Saturday, 9 April 2011

Toiletpaper Problem

A Toiletpaper Problem

To truly let this blog live up to its name, I propose the following toiletpaper problem, inspired by real life:

I'm on the toilet (number 2, if you must know) and, because the paper is rather thin, I tear off a good long section to be able to double it over. Upon folding it in half, however, I realize that the piece I tore off is still too long to use! What to do?

WELL: I could tear this folded over peice in half, but this would lead to the unfortunate situation in which the one section would have two layers, unconnected by a fold. As we all know, the layers of this cheap toiletpaper would seperate in such a case.

The problem becomes: how to tear this piece in half such that the two halves end up folded in half and of the same size.

The solution for this was pretty obvious: I ended up unfolding it, tearing it in half, and then folding each half in half.

BUT this gave rise to the question: what if the piece you tore off originally is 3 times the length you want? 4 times? N times?

The algorithm above takes N folds and N-1 tears. But you can do better than this.

Give an algorithm that takes:
N folds and one tear
1 fold and O(log(N)) tears
O(log(N)) folds and one tear

NOTE: O(log(n)) means "order of log(N)" This means that the number of folds grows roughly logarithmically but may be slightly different from what your calculator would say for "log base 2 of N" For example: f(m) = log2(m) + 4; O(f(m)) = O(log(m)). The constant goes away.

Friday, 1 April 2011

The Antithetical Scene

An Analysis of Vernon God Little and Water

The Hungarian psychologist Mihaly Csikszentmihalyi, in his work on the subject, proposed that the optimal experience is a state of “flow.” (1) According to Csikszentmihalyi, a state of flow is characterized by the loss of the sense of self and the merging of the emotional and intellectual towards the task at hand. Flow is only achievable if the task is challenging but satisfying.

In the 1930’s Antonin Artaud set out to establish an absurdist theatre of cruelty. This cruel theatre made as its aim the unsettling of the audience to dispel the “shroud over our perceptions” (2). To shatter the audience’s illusions, Artaud argues, the play must bring the audience into the emotional scene and then “cruelly” destroy that false reality.

Bertolt Brecht’s Dialectical Theatre was opposed to this emotional embrace of the audience. Watching the Brechtian stage, the audience is constantly aware that they are watching a play. They are never allowed to enter the world of the play because it is the dialog between the play and the outside world that allows the performance to speak.

To the modern audience, however, neither of these forms of theatrical scene is likely to provide a very satisfying experience, and is through analysis of “flow” that we understand why.

While the typical West-End musical certainly creates an enjoyable experience, it is unlikely to challenge the audience. Absurdist theatre, while certainly challenging, remains unenjoyable. Brechtian theatre, meanwhile, prevents the audience from ever losing its sense of self. For Csikszentmihalyi, and sadly for many of us, this prevents a state of flow.

Today’s audiences expect and deserve to be put into a state of flow: to be challenged, provoked and to still enjoy the experience! To ensure a play’s success in today’s competitive cultural economy[1] and within the audience’s own mental economy[2] a play must do this.

The scenography of two recent productions in London, Vernon God Little (3) and Water (4), merge the gap between the dialectic and the absurd, allowing the audience to experience a state of flow, leaving them both shocked and entertained. Their scene is the creation of a theatrical space that runs directly against the narrative of its story. This contradictory scene derives its voice from a sort of Brechtian Dialectic, where instead of leaving one voice to the audience, it instead presents both voices. One voice comes from the plot that is unfolding onstage and one voice comes, as it were, from the theatre or ensemble itself through a series of strong scenographic choices that directly contradict the voice of the story. This is the essence of the antithetical scene.


Water is a play of missing connections. Graham is separated from his father by space and from his brother, Chris, by time. Claudia separates herself from Joe out of fear and both isolate themselves from the world in their pursuit of greatness[3]. Claudia’s isolation drives Joe away, despite the fact that she carries his child. Joe’s isolation and ego cause him to go on a suicidal dive, and Chris is left with no real family despite the social status he’s carefully cultivated (a fate all the characters share).

