Entropy, Negentropy and Chaos in Tom Stoppard’s Arcadia: Must We Face the Music or Can’t We Just Dance?

Entropy, Negentropy and Chaos in Tom Stoppard’s Arcadia:

Must We Face the Music or Can’t We Just Dance?

Burton Weltman

“Hegel remarks somewhere that all facts and personages of great importance in world history occur, as it were, twice.  He forgot to add: the first time as tragedy, the second as farce.”    Karl Marx.  The Eighteenth Brumaire of Louis Napoleon.

Prologue: Dancing in and out of time.

Tom Stoppard’s play Arcadia is the story of a family and some of the family’s friends that takes place in two different time periods, the early 1800’s and the early 1990’s.  The play is billed as a dramatization of the theories of entropy in physics and Chaos in math.  The characters and events of the later period appear to be pale reflections of those in the earlier period.  Their seeming insipidity could arguably be a result of entropy, that is, the eventual decline of the universe from vividness and order into blandness and disorder, as predicted by the Second Law of Thermodynamics.  But, maybe not.  Arcadia is a funny play, full of witty byplay and intellectual conundrums.  It challenges our minds, hearts and funny-bones, and leaves us much to ponder.

At the end of the play, two couples, one from each time, are dancing.  The first couple consists of a sparkling intellectual in his early twenties and a brilliant girl of sixteen from the 1800’s.  They are waltzing gracefully in time to the music.  We know that the girl will tragically die in a fire later that evening, and that the man will then spend the rest of his life as a hermit.  The second couple consists of a run-of-the-mill scholar in her late thirties and a mute boy of fifteen from the 1990’s.  They are dancing awkwardly, and they are often out of time to the music.  The difference in the ages of the people in this second couple, along with their clumsiness, makes them look almost farcical.  We don’t know what will become of them in their futures.

So, is this a funny but depressing play about human history repeating itself in cycles that descend toward decrepitude?  Are we supposed to perceive the moral of the story as the inevitability of entropy in human affairs?  In this context, must we see the waltzing of the first couple as a symbolic evocation of Irving Berlin’s melancholic “Let’s Face the Music and Dance,” as one critic has suggested?  Is their dancing an omen of the end of things, and a warning that we must stoically resign ourselves to it?[1]

Or might we instead focus on the efforts of the second couple, and maybe see their stumbling about as the first tentative steps toward a new way of dancing, something less formal than a waltz, but perhaps more energetic. Something like “rock & roll,” not as graceful as a waltz, but reeking with negentropy, the opposite of entropy.  In sum, does this last scene foreshadow the inevitable decline of humanity, or might it be a sign and source of hope for the future?  The conventional view of the play takes the former view.  I take the latter, and I think it matters.

Fractals, Feedback Loops, Self-Similarity, and Strange Attractors: Chaos in Action.

Stoppard has said that Arcadia was inspired by James Gleick’s book Chaos: Making a New Science in which Gleick explains the origins and evolution of Chaos Theory in mathematics.  It is a relatively new theory because it requires an immense number of calculations to apply it, and it is only recently that computers have been developed that can effectively perform those calculations.  The play discusses Chaos Theory, but also exemplifies it in many ways.

Chaos Theory (capital “C”) is an attempt to find order in what seems to be disorder and, as such, is not the same as chaos (small “c”), which is actual disorder.  Chaos Theory is an antidote to the helplessness and hopelessness of what seems to be chaos in those cases where order actually prevails beneath apparent disorder.  It is also, thereby, arguably a counter to theories of entropy that take every appearance of disorder as an instance of the descent of the universe into universal randomness, blandness, and disarray.  The moral of Chaos Theory seems to be that all may not be as bad as it seems.

Gleick says that while “the Second Law [of Thermodynamics] is a rule from which there appears no appeal,” it is still the case that “Nature forms patterns.  Some are orderly in space but disorderly in time, others orderly in time but disorderly in space.”  It is the goal of Chaos Theory to identify patterns where they least seem to exist.[2]  In the course of the play Arcadia, the waltzing teenage girl from the early 1800’s, whose name is Thomasina, ostensibly discovers the basic ideas of both the Second Law of Thermodynamics and Chaos Theory.  Lacking computers, she is unable to fully develop her ideas.  It remains for later generations with adequate technology to rediscover these theories and be able to develop them.

