STEPHEN D. ABBOTT Turning Theorems into Plays

fter overhearing the gossip of the house staff, the young turned under in favor of gothic ruins; and Thomasina is A Thomasina Coverly interrupts her algebra lesson on perplexed by the fact that no matter what she does with her Fermat’s Last Theorem to ask her tutor, Septimus Hodge, spoon, the red jam in her rice pudding eventually turns the the meaning of “carnal embrace.” Septimus’s first explana- entire dish an even shade of pink. “Do you think this is tion, “Throwing one’s arms around a side of beef,” proves odd,” she muses, “you cannot stir things apart.” And so we unacceptable as Thomasina points out that it was a certain have our second hint that, like nearly all of Stoppard’s writ- Mrs. Chater who was discovered in carnal embrace in the ing, this comedy is really a play of ideas. Throughout his garden gazebo. “I don’t think you have been candid with me work, theorems of mathematics and laws of physics habitu- Septimus,” Thomasina insists. “A gazebo is not, after all, a ally appear unannounced in the most unlikely places, and it meat larder.” “Ah yes, I am ashamed,” Septimus finally con- is with Arcadia that Stoppard’s affinity for the mathematical cedes. With blunt, almost medical precision, he then pro- sciences reaches its pinnacle. By creating a visual image of vides his talented pupil with a terse description of inter- entropy in rice pudding, and by pushing Thomasina’s ro- course, explaining that carnal embrace is actually sexual con- mantic education incongruously up against her lesson in num- gress between males and females... ber theory, Stoppard is setting the stage for what is to be a provocative exploration of the human implications inherent SEPTIMUS: ... for purposes of procreation and pleasure. in the confrontation of classical Euclidean geometry and Fermat’s last theorem, by contrast, asserts that when x, y, Newtonian physics with chaos theory and the second law of and z are whole numbers each raised to the power of n, thermodynamics. the sum of the first two can never equal the third when n is Arcadia is just one of over 40 scripts that Tom Stoppard greater than 2. has written for the stage, radio, television and film. His re- THOMASINA: Eurghhh! cent Academy Award for Shakespeare in Love has no doubt SEPTIMUS: Nevertheless, that is the theorem. boosted his public recognition, but critics of modern theater THOMASINA: It is disgusting and incomprehensible. have for several decades regarded Stoppard among the lead- ing active playwrights writing in English. Ironically, this ex- This delightful exchange from the opening moments of Tom tremely British author was born Tomas Straussler to Czecho- Stoppard’s Arcadia offers a vivid example of why the play- slovakian parents in 1937. The family lived for a while in wright himself would wonder aloud if his writing is best de- Singapore, and then evacuated to India before World War II, scribed as “seriousness compromised by my frivolity, or ... although Tom’s father stayed behind and was killed in the frivolity redeemed by my seriousness.” The frivolous charm ensuing Japanese invasion. In 1946, Tom’s mother married of this scene is easy to appreciate. What is not so obvious is Major Kenneth Stoppard, a British army officer on duty in that this banter between Thomasina Coverly and her tutor is India, and the new family eventually found its way to Bristol, our first clue to the ensuing debate between what can loosely England around 1950. Adding to the confusion is that this be categorized as the classical and the romantic. Arcadia opens writer of high ideas actually quit school at age seventeen to in the Coverly family’s stately home. The year is 1809 and become a journalist, and eventually theater reviewer, for the Thomasina, along with the rest of western culture, is emerg- Bristol Evening World. When asked, Stoppard unequivocally ing from the logical rigors of the Enlightenment to discover asserts that he is an Englishman, but this has not prevented the allure of the Romantic era. Lord Byron is a house guest proliferation of the theory that only someone with an exter- (though we never meet him); the pastoral gardens are being nal perspective on the culture could write dialogue with such a mastery of British language and nuance. In a similar way, being self-taught has meant Stoppard’s understanding of mathematical and philosophical concepts has come without the bias and clichés of any standard approach. The results STEPHEN D. ABBOTT is Assistant Professor of Mathematics at are a refreshing and often hilarious interpretation by the Middlebury College. artist of some of science’s great achievements.

