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    It’s wanting to know that makes us matter.

Page 2

    Director’s Note

What we know is not much. What we do not know is immense.

    Rehearsal is a process of discovery. And interestingly enough, what we discovered, as we rehearsed Arcadia is that the play itself is about the process of discovery.

    It asks the questions mankind has been asking ever since we wiped the primordial soup of our shoes. Who are we? Why are we here? What’s it all about?

    But fear not. Since it’s Tom Stoppard who’s doing the asking, the funny bone is engaged as frequently as the mind.

Part detective story, part love story, part comedy of errors, Arcadia is also a crash course

    in mathematics, landscape gardening, literature, Romantic poetry, the second law of thermodynamics, oh, and lest things should get dull, chaos theory. The action is set in the thschoolroom of Sidley Park, Derbyshire, inhabited by the Coverly family in the early 19

    century, and simultaneously in the present day by their descendants Valentine, Chloe and the ever-silent Gus.

    While a wildly comic series of events unfolds in 1809 and 1812, involving, among other things, Romantic trysts in gazebos, duels at dawn, mysterious hermits, rice pudding, mediocre poets, steam heated engines and overheated aristocrats, a pair of rival literary researchers works doggedly and with haphazard success, to unravel them in the present.

    Will we ever find out what really happened? Is it possible to really know the past? Is it possible to really know anything? What Arcadia taught us is it’s not the answers that

    matter. It’s asking the questions. As Hannah Jarvis observes, “It’s wanting to know that

    makes us matter.”

It doesn’t matter that we’re all looking for different things. And that being human and

    fallible, we don’t always get it right. That we chase after red herrings and chimera, led

    by our hearts as often as our heads. Faced with the possibility that, after all our striving, we may never know the answers. That the “theory of everything” will always elude us.

    That there will always be an unknowable mystery at the heart of things -- like a fifteen year old boy who never speaks.

But we keep looking because we want to know.

We hope you find the search as exhilarating as we do.

Ave Lawyer

Classicism vs. Romanticism in Mathematics and Physics

“What’s going on here?”

    Bernard Nightingale, Scene 2

    And he might well ask. Is life a series of conflicts between thinking and feeling, between order and disorder, between the Classical and the Romantic? Arcadia suggests that our

    personalities, our lives, our relationships, our aesthetic preferences and perhaps even our picture of the physical universe is driven by this dichotomy.

    The Classical world is one ruled by the mind -- orderly, predictable, balanced, unchangeable and unchanging.

    The Romantic world is ruled by the heart chaotic, irregular, unpredictable,


    The changes in thought and taste in mathematics, physics, poetry and landscape gardening that reveal themselves as time bounces back and forth in the Sidley Park schoolroom reflect a larger shift from a traditional (Classical) to a modern (Romantic) view of the universe.

    Our guide on this journey is the young genius Thomasina Coverly, who makes three amazing discoveries.

There’s more to the world than meets Euclid’s eye

    She instinctively realizes that the classical geometry of Euclid, limited to straight lines, right angles and “regular forms” is too limited to be able to describe the “irregular” shapes of nature. It can describe the curve of a bell, but not a bluebell. So, by trial and error, she moves past the classical towards the Romantic, discovering what she jokingly refers to as The New Geometry of Irregular Forms” which we today know as fractal

    geometry associated with Bernard Mandelbrot. And tipping her hat to what is now called chaos theory.

    She begins by picking up an apple leaf and saying “I will plot this leaf and deduce its equation. She has obviously found the equation and explored its applications by 1812. It is what she describes as a “rabbit equation” …which “eats its own progeny”. in the homework assignment that Septimus returns to her. The "rabbit equation" is an iterated

    algorithm a process of equations that describe an apple leaf. (The method used to find it involves constantly feeding a solution back into the equation, like a rabbit continuously generating then devouring its offspring. This process of feedback is called iteration.

    Thomasina goes as far as she can with the tools at her disposal, but somehow she can see the end result that her algorithm will create a picture of the apple leaf. As Valentine is to discover in 2008 when he plugs Thomasina’s rabbit equation into a computer and, just

    as she predicted, the numbers “draw” a picture of the apple leaf. (see below)

     Fractals are the This picture of the apple leaf drawn in this way is a called a fractal.

    visual objects which result from iterated algorithms, and they have the characteristic that

    they are "self-similar" in the sense that if you change their scale and look at them, they appear exactly as they did before. Each of the smaller shapes looks just like the big one, and each of theirs looks like them, and so on down the line. Thomasina’s new irregular

    'fractal' geometry is beautifully suited to describing the messy bits and behaviour of the real world. Clouds, lungs, mountain ranges and cauliflowers are fractal objects, ones that reveal similar shapes and motifs at every level of magnification.

