On Friday, 16 July, Diana and I met uptown at the David H. Koch Theater, the former New York State Theater, at Lincoln Center to see A Disappearing Number by the London-based theater troupe Complicite. (Home of New York City Ballet and New York City Opera, the Koch was renamed in 2008 when its renovation was initiated with a grant from the billionaire philanthropist. Part of the campus-wide reconstruction, the theater reopened in 2009.)
Founded in 1983 as the Théâtre de Complicité by Simon McBurney and two friends who were all trained in the physical theater style of Jacques Lecoq, Complicite has become the vision of McBurney, its artistic director. It works collectively to create its productions, usually based on non-dramatic material—though not always (Ionesco’s The Chairs was a hit on Broadway in 1998), but McBurney is nearly always the director and shaper of the stage performance. Complicite is firmly in the world of avant-garde and makes extensive use of multi-media and technical effects for its productions, especially projections. I last saw the company in ‘98 at an earlier Lincoln Center Festival with The Street of Crocodiles, the adaptation of a 1934 collection of surrealistic short stories by Polish writer Bruno Schultz, which I recall as being an amazing (and somewhat disorienting) experience. A Disappearing Number, inspired in part by G. H. Hardy’s A Mathematician’s Apology (1941), won the 2008 Laurence Olivier Award for Best New Play.
The short description of Number, which first played in Britain in 2007, is that it’s the tale of self-taught Indian mathematician Srinivasa Ramanujan (1887-1920) and his seven-year collaboration with Cambridge math (or “maths,” as the Brits have it) professor Godfrey Harold Hardy (1877-1947) from the years just before to just after World War I. (The character of Dr. Amita Ramanujan in the U.S. TV series Numb3rs was named for the Indian mathematician.) Like Proof and Jumpers, two other “math plays,” Number isn’t really about mathematics—though it is about numbers, in a philosophical sense. (Wait, it gets denser!) In fact, except for a brief opening set piece, you don’t even have to be able to add or subtract. (There is a math trick at the beginning, too, in which the audience is asked to do some of that—but it’s a demo and you don’t have to participate to get the point. Besides, it’s over quickly.)
Okay, I’m deliberately teasing you. I should say right away that I found this play wonderfully fascinating and intriguing—and I can’t balance my checkbook. I confess, I’m not sure what it’s about thematically—I have some guesses, which I’ll share momentarily, but I’m still searching. Theatrically, however, it’s one of the most engaging productions I’ve seen in a long time. If you’ve read some of my other articles on theater and performance, you’ve run into my personal criteria for “good theater”: it has to do more than tell a story, and it must be theatrical. (I’ve defined ‘theatrical’ before, too: using all the attributes of live performance. It’s akin to what Tennessee Williams called “plastic theater” except that he put it in the control of the dramatist and I put it in the hands of anyone who makes theater. See my essay “’The Sculptural Drama’: Tennessee Williams’s Plastic Theatre,” Tennessee Williams Annual Review no. 5 , http://www.tennesseewilliamsstudies.org/archives/2002/3kramer.htm.) Well, A Disappearing Number meets these criteria in spades. (I should add that a performance can meet the criteria and still not be good theater—Teorema did, or tried to—but if it fails to meet one or both, it can’t be good theater, at least not for me.)
Not everyone agreed with me, though. Charles Isherwood called Number a “quietly mesmerizing play” and an “engrossing inquiry” in the Times, but Michael Feingold of the Village Voice, who doesn’t like Complicite—he characterized the troupe’s work as “a watery paste of image theater and narrative, usually with some kind of scientific or historical material dropped in to provide a hint of substance, and heavily decorated with multimedia effects”—concluded that the play’s “pretty patterns may all mean something mathematically; artistically, they don't.” (Feingold went on to raise objections like why Hardy didn’t hook Ramanujan up with other Indians in Britain and find him some British vegetarians—he named Shaw as a prominent example—to ease the Indian’s cultural disorientation. Please! What’s the point of asking such a question 100 years after the fact? It suffices that Hardy didn’t; that’s not Complicite’s fault! If Feingold wants to indict Hardy, he’s free to try, but it’s hardly a legit criticism of the play.)