© Mathematical Association of America Math Horizons September 1999 5 efficiency by employing four men. It takes them two years to paint the bridge, which is the length of time the paint lasts. This new paint will last eight years, and so we only need one painter to paint the bridge by himself. After eight years, the end he started at will be just ready for re- painting. The savings to the ratepayers would be £3,529 15s. 9d. per annum. The mathematics is not simply incidental; nothing is in- cidental in Stoppard’s scripts. The rigidity of the algebra of this eighth-grade word problem is accented by the backdrop of the steel beams of the “fourth biggest single-span double- track shore-to-shore railway bridge in the world bar none—”. Albert, meanwhile, is an amorphous soul who is utterly se- duced by the definitive, angled, visible grandeur of the bridge. FITCH: I’m the same. It’s poetry to me—a perfect equation of space, time and energy— ALBERT: Yes— FITCH: It’s not just slapping paint on a girder— ALBERT: No— FITCH: It’s continuity-control-mathematics. /Solo ALBERT: Poetry. FITCH: Yes, I should have known it was a job for a university Daily Mail Daily

© man... You’ll stick to it for eight years will you? Tom Stoppard ALBERT: Oh, I’ll paint it more than once. Some of the play’s most comic moments occur when Albert “It’s poetry to me.” is joined by Fraser, a would-be suicidal personality who, ev- ery time he climbs the bridge to jump is so calmed by the To be sure, the themes explored in Stoppard’s plays are by perspective that he loses the desire to kill himself. Albert is no means limited to those in the sciences, nor do they re- profoundly annoyed by this habit, and it is during their con- spect the usual boundaries between academic disciplines. The versations that the flaw in Fitch’s algebra is slowly revealed. characters in Travesties (1974) include Lenin, James Joyce, After two years, Albert has painted only a quarter of the bridge, and Tristan Tzara, one of the founders of the artistic move- leaving three quarters of the bridge exposed under cracking ment Dada. But mathematical allusions are ubiquitous, even two-year paint. As the town revolts at the sight of the decay- in Stoppard’s earliest work. Albert’s Bridge is a radio play first ing girders, Fitch’s panicked solution is to send an army of performed in 1967 about a philosophy graduate (Albert) painters out to finish the job in a single day. Forgetting to whose chronic disinterest in the world leads him to take a break stride as they march onto the top of the bridge, the job working with three working class types painting the resonating frequencies of the 1800 collective footsteps brings Clufton Bay Bridge. (It should be pointed out now that aca- the bridge, Albert, and the play to a crashing end. demics and other victims of higher education never fare very well in Stoppard’s plays.) The particular paint they use re- “It must be indicative of something quires re-painting every two years which is precisely the length of time it takes the four of them to complete the job. Thus, besides the redistribution of wealth.” whenever the team finishes the last steel girder in the span, they return the next morning to the other side and begin all Stoppard’s first major success as a playwright, and probably over again. What has been a twenty-year Möbius nightmare still his best known work, is Rosencrantz and Guildenstern Are for Dad, the oldest of the painters, is actually a great relief to Dead, first performed in its present form in 1967. The play Albert who finds his only solace in the concreteness of his tells the story of Hamlet from the point of view of Shakespeare’s work high above the city. Consequently, it is Albert who gladly two minor characters charged with investigating the source volunteers for the lonely duty required in a money-saving of Hamlet’s lunacy and ultimately responsible for delivering plan hatched by Fitch, the “clipped, confident, rimlessly- the prince to England to be killed. The curtain rises (in eyeglassed” town supervisor. Stoppard’s script) to find the two misplaced Elizabethans betting on the flip of a coin; heads and the coin goes to FITCH: You see, to date we have achieved your optimum Rosencrantz, tails and it belongs to Guildenstern. It is im-