The development of Chaos Theory was inspired in recent years in large part by the inability of meteorologists to reliably predict the weather more than two days in advance, despite having computers and algorithms that can accommodate a myriad of factors that make up the weather.  Beyond two days, the algorithms go wild and chaos ensues in the calculations.  This apparent chaos in the weather, and in other systems that are similarly unpredictable, seems to be a function of two main factors.[3]

First, systems that do not have strong foundations and/or built-in inertia are liable to undergo big changes in their behavior as a consequence of small changes in their surrounding conditions, and long-range predictions thereby become precarious.  Since most systems inevitably experience at least some small changes in their operating conditions, long range predictions about those systems will be thrown off unless they have strong foundations and/or inertia.  This is the problem with predicting the weather.  A host of volatile elements determines the weather, and small changes in any of those elements can throw off weather forecasting.  The oft cited example is that of a butterfly flapping its wings in Brazil leading to a typhoon in Asia.

Chaos Theory seemingly has democratic implications.  It claims that the smallest actions can initiate the biggest results, such as the flapping of a butterfly resulting in a typhoon.  It is, thereby, bottom-up in its implications.  It stresses the importance of little guys and factors that are often considered too unimportant to be respected.  In this regard, Chaos Theory can be regarded as a cautionary tale, akin to the warning sounded by Cinderella in Stephen Sondheim’s musical Into the Woods, “You move just a finger, Say the slightest word, Something’s bound to linger, Be heard.”  But it can also be taken as a hopeful idea, as in Dr. Seuss’s Horton Hears a Who, in which the slightest squeak by the smallest Who is enough the save the universe of the Whos.  So, when Gus and Hannah dance at the end of the play, maybe the song is “This Could Be the Start of Something Big?”

A second factor involved in creating chaos is the feedback that a system encounters.  If the feedback that results from a system’s operations is stronger than the system’s foundations and/or inertia, then the system’s patterns and predictions will be thrown off.  This is the case with weather.  A strong wind can literally blow a weather system in a different direction.[4]  At the same time, implicit in this theory is the hope that if you build a strong enough foundation, your system or structure may withstand the whirlwinds of change.  And that foundation may be democratically made up of many small individuals or things, as represented in the political slogan “The people united cannot be defeated.”

It is not the case, however, that chaos is always disorderly.  Chaos theorists claim that one can often find orderly patterns underneath the superficial disorder of many systems, albeit they are likely to be patterns that are unstable and cannot be predicted in advance.  Chaos Theory holds that systems may behave in logical and deterministic ways, even though their patterns can only be discerned in retrospect.   And the patterns may change in an instant.  Gleick notes that Chaos (capital “C”) is “a delicate balance between forces of stability and forces of instability.”[5]

Two of the main types of Chaos patterns are fractals and attractors, which can exist separately or can combine to make what is called a strange attractor.  It is not possible to predict the behavior of either fractals or attractors in advance, but they can be seen in retrospect as orderly and deterministic.  A fractal is a shape that reproduces itself through self-similarity.  A fractal can be successively subdivided, with each iteration essentially the same as the previous one, albeit slightly different and smaller than the last.

Fractals can be fitted together like pieces of a puzzle so that an infinite number of ever smaller replications can be fitted within a delimited space.  Fractals are, thereby, the most efficient way to maximize the coverage of the surface of a space with shapes.  Fractals are also the most efficient way to create a complex orderly pattern because all that needs to be done is to replicate the initial shape in decreasing sizes that fit in with the rest.  Blood vessels in a human body are spaced in a fractal pattern, thereby most efficiently distributing blood throughout the body.  Veins in a leaf are also spaced in a fractal pattern, as are many other natural systems.

A formula for producing fractals is to take the solution of an “X & Y” equation, plug the “Y” back into the equation as the new “X” and repeat the equation, then do this again and again ad infinitum.  When you plot the results of the equation on a graph, you get new shapes that are similar but not the same as the previous ones, thereby adding a new layer of complexity to the system.  This is the formula that Thomasina ostensibly discovered during the early 1800’s.  In the case of fractals, smaller does not mean lesser.  The new shapes are as complex as the previous ones.  And there are an increasing number of the new shapes as they decrease in size.  Fractals can seemingly, therefore, function as agents of negentropy, as they energetically reproduce themselves in an ongoing and orderly complexity toward infinity.