The Complicite productions I know of aren’t linear narratives. (I’m not sure you can even discuss linearity in terms of Ionesco because he’s . . . well, absurd. Linearity doesn’t apply. Beckett’s Godot goes around in circles—is that linear? I say it’s apples and pedicabs . . . .) Nevertheless, there is a story—it’s just told . . . ummm, non-linearly. (Even McBurney’s program note is non-linear! I suspect he thinks that way.) Actually, there are two stories that wind together like a DNA helix. One is the factual history of Hardy (David Annen) and Ramanujan (Shane Shambhu) and the Indian mathematician’s odyssey from obscurity in India to prominence in England and back again to India for his death at 32 in 1920. Along the way, Ramanujan changes theoretical math forever in ways that are still being felt today. (Some of the ideas he proposed in 1913 are only now being fully explained.) The other tale is the modern, mid-life love story of Ruth Minnen (Saskia Reeves), a math lecturer at a British university, and Al Cooper (Firdous Bamji), an East Indian-American futures trader from L.A. Narrating both tales, and bridging them, is Aninda Rao (Paul Bhattacharjee), a physicist who, appropriately, specializes in string theory—otherwise known as “the theory of everything.” (I find that cognomen wonderfully arrogant.) The goal of string theory, as Rao explains, is to find how everything in the universe connects to everything else—a suitable perspective for the narrator of a play that jumps across time and space: between India and England; the second decade of the 20th century and the first decade of the 21st; research, creativity, and love; discovery and loss; science and beauty (which, Hardy and the play assert, aren’t so very separate); numbers, words, and emotions; past, present, and future (distinctions, McBurney notes, Einstein said were illusions anyway); infinity and the finite; and other unlikely juxtapositions. In one way, at least, that the play is about math is apt: pure math, after all, deals with real numbers, imaginary numbers, irrational numbers . . . and infinity. An infinity of infinities, as Ruth points out. (I won’t go into it now, but while I found little in A Disappearing Number that connected to David Auburn’s 2000 play Proof, I did find myself thinking of Tom Stoppard’s 1972 Jumpers. In a very broad sense, Number explores dramatically what Jumpers looks at comically.)
Briefly, G. H. Hardy receives a letter in 1913 from a 26-year-old, 20-rupee-a-month clerk in the Madras Port Authority. Ramanujan had written to other mathematicians and been dismissed by every one until Hardy. Not only is he barely educated—he’d had to leave college because he couldn’t pass his non-math courses—with no formal training in math, but he’s proposing theorems that seem on the surface to be crack-brained. One, for instance, is that 1+2+3+4+5+ . . . = -1/12. To most people (like . . . well, me), this makes no sense—but Hardy recognizes it as the application of some advanced developments in Germany, which Ramanujan has apparently lit upon on his own. The Cantabrigian knows the Indian’s not a crank but a genius and invites Ramanujan to come to Cambridge, but Ramanujan’s Brahmin faith doesn’t permit him to travel abroad. Eventually, he finds a way around the restriction and spends seven years with Hardy, making mathematical history. The intuitive, instinctual Indian conjures the insights and the logical, formalist Englishman provides the proofs. Together they push pure math into new realms with discoveries that form the foundation of string theory in the present. Hardy, the painfully reserved don, writes that the collaboration is "the one romantic incident in my life." In 1920, Ramanujan returns to Madras where he becomes ill with a liver infection, which ironically he may have contracted in Britain, and dies before his thirty-third birthday.
Ramanujan, of course, is a truly displaced person: an outsider, an alien, an “other.” He’s an Indian among Brits, a dark-skinned Asian among white Europeans, a vegetarian among meat-eaters, a Hindu among Christians, an unschooled intuitive among highly educated formalists, a young man among the middle-aged. His new colleagues, including Hardy, know little about him beyond his name and, as Rao observes, they even get that wrong. (The Indian genius is called Ram-a-NOO-j’n in the play, though the name should probably be pronounced Ra-MAHN-u-jan—like the TV character.) He has trouble with the British diet, especially the scarcity of fresh vegetables, and the English climate, which is cold and damp for a man from subtropical southern India. While Ramanujan’s spiritual and a devout Hindu—he attributes his insights to his family goddess, Namagiri—Hardy’s a committed atheist. Ramanujan is diffident and a loner, but Hardy’s no help because the Englishman himself is shy and makes friends only with difficulty. Still, both men buck their respective establishments to form the collaboration. Ramanujan defies his Brahmin caste and travels across the ocean to England, making himself an outcast at home; Hardy sponsors his collaborator for a fellowship at the college and membership in the Royal Society despite opposition among his English colleagues because Ramanujan is young, foreign, and uneducated. The displacement disorients Ramanujan so much that he becomes ill and tries to commit suicide by jumping onto the tracks of the London Underground. Nonetheless, their partnership is characterized as the intellectual equivalent of Edmund Hilary and Tenzing Norgay’s mountain-conquering alliance.