6 Math Horizons September 1999 © Mathematical Association of America GUIL: One, probability is a factor which operates within natural forces. Two, probability is not operating as a factor. Three, we are now within un-, sub- or supernatural forces. Discuss. But the heady Guildenstern is not done yet. Moments later, in true Lewis Carroll fashion, he attempts to turn his own logic back on itself. GUIL: ...If we postulate, and we just have, that within un-, sub- or supernatural forces the probability is that the law of probability will not operate as a factor, then we must accept that the probability of the first part will not operate as a factor, in which case the law of probability will oper- ate as a factor within un-, sub or supernatural forces. And since it obviously hasn’t been doing so, we can take it that we are not held within un-, sub- or supernatural forces after all; in all probability, that is. The coin is a multifaceted device. In addition to setting the existential tone in its refusal to obey the law of large numbers, it also points toward the symbiotic relationship between Stoppard’s script and the script of Hamlet. As the Player, who is also present in both plays, says, “[It] is a kind of integrity, if you look on every exit being an entrance some- Alex Cranmer and Richard Price as Rosencrantz and Guildenstern in where else.” In fact, the coin does eventually come up tails—at a Middlebury College production. Photo by Alex Fuller. precisely the moment when Hamlet and Ophelia swoon on- stage and the action is taken over by Hamlet, Act 2, Scene 1. mediately clear that something is amiss. Each flip we witness The Player’s line in context is explicitly about his own life turns up heads, and Rosencrantz’s heavy bag of coins indi- as a traveling actor, but it is also clearly intended as a com- cates that this has been happening for quite some time. ment on the R&G–Hamlet relationship. This is just one of Rosencrantz is embarrassed to be taking so much money from the many ways Stoppard’s play finds to talk about itself. Ad- his friend, but seems uninterested in considering the matter vertising his troop’s talents, the Player asserts, “It costs little much further. Guildenstern could care less about the money to watch, and little more if you happen to get caught up in the but is clearly disturbed by the implications. action.” These self-referential moments abound and suggest a sympathy on the part of Stoppard for the type of recursive GUIL: This must be indicative of something, besides the thinking beloved by mathematicians and crucial to such logi- redistribution of wealth. List of possible explanations. One: cal delights as Russell’s paradox and Gödel’s incompleteness I am willing it. Inside where nothing shows, I am the theorems. At one point, Rosencrantz and Guildenstern stumble essence of a man spinning double-headed coins, and bet- upon the troop of players rehearsing the production of The ting against himself in private atonement for an unre- Murder of Gonzago requested by Hamlet to “catch the con- membered past. science of the king.” Their play, however, is no less than a ROS: Heads. mimed Hamlet which ends with a provocative scene of GUIL: Two: Time has stopped dead, and the single experi- Rosencrantz and Guildenstern unsuspectingly witnessing a ence of one coin being spun has been repeated ninety portrayal of their own murders at the hands of the English times...(He flips a coin and tosses it to Ros.) On the whole king. In the film version of R&G, Stoppard even adds a doubtful. Three: divine intervention... Four: a spectacu- puppet show of Gonzago as part of the troops’ rendition of lar vindication of the principle that each individual coin Hamlet happening within Stoppard’s R&G which is inside spun individually (he spins one) is as likely to come down Shakespeare’s Hamlet. All of this is, of course, taking place heads as tails and therefore should cause no surprise each in front of an audience, who, judging from the fact that individual time it does. (It does. He tosses it to Ros.) Rosencrantz and Guildenstern are caught unaware in this strange loop, should not necessarily assume that the recur- The mathematical aura of this scene runs deep. Beyond sive levels end with the theater in which they sit. the explicit references to probability, Guildenstern (who is acting like the analytical “heads” to Rosencrantz’s obtuse “tails”, at least at this point in the play) proposes that the “Saint Sebastian died of fright.” “scientific approach to the examination of phenomena is a defense against the pure emotion of fear,” and begins orga- Jumpers, which followed R&G in 1972, is the staging of a nizing his arguments into logical syllogisms. debate, both serious and farcical, over the question of whether

