Tag Archives: moral certainty

Probability Theory, Moral Certainty, and Bayes’ Theorem in Shakespeare’s OTHELLO

Marionet Teatro
Theatre about Science Conference
University of Coimbra, Portugal
November 25-27, 2021
Edwin Wong

Probability Theory, Moral Certainty, and Bayes’ Theorem in Shakespeare’s Othello

Thank you to the organizers for putting this wonderful event together and thank you everyone for coming. It’s great to be here. I’m Edwin Wong. I specialize in dramatic theory based on chance, uncertainty, and the impact of the highly improbable. My first book, The Risk Theatre Model of Tragedy, presents a new theory of tragedy where risk is the dramatic fulcrum of the action. The book launched The Risk Theatre Modern Tragedy Playwriting Competition, the world’s largest competition for the writing of tragedy, now in its fourth year (risktheatre.com). Today, I’ve come all the way from Victoria, on the west coast of Canada, to talk about the intersection between theatre and probability theory in a play we all know and love: Shakespeare’s Othello.

Now, the first thing people ask when I say “theatre” and “probability theory” is: “How do you bring probability theory to theatre? How would you know the odds of something happening or not happening? —every event, even chance events, are purposefully written into the script by the playwright.” They ask: “Where is the probability in theatre?”

It’s there. Look at the language of probability in Othello. In Othello, Shakespeare talks of “proof,” “overt test,” “thin habit and poor likelihoods,” “modern seeming,” “probal [i.e. probable] to thinking,” “exsufflicate [i.e. improbable] and blown surmises,” “inference,” “prove it that the probation bear no hinge nor loop,” “I’ll have some proof,” “living reason,” “help to thicken other proofs that do demonstrate thinly,” “speaks against her with the other proofs,” and so on. The language of probability permeates the play.

The language of probability permeates Othello because, in this play, no one is as they seem. “I am not what I am,” right? Iago seems honest; he’s anything but. Othello seems a man for all seasons; he is, however, quite fragile. Desdemona seems unfaithful; she is, however, true. Emilia seems to have loose morals; she sticks to her morals, however, even when threatened with death. There’s a disjunction between seeming and being. Othello and Iago talk about it: “Men should be what they seem,” says Iago, “Or those that be not, would they might seem none.” Because seeming and being are at odds, you can guess what a person’s intentions are, but you may never know.

This brings us to the crux of the play: your best friend who you’ve stood shoulder-to-shoulder with in wars and who’s known for his honesty, is telling you your wife is getting it on with your lieutenant. You’re a little bit older, having “declined into the vale of years.” Your wife is young, as is your lieutenant. But, you love your wife very much and she seems constant. At the same time, you also trust your best friend. What do you do?

This is what Othello decides. If the allegations are true, he’ll kill Desdemona and Cassio. If they’re false, he’ll kill Iago. Someone will die. The problem is, how does he decide who dies? There’s no proof. Nor is proof forthcoming: Iago and Othello establish that Desdemona and Cassio, if they’re guilty, aren’t going to confess. And, because they’re subtle lovers, Othello’s not going to catch them in the act. In the real world, you could probably catch them, sooner or later. But that’s not the world of the play that Shakespeare’s created: in this play, there’s only seeming.

So, Othello will kill. Who he kills will be based on belief and probability. He can’t decide. But Iago helps him. He comes up with the test of the handkerchief. Now, the test of the handkerchief isn’t certain, but in the world of the play, nothing is certain; there’s only probability. Othello has given Desdemona a special handkerchief. Iago suggests that, if the handkerchief makes its way into Cassio’s hands, then Othello can take this as proof. Conversely, if Iago cannot demonstrate this, Othello can take this as proof Iago is lying. Lives hand in balance.