An attractor is the locus of another form of Chaotic pattern.  It is a point around which successive iterations of a loop swirl.  It represents a form of topology, which is the twisting and stretching of a loop into an everchanging series of shapes.  The loops that swirl around an attractor can take on weird shapes that seem unrelated except that they focus on the attractor point.  The loops may or may not decrease in diameter as they replicate, and may or may not descend toward the point.  Weather patterns apparently swirl around attractors.  Finally, there are strange attractors that combine a swirling motion with a fractal structure.[6]

So, what does all this have to do with Arcadia?  The question is whether the plot of the play might be interpreted as exemplifying entropy theory, Chaos Theory, or both.   And if the plot exemplifies Chaos Theory, is it in the form of an attractor, a fractal, or both as a strange attractor?  I think the answer to both questions is “both” and, again, it matters.

The Plot: Back to the Future, Back to the Past, Again and Again.

Arcadia is set in a mansion on the English country estate of Sidley Park.  All of the action takes place in one room, and cycles back and forth in that room between the early 1800’s and the early 1990’s.  There are four main human characters in each period.  The estate of Sidley Park also functions as a major character in the play, in that it is, I think, the strange attractor around which the play revolves.  It is a place of civility that fosters intellectual curiosity and honest, if sometimes heated, debate.  It is also a locus of romance and amorous adventures.  The two different time periods are like loops that whirl around an attractor, and the human characters and events are like fractals, that is, iterations which are similar but still significantly different.

The main character from the early 1800’s, and for the entire play, is Thomasina, a precocious teenager who critiques the conventional Newtonian physics of her time by asking why when she stirs jam into her pudding, she cannot then unstir it.  Likewise, when a pudding has cooled down, why won’t it ever spontaneously heat back up.  “Newton’s equations,” Thomasina contends, “go forwards and backwards, they do not care which way.  But the heat equation cares very much, it only goes one way.”  Based on her pudding question, and speculations on why steam engines run down, she ostensibly discovers what was later known as the Second Law of Thermodynamics.

Similarly, based on her critique of conventional geometry, which focuses on simple shapes such as squares that go through predicable changes, Thomasina develops the formula described above for creating self-replicating fractals. Fractals are complex geometric shapes that go through unpredictable changes based on repeatedly taking the “Y” from an “X & Y” equation and plugging it back into the equation as the new “X.”  Thomasina takes a leaf and proposes to graph it using her new ideas.  The formula she ostensibly developed is a mainstay of Chaos Theory.

The second key character from that time is Septimus, who is Thomasina’s tutor.  He is a genial Enlightenment intellectual and a friend of the poet Byron, who is himself an unseen visitor at Sidley Park.  A third character is Chater, a second-rate poet with whose wife Septimus has been sleeping.  He provides a frequent target for Septimus’ wit.  The fourth main character is Noakes, a landscape architect who is transforming the Sidley Park terraces from a Classical formal garden into a Romantic wilderness, complete with an ersatz hermitage.  This change is taken by characters in both the earlier and later periods to symbolize the decline of reason and orderliness and the rise of emotional and intellectual disorder.

The main characters in the later period are similar to those in the earlier, almost fractal-like, but with different genders and roles.  The central character is Hannah, a second-rate historian who has written a biography of one of Byron’s mistresses.  She is doing research on a hermit who might have lived in the hermitage in the Sidley Park gardens during the early nineteenth century.  She is a mundane but solid thinker, and is intellectually similar to Septimus but less brilliant.

Hannah’s main foil is Bernard, a second-rate literary critic who is doing research on the poet Chater, and is trying to prove that Byron killed Chater at Sidley Park in a duel over Chater’s wife.  He is a bold thinker, like Thomasina, but a cad and usually wrong in his speculations.  He is an egotistical and cynical proponent of the idea that nothing ever really changes.

Valentine is a graduate student in zoology and a computer geek, who is trying to apply Chaos Theory to the reproductive cycles of grouse.  He comes to realize that Thomasina developed the basic ideas of entropy and Chaos Theory before her time, and before there were computers that could do the complex mathematics required to fully explicate and apply those theories.  Valentine explains the theories to Hannah and to the audience.  He is a proponent of the idea that things really do change, and that science makes a positive intellectual difference.