© Mathematical Association of America Math Horizons September 1999 7 virtue is a social convention that has evolved as a means to triviality. What is fascinating is to see how heavily the un- keep society running smoothly (and so is open to arbitrary trained Stoppard relies on mathematics to help George ana- changes) or if goodness is absolute, existing unaltered out- lyze his opening question, “Is God?” The main attraction side of the human frame of reference. Making the case for seems to be mathematicians’ extensive experience working the existence of moral absolutes is George Moore, a professor with the infinite. Making a loose analogy between the open of philosophy and so, consequently, a bumbling fellow. Ulti- interval from zero to one and the infinitude of time and mately, though, his views are probably closest to Stoppard’s space, George surprises himself by noticing, “But the fact is, own and so he is given moments of sense and sympathy the first term of the series is not an infinite fraction but zero. during the intermittent occasions throughout the play when It exists. God, so to speak, is naught. Interesting.” He (some- he dictates his speech to be given at the evening’s sympo- what cryptically) cites Georg Cantor and Bertrand Russell, sium, “Man—Good, Bad or Indifferent.” Meanwhile, pro- and then aggressively sets his sights on the classical para- viding context for the academic discussion, George’s debat- doxes of Zeno. One of Zeno’s paradoxes states that “a tor- ing partner’s mysteriously murdered body is hanging on the toise, given a head start in a race with, say, a hare, could back of his bedroom door. It is being concealed by his po- never be overtaken.” This is so, Zeno argued, because every tentially guilty wife who is possibly having an affair with Sir time the hare reaches the place where the tortoise was, the Archibald Jumper, George’s philosophical adversary and tortoise has meanwhile moved ahead ever so slightly. For coach of a gymnastics team consisting roughly of the mem- effect, George has brought a tortoise and a hare to assist with bers of the philosophy department. a demonstration but Thumper, the hare, has escaped from The comic twists of George’s long dictation keep the audi- his box. George has also brought his bow and arrow to illus- ence entertained, but some underlying substance is required trate another paradox of Zeno who, in George’s summary, to keep the argument, and the play, from collapsing into said that “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, as I will now demonstrate, that though an arrow is always approaching its target, it never quite gets there, and Saint Sebastian died of fright.” George’s argument for God as the “First Cause” is threat- ened by Zeno’s notion of an infinity without an end or a beginning. To dramatically lay to rest any doubt that an infi- nite number of events can occur within a finite amount of time and space, he confidently notches the arrow in his bow but, startled by his wife’s cry for help, fires it over the ward- robe where—as we sadly discover at the end of Act 2—it fatally impales poor Thumper.

“You get what you interrogate for.”

Stoppard has said that the easiest part of creating plays is writing dialogue and the hardest part is finding material about which to write. As we have seen, Stoppard often piggy- backs off of other texts, and several times he has used histori- cal figures in his writing. Another recurring device in Stoppard’s work is the development of extended metaphors. In 1984, Stoppard wrote Squaring the Circle, a drama-docu- mentary for television about Lech Walesa and the Solidarity movement in Poland. In the opening scene the narrator ex- plains, “Between August 1980 and December 1981, an at- tempt was made in Poland to put together two ideas that wouldn’t fit, the idea of freedom as it is understood in the West, and the idea of socialism as it is understood in the Soviet empire. The attempt failed because it was impossible, in the same sense as it is impossible in geometry to turn a circle into a square with the same area—not because no one has found out how to do it but because there is no way in which it can be done.” Now in this case it is clear that the The Metropolitan Museum of Art, Gwynne Andrews, Rogers and Harris Brisbane Dick Funds, 1948. Funds, Dick Brisbane Harris and Rogers Andrews, Gwynne Art, of Museum Metropolitan The subject matter of the play came first and that the analogy to Saint Sebastian, dead of fright. By Francesco Botticini geometry occurred as an afterthought. However, in the case

