An Unlikely Pairing

Mathematics and Shakespeare a combination liable to make members of both academic factions run in fear.  They are, however, surprisingly compatible.  Statistics, probability, and logic pair nicely with verse analysis, staging, and doubling.  For the past two weeks this bizarre intersection has been the focus of my work in the education department. Using Internet Shakespeare Editions, (http://internetshakespeare.uvic.ca/Foyer/plays.html). Minitab 16 (http://en.wikipedia.org/wiki/Minitab), and a TI-84 plus (http://en.wikipedia.org/wiki/TI-84_Plus_series) I have determined the probability of randomly generating verse lines, and I have also discovered why twelve is the ideal maximum number of actors on the Blackfriars stage.  For those with the guts to face irrational numbers and irregular lines, here are my findings.

Is Iambic Pentameter a Coincidence?

Coin flips are a favorite probability simulator of math teachers everywhere.  Each flip has two outcomes—heads or tails—both of 0.5 probability.  From there the textbook, teacher, or worksheet can set up various scenarios to test: what is the probability of  ten flips yielding eight heads and two tails, six heads in a row, etc?  If we replace the coin with a syllable, we can calculate the likelihood of accidentally writing a regular line of iambic pentameter.  Each of the ten syllables represents a coin flip and stressed and unstressed syllables represent heads and tails. This problem assumes there is a 50/50 chance of stressing a syllable.  In order to determine the probability of randomly generating an unstressed-stressed-unstressed-stressed pattern for ten syllables in a row, we must multiply the probabilities of each outcome in the desired order.  Since both unstressed and stressed have the same probability of occurrence—0.5—the problem looks something like this: 

0.5*0.5*0.5*0.5*0.5*0.5*0.5*0.5*0.5*0.5 = 0.000977 or 0.5^10 = 0.000977

In other words, under these conditions, there is a 0.0977% chance of randomly generating a single line of iambic pentameter.  What is the probability of generating a full sonnet’s worth of pentameter?  In that case we want one-hundred-forty alternating unstressed-stressed syllables, fourteen lines of ten syllables.  The equation is 0.5^140 = 7.175*10^-43.  For readers unfamiliar with scientific notation that is 0.0000000000000000000000000000000000000000007175, essentially zero.  Iambic pentameter is not coincidental. 

How Many Staging Permutations are there for the Blackfriars Playhouse?

            The answer to that question changes according to how many actors are involved.  Fortunately, after establishing the number of positions available to one actor we can create a formula applicable to any number of people.  The stage is twenty-nine feet wide by twenty-two feet deep.  For the purposes of this problem we ignore the presence of the gallant stools.  The groups of four X’s represents the space occupied by an actor, for the purposes of this equation four square feet.

X

X

X

X

Under these assumptions, there are 588 different positions for a single actor.  21*28 = 588.  We multiply by one less than the actual dimensions because that is how many different positions two feet (one side of a four foot square) can occupy within 22 or 29 feet.  The numbers one through twenty-two represent to depth of the stage.  We are trying to figure out how many ways there are to place two consecutive feet within that range, feet one and two, feet two and three, etc.  We end up with twenty-one combinations.  Doing the same with twenty-nine feet yields twenty-eight combinations.

1.        1 2

2.        2 3

3.        3 4

4.        4 5

5.        5 6

6.        6 7

7.        7 8

8.        8 9

9.        9 10

10.    10 11

11.    11 12

12.    12 13

13.    13 14

14.    14 15

15.    15 16

16.    16 17

17.    17 18

18.    18 19

19.    19 20

20.    20 21

21.    21 22

Things get more complicated for the second actor.  Actor One occupies a four square foot space somewhere on the stage which Actor Two cannot also occupy.  The 588 possibly positions assumed the actor could be anywhere on stage, which means several of those options overlap by one or more units.  This means that we must take out the spot occupied by Actor One and all overlapping positions when calculating the number of possibilities for Actor Two. 

The diagram below illustrates the need to account for overlap.  Each cell is a square foot.  The center Xs represent the occupied space.  The surrounding Ys indicate parts of other four foot units that overlap with the occupied square.