    Engaged in his own research, Valentine is attempting to understand the rise and fall of grouse populations using iteration. As heir to Sidley Park, part of his inheritance is a complete set of game books detailing the precise number of grouse shot at the estate each year. He is trying to extrapolate from this to predict the populations in the future using . ideas from chaos theory. Valentine is amazed to find that Thomasina was doing exactly

    what he is doing, except in reverse. It makes him furious to think (and he refuses to admit) that a schoolgirl in 1800’s Derbyshire could possibly be using a sophisticated modern technique like iteration.

Newton didn’t know it all

    In Arcadia, simple Newtonian physics represents Classicism. Isaac Newton’s

    "clockwork" view of the universe considers forces between a small number of objects in a controlled environment, and provides a metaphor for control, logic, and the picture of the world as orderly and unchanging.

    Watching what happens when she stirs jam into her bowl of rice pudding, Thomasina begins to doubt how completely the classical physics of Sir Isaac Newton can truly explain the world. Newton’s Laws of Motion are insensitive to time – they apply

    whether an object is moving in one direction or another. For example, in a movie of a ball thrown in the air, the ball follows certain rules of motion and behaves in a predictable fashion, whether the film runs forwards or backwards.

    But once she stirs the jam into her pudding, Thomasina notices, it doesn’t behave

    predictably at all .

    “When you stir your rice pudding, Septimus, the spoonful of jam spreads itself around…But if you stir backward the jam will not come together again. Indeed, the pudding does not seem to notice and continues to turn pink as before… You cannot stir

    things apart.

    She notices two things.

    One that the tendency is for disorder to increase.

    Two that it is doing so in an irreversible fashion.

    The trails of jam move toward a larger disorder that cannot be stirred back together by going the other direction. i.e. the bowl of rice pudding goes into a disordered state that cannot be reversed.

    Which leads her to believe that, (as modern scientists have proved) that all systems in the world do not follow Newton’s law. Thomasina finds proof for her hunch that some

    processes tend irreversibly towards disorder, in a discovery made in the field of thermodynamics.

    Thermodynamics (the action of bodies in heat) is the study of heat and its conversion to other forms of energy. In a typical thermodynamic system, heat moves from hot (boiler) to cold (condenser) and work is extracted.

In the 19th century a French scientist named Nicolas Lonard Sadi Carnot was the first

    to discover the Second Law of Thermodynamics: essentially, that over time systems go

    into disordered states because heat only goes one way it travels to cold objects and

    will not travel to hot objects. This means that in the creation of energy, a motor will

    create heat, which will be lost into the colder air around it.

    Reading this in an essay and applying it to the world around her, Thomasina cheerfully informs the landscape gardener, Mr. Noakes that, because of this the performance of his prized Newcomen Steam Pump, laboring away outside the French door, will always be less than 100% efficient.

When Valentine finally unravels the mystery of Thomasina’s heat engine diagram, he

    understands that what she has done is essentially applied the notion of the

    thermodynamic arrow of time.

    If time were perfectly symmetric (i.e., moved forwards and backwards as Newton suggested) then it would be possible to watch a movie taken of real events and everything that happens in the movie would seem realistic whether it was played forwards or backwards.

    While a movie of the planets orbiting the sun would look equally realistic run forwards or backwards, one showing a cup falling off a table, while realistic running forwards, would be unrealistic running backwards.

Similarly, the thermodynamic arrow of time runs in one direction only, because, as

    The Second Law of Thermodynamics tells us, heat moves in one direction only, so a system will always become more disordered over time.

    Taking a typical giant step from steam pumps to the universe itself, Thomasina sees the implications of the Second Law when applied to all the atoms in the universe. If disorder increases, and heat continues to be lost, the temperature at each location in the universe will eventually even out. In the final, climactic moment of the plot, Stoppard beautifully combines the realization of death with an understanding of Thomasina's heat diagram.

    Even though she is the creator of a frightening picture of mortality, Thomasina yearns passionately to dance. The heat of love and carnal knowledge, the playwright suggests, might help one avoid the empty shore.

