Atmospheric wave wall,” Olafur Eliasson, Chicago 2021. Image from Colossal

“Atmospheric wave wall,” Olafur Eliasson, Chicago 2021. Image from Colossal

Detail of “Atmospheric wave wall.” Image from Colossal.

Detail of “Atmospheric wave wall.” Image from Colossal.

The artist has this amazing quote about the piece:

“What we see depends on our point of view: understanding this is an important step toward realizing that we can change reality.”


The geometry originates in something called Penrose tiling, and is based on pentagons.  Image from Wikipedia

The geometry originates in something called Penrose tiling, and is based on pentagons. Image from Wikipedia

As tiling squares produce an infinite and democratic grid of space, tiling a five sided shape makes unique evolutions. You can sense the mathy Islamic geometries in there. Spying the hem of God or Allah in the numbers. I love waking up to the idea that these blooming patterns compose the entire world, constantly dawning. A new aubade shaping us every morning.

Beyond tiling as a mathematical generator of spherical patterns, architecture has taken inspiration from pieces of spheres from the earliest domes to the fractured pieces of the present.

The Pantheon in Rome; a half dome containing a full sphere.

The Pantheon in Rome; a half dome containing a full sphere.

The shells of the Sydney Opera House could be described as wedges mined from an imaginary sphere.

The shells of the Sydney Opera House could be described as wedges mined from an imaginary sphere.

Fuller’s tessellated dome in Montreal. Diaphanous presence of space.

Fuller’s tessellated dome in Montreal. Diaphanous presence of space.

Epcot Center in Disneyworld, Orlando. The sphere as a mysterious volume containing the future.

Epcot Center in Disneyworld, Orlando. The sphere as a mysterious volume containing the future.

Amazon HQ in Seattle: The new workplace biosphere.

Amazon HQ in Seattle: The new workplace biosphere.

Richard Serra: Between the Torus and the Sphere, 2001. Geometry in the rough hands of a sculptor, assisted only by gravity.

Richard Serra: Between the Torus and the Sphere, 2001. Geometry in the rough hands of a sculptor, assisted only by gravity.

Richard Meier’s  Jubilee Church, Rome, 2003. Delaminated slices of spheres, peeled apart to let the light in.

Richard Meier’s Jubilee Church, Rome, 2003. Delaminated slices of spheres, peeled apart to let the light in.

Daniel Libeskind’s Imperial War Museum, Manchester. Shards of spheres useful perhaps only for their brokenness.

Daniel Libeskind’s Imperial War Museum, Manchester. Shards of spheres useful perhaps only for their brokenness.

God may have been a part of the equation of the sphere back when: The Point at the center, where all extents of the reach are within His grasp. The sublime creeps over our thoughts like a thunderhead: the dome of the night sky and its scaffold of stars. But I think the sculptors, Eliasson and Serra, are using the equations differently, and find a different sublime. Their works include us, wherever we happen to encounter them spatially. Sure, there is math and structure and all the confidence displayed in that. But there is also variability, uncertainty, questioning, and a renewed wonder of it all.