As this saga’s unfolding in discontinuous scenes, the story of Ruth and Al plays out. Ruth, who’s inspired by Ramanujan, has just finished lecturing when Al approaches her. He’s wandered into her session and finds himself taken with the math teacher even though he doesn’t understand a thing about numbers. Al pursues Ruth and they eventually marry; Ruth becomes pregnant, but she loses the baby, a tragedy with which she never comes to terms. She makes a solo trip to India to follow Ramanujan’s footsteps and collapses on a train, felled by a brain aneurysm. Al, whose parents were Indian (he was born in the U.S. and had never been to the land of his heritage), travels to India to scatter Ruth’s math books in the Cauvery River, “the Ganges of the South,” thinking it will bring her close to Ramanujan in death—and help him understand what captivated her so much about the math legend. (Feingold points out parenthetically that the play “perhaps unconsciously” links going to India with dying. Now, Al does meet Aninda Rao in India on a journey to do the same mitzva for his aunt’s ashes, but both Al and Rao have traveled to India without perishing! Also, you could say that leaving India is what killed Ramanujan. I’m not inclined to buy Feingold’s correlation.) The two narratives are almost parallels—both romances of a sort, one intellectual and one emotional—though the nationalities are reversed: the suitor in the math romance is British; the pursuer in the “heart” story is Indian(‑American). Further, they also travel in opposite directions: Ramanujan goes west from India to England and then returns home to die; Ruth goes east, followed after her death by Al who metaphorically returns “home.” The terms of the equation are inverted, you might say—but, according to the little math I remember, A+B = B+A. (It’s significant to note that these are patterns, a concept that will turn up momentarily.)
Michael Levine’s set for Number shape-shifts much as the play itself does. It opens on a lecture hall with a long whiteboard that stretches almost across the whole stage on which Ruth is writing an inscrutably complex and apparently endless equation, then morphs into Hardy’s office where he receives Ramanujan’s letter. Rao, who sometimes performs the function of Wilder’s Stage Manager in Our Town, demonstrates that nothing we see is real—except the math. (He amends his assertion quickly as Hiren Chate, the musician, emerges to set up his instruments: the music is real, too, Rao acknowledges.) He proceeds to shift the panels making up the walls, opens doors to nowhere, raises the whiteboard out of sight, and points out that all the people are really actors playing parts. Over the two-hour, intermissionless performance, the set mechanically reconfigures itself like the sci-fi movie Dark City without the menace, shifting from Cambridge to Madras to a hotel room in England to a train in India and to various locations beyond time and place, greatly assisted by Paul Anderson’s fluid lighting. All the while, videos of scenes (like a taxi ride through the streets of Madras), random images, silhouettes and shadows, or equations and numbers are projected on the back of the stage (courtesy of Sven Ortel’s conception). (The white-on-black digits, which one reviewer said seemed to “snow down across the walls” of the set, along with the voice over a PA system counting backwards, kept making me think of Tom Lehrer’s "Wernher von Braun": “’In German oder English, I know how to count down / Und I’m learning Chinese,’ says Wernher von Braun.”)