Gus is a mute teenage member of the Sidley Park family.  He gives Hannah an apple that she puts down on a table, and that is eaten by Septimus later in the play, albeit earlier in time, which is a paradox.  The apple incident seems to be an instance of time working backwards as well as forwards which, in turn, seems consistent with Newtonian physics and contrary to the Second Law of Thermodynamics.  Gus does not talk, but his actions provide a link between the two periods, and they are perhaps vehicles of energy and a symbol of negentropy.

The main action in the earlier period centers around Thomasina’s scientific discoveries and Septimus’ amorous adventures.  Septimus is repeatedly confronted by Chater for having slept with Mrs. Chater, and for having written a scathing review of Chater’s poetry.  Septimus also later sleeps with Thomasina’s mother before finally falling in love with Thomasina.  There is a lot of witty dialogue among the characters in this earlier period, full of high cultural references.

The main action in the second period centers around Bernard’s researches and theories as to Byron and Chater, and Hannah’s researches on the alleged hermit.  Bernard makes some shrewd initial deductions about Byron being at Sidley Park in 1809, but then his thinking goes awry as conflicting evidence overwhelms him, and he repeatedly misconstrues the evidence.  His theories about Byron killing Chater prove to be nonsense.  It is much like what happens to weather forecasting when you try to extend your predictions too far.  Under persistent challenging from Hannah, he is finally forced begrudgingly to admit the failure of his theories.

Meanwhile, Hannah comes to the correct conclusion that Septimus was the hermit who was reported to have lived in the garden, and that a mass of papers covered with odd scribblings that had been discovered in the hermitage were his futile attempts to work out Thomasina’s theories by hand.  Hannah’s work is conducted in a less speculative way than Bernard’s, and she gets assistance from Valentine in explaining entropy and Chaos Theory.

Much of the dialogue in the later period consists of insulting repartee between Hannah and Bernard, civil but biting.  Hannah wins that battle.  There is also some unconsummated sexual tension between Hannah and Bernard, and a pervasive sextual tension among the other characters, with an occasional offstage consummation.  This keeps things lively in the house and in the play despite all the talking.

But the brilliance of the characters and conversation in the earlier period are in sharp contrast with the more desultory dialogue in the later period.  The earlier period is filled with poets and innovators.  They are creators.  The second period is dominated by historians and critics who merely study the work of past creators, and a guy who is studying the mating habits of grouse.

The play ends with the characters in the earlier period having a formal ball, and the characters in the later period having a costume ball in which they dress up as imitations of people in the earlier period.  Characters from both periods are on stage at the same time, but are seemingly unaware of each other.  The universe of the play seems to be winding down until, I contend, Gus asks Hannah to dance.

Conventional Interpretations: Facing the Music.

“Soon, we’ll be without the moon…So while there’s moonlight and music and love and romance, let’s face the music and dance.”  Irving Berlin.  Let’s Face the Music and Dance.  [7]

Arcadia is widely considered to be “a masterpiece.”[8]   It has been hailed as “the finest play written in my lifetime” by Brad Leithauser[9] and “the greatest play of our age” by Johann Hari.[10]  Like Hari, most critics see the play as “a laugh-filled tragedy”[11] with a depressingly resigned conclusion about life, the universe, and everything.  Entropy is the reason for this.

Early in the play, when Thomasina explains her theory of entropy to Septimus, he complains “So we are all doomed!”, to which Thomasina replies “Yes.”  Similarly, later in the play, after Valentine has explained entropy to Hannah, she asks him “Do you see the world as saved after all?” and he replies “No, it’s still doomed.”  Thomasina’s and Valentine’s replies have been taken by most critics as reflecting the viewpoint of the play that entropy is unstoppable and irreversible.  The play, says Leithauser, is “a sort of dance to the music of time,” and the song is Irving Berlin’s melancholic “Let’s Face the Music and Dance.”[12]  “The elegance of the past is gone,” was similarly the summary of the play by another reviewer.[13]  “Ergo, the future is disorder,” concluded yet another.[14]  The play, in this view, is all about entropy, and about history repeating itself in cycles that spiral downward, with each iteration duller and deader than the last.

The moral of the story according to these critics is that since entropy is humanity’s fate, the play’s main message is a challenge to our courage.  The play forces us to face the question of “How should we live with the knowledge that extinction is certain – not just of ourselves, but of our species?”[15]  In this conventional view, the play’s answer is contained in Hannah’s stoical statement that “It’s the wanting to know that makes us matter,” even if we are doomed.  For most critics, the play confronts us with the tragedy of knowing our fate and being unable to do anything about it.  I don’t agree.  I think these critics missed the point that the play is not only about entropy, but is also about Chaos.