8 Math Horizons September 1999 © Mathematical Association of America of Hapgood (1988), Stoppard’s cold-war espionage thriller, In the play’s denouement, Hapgood is forced to shoot the situation is certainly reversed. Ridley and there is a brief but poignant moment after the The central metaphor of Hapgood is the wave/particle stretcher is taken away when she hopelessly asserts, “It was duality of light described in quantum theory. A Russian sci- the shoulder.” The point is that in creating Celia, Hapgood entist named Kerner who is supposedly working for British has “made up the truth.” As Kerner says early in the play, intelligence as a double agent is suspected of leaking his top “The one who puts on the clothes in the morning is the secret research back to Moscow. When confronted for the working majority, but at night—perhaps in the moment be- truth, he responds with a poetic description of the famous fore unconsciousness—we meet our sleeper—the priest is double-slit experiment where light from a laser passing visited by the doubter, the Marxist sees the civilizing force of through the two slits forms either an interference pattern the bourgeoisie, the captain of industry admits the justice of (unique to waves) or a double-peaked distribution (indicative common ownership.” of particles) depending on how the experiment is conducted. He then concludes with the famous adage, “The act of ob- serving determines the reality... There is no explanation in “Armed thus, God could only make a classical physics. Somehow light is both wave and particle. cabinet.” The experimenter makes the choice. You get what you inter- rogate for.” But this lesson in nuclear physics is not just to The science in Stoppard’s spy-thriller/melodrama had a some- help us understand the nature of double agents; it is meant what intimidating effect on audiences, and Hapgood has been to be applied to human personality in general. Elizabeth significantly revised since its first production. This was not Hapgood is a tough and classy agent who plays chess with- the case at all for Arcadia which has met with glowing reviews out a board and runs an otherwise all-male British intelli- since its debut in 1993. One of the major influences cited by gence office. Kerner was “turned” by Hapgood, and we learn Stoppard for Arcadia is James Gleick’s Chaos, the first chap- that not only did she fall in love with her scientist but that he ter of which describes the frustrating attempts of Edward is also the father of her twelve year old son, Joe. When the Lorenz to build a computer model capable of predicting the goods from an intricately choreographed drop-off get myste- weather. The non-linearity of Lorenz’s equations produced a riously switched, Hapgood suspects an abrasive, somewhat phenomenon now popularly called the “butterfly effect” crude agent named Ridley. Her suspicions gain momentum whereby two runs of the computer model starting with only when, in a moment of what might be termed gratuitous math- tiny differences in the initial input produced unrecogniz- ematics, she learns that there are actually two of them. ably different output. KERNER: An ancient amusement of the people of Königsberg To portray the butterfly effect on stage, Stoppard sets was to try to cross all the seven bridges without crossing Arcadia across two time periods. The play opens in 1809 in any of them twice. It looked possible but nobody had solved the Coverly family’s large country house where the daughter it... Leonard Euler took up the problem of the seven Thomasina is being tutored by Septimus who, when he is not bridges and he presented his solution in the form of a teaching his talented student the classics, is engaging in car- general principle based on vertices... When I looked at nal embrace in the gazebo with Mrs. Chater, the wife of a Wates’s diagram (of Ridley’s path during the opening drop- poet whose book he has just panned. The second scene of off) I saw that Euler had already done the proof. It was the the play takes place in the same room, but in the present, bridges of Königsberg, only simpler. where three academics are each trying to recreate what has taken place in this house 180 years earlier. The most laugh- HAPGOOD: What did Euler prove? able of the three is Bernard, an historian whose tiny errors in KERNER: It can’t be done, you need two walkers. initial conditions lead him to conclude that Lord Byron Thus, like an electron whose location is not uniquely speci- fought a duel and killed the poet Chater before fleeing En- fied by the laws of nuclear physics, Ridley has for years been gland. Hannah is also an historian, but is interested in the serving as his own alibi. Ridley’s twin, however, is not as history of the gardens which during Thomasina’s time were interesting as Hapgood’s. In a plan to snare Ridley, Hapgood being transformed from smooth, undulating meadows to the creates her own foul-mouthed twin-sister named Celia who “picturesque style” characterized by gloomy forests, craggy conspires with Ridley to help rescue Hapgood’s son from ruins, and a hermitage in place of the infamous gazebo. As (fabricated) Russian kidnappers. The irony is deep though, Hannah says, “It’s a perfect symbol [of] the whole Romantic as it is the “bad guy” Ridley’s fondness for Hapgood that shame... A century of intellectual rigor turned in on itself... makes him willing to risk himself to save young Joe while The decline from thinking to feeling, you see?” Central to Hapgood’s superior shows no scruples about using the child Hannah’s thesis is the hermit, “a savant among idiots, a sage as bait. Hapgood begins to realize this and—through the of lunacy,” who when he died left the hermitage stuffed with voice of Celia—attempts to warn Ridley. Unable to compre- thousands and thousands of pages of mathematical proofs at- hend the paradox of what is happening, Ridley is confused tempting to “save the world through good English algebra.” to the point of shouting “Who the hell are you!” “I am your The third academic is Valentine, a mathematician and dreamgirl Ernie,” she replies. “Hapgood, without the brains member of the Coverly family who is using the data in the or the taste.” game books to model the grouse populations as a chaotic