The separation and isolation continues on the meta-narrative level, where the parallel plots of Graham and Claudia never intersect. Both characters stay at the same Canadian hotel and at one point they both board the same lift. The audience fully expects the transcendent moment of suddenly intertwined narratives that the production has been careful to set up. The plot, however, denies the characters even that connection and the audience feels cheated and empty when the play ends with neither character ever becoming aware of the other.

However, even as Claudia is unable to work with the international community towards a higher goal (combatting global warming), her actress is busy dashing about the stage becoming in turns a receptionist, a stewardess, even a breathing apparatus, in a highly choreographed meta-scene.

What Water does, in a seemingly Brechtian move, is lay bare the process of theatre-making. There are no curtains hiding the stage crew, no hiding the actors as they deftly switch roles, and the sound effects (an intricate, rhythmic and meaningful music) are not created remotely but are made on stage, in plain view.

Critic Ian Foster noted that the inventive soundscape was created “in the most varied of manners … finding connections in the most disparate of things.” (5) Indeed every sound arising naturally in the scene eventually found its way into Tim Phillips’ music, finding connections with other sounds, other characters and even other scenes.

In a marked contrast to the disjunction of the plot, the scenography of the performance itself is very connected. The very embodiment of Baugh’s “scene-as-machine” (6) each scene gives way to the next as easily and powerfully as the tide. Yet even as we see these wondrous, fluid transformations of space and hear Phillips’ beautiful music this image of effortless power is grounded in the production’s flaunting of the human hands and effort which run that machine.

The story of Water presents a rather bleak narrative of man’s inability to connect and the suffering that surely awaits him. The scene around that story presents the audience with an antithetical narrative: the beauty and puissance that comes from the successful collaboration of the people running the theatre. It is in creating a dialog between the story and the scene that Water finds its voice and simultaneously disturbs and consoles. The story leaves the audience shaken by a sense of futility, but the scene offers the chance of redemption: if only the characters could come together and see (or perhaps hear) the beauty and connections in the scene around them.

Vernon God Little

Vernon God Little presents the opposite relationship between the scene and the story. While in Water the scene contradicts the plot, in Vernon God Little it is the story that undermines its scenography.

Vernon is a play of manipulation and perception[4]. Before the action of the play, Vernon’s best friend, Jesus, doubly outcast from Texan society by being Mexican and gay, goes on a murderous rampage, killing sixteen of their classmates before turning the gun on himself. As the town looks for someone to blame, they turn on Vernon: a move facilitated by the opportunistic sleaze-ball Lally. In a cycle of injustice, Vernon is forced to run, each step incriminating him more in the media-informed eyes of the spectacle-hungry public. Vernon is eventually caught in Mexico when his own sexual desires are manipulated by Taylor, and it isn’t until, on death row, when Vernon decides to “give the people what they want” that his tragedy ends and he can return home exonerated.

Such a story could easily become pathetic melodrama were it not continuously undermined by antithetical scenography. While the story asks us to pity Vernon, a raucous blue-grass band stomps about stage celebrating Vernon’s pain. In the grossly unfair mistrial that condemns Vernon, glittering beads and a gospel singing judge exuberantly endorse this spectacle of justice. And when Vernon’s triumphant resurrection and return home is undercut by his mother’s new fridge, the scene legitimizes her inhuman selfishness by allowing the radiant symbol of consumerism to literally upstage Vernon.

Clearly the production is not asking us to exchange our empathy for Vernon for a fridge. What this antithetical scene presents us with is the story through the eyes of the story’s society. A caricature of mediatized sensationalism, populist blood-lust and rampant materialism, the scene mercilessly reminds us how we would feel about the story had we not the advantage of Vernon’s perspective.

