The 'Infinity Room': One of Many Ways to Imagine Infinity

The "Infinity Environment," an installation art piece by Doug Wheeler on display at the Doug Zwirner Gallery in New York City. Credit: Tim Nighswander/IMAGING4ART, courtesy of David Zwirner, New York (c) 2012 Doug Wheeler
The "Infinity Environment," an installation art piece by Doug Wheeler on display at the Doug Zwirner Gallery in New York City. (Image credit: Tim Nighswander/IMAGING4ART, courtesy of David Zwirner, New York (c) 2012 Doug Wheeler)

As I stepped into the Infinity Environment on Wednesday morning (Feb. 1), I heard faint gasps from those around me. With apprehension, we entered a stark white, brilliantly lit room with no edges. The curved walls and angled lighting minimized shadows, giving the illusion that we were staring into a continuum. With no visual reference points anywhere in the room, my eyes flickered about, desperate for something to focus on; it was impossible to tell how far space extended, if at all. In seeming infinite, space ceased to exist beyond my eyelashes and nose.

"There is no other time in your life when you will look out and see nothing at all," one young woman, an art student, whispered.

The Infinity Environment, an art piece by Doug Wheeler, is currently on display at the David Zwirner Gallery in New York City. It's an artist's valiant effort to realize infinity, a concept that has been known to humanity for thousands of years, but, for most of us, remains difficult to grasp. Ancient Indian philosophers understood it as the entity from which a part can be removed, or another part added, only to have it remain the same. The ancient Greeks conceived of it as the boundless set of prime numbers. Both are true descriptions, but neither evokes a visceral understanding of the true nature of the beast.

Art is one way to grapple with infinity. Mathematicians, physicists and philosophers, many of whom routinely deal with the concept, describe how they conceive of this elusive entity. [Album: Visualizations of Infinity]

Andy Albrecht, a cosmologist and the chairman of the physics department at the University of California, Davis, has used the same analogy since he was a student. Albrecht also imagines a room, but unlike the Infinity Environment, it appears infinite by way of immense size rather than illusion.

"In the case of the [art installation], the sense of it being infinite is just an optical illusion, because you could bring a ball and throw it against the wall and discover quite quickly that the room is finite," Albrecht said. "But you can imagine a bigger room where you can throw a ball and it wouldn't come back. The ball would have to travel so far to hit the opposite wall that you'd give up waiting for it. Maybe that would be good enough to represent infinity.

"Or, if your measuring device is the range finder on a camera, then the warehouse would have to be much bigger to seem effectively infinite. At some critical size the signal would get dispersed and the range finder could no longer find the signal bouncing back to it," he said. Just as if it were infinitely large, at that point the warehouse's actual "size" becomes meaningless; if it were twice as large, you wouldn't know.

It may seem overly simplistic to equate an extremely large-but-finite space with an infinite one, but in physics the two are effectively equivalent, Albrecht said. When calculations in field theory, quantum mechanics or other branches of physics are done under the assumption that the universe is infinitely large, and then when the calculations are done under the assumption that the universe is huge but finite, the difference in the outcomes is immeasurably small. Thus, infinity is just a handy tool to simplify calculations; "It's not a reality," he told Life's Little Mysteries, a sister site to LiveScience.

But others think it might be. Michael Ibison, a senior research physicist with the Institute for Advanced Studies at Austin, Texas, explained that the traditional, conservative view of the universe is that it is "closed." In this model, space-time (the fabric of the universe) is ever-so-slightly curved, like the surface of a vast sphere, such that if you moved along it in one direction for long enough, you'd get back where you started. However, the more data astrophysicists gather from the cosmos, the more it looks as if it might be "open." In this model, space-time is flat, extending forever in all directions, and what goes around never comes around.

"The amount of precision they've got from the astrophysical data is not sufficient to know which description of the universe is correct," Ibison said. For all we know, the universe is flat, or it is a sphere so large that it appears flat. But if the universe is flat, then it is infinite in size, and infinity is, in fact, a physical reality. On the other hand, if the universe is a sphere, then it is finite, and infinity is just an abstract creation of the human mind — a concept for mathematicians, philosophers and artists. Though no one yet knows which version of the story is the right one, Ibison said he is "personally empathetic" to the idea of closed space-time.

However, if the universe is in fact flat and space-time does go on forever, he recommends this analogy: "You can think of a rubber sheet being stretched in all directions. But rather than imagining people holding the edges and stretching it, you must think of a rubber sheet that's already infinite, expanding more."

Regardless of whether infinity is real, it nevertheless exists in the abstract. The integers, for example — 1, 2, 3 and so on — go on forever. More perplexing still, mathematicians have proven there are many different kinds of infinities, all of different sizes. "Mathematicians have been investigating questions about various higher levels of infinity. There are, perhaps unsurprisingly, infinitely many of these so-called transfinite numbers," said Rudy Rucker, a mathematician, philosopher and author of the book "Infinity and the Mind" (Princeton University Press, 1995). [5 Seriously Mind-Boggling Math Facts]

While the notion of different types of infinity may be truly inconceivable, Rucker says there are many methods for imagining the concept of infinity in general, and each is as valid as the next. "A rationalist says that infinity is inconceivable, although it may be that we can prove certain things about it. A mystic says that, by fully opening one’s mind, it’s possible to merge into the cosmic whole and thus experience infinity in a direct and personal way," he wrote in an email.

The story of infinity reminds Rucker of the story of the blind men and the elephant. "Each group of thinkers sees infinity in a different way," he wrote. "I was trained as a mathematician, and I do like the intricate games that mathematicians can play with infinity. The concept that our physical universe might indeed be infinite is of course staggering. It's pleasant to imagine or to experience a temporary merger with the infinite One mind. And it's interesting to hear theologians speculate about how a finite, created mind manages to experience an infinite God's love."

Follow Natalie Wolchover on Twitter @nattyover. Follow Life's Little Mysteries on Twitter @llmysteries, then join us on Facebook.

Natalie Wolchover

Natalie Wolchover was a staff writer for Live Science from 2010 to 2012 and is currently a senior physics writer and editor for Quanta Magazine. She holds a bachelor's degree in physics from Tufts University and has studied physics at the University of California, Berkeley. Along with the staff of Quanta, Wolchover won the 2022 Pulitzer Prize for explanatory writing for her work on the building of the James Webb Space Telescope. Her work has also appeared in the The Best American Science and Nature Writing and The Best Writing on Mathematics, Nature, The New Yorker and Popular Science. She was the 2016 winner of the  Evert Clark/Seth Payne Award, an annual prize for young science journalists, as well as the winner of the 2017 Science Communication Award for the American Institute of Physics.