© Mathematical Association of America Math Horizons September 1999 9 VALENTINE: Yes, there was someone, forget his name, 1820s [Pierre Simon de Laplace], who pointed out that from Newton’s laws you could predict everything to come—I mean, you’d need a computer as big a the universe but the formula would exist. CHLOE: But it doesn’t work, does it? VALENTINE: No, it turns out the maths is different. CHLOE: No, it’s all because of sex.

“Ah,” Valentine concedes. “The attraction that Newton left out.” Mirroring this exchange is a similar one between Thomasina and her tutor.

THOMASINA: Well! Just as I said! Newton’s machine which would knock our atoms from cradle to grave by the laws of motion is incomplete. Determinism leaves the road at ev- ery corner, as I knew all along, and the cause is very likely ... the action of bodies in heat.

The pun is certainly intended, but the 16-year-old genius Fractal leaf. Courtesy of Daniel Scharstein, Middlebury College. is actually referring to the yet-to-be-formulated second law of thermodynamics. Contradicting everyone’s attempts to look backwards in time, the second law of thermodynamics states system. In addition to explaining the essential nature of that the universe is a “one-way street.” In every physical pro- Chaos theory to Hannah (and the audience), his main ser- cess there is an inherent inefficiency—energy lost in the form vice is to serve as translator for Thomasina’s lesson books. of heat—and the disorder in the system increases. Without No ordinary student, Thomasina grows restless with Septimus’ the mathematical vocabulary to express herself, Thomasina classical geometry of plotting “xs against ys in all manner of draws a diagram illustrating the principle of increasing en- algebraic reason. Armed thus,” she frets, “God could only make a cabinet.” A century and a half before Benoit Mandlebrot tropy which, through the magic of the stage, is studied by coins the term “fractal,” Thomasina plucks a leaf from an apple both Septimus and Valentine doubled in time. and declares that she “will plot this leaf and deduce its equa- SEPTIMUS: So the improved Newtonian Universe must cease tion. You will be famous for being my tutor when Lord Byron is and grow cold. Dear me. dead and forgotten.” One hundred and eighty years later, Val- entine runs Thomasina’s leaf equation through his laptop while VALENTINE: The heat goes into the mix. Hannah reads the Fermatian passage from Thomasina’s primer: THOMASINA: Yes, we must hurry if we are going to dance. “I, Thomasina Coverly, have found a truly wonderful method VALENTINE: And everything is mixing the same way, all whereby all the forms of nature must give up their numerical the time, irreversibly... secrets and draw themselves through number alone. This mar- gin being too mean for my purpose, the reader must look else- SEPTIMUS: Oh, we have time, I think. where for the New Geometry of Irregular Forms, discovered by VALENTINE: ...till there’s no time left. That’s what time Thomasina Coverly.” means. Thomasina is as passionate as she is prodigious, at one SEPTIMUS: When we have found all the mysteries and lost point crumbling at the thought of the losses incurred when all the meaning, we will be alone, on an empty shore. the ancient library of Alexandria was burned. Septimus con- soles her with the argument that “we shed as we pick up, like THOMASINA: Then we will dance. Is this a waltz? travelers who must carry everything in their arms, and what Amid