Theorems Into Plays

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 Fermats Last Theorem to ask her tutor, Septimus Hodge, spoon, the red jam in her rice pudding eventually turns the the meaning of carnal embrace. Septimuss first explana- entire dish an even shade of pink. Do you think this is tion, Throwing ones 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 Stoppards 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 dont 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 Stoppards 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 Thomasinas 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 Fermats 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- Stoppards 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 Toms father stayed behind and was killed in the frivolity redeemed by my seriousness. The frivolous charm ensuing Japanese invasion. In 1946, Toms 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 familys 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 Stoppards 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 sciences 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 incidental in Stoppards 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: Im the same. Its poetry to mea perfect equation of space, time and energy ALBERT: Yes FITCH: Its not just slapping paint on a girder ALBERT: No FITCH: Its continuity-control-mathematics. /Solo ALBERT: Poetry. FITCH: Yes, I should have known it was a job for a university Daily Mail Daily © man... Youll stick to it for eight years will you? Tom Stoppard ALBERT: Oh, Ill paint it more than once. Some of the plays most comic moments occur when Albert Its poetry to me. is joined by Fraser, a would-be suicidal personality who, every time he climbs the bridge to jump is so calmed by the To be sure, the themes explored in Stoppards 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 Fitchs 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 Stoppards earliest work. Alberts Bridge is a radio play first ing girders, Fitchs 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 Stoppards 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 Stoppards 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 Shakespeares 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 Hamlets 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. Stoppards 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 operate as a factor within un-, sub or supernatural forces.

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