An Alternative Interpretation: Dancing in the Streets.

  “Callin’ out around the world, are you ready for a brand new beat?”                        Marvin Gaye.  Dancing in the Streets.[16]

“Septimus, what is carnal embrace?”  This is the opening line of the play, spoken by thirteen-year-old Thomasina to her tutor Septimus.  She goes on to say that she had heard the butler saying that Mrs. Chater had been discovered in a carnal embrace in the gazebo, and she wants to know what that means.  Septimus is nonplussed.  He has set Thomasina the task of finding a solution to Fermat’s famous Last Equation, which was still unsolved in the early 1800’s.  It is clearly not a problem that he expects her to solve, and the task is merely intended to keep her busy while he is doing other things.  But Thomasina finds questions about sex more interesting.

Sex and sexual tension play a big role in this play.  There is a lot of sexual attraction and action.  It keeps the characters in motion, and keeps up the audience’s interest, in the midst of all the mathematical, historical and philosophical discussions that are the meat of the play.  In turn, while sex is a source of confusion and disorder in the play, and in human society generally, it is also a vehicle for bringing couples together and a means of fractal-like human reproduction.

Thomasina’s opening question, therefore, introduces the basic themes of entropy and negentropy, and order and disorder, that the play explores.  The subsequent dialogue between Thomasina and Septimus is itself like a Chaos pattern spiraling toward an attractor.  Septimus wants to avoid her question about carnal embrace, but Thomasina persists.  Their discussion circles around and around the definition of sex, and around what Septimus has been up to with Mrs. Chater.  It homes in eventually on the point to which it has been tending, a biological explanation by Septimus of sexual intercourse and an admission by him that he has had sexual intercourse with Mrs. Chater in the gazebo.

Sex is an attractor in this instance and throughout the play.  It is an unpredictable wildcard that can disrupt the most orderly patterns of life.  But it is also follows a pattern, especially in the case of Mrs. Chater, who will seemingly sleep with any male in sight.  There is an underlying order and a negentropic energy to life with her around.  But the same is the case with the others in the play, as the characters buzz around each other like bees in a Sidley Park flower bed.

Entropy in the universe seems to be accepted as a universal law in and by the play but, I would contend, entropy in society and human affairs is not.  While the characters in the later period of the play are less interesting than those in the earlier period, people of that later time have computers that can deal with the mathematics of Chaos and entropy that people in the earlier time couldn’t.  Valentine can do computations in a minute that Septimus apparently could not do in a lifetime.  And women like Hannah in the later period do not have to hide their lights under a bushel, as did Thomasina in the earlier period.  This addition of women to full equal status might make for greater social chaos in the 1990’s, but also for complexity in the play that is energizing.

I think that Septimus’ message to Thomasina about things that are seemingly lost in history trumps Hannah’s resignation to historical entropy. When Thomasina laments that so many of the great books in the ancient Library of Alexandria have been lost to us because of the destruction of the Library, Septimus says that nothing is lost in the long course of history.  “The missing plays by Sophocles will turn up piece by piece,” he says, “or be written again in another language,” as will everything else that makes life interesting.  Things come and go, and come again, just as good and maybe even better.  This is exactly what happens in the course of the play as Thomasina’s lost copy books that contained her ideas turn up, and it turns out that her lost ideas had been perfected by subsequent generations.

Chaos Theory is two sided as to the ability of humans to predict and plan.  On the one hand, it introduces uncertainty in planning by telling us that many things tend to fall apart at the slightest touch and then seemingly become chaotic.  On the other hand, it provides us with some measure of comfort by telling us that what seems like chaos may in fact be orderly, albeit unpredictable. That things can’t be exactly predicted does not mean they can’t be planned and prepared for.  And a way to avoid chaos in the first place is to construct systems that have foundations strong enough to withstand changes in conditions and blowback, whether they be social systems, computer programs, political organizations, healthcare plans, or whatever.  In the play, this seems to be the case with Sidley Park, despite periodic changes to the gardens.

I think the moral of the play may be that just when things looked bleak, in the midst of a costume party in which characters from the 1990’s were dressed up as pale imitations of characters from the early 1800’s, a mute boy gets up and dances with a pretty woman.  And maybe, you get yet another rebirth of an even better rock ‘n roll.  That, I think, is a better interpretation of the play.