There is also Indian dance, performed by Shambhu, otherwise appearing as Ramanujan, and Divya Kasaturi, who plays other roles as well. More than the music, which underscores the action, the dance interludes function contrapuntally—moments of pure, but foreign, aesthetics amidst the relentless logic of the math. That the dancers are sometimes dressed in western garb makes the Indian dance sections more exotic and out of place—the way Ramanujan must have felt a lot of the time. The projections—which also include images from an overhead projector in Ruth’s lecture hall displaying images of Al’s hand and a bee he just swatted—aren’t just background pictures but an essential part of the production’s atmosphere and dynamic. The projections are usually accompanied by Indian music (composed by Nitin Sawhney), played live by Chate sitting just off the set at stage right, or the voice-over, sometimes in Hindi, which works like a soundtrack that’s integral to the production, not incidental to it. Together, the voice, music, dance, and projections form an alternative, parallel text. The effect of all the production elements is cumulative—the result, if you’ll pardon a mathematical metaphor, is greater than the sum of the parts. Everything adds a level and even if I can’t define or even describe the effect of each aspect—I may not even have noticed them all—removing one would diminish the whole the way taking off one of a car’s wheels destroys the vehicle’s effectiveness.
As I said, I’m not sure what Number is supposed to mean. Many of the reviews offered interpretations that I didn’t catch. I took away some thoughts I’m not sure were the intended point (which doesn’t make them invalid, or even unwanted—just not the main idea). Feingold of the Voice pretty much dismissed the whole effort, of course, and Isherwood bought into the idea that Rao articulates at the end: “All beautiful theorems require a very high degree of economy, unexpectedness and inevitability,” which Isherwood says is also true of theater and that McBurney meets the requirement. McBurney wrote that the play is as much “enquiry” as narrative “about our relentless compulsion to understand” (not far from what I contend is Stoppard’s prevailing theme), which allows me to free-float unreservedly. A lot of what I came away with—or sat there thinking about as I was watching and listening—were almost random thoughts. In most plays when my mind wanders, it’s because I’m bored or confused. Occasionally, it’s because the play sparks my imagination, starts me on a mental journey and, try as I might, I can’t stop myself. I don’t know if that’s good or bad—it certainly makes it hard to articulate later what I saw and heard—but it can be exhilarating. That’s what happened to me at A Disappearing Number.
I can’t sort all this out in any kind of cogent order, so I’m just going to ramble—the way my mind did while I was watching the show and right after as I was making my way home. (The New York Times reviews of both Number and Teorema came out the next day and I read them on the bus to Washington, starting me off again ruminating on the plays, especially Number.) Writing this report has spurred more thoughts, or connections among some I already had.
At the start of the play, Rao comes out while Ruth is lecturing on numerical series, scribbling ever more fantastical formulæ on the whiteboard. Before Rao shifts the set, he jokes that the play won’t all be like what the math prof is doing. Then he launches into the math gag I mentioned: Pick a number, he tells us. “Now double your number. Add 14 to the new number. Divide this number by 2. Finally, subtract the first number you thought of.” There were laughs in the audience when Rao reveals that we were all now thinking of the number seven. The math is pretty simple, of course (even I figured it out, after all), but the point seemed to be that numbers, even in so silly and simple an application, are magical. Like romance and creativity, they’re mysteries—and that’s what Number explores: the mystery of romance, both intellectual and emotional, and creativity, both artistic and scientific. Feingold complained that we never learn what attracts Al and Ruth to one another since they don’t share her obsession with math. I saw this as part of the mystery of numbers: Al is inexplicably but inexorably drawn first to her lecture, even though he doesn’t understand it, and then to her. Hardy proclaims, “A mathematician, like a painter or a poet, is a maker of patterns” equating the creativity of logic with the creativity of art. Ruth continues the quotation: “[T]he mathematician's patterns must be beautiful.“
Feingold, of course, disparaged the claim to creativity: a math theorem can’t equal the accomplishment of painting Guernica or writing Leaves of Grass, he insisted. I’m not so sure: when I was in college, the hardest course in the curriculum was generally agreed to be organic chem. The prof, an amateur actor and playwright, used to give points on his exams for “elegance,” even if the answer was factually wrong. A scientist, he rewarded creative thinking even over correctness. I reject this particular distinction between science and art. (The debate surfaces even within art. There’s a persistent argument among some whether actors and directors are “creative” or “interpretive” artists. I say it’s an artificial dichotomy.) What Hardy was saying, and what Number illustrates, I believe, is that there are different kinds of creativity. One kind makes something where nothing existed before—that’s what artists do, as Feingold observed. But scientists engage in a different kind of creativity. They discover things that already exist, but they use creative methods to identify them, reveal them, explain them, and use them. How is it possibly not creative when a physicist predicts the existence of particles no one has ever seen because her mind made the logical and reasoned connections that revealed their presence? Or an astronomer who “discovers” a new planet even before it’s rendered visible because he’s interpreted the evidence of its existence creatively? How is it not creative to conceive of such a thing as an imaginary number? Here’s how McBurney reconstructs the conception (a word, you’ll note, we also use to decribe the creation of a baby):
[O]ne day some mathematician simply said, “. . . We need a square root of minus one, and if we imagine it, it will exist.” And so they did. It was a leap of the imagination and they called it “i,” the imaginary number. And this “leap” gave us complex numbers. And without complex numbers, we would not be able to describe electromagnetic behavior or create digital technology in the way that we have. We would have no radio, no television, nor the mobile phone . . . . A leap of the imagination.