	Y	Y	Y	Y
	Y	X	X	Y
	Y	X	X	Y
	Y	Y	Y	Y

Including the central square there are nine positions in and around the Xs which Actor Two cannot occupy.  588 – 9 = 579 spaces available to Actor Two.  We find the total number of possible stage pictures by adding Actor One’s possibilities (588) and Actor Two’s possibilities (579).  588+579 = 11,667.  Please note that this equation assumes the first actor’s position was not on the edge of the stage, as such a position would reduce the number of positions eliminated after placing Actor One.

If the number of positions available goes down by nine with each actor added to a scene, we can generate a formula to calculate the number of staging possibilities.  588+Σ(588-(n*9)), where n = the number of actors on stage previous to the actor being placed.  The Σ symbol means “sum of.”

Stage configuration has a huge affect on ideal blocking.  The Blackfriars Playhouse features a thrust stage, meaning it has audience on three sides (four if you count the balcony).  Angles are the rule for thrust stages.  As long as actors form diagonal lines, triangles, etc., then every audience member is able to see at least one of them. 

            In order to figure out how many angled combinations there are we follow a similar formula as the one above but with more positions removed.  After removing the occupied position and the eight surrounding squares from the pool we also remove the column and row containing the selected position. 

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As previously stated, there are twenty-one and twenty-eight different positions in each row/column.  Placing an actor removes three of those, leaving eighteen and twenty-five.  18+25+9 = 52.  Under these conditions the formula becomes 588+Σ(588-(n*52)).

            Up to a certain number of actors, the number of staging possibilities grows with each additional actor on stage as we add some number less than 588 to 588.  At and beyond twelve actors, however, the number of permutations shrinks with each addition.  The eleventh actor adds sixteen possible configurations because 588-(52*11) = 16.  The twelfth actor removes thirty-six configurations, 588-(52*12) = -36.  Scholars debate the exact size of early modern acting companies; however, the general consensus is that the troupes were between eleven and fifteen actors.  These calculations support the lower end of that range, at least for indoor stages like the Blackfriars Playhouse.  The larger outdoor stages such as the Globe may have allowed for larger casts.   

The majesty of the creature in resemblance of the Mother.

            Mothers. We all have them, or did at some point. There are many different types of mothers: biological, adoptive, absent, neglectful. In honor of this upcoming Mother’s Day, let’s take a look at all the different mothers who appear (or critically do not appear) in the shows currently on during the Spring season at the Blackfriars Playhouse. The unwillingly absent but eternally loving Hermione in The Winter’s Tale, the self-interested and transgressive Annabella in ‘Tis Pity She’s a Whore, and the Indian votaress in A Midsummer Night’s Dream all have one thing in common: they do not get to raise their children. But does that mean they are not mothers?

            When Hermione is with her children, she is happy and content, a loving mother and a normal one. She gets annoyed at Mamillius a time or two, telling her lady to “take the boy to you; he so troubles me / ‘tis past enduring” (2.1.1-2) – but it’s hardly unusual or unnatural for a mother to occasionally be wearied by her rambunctious ten-year-old. But when Leontes’s jealousy removes her from her family, resulting in her son’s death and her daughter’s banishment (and presumed death), we see the full pain of a grieving mother.

Hermione never grieves for herself. Even after Leontes throws Hermione in jail, where she endures the pain of childbirth alone in a dirty cell, and then is “hurried / here to this place, i’ th’ open air, before / I have got strength of limit” to stand trial before her husband for her supposed crimes, she never weeps or pleads for her life (3.2.104-6). “Sir, spare your threats,” she says to Leontes. “The bug which you would fright me with, I seek” but not because she has been “on every post proclaim’d a strumpet.” Her first sorrow is the loss of her husband’s love, and hard by is “my second joy / and first fruits of my body, from his presence / I am barr’d, like one infectious.” What cares she for life, if she does not have her son? On top of that, “my third comfort … is from my breast … hal’d out to murder.” Her desire for death stems not from pride or slander but from the loss of her children – every mother’s nightmare. “Tell me what blessings I have here alive,” she tells Leontes, “that I should fear to die?”

And die she does, at least for awhile, when she loses Mamillius for good. When she is not a mother, she simply ceases to exist. Whether she is dead or in hiding with Paulina is not important: the only important thing is that she is not there. It is not until her daughter Perdita reappears, restoring her title of “mother,” that Hermione herself can exist again. She is a mother more than she is a woman, a wife, or a queen. If she can’t be a mother, she’s nothing.