In their rush to dinner, Othello and Desdemona accidentally drop the handkerchief. Emilia, by chance, finds it, and, knowing that Iago is always asking about it, gives it to Iago. Iago plants the handkerchief in Cassio’s bedroom where Cassio finds it and asks his ladyfriend Bianca to copy the design: the napkin is of an unusual provenance, “spotted with strawberries.” Bianca, however, thinking the handkerchief a gift from some new woman, gets jealous and squabbles with Cassio. Iago, meanwhile, has set things up so that Othello sees Cassio with the handkerchief. Once he sees the handkerchief, he’s convinced: Cassio and Desdemona are getting it on.

Is Othello, jumping to this conclusion, being reasonable? The first great Othello critic, Thomas Rymer, found Othello’s actions laughable. He came up with a jingling couplet to express his distaste, saying: “Before the Jealousie be Tragical, the proof may be Mathematical.” Most people, I believe, would agree with Rymer and say: “Othello, what are you doing?!?”

Enter probability theory. In probability theory, there’s a tool called Bayes’ theorem. It’s used to calculate conditional probabilities. With it, you can revise probability estimates as new information comes to light. This is exactly what happens in Othello: new evidence—the handkerchief—comes to light that makes Othello revise his initial probability estimate. In Iago’s words, the napkin “speaks against her with the other proofs,” or the napkin “may help to thicken other proofs / That do demonstrate thinly.” How much does it thicken the other proofs? Let’s find out. We can throw some numbers figures into Bayes’ theorem, and it will tell us, in percent, how certain Othello is after he sees Cassio with the napkin.

We start off with what is called the prior probability. That is the initial probability before he receive new information. Now, before the test of the handkerchief, Othello says:

Othello. By the world,
I think my wife be honest, and think she is not,
I think that thou [meaning Iago] art just, and think thou are not.

It seems that he views the odds that he has been cuckolded as 50:50. His mind is evenly divided. So, we enter this into the formula.

Next, we need to come up with a probability value that represents the chance that Cassio has the handkerchief given that Othello has been cuckolded. The dialogue between Othello and Iago suggests that we should assign a high percentage to this figure, which, while not 100%, must approach 100%. Call it 90%. We enter this into the formula.

The final probability value we require is the chance that Cassio should have his handkerchief given that Othello has not been cuckolded. Although Iago suggests that lovers give away their tokens all the time, Othello’s reaction suggests he strongly disagrees. So, we can call the likelihood that Cassio has the napkin and nothing untoward has happened something low, in the order of magnitude of say 1%.

We plug all these values into Bayes’ theorem, and it gives us an answer: if Othello’s mind had been evenly divided on Desdemona’s guilt, once he sees the handkerchief in Cassio’s hand, he can be 98.9% certain that he has been cuckolded. So, it would appear, contrary to Rymer, that the “Jealousie was Tragical because the proof is Mathematical.” A certainty test of 98.9% is certainly high. Modern statisticians use a 5% certainty test to establish moral certainty, or, the threshold at which one has the right to act. Othello is well within this 5% range.

We can also play with the numbers to arrive at different results. Some might say, for example, that a 50% initial probability that he is a cuckold is way too low. Look, if your best friend—who is known for honesty—and your wife’s father himself is telling you to watch out, then the initial probability you are a cuckold is likelier closer to 80%. If this is the case, then, after the napkin test, the chances you are a cuckold go up from 98.9 to 99.7%. That’s equivalent to the three-sigma test that physicists, up to recently, use to confirm that their experiments are the real deal, and not an artifact of chance. 99.7% is quite confidence inspiring, and shows that Othello, after seeing the napkin, could be quite sure.

Of course, everyone says Othello was too rash. He should not have killed Desdemona. I get this. But then, should he have killed Iago? Remember, the play is set up so that he has to kill someone, whether Desdemona or Iago. This is where probability gets interesting. The question the play asks is: how high a degree of confidence must we have to act? Those who contend Othello achieved moral certainty also have to contend with the fact that he was wrong. Those who contend that Othello failed to achieve moral certainty have to wonder how today’s insurance, medical, and consumer safety industries—not to mention courts—often hang matter of life and death on less stringent significance tests.

