Hilbert's Hotel, Other Paradoxes, Come to Life in New "Math Play"

September 30, 2003


Infinities is deeply tied to the space in which it was developed and performed: an old warehouse in Milan, once used as storage for La Scala productions.

Kirsten Shepherd-Barr

"Mathematics provides a new language for the theatre," says Luca Ronconi, director of John D. Barrow's exciting play Infinities, which finished a second successful run in Milan in May. Barrow's play does for mathematics what Michael Frayn's Copenhagen did for physics. Infinities actually enacts some of the great paradoxes or "thought experiments" about infinity: the Hotel Infinity in all its vastness, the notion of time-travel, the idea of living forever, Borges's Library of Babel with its endless corridors of books. Watching Infinities brings such concepts to life in a stunning combination of mathematics, philosophy, science, and theatre. For those who felt that David Auburn's play Proof was only tangentially and incidentally about mathematics, here is a play that truly engages the subject, for specialists and general audiences alike.

Barrow provided the text, a mixture of original passages and selections from essays on infinity of his own and other people, ranging from Nietzsche to Borges to Hawking. The acclaimed Italian director Ronconi developed the staging in conjunction with the Teatro Piccolo and Sigma Tau Foundation in Italy. The result is a play that demonstrates the very concepts it deals with, and takes the genre of "science plays"---so popular in recent years---to a new level.

The play presents five scenarios on different ideas of infinity, and it deliberately rejects such mainstays of traditional theatre as plot and characterization. Watching it, we breathe the air of ideas and abstractions that are magically brought to life through the material possibilities of the stage-and what a stage it is. Infinities is deeply tied to the extraordinary space in which it was developed and is performed: an enormous old warehouse in Milan's Bovisa district in which sets and costumes for La Scala productions were once kept. The audience is led through this vast space, which is divided into five very different stages for each of the five scenarios on infinity. We are admitted to a new scenario in small groups every fifteen minutes, making the play theoretically infinite in its structure as it lacks a beginning, middle, and end---an open-endedness that neatly captures the thematic core of the play.

Although some of the scenarios work better than others, Infinities as a whole offers a new experience, for actors and audience alike, in which the language of drama and the language of science meet spectacularly.

Scenario 1, "Welcome to the Hotel Infinity," dramatizes a famous mathematical thought-experiment. At Hilbert's Hotel, an overwrought manager with an infinite number of rooms must accommodate increasing numbers of guests in increasingly complex numerical arrangements, from one new guest to whole galaxies of new arrivals. The actors explain the complex mathematics with the help of a huge monitor displaying the equations necessary to work it all out. With tongue only slightly in cheek, Barrow concludes with a cosmological moral: Hotel Infinity to Hotel Zero? If the universe is infinite and began from nothing, maybe it will one day return to nothing after it gets too complicated and unmanageable to be kept running any longer.

In one of the play's five scenarios, the manager at Hilbert's Hotel has an infinite number of rooms in which he must accommodate increasing numbers of guests in increasingly complex numerical arrangements. The actors explain the underlying mathematics with the help of a huge monitor. Photographs by Serafino Amato.

The audience's next stop (for those of us in this particular group) is about living forever. We are in a claustrophobia---inducing black box full of impossibly old people languidly reading in their wheelchairs or sitting under salon-style hair-dryers. The stifled atmosphere and long monologues create a monotony that effectively conveys the idea of perpetuity, and how unappealing it would be to go on living forever.

Another of the play's scenarios dramatizes the Library of Babel of Jorge Luis Borges. Mirrors help create the illusion of an infinite library, and the appearance of increasing numbers of identically costumed actors addresses the Duplication Paradox.

Scenario 3 dramatizes Jorge Luis Borges's parable of the Library of Babel. Visually inventive staging, involving the use of mirrors at the ends of several corridors lined with drawers large enough to hold a human body, creates the illusion of an infinite library, and the audience is invited to wander from corridor to corridor while the voices of the actors resound around them. Another neat trick is the appearance of an increasing number of identically masked and clothed actors---a disturbing effect as the text addresses the Duplication Paradox, suggesting the impossibility of uniqueness and individuality. The actors' endless replications of themselves underscore the message of the text.

The fourth scenario stages the famous conflict between the nineteenth-century mathematicians Cantor and Kronecker. The textual narrative of Cantor's troubled life is illuminated visually by a wheelchair-bound actor, swathed in white bandages, who sits immobile under the rantings of his assailant, Kronecker. All this takes place on the tables of a simulated classroom, with the audience seated at the tables among real students from the polytechnic; now and then, students rise to paint the mathematical equations and names of the great mathematicians referred to in the text on huge white sheets of paper on the walls.