So why does it matter?  It is not appropriate to read things into a play that are not there.  But when one can interpret the play as proposing either that the glass is half empty, which is the conventional view of Arcadia, or that it is half full, which is mine, I think it is important to at least recognize the plausibility of the latter interpretation.  It matters because we live in an age that seems to have abolished utopian ideals, big dreams of social justice, and theories of universal harmony that energized people during the nineteenth and early twentieth centuries.  We no long hear much about fulfilling the political ideals of liberty, equality and fraternity, or the ethical ideal of doing unto others as you would have them do unto you, or the social ideal that the self-development of each should be the basis of the self-development of all.

As exemplified by the conventional interpretations of the play Arcadia, we seem to be overwhelmed with weltschmerz and demoralized by the idea of entropy.  But Arcadia seems to say that this is a self-fulfilling prophecy.  The big ideals that we think we have left behind, that we think we are too mature to entertain any longer, are promoted and practiced in the play by the characters at Sidley Park and by the place itself as an institution.

Marshall McCluhan used to claim that the medium was the message, and I think that is the basic message in this play.  Underneath all of the swirling and the cyclical recurrences that characterize the people and events in Arcadia, the hopefulness of the place, Sidley Park, is the underlying message of the play.  And it is the sort of place that can perhaps be replicated on ever larger scales, so that the great ideals and the big negentropic dreams of the past might in the future be resurrected and implemented.

Postscript: Karl Marx and Historical Cycles.

Karl Marx is more commonly known for his economic theories of capitalism, and for having his name misappropriated in support of oppressive Communist regimes, than for the historical and political writings for which he was better known during his own day.  Marx was for many years a highly regarded foreign correspondent for Horace Greeley’s New York Tribune newspaper, and was well known in the United States for his analyses of political events in Europe.[17]

Marx’s famous comment that history repeats itself, occurring first as tragedy and then as farce, was directed at the ascension of Napoleon III to the title of Emperor of France in 1851, a title previously held by his Uncle Napoleon I during the early 1800’s.[18]  The tragedy to which Marx was referring was the overthrow of the first French Republic in the early 1800’s by Napoleon I.  That republic had emerged out of the French Revolution against King Louis XVI in the early 1790’s, and had reflected the hopes of the revolutionaries for a society based on the political ideals of liberty, equality and fraternity.  Napoleon I was a villain, but he was a great villain who did enormous things, until he was himself overthrown as a result of losing the Napoleonic Wars (he even had a twenty-year series of wars named after him), and he was replaced by a new King.

Napoleon III became emperor by overthrowing the second French Republic that had emerged after a second French Revolution, this time against King Louis Philippe.  The second republic had projected even greater social goals than the first, with economic justice as well as political democracy as one of its aims.  Napoleon III was a villain, but a pale and paltry replica of his uncle.  Marx, with his comment about history repeating itself, was mocking this cycle of kings, republics, and emperors, that had resulted in the poltroon Emperor Napoleon III.

In proposing that history repeats itself, occurring first as tragedy, then as farce, Marx did not suggest what the third, fourth and subsequent cycles of history would be like.  When he wrote about the ascension of Napoleon III in 1852, he could not have foreseen the way in which the cycles would continue in France.  What actually happened was that Napoleon III was overthrown in 1871 as the result of losing a war with Prussia.  He was followed by another French Republic, which was itself overthrown by the Nazis and the dictatorial Petain government during World War II.

The Nazi and Petain regimes were, themselves, then overthrown as a consequence of losing the war, and were replaced by yet another French Republic.  This republic extended its goals even further than the previous republics to encompass religious, ethnic and gender justice, but it has wavered between more and less democratic forms to the present day.

Marx’s comment about history repeating itself came at only the beginning of this cyclical series of absolutist and republican, authoritarian and democratic, progressive and reactionary regimes in France.  Similar cycles ran their courses in other parts of the world.  Do these cycles represent entropy, with the later regimes invariably paler and farcical reflections of the earlier.  Are these cycles evidence of an entropic decline of society into lameness and listlessness?