The intersection between probability theory and theatre is one of the richest crossroads in research today. Not only can we talk about whether Othello should or shouldn’t have acted, we can compare Othello to, say Hamlet. Hamlet is told by the ghost that his uncle killed his dad. As Hamlet himself realizes, the ghost is much less trustworthy than a best friend. Next, just like in Othello, Hamlet stages the mousetrap, the play within the play, to determine, on a probabilistic basis, whether his uncle is guilty. Like the test of the napkin, Hamlet’s mousetrap isn’t perfect. But for some reason, we allow Hamlet to act. Why is that? These are all fascinating questions that arise when we examine theatre from the perspective of probability theory.

I’ve always believed that theory should service practice. How can probability theory add to the performance of drama? I saw an Othello this year, a fast-paced one, big-budget production. But watching it, I felt some lines were missing. It turns out, after checking the text, parts of the text were missing: the beginning of act one, scene three where the sailor gives conflicting accounts of the size and heading of the attacking Turkish fleet. I learned later that this section is quite often omitted from performances. What a shame: the scene illustrates how, so often in the most critical affairs, though we want certainty, we must act based on probability. This moment sets the scene for the entire play: Othello too wants certainty, but must act on probability. By bringing science to the theatre, I offer a powerful reason for including this scene in future productions: this scene unlocks the play.

If you would like learn more about chance in theatre, pick up a copy of my book: The Risk Theatre Model of Tragedy: Gambling, Drama, and the Unexpected, published by Friesen in 2019. This talk is based on a new book chapter that came out a few months ago called: “Faces of Chance in Shakespeare’s Tragedies: Othello’s Handkerchief and Macbeth’s Moving Grove.” It’s in a book called: Critical Insights: Othello, edited by Robert C. Evans and published by Salem Press. Follow me on Twitter @TheoryOfTragedy.

Thank you.

BAYES’ THEOREM

P(C) initial probability Othello is a cuckold 50%
P(~C) initial probability Othello is not a cuckold 50%
P(H C) chance Cassio has the handkerchief if Othello is a cuckold 90%
P(H ∣ ~C) chance Cassio has the handkerchief if Othello is not a cuckold 1%

                                                               P(H ∣ C)
P(C H) = P(C) * _____________________________________________________________

                                          {P(H ∣ C) * P(C)} + {P(H ∣ ~C) * P(~C)}

Putting it all together yields this result:

                                                               0.90
0.989 = (0.50) * _____________________________________________________________

                                          {0.90 * 0.50} + {0.01 * 0.50}

– – –

Don’t forget me. I’m Edwin Wong and I do Melpomene’s work.
sine memoria nihil

A Risk Theatre Reading of Shakespeare’s OTHELLO

Playwrights explore chance in its many guises. To create a play, playwrights collide want, will, and intention with accident, chance, and fortune. In the no-man’s land between accident and intention, drama arises. Where accident intensifies the protagonist’s will, comedy results. Where accident eclipses the protagonist’s will, tragedy results. Chance is a playwright’s plaything because uncertainty, being unknown, is inherently dramatic.

In the tragedy Othello, Shakespeare explores chance by asking: “How high a degree of probability must one attain to have a sufficient basis for judgment?” Shakespeare sets the backdrop by crafting characters who are not what they seem. Their actions, reputations, and speech belie their being. When seeming and being are at odds, certainty goes out the window. Only the uncertain parts and probable fragments are left behind. In this world, there is no knowing, only thinking:

IAGO. My lord, you know I love you.

OTHELLO. I think thou dost. (3.3.119-20, emphasis added)

The play follows Othello as he pieces together broken probabilities, looking for the chance event so convincing that it rules out every doubt. He looks for a tattered proof known as moral certainty.