It is the cognitive dissonance between the story as we know we should experience it and the story as we are asked to experience it by the scene-as-society that allows Vernon God Little to act as an intervention. In true Artaud fashion the audience’s normal view is made grotesque and disgustingly false, disturbing the audience both with the distance between perception and reality and by the knowledge that we often do perceive the world in this way.

Foil Characters and achieving Flow

Clearly the antithetical scene has opened new vistas of theatrical expression for these productions, but how does this antithetical scene achieve a state of flow? A naïve but partially correct explanation is that in both Vernon and Water the smooth, unbroken, dreamlike transition from scene to scene helped the productions to flow[5].

In the Csikszentmihaly model, viewing a play is the task of coming to a clearer understanding of the world by grappling with the conflicts and contradictions the play presents. To experience a play in a state of flow, the audience must engage with the task (with both sides of a conflict) at both the reflective (intellectual) and visceral (emotional) level: empathizing with and projecting onto both sides so strongly that the sense of self is lost.[6]

Plays that achieve this typically do so through characterization. In Frankenstein (7), the foil characters of the scientist and the monster as well as the opposing forces of the individual (as represented by both characters) and society as a whole (as represented by the rest of the ensemble, particularly Elizabeth) are each so identifiable and understandable that we cannot help but be moved and absorbed by the conflict between them.

In Water and Vernon God Little it is the representation itself and its opposing presentation that provide us the “foil characters” on which to project our views. In Water we identify with the plight of the characters, and with the hopeful beauty of its soundscape. In Vernon we identify not only with Vernon and Jesus, but unfortunately with the dehumanized, sensationalist presentation which has come to be all too familiar today.

Using the idiosyncrasy of Artaud’s absurd and Brecht’s awareness of the dual layers of representation and presentation, the theatre of antithesis turns its own theatricality into its vehicle of expression: able to simultaneously disturb and console; inform and delight, all the while maintaining its sense of flow.


1. Csikszentmihalyi, Mihaly. Flow: The Psychology of Optimal Experience. New York : Harper and Row, 1990.

2. Artaud, Antonin. The Theatre and its Double. 1938.

3. Norris, Rufus. Vernon God Little. Young Vic, London : s.n., February 2011.

4. Farr, David. Water. Tricycle Theatre, London : Filter and Lyric Hammersmith, February 2011.

5. Foster, Ian. Review: Water, Filter at Tricycle Theatre. There Ought To Be Clowns. [Online] February 5, 2011. [Cited: March 29, 2011.]

6. Baugh, Christopher. Theatre, Performance and Technology. New York : Palgrave MacMillian, 2005.

7. Dear, Nick. Frankenstein. The National Theatre, London : s.n., 2011.

8. Boorstin, J. The Hollywood Eye: What Makes Movies Work. New York : Cornelia & Michael Bessie Books, 1990.

9. Norman, Don. Emotional Design. New York : Basic Books, 2004.

[1] Plays are competing with cinema and other art forms that already do this very successfully. See footnote 6

[2] What I’m suggesting here is that a play’s goal is to be long remembered by those who see it. A play that is enjoyable but not profound will be quickly forgotten for more recent, pleasant experiences. A play that is profound but not enjoyable will not long be contemplated because of its negative emotional associations. Only the play that is both enjoyed and disillusioning will be long remembered.

[3] In this way the fate of Claudia and Joe parallels that of Dr Frankenstein: damned by their individualist pursuits of greatness; while Graham’s parallels that of the creature: doomed to separation from his bookish progenitor. (7)

[4] As such, it seems to be almost obvious that they should choose to present these themes at the meta-theatrical level.

[5] In this sentence I use flow in both Csikszentmihalyi’s sense and the more quotidian sense.

[6] This is a connection between the work of film critic J. Boorstin and psychologist M. Csikszentmihalyi that I came across in cognitive scientist Don Norman’s book Emotional Design. Its extension into the theatrical realm is, I feel, obvious. (1) (8) (9)