the mathematical and scientific fireworks, Arcadia we let fall will be picked up by those behind.” Septimus be- works as storytelling because, in the end, it is heart-break- lieves in the perpetual mechanical wheels of the Newtonian ing. Thomasina and Septimus do finally dance, gracefully universe, and it is clear that Stoppard is fascinated by the challenges Newton’s deterministic system has sustained over and to their mutual delight, passionately. But the audience the centuries. In Hapgood he explores the loss of “objective has learned midway through the play that, like the library in reality” via the uncertainty inherent in quantum theory. In Alexandria, Thomasina dies in a fire that night, on the eve Arcadia, determinism is discussed repeatedly, once even by of her seventeenth birthday. Watching the lovers dance as Valentine’s lascivious sister Chloe. the curtain falls, it is finally clear that it is the devastated Septimus who is Hannah’s hermit, living out his years in the CHLOE: The future is all programmed like a computer— hermitage, insanely trying to rescue his pupil through her that’s a proper theory isn’t it? own discoveries. Septimus’s plight is still relevant. The ques-

10 Math Horizons September 1999 © Mathematical Association of America tion of how complex structures arise in the face of the down- poetry are related in ways we do not acknowledge and ulti- hill current caused by the second law of thermodynamics is mately matter greatly in the way we choose to understand considered by many to be the fundamental issue presently ourselves. Arcadia is a celebration of this point. Where Ber- sitting at the forefront of science. For some, the most encour- nard is mostly bluster, Hannah and Valentine are redeemed aging clues are hidden in the equations of chaos theory. Pon- by their own passionate reasons for what they do. Stoppard dering over Thomasina’s leaf equation on his computer, Val- often hides behind his characters saying that “writing dia- entine explains to Hannah, logue is the only respectable way of contradicting yourself,” but it is impossible not to believe we are hearing the VALENTINE: See? In an ocean of ashes, islands of order. playwright’s voice when Hannah confides to Valentine, “It’s Patterns making themselves out of nothing ... all trivial—your grouse, my hermit, Bernard’s Byron. Com- HANNAH: Do you mean the world is saved after all? paring what we’re looking for misses the point. It’s wanting VALENTINE: No, it’s still doomed. But if this is how it to know that makes us matter.” started, perhaps it’s how the next one will come. Acknowledgments: I would like to thank professor/director Tom Stoppard has made it clear that his plays are events Cheryl Faraone and the 38 students whose contributions to to be enjoyed, insisting that he does not write for scholars to the winter term course, “Stoppard, Science and Spirituality,” pore over his work in search of dissertation topics. But the (Middlebury College, January 1998) greatly shaped the con- fact that the playwright has little use for the academic does tent of this essay. not make the opposite proposition any less true. A journey All quotations from Tom Stoppard in this article are taken through the rich ideas concealed in Stoppard’s plays brings from Conversations with Stoppard by Mel Gussow, Grove Press, to life the notion that mathematics and art and science and New York, 1995. n

© Mathematical Association of America Math Horizons September 1999 11