Je Est Un Autre or “I is Another”

Come on, come on, you are pictures out of doors,
Bells in your parlours, wild-cats in your kitchens,
Saints in your injuries, devils being offended,
Players in your housewifery, and housewives in . . .
Your beds! (2.1.109-13)

“Men should be what they seem,” says Iago, “Or those that be not, would they might seem none” (3.3.129-30). But that is not the case here. By cleaving apart seeming and being, Shakespeare creates a setting to explore chance. In Othello—to take poet Arthur Rimbaud’s memorable idea, Je est un autre (“I is another”)—each character is also “another.” Appearances deceive. When characters seem to be such, but are, in reality, another, understanding and certainty become best guesses. By cleaving seeming and being, Shakespeare takes the audience into a world of probability, a world where there is a chance of being correct and a chance of being incorrect. In this indeterminate world, characters weigh probabilities, form plans “probal to thinking” (2.3.333), and search for moral certainty, the probability that is so high that, even though uncertain, is called by the name of certainty. The tragedy is that even moral certainty is less than certain. Like bells in the parlours or men who might seem none, moral certainty only seems to be the real thing.

Iago seems honest. His epithet is “Honest Iago.” “Honest Iago,” says Othello, “My Desdemona I must leave to thee” (1.3.295-6). Roderigo entrusts him with his wealth and fastens each hope to him (1.3.363-80). Desdemona confides in him (3.4.133-41). “I never knew,” says Cassio, “A Florentine more kind and honest” (3.1.40-1). Iago’s seeming, however, belies his being. “I am not what I am,” he says, “but seeming so” (1.1.59 and 64).

Desdemona seems dishonest. “I do beguile,” she says, “The thing I am by seeming otherwise” (2.1.122-3). “Look to her, Moor, if thou has eyes to see,” warns her father Brabantio, “She has deceived her father, and may thee” (1.3.293-4). “Swear thou art honest,” demands Othello, “Heaven truly knows that thou art false as hell” (4.2.39-40). Her seeming, however, belies her being. She is a true heart.

Emilia seems bawdy. “She’s a simple bawd,” says Othello (4.2.20). In between Cassio’s kiss and his suspicions of her infidelity, Iago remarks her services are for the common use:

EMILIA. I have a thing for you.

IAGO. You have a thing for me? it is a common thing—

EMILIA. Ha? (3.3.305-7)

Though seen as a bawd who would sell great vice for a small price, she ends up buying virtue at the cost of her own life, at the last standing between Iago’s maleficence, Othello’s rage, and Desdemona’s helplessness, exposing the wickedness of both her husband and Othello. Not even Othello’s sword can silence her virtue:

EMILIA. Thou hast done a deed [He threatens her with his sword.]
—I care not for thy sword, I’ll make thee known
Though I lost twenty lives. Help, help, ho, help! (5.2.160-2)

Her surface appearances belie her core values. By judging her by her surface appearances, Iago, who knew her best, seals his doom.

Othello seems a man for all seasons. The assembled Venetian senate regales him as “all-in-all sufficient,” “a nature whom passion could not shake,” and one whose virtue lay beyond “the shot of accident” (4.1.264-8). He is of such steadfast repute that, when Emilia inquires whether he is jealous, Desdemona replies: “Who, he? I think the sun where he was born / Drew all such humours from him” (3.4.30-1). His seeming, however, belies his being. In reality, he proves insufficient, full of passion, and most susceptible to accident and chance.

So too, in the play’s macrocosm, the invading Turkish fleet seems sometimes smaller, sometimes larger. And, whether larger or smaller, sometimes it seems to bend for Rhodes, and sometimes for Cyprus. Its size and trajectory belie its intentions (1.3.1-45). Though the senate would rather act on certain, rather than probable intelligence, because the enemy projects a false gaze more full of seeming than being, the senate must act on probabilities. So too, Othello, Roderigo, Desdemona, and the other characters looking on at the grand pageant must hazard the probability of being caught on the wrong side of seeming and being.