It’s not what they discover—it’s how they get there. No, what Hardy’s saying, in McBurney’s rendering, and what the play is meant to show is that aesthetic creativity and intellectual creativity are aspects of the same impulse. We know, for instance, that music, which figures significantly in Number, and math are related; McBurney points out that in the middle ages, people saw music as audible arithmetic. But string theory posits that everything is connected—math and painting and poetry and music and perhaps even love and friendship. (In that TV series, Numb3rs, the main character, a math genius who uses his skills to solve crimes, actually wrote a popular book about the mathematics of friendship and there’s a book on store shelves called The Mathematics of Marriage.) The artist makes things that didn’t exist before; the scientist thinks things that no one had ever thought before. The creativity Hardy sees is the working of the human mind, not the human hand. Archimedes was creative; Columbus was creative; Copernicus was creative; Galileo was creative; Newton was creative; Einstein was creative; Heisenberg was creative; Hawking is creative. Feingold found this to be a “gap in Hardy’s reasoning,” but it’s his definition of creativity that’s crabbed and narrow—and that’s his problem.
The mystery of numbers is also elegant—in its symmetry for example. Whatever’s true on one side of zero is also true on the other. (As I noted, Ruth states that there are an infinity of infinities. For instance, there are an infinity of positive numbers and an infinity of negative numbers. QED.) Numbers are also mysterious and elegant in their vastness. Ruth also invokes the axiom that there are an infinity of numbers between 1 and 2: 1.1, 1.2, 1.3, 1.4, and so on. But there are also an infinity of numbers between 1.1 and 1.2: 1.11, 1.12, 1.13, and so forth. This is where I began flashing onto Jumpers: “Cantor’s proof that there is no greatest number ensures that there is no smallest fraction.”
Ruth carries this consideration further. She asserts to an incredulous Al that 1+1/2+1/4+1/8+1/16 . . . ∞ = 2. It’s not possible, insists Al (to the silent agreement of the audience, I’d wager). Of course, Ruth explains, only at infinity would the series equal 2, otherwise, it only gets closer and closer. Jumpers, again:
[I]t was precisely this notion of infinite series which in the sixth century BC led the Greek philosopher Zeno to conclude that since an arrow shot towards a target first had to cover half the distance, and then half the remainder, and then half the remainder after that, and so on ad infinitum, the result was . . . that though an arrow is always approaching its target, it never quite gets there, and Saint Sebastian died of fright.
Of course, there’s a bit more to this proposition than the mathematical mystery of it. The people in Number are always approaching one another but never quite connecting. Hardy and Ramanujan, though they differ in many significant respects, aren’t precise opposites. In addition to their shared passion for math, they are both solitary men. Yet they never become friends beyond their collaboration. Ruth and Al don’t seem suited to each other, but they do love one another. Yet they don’t really come together, either, sending Al off to search for the missing connection in India after Ruth dies. Like the fractions approaching 2, they never quite get there . . . .
It seems, however, that you can do anything with math, even if it defies ordinary logic and common sense. (And isn’t that magic?) In the world of math, however, it’s still true. And that’s another place my mind went. The infinty of fractions between 1 and 2, for instance, is the source of this thought from Jumpers:
Furthermore, . . . before reaching the half-way point, the arrow had to reach the quarter-mark, and before that the eighth, and before that the sixteenth, and so on, with the result, remembering Cantor's proof, that the arrow could not move at all!