If one looks at the stature of the leading characters involved in these changes, one might answer this question with a “Yes.”  With respect to France, comparing Napoleon I with Napoleon III, or Charles de Gaulle with Emmanuel Macron, the differences seem obvious.  But if one looks at the lot of ordinary French citizens, comparing the lives of most people during the eighteenth and nineteenth centuries with the lives of most French people today, I think one must conclude with a “No.”  As part of each cycle, republican governments have become socially and politically more progressive.  And this has been the case in most places around the world, despite problems of poverty, oppression and warfare that many people in many countries are still forced to endure.

Life is less oppressive today, and living standards are higher, for a higher percentage of the world’s population than in the past, and life is also more complex.[19]  While the physical universe may be falling prey to entropy, the social universe seems to be subject to negentropy.  The relatively simple order of a slow-moving agricultural society has been replaced in most parts of the world by the complex structures and the high-powered energy of urban, industrial and post-industrial societies.  The setting of Arcadia in Sidley Park exemplifies this change.  In the early 1800’s, places like Sidley Park were at the economic, social and political center of English society.  In the 1990’s, Sidley Park is merely a resort for recreation and reflection, surviving on the fringes of an urban society.

This is by no means to say that life has become the best in the best of all possible worlds, or that things might not get much worse rather than better.  The political cycle in the United States that has given us the horrendous farce of President Donald Trump following close upon the tragedy of President George W. Bush, with the decency of President Barack Obama as an interlude, is proof of this.  The problem we most urgently face today, however, is not the entropic death of a cooling universe, but the negentropic heat-death of a nuclear war or global warming.  It is the catastrophic danger of too much heat, not too little, that is the problem.

When facing the possibility of disaster, finding hope where it can be sighted is an important part of trying to avoid catastrophe.  In this context, conventional interpretations of Acardia that pessimistically focus on the inevitability of entropy seem not only wrong but wrongheaded in contributing to the disaster the critics bemoan.  Even if history is sometimes tragical and sometimes farcical, sometimes for better and sometimes for worse, Arcadia seems to support the conclusion that as unpredictable as historical comings and goings may be, there is hope for a better future.  So long as the music plays on and people continue to dance.

[1] Brad Leithauser. “Tom Stoppard’s ‘Arcadia,’ at Twenty.”  The New Yorker. 8/8/13.

[2] James Gleick. Chaos: Making a New Science. New York: Penguin Books, 2008. p.308.

[3] James Gleick. Chaos: Making a New Science. New York: Penguin Books, 2008. p.20.

[4] James Gleick. Chaos: Making a New Science. New York: Penguin Books, 2008. p.284.

[5] James Gleick. Chaos: Making a New Science. New York: Penguin Books, 2008. p.309.

[6] James Gleick. Chaos: Making a New Science. New York: Penguin Books, 2008. pp.103-105, 109, 139, 227.

[7] Irving Berlin. Let’s Face the Music and Dance. 1936.

[8] Chris Jones. “’Arcadia’ brims with intelligence in Writers’ bright new house.” Chicago Tribune. 3/24/16.

[9] Brad Leithauser. “Tom Stoppard’s ‘Arcadia,’ at Twenty.”  The New Yorker. 8/8/13.

[10] Johann Hari. “Is Tom Stoppard’s Arcadia the greatest play of our age?” Independent. 5/21/09.

[11] Johann Hari. “Is Tom Stoppard’s Arcadia the greatest play of our age?” Independent. 5/21/09.

[12] Brad Leithauser. “Tom Stoppard’s ‘Arcadia,’ at Twenty.”  The New Yorker. 8/8/13.

[13] Sharon Kilarski. “Theater Review: ‘Arcadia.’” Epoch Times. 8/31/16.

[14] Chris Jones. “’Arcadia’ brims with intelligence in Writers’ bright new house.” Chicago Tribune. 3/24/16.

[15] Ben Brantley. “The 180-year Itch, Metaphysically Speaking.” The New York Times. 3/17/11.”

Johann Hari. “Is Tom Stoppard’s Arcadia the greatest play of our age?” Independent. 5/21/09.

[16] Marvin Gaye. Dancing in the Streets. 1964.

[17] Isaiah Berlin. Karl Marx: His Life and Environment. New York: Oxford University Press, 1959. pp.184-185.

[18] Karl Marx. The Eighteenth Brumaire of Louis Napoleon. New York: International Publishers, 1963. p.15.

[19] Richard Easterlin. “The Worldwide Standard of Living Since 1800.” Journal of Economic Perspectives, Vol.14, #1. Winter, 2000. pp.7-26.

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