    The play ends on a life-affirming note. Though we discover with Thomasina that the world must cool and end in entropy or heat loss it’s written in the “secrets of nature” –

    we discover with Valentine that there is order in the disorder. And if this is how this world came, perhaps its how the next will be born.

Classicism vs. Romanticism in the Sidley Park Garden

    Hannah: “The whole Romantic sham. It’s what happened to the Enlightenment, isn’t it? A century of intellectual rigor turned in on itself. The history of the garden says it all beautifully.”

    The grounds of Sidley Park, the house which provides the setting for Arcadia, are a

    canvas on which all three of the main styles of eighteenth and early nineteenth-century landscape gardening have at one time or another been inscribed.

    These three different styles of gardening were treated by some contemporary commentators as mere changes in fashion, and they were frequently compared with changing fashions in dress, particularly in women's dress. For others, however, they were like fashion itself -- part of a complicated story of social and political change.

The Classical Italian Garden

    The formal Italian garden reflects the Age of Reason or the Enlightenment. It was probably planted by Thomasina’s great-grandfather.

    Until the 1740s, the garden was laid out according to an aesthetic which saw beauty only in symmetry, in the geometrical pattern made by circular pools and the intersecting straight lines of avenues, alleys, terraces, hedges.

Hannah says: “The house had a formal Italian garden until about 1740”

    “…that makes you want to weep. Paradise in the Age of Reason….topiary, pools and

    terraces, fountains, an avenue of limes. sublime geometry…the best box hedge in


1740-1809: The Natural English Park

    The formal Italian garden is replaced by the “natural English park” for which Launcelot “Capability” Brown was famous. This was probably done at the instigation of

    Thomasina’s grandfather.

    Around 1740 or so tastes changed and this formal Italian design was dug up and “improved” by Lancelot "Capability" Brown. Brown’s goal was to create open vistas

    which made the park and its surrounding countryside seem part of one harmonious landscape which ran unbroken to the horizon and beyond.

    One way to make the landscape appear to flow seamlessly, was to remove anything that appeared “unnatural” or “man made” like topiary, pools and terraces, fountains and an

    avenue of limes. The” best box hedge in Derbyshire” was dug up and replaced by a “ha ha” (a ditch used to keep cows off the lawn.) “The grass went from the doorstep to the

    horizon so the fools could pretend they were living in God’s countryside….”

This is the way the garden looks in Lady Croom’s time, and it is just to her taste.

1810 The Fake Gothic Wilderness

    The Gothic Garden reflects the Age of Romance.

    Lord Croom, Thomasina’s father, has hired Mr. Noakes, the landscape gardener to tear

    up the natural English landscape that Lady Croom so cherishes and replace it with a faux Gothic wilderness in the “picturesque” style.

    As Arcadia opens in 1809, the English park that Lady Croom so admires is about to give way to the "picturesque" or “Romanticstyle favored by Mr. Noakes. The picturesque

    was an aesthetic of irregularity, of "Romantic" wildness, in which the natural, flowing lines of Capability Brown were deliberately broken and obscured by sudden declivities, jagged shapes, ruined buildings and statuary, and the shadows of rocks and unkempt trees. Lady Croom finds it utterly distasteful but her protests were obviously in vain, because by 1812, the process of transformation is under way, under the auspices of Mr. Noakes and his noisy “Newcomen steam pump”. .

    Hannah, who is all geometry and reason, hates the whole “Romantic sham” of the Gothic

    landscape. She particularly dislikes the fact that the Gothic landscape, when plunked down in England, stands out like a sore thumb -- stagy and fake and artificial. “…a setting of cheap thrills and false emotion”.

Pg 5

    The pleasure of finding things out

    The men and women in “Arcadia” are driven by the same impulse as Nobel laureate

    Richard Feynman -- “the pleasure of finding things out”. Feynman always said that he

    did physics not for the glory or for awards and prizes, but for the fun of it, for the sheer

    pleasure of finding out how the world works, what makes it tick.

     “…the kick in the discovery”…the sudden feeling, akin to an epiphany, that I had

    grasped a wonderful new idea, that there was something new in the world, that I was present at a momentous scientific event, no less dramatic and exciting than Newton’s feeling when he realized that the mysterious force that caused that apocryphal apple to land on his head was the same force that caused the moon to orbit the earth….

    …that’s why scientists persist in their investigations, why we struggle so desperately for every bit of knowledge, stay up nights seeking the answer to a problem, climb the steepest obstacles to the next fragment of understanding, to finally reach that joyous moment of the kick in the discovery, which is part of the pleasure of finding things out.”