Annabella and Giovanni, from John Ford’s ‘Tis Pity She’s a Whore, notably lack such a motherly presence. Annabella’s maid, Putana, is a poor substitute, and their father is too preoccupied with arranging Annabella’s wedding to one of her many suitors to notice that she is sleeping with her brother. In fact, there are no mothers in the play at all – except Annabella herself, who becomes pregnant with Giovanni’s child.

Her pregnancy, the play’s only concession to motherhood, is a calamity. There is no joy in the prospect of this child. Putana’s way of telling Giovanni the unhappy news is to wail that his sister is undone and shamed forever. When Giovanni anxiously asks her if Annabella has died, Putana says, “Dead? No, she is quick; ‘tis worse, she is with child” (3.3.9-10). Even Friar Bonaventura has no pity for the scared expectant mother. “You have unript a soul so foul and guilty / as, I must tell you true, I marvel how / the earth hath borne you up” (3.6.2-3). Annabella makes one tender to reference to her unborn child, telling her already-cuckolded though newly-wed husband Soranzo cryptically of “the man… that got this sprightly boy / for this a boy, that for glory, sir” and then launches into praises for her anonymous baby daddy (4.3.33-4). No one speaks another word about the gestating child until Giovanni stabs Annabella in a jealous rage and, as an afterthought, realizes he has also killed his son.

But lest you think all early modern plays take such a dire view of motherhood, you must remember A Midsummer Night’s Dream. Certainly Athens has moments where a much-needed mother is absent – notably Hermia’s mother, who might have been able to tell Egeus not to kill their daughter for wedding her true love Lysander – but the fairy world of Oberon and Titania is different. Titania is parenting a little Indian boy, son of a votaress who died during childbirth. (Hear more about this in Dr. Ralph’s podcast here.) Titania loved the woman and tells Oberon, “for her sake do I rear up her boy / and for her sake I will not part with him” (2.1.136-7). Oberon wants the boy for his own page for unclear reasons, and the fairy subplot hinges on their fight over him.

Take out the supernatural elements and you find a very modern familial situation. Titania and Oberon were lovers once but now, divorced as they are, their main and most vicious battle is over custody. Oberon may want the boy out of jealousy of his beauty or just to annoy his ex, but Titania loves him as if he were her own. “The fairy land buys not the child of me,” she tells Oberon (2.1.122). Does the lack of Titania’s blood in the boy’s veins make her any less his mother? Perhaps not, but does her love for him nullify his connection to his birthmother, the Indian votaress who died giving birth to him? Doubtless if she had lived she would love him just as much as Titania does – but she did die, and Titania loved her, and for her sake will raise her boy to remember her. Had she left him behind, he would be motherless. By taking him with her, she gave him two mothers – herself and the memory of the votaress.

This Mother’s Day, honor all the mothers in your life. Not all mothers get to raise their own children. Maybe they are separated from their children through unfortunate circumstances, like Hermione. Maybe they are never born, like Annabella’s. Maybe someone else raises them, due to the birth mother’s death, like the Indian votaress’s. Likewise, not all mothers give birth to their own children, like Titania. Yet, all of these women are mothers, and they all deserve recognition on Mother’s Day.


--Lia Razak

Game of Whores

Forbidden love, callous murders, frantic bids for power, innocence shattered, impulsive actions with disastrous consequences, a rotten world falling to pieces at the slightest touch -- is this a 21st century fantasy series, or a 17th century tragedy? Both, as it turns out -- 'Tis Pity She's a Whore and Game of Thrones both explore some of the darkest twists of the human heart and the most depraved and desperate actions of our minds. The titillation of watching such egregious violations of societal taboos is as strong now as it was four hundred years ago. We've assembled a list of some of the greatest similariites between the shocking HBO series and John Ford's equally astonishing play, in our very own Game of Whores! Are you a fan of Game of Thrones? Then go check out Game of Whores, and join us at the Blackfriars Playhouse for 'Tis Pity She's a Whore and see the temptation and turmoil live instead of on a screen -- we're HD and 3D with no extra upcharge. 

WARNING: The Game of Whores contains SERIOUS SPOILERS for both Game of Thrones and 'Tis Pity She's a Whore. Read at your own risk!