Think about it. Perfectly logical, right? But impossible! The play sets up a dichotomy between pure math and the real world. In our regular existence, numbers represent mundane things we work with every day: money, telephone numbers, taxi registrations, room numbers, time on a digital clock. All those appear in Disappearing Number, some with more import than others. We know what all those mean to us and they don’t seem mysterious or inscrutable. They also don’t always follow the rules. In math, one and one make two. But in life, one woman and one man, say Ruth and Al, can combine to make three—and then, unlike the regular and predictable world of math, three reverts to two and then to one again. In the other narrative, one and one, Hardy and Ramanujan, make impossible discoveries that continue on into an unforeseeable future and proliferate beyond anyone’s ability to predict or even comprehend. The creativity that Feingold doesn’t recognize was the sum of Hardy’s discipline and precision plus Ramanujan’s insight and intuition—and it eventually helped give rise to “the theory of everything.” (How is that not as much a masterpiece of human creativity as Guernica or Leaves of Grass?) But without Hardy, Ramanujan was just a 20-rupee-a-month clerk; and without Ramanujan, Hardy was just a math don. (Hardy spent the remainder of his life after Ramanujan’s death—another 27 years—largely promoting the products of their remarkable collaboration.)
This doesn’t mean that the play is perfect. (McBurney did considerable retuning of the script and production between performances in Europe—where he played Al—and the transfer to the West End.) A few reviewers dismissed Number as insufficiently beefy, relying on too much intellectual verbiage and not enough drama. (This is short of Feingold, who rejected the entire effort.) Coincidentally, that’s the same criticism Tom Stoppard gets—and he’s one of my favorite playwrights. (For the record, I reject the judgment in both instances.) It wasn’t hard to sit for the two hours without intermission, but I always feel that the optimum length for a long one act is 90 minutes. The center of the script could be trimmed, eliminating some of the sections that don’t seem to contribute to the sweep of the play’s principal themes. There’s an extraneous discussion, for instance, of “colony collapse disorder” among bees in America that appears to be presented as a metaphor for the situation of the play, but the scene doesn’t really relate. There are also some ideas that were introduced but weren’t developed or used as strongly as they ought to have been. One, for example, is Al’s profession, a futures broker, which entails, he says, predicting the bad fortune of some enterprise and essentially betting on the failure—but in a play that contends so much with time, past and present in particular, the future orientation of Al’s work seems to have been dropped in for balance and then forgotten.
The star of this show is McBurney, who both conceived it after a friend introduced him to Hardy’s book over a decade ago and directed the company through the creation of the piece and in the resulting production. He’s very practiced, of course, at this kind of highly theatrical presentation; it’s what Complicite does. But that doesn’t mean the actors were mere automatons moved about the stage to make McBurney’s pictures come to life. (The cast did create the text together, after all.) The whole company was good; no one hit a false note, but a few deserve special commendation. Saskia Reeves portrays a touching and warm Ruth who, for all her scientific distance, wants to be a wife and mother—and wants her non-mathematician husband to understand and appreciate her subject. That they never connect makes her all the more engaging as a character. Reeves allows Ruth to be girly, despite the character’s age and intellectuality. Paul Bhattacharjee’s Rao is light-hearted and funny, in contrast with the profundity of his main subject—finding the connectedness of everything in the universe is surely a daunting responsibility!—and lends a palpable humanity to the story of Hardy and Ramanujan that it might otherwise miss. One of the best performances isn’t even visible. After Ruth’s death, Al tries to get her cell phone number (which she makes a deal of when they first meet) transferred to his name, to keep a part of her—a number—close to him. On the phone with “Barbara Jones” at the company’s customer service center, he is exasperated with the lack of comprehension he encounters. Of course, it turns out that “Barbara” is really Lakshmi in Bangalore and, as voiced by Chetna Pandya, provides a delightful progression of obliviousness, understanding, sympathy, and finally empathy with Al’s loss, for she has lost her job when the phone company relocates the call center back to Britain.
[A Disappearing Number was at the Lincoln Center Festival for only five performances, a disappointingly short stay. But it will be part of the National Theatre’s program of live broadcasts of performances to movie theaters (and other venues) worldwide on 14 October.]