Nineteenth-century dissension brought to the stage: One Infinities scenario has an immobile, wheelchair-bound Georg Cantor assailed by Leopold Kronecker.

Just when we think the play can't possibly get any more inventive, we enter the gigantic open space of the final scenario, which is about time-travel. A grandmother teeters across the stage, at one point narrowly missing the grandson speeding toward her in his wheelchair (illustrating the Grandmother Paradox). An actor leaps effortlessly through time, which is symbolized by a long span of book-filled crates. The concept of time-travel is further literalized through the use of a train car complete with pre-set pop-up dining tables at which passengers sit facing in both directions.

Although visually striking, these are some of the director's few concessions to audience expectations of realism. He prefers to rely on more abstract elements---such as symbolic movement: straight lines (actors moving perpetually forward and backward) or circles (actors sitting or walking endlessly around)---that perform infinity. He also avoids realism by shielding many of the actors in gray wigs and white half-masks (leaving the mouth and eyes visible but grotesquely exaggerating the cheeks and nose).

Infinities places exhaustive demands on its actors. They often have to rush from one scenario to another, and whether hanging upside down from the ceiling or leaping across a vast expanse of books, they need to have the agility and stamina of acrobats. They take turns rotating roles throughout the run of the show to avoid becoming complacent and predictable. There is a great deal of complicated text to memorize, yet no linear plot and no characterization.

Speaking to me through an interpreter in his sunny, plant-lined office at the Teatro Spehler in Milan, Ronconi explains that he wanted a kind of theatre that would challenge the audience and the actors alike. "We must leave at home traditional notions of character, story, and plot, and the idea of continuous attention from the audience." In Infinities, the actors and the audience are in the same boat. "This kind of theatre is looking for hypotheses, rather than starting with them. We don't know the final answer. The actors are not above the audience---they often don't understand the text that well, the math, either." Ronconi deliberately puts us in a vulnerable position, as the intermingling of audience and actors makes us feel as visible as the performers.

Ronconi is very interested in time and temporality in the theatre. He jumped on the idea of infinity/infiniteness because he could destroy the apparent coincidence between the time of the play and the time depicted in the play. It's a running show, not a whole package that is complete, but open-ended. It avoids the illusion of "complete information" that the audience gets in traditional theatre.

Infinities succeeds because its staging and its structure convey its ideas. We in the audience are not attending a lecture on mathematics, we are participating in a vivid and imaginative demonstration of stimulating thought-experiments. Whether we understand every nuance of these paradoxes is not the point; it is the unmediated immersion in them that matters. What sticks to us once we've emerged from the theatre is part of the suspense.

Kirsten Shepherd-Barr, an associate professor of English at North Carolina State University, is currently on academic leave in England, where she is working on a book about theatre and science. Her articles about science in the theatre have appeared in American Scientist and Interdisciplinary Science Reviews, among other publications.

A Note About the Playwright
John D. Barrow, the author of Infinities, the play reviewed in the accompanying article, was named Research Professor of Mathematical Sciences in the Department of Applied Mathematics and Theoretical Physics at Cambridge University in 1999. In the same year, he began an appointment as director of the university's Millennium Mathematics Project, an initiative undertaken to increase understanding of mathematics and its applications among young people and the general public. For examples of the project's output, see http://www.connectspace.co.uk.

Barrow's "public awareness" activities have included numerous community lectures, given worldwide on topics related to his research interests, in particle physics and cosmology, cosmological models, and cosmological aspects of gravitation theories. He is also the author of 15 general-audience books (translated into 28 languages). Among the titles are Theories of Everything, Pi in the Sky, The Artful Universe, and, most recently, The Constants of Nature: From Alpha to Omega (Pantheon Books, 2003).

To date, Infinities has been performed in Italian and Spanish (at the Valencia Festival, in a sister theatre to Milan's Piccolo); there are plans for a performance in Arabic, at the recently restored Library of Alexandria. A symposium on the play was held at the Theatre Populaire in Lyons, France. Barrow, who interacted with director Luca Ronconi during a long period with regard to sets and staging, reports that about 33,000 people have seen the production in Milan, and he hopes that it will run again at the Teatro Piccolo next year. Regrettably, he is not aware of any plans for an English-language performance.


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