    The term Arcadia is used to refer to an imaginary and paradisiacal

    place. In reality is was a region of ancient Greece in the central Arcadia. Peloponnesus. Its inhabitants, somewhat isolated from the rest of the world, proverbially lived a simple, pastoral life.

    A county in central England Derbyshire

    A book that covers the basic elements of a subject. primer.

    Plump, chicken like game birds with mottled brown or grayish grouse plumage found in the Northern Hemisphere.

    Latin for flesh or meat. caro, carnis

    The son of Judah in the Bible (Genesis 38:9). Onan is remembered for spilling his seed on the floor and is associated with masturbation Onan

    and coitus interruptus.

    Pierre de Fermat, a French mathematician and magistrate who lived from 1601 to 1665. He was a founder of modern number and Fermat

    probability theories.

    nnnFermat stated that the equation x + y = z, where x, y, and z are

    nonzero integers, has no solutions for n when n is an integer greater Fermat's Last

    than 2. It wasn’t until 1993 that British mathematician Andrew Theorem

    Wiles found a proof of the conjecture.

    Latin, from the Greek word eros meaning sexual love. In psychiatry, it refers to the sexual drive. Eros was the son of Aphrodite and the Eros

    Greek god of love.

    A freestanding, roofed and open-sided garden structure providing a gazebo shady resting place.

    The late 18th century movement driving British landscape the picturesque architecture.

    The English mathematician and scientist (1642-1727) who invented

    formulated among other things, the theories of universal gravitation, Sir Isaac Newton,

    terrestrial mechanics, and color. Of apocryphal apple fame.

    Refers to Mechanics, the branch of physics concerned with the motion of objects and their response to forces. For normal phenomena Newton's laws of motion remain the cornerstone of Newtonian

    mechanics. However, Newton's laws have been superseded by quantum mechanics and Albert Einstein's theory of relativity.

    The largest and most famous of England's public schools (in England, "public schools" are the equivalent of "private schools" Etonian

    here in the US.

    Isaac Newton developed three laws of motion: (1) a body at rest Newton's law of

tends to remain at rest, or a body in motion tends to remain in motion

    motion at a constant speed in a straight line, unless acted on by an outside force; (2) the acceleration of a mass by a force is directly proportional to the force and inversely proportional to the mass; (3) for every action there is an equal and opposite reaction.

    (1608-1674) The English poet and scholar who is best known for the John Milton epic poem Paradise Lost, perhaps the greatest epic poem in English.

    British writer (1774-1843) known for his Romantic poetry, criticism, Robert Southey and biographical works.

    Scottish literary critic and jurist (1773-1850) who co founded and

    edited the Edinburgh Review and was known as a harsh critic of Lord Jeffrey


    Henry Richard Vassall Fox, 3d Baron (1773-1840) was a British

    statesman and writer. A liberal Whig supporter, he was lord privy Lord Holland seal from 1806-7 until the fall of the Whigs. He is best remembered for his writing and his wife's literary salon gatherings.

     The Piccadilly

    A fictional publication reviewing and satirizing literature. Recreation

    Scottish novelist and poet (1771-1832) who wrote romances of Sir Walter Scott Scottish life, the most famous being Ivanhoe.

    The rectangular area, 22 yards long, between the wickets in cricket,

    an outdoor game played in Britain with bats and a ball by two teams cricket pitch

    of 11 players each.

    A district of western Greater London on the River Thames where the famed Royal Botanic Gardens were established in 1759. The gardens Kew contain thousands of plant species and include museums,

    laboratories and hothouses.

    A tall, four-sided stone shaft, usually tapered and monolithic, that terminates in a point. The ancient Egyptians dedicated them to the sun god and placed them in pairs before temple portals. Hieroglyphs obelisk

    commonly ran down each of their sides. Many obelisks were taken from Egypt.

    A small brook or rivulet. rill

    "Even in Arcadia, there am I" (the "I" refers to death). A famous

    painting by Nicholas Poussin called Shepherds in Arcadia shows a Et in Arcadia ego

    group standing around a tomb on which the words appear.

    (1764-1823) A British writer of Gothic novels Ann Radcliffe

    The 4th Earl of Orford, 1717-97, noted for his Gothic romance, The

    Castle of Otranto (1765). Strawberry Hill, Walpole's Gothicized Horace Walpole cottage, is credited with starting the Gothic/picturesque craze in English landscape design.

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