In this play populated by topsy-turvy Je est un autre types, Iago presses the confusion forwards. Iago is an obsequious go-getter. His primary weapon is dissimulation. To enrichen himself, he plays panderer to Roderigo, though he panders nothing. To rise up the chain of command, he devises a way to cashier Cassio, Othello’s lieutenant. He will persuade Othello that Cassio cuckolds him. To this end, he employs a series of strategies. When convenient, he spreads rumours that Cassio is having an affair with Desdemona, Othello’s younger wife. He starts with Roderigo:

IAGO. Lechery, by this hand: an index and obscure prologue to the history of lust and foul thoughts. They met so near with their lips that their breaths embraced together. Villainous thoughts, Roderigo: when these mutualities so marshal the way, hard at hand comes the master and main exercise, th’incorporate conclusion. (2.1.255-61)

and then moves to Othello:

IAGO. I lay with Cassio lately
And being troubled with a raging tooth
I could not sleep. There are a kind of men
So loose of soul that in their sleeps will mutter
Their affairs—one of this kind is Cassio.
In sleep I heard him say ‘Sweet Desdemona,
Let us be wary, let us hide our loves,’
And then, sir, would he gripe and wring my hand,
Cry ‘O sweet creature!’ and then kiss me hard
As if he plucked up kisses by the roots
That grew upon my lips, lay his leg o’er my thigh,
And sigh, and kiss, and then cry ‘Cursed fate
That gave thee to the Moor!’ (3.3.416-28)

If there is a kernel of truth Iago can explode into reckless speculation, he will do so:

IAGO. She did deceive her father, marrying you,
And when she seemed to shake, and fear your looks,
She loved them most.

OTHELLO.                     And so she did.

IAGO.                                                   Why, go to, then:
She that so young could give out such a seeming
To seel her father’s eyes up, close as oak—
He thought ‘twas witchcraft. But I am much to blame,
I humbly do beseech you of your pardon
For too much loving you.

OTHELLO. I am bound to thee for ever. (3.3.209-17)

When all else fails, Iago practices psychological warfare. Through insinuation, he gets Othello to convince himself. Conclusions drawn when one convinces oneself root more firmly than persuaded proofs:

IAGO. Did Michael Cassio, when you wooed my lady,
Know of your love?

OTHELLO.                    He did, from first to last.
Why dost thou ask?

IAGO. But for a satisfaction of my thought,
No further harm.

OTHELLO.        Why of thy thought, Iago?

IAGO. I did not think he had been acquainted with her.

OTHELLO. O, yes, and went between us very oft.

IAGO. Indeed?

OTHELLO. Indeed? Ay, indeed. Discern’st thou aught in that?
Is he not honest?

IAGO. Honest, my lord?

OTHELLO. Honest? Ay, honest.

IAGO. My lord, for aught I know.
What dost thou think?

IAGO. Think, my lord?

OTHELLO. Think, my lord! By heaven thou echo’st me
As if there were some monster in thy thought
Too hideous to be shown. (3.3.94-111)

Despite the rumours, speculations, and insinuations, Othello sees, or believes he sees, Desdemona’s true heart:

OTHELLO. What sense had I of her stolen hours of lust?
I saw’t not, thought it not, it harmed not me,
I slept the next night well, fed well, was free and merry;
I found not Cassio’s kisses on her lips. (3.3.341-4)

Beginning to suspect foul play, he retains enough good sense to demand proof from Iago, telling Iago to provide proof, or his life:

OTHELLO. Villain, be sure thou prove my love a whore,
Be sure of it, give me the ocular proof, [Catching hold of him]
Or by the worth of man’s eternal soul
Thou hadst been better have been born a dog
Than answer my waked wrath! (3.3.362-6)

Nothing improper has transpired, and, as a result, Iago has no proof, cannot come up with a proof. He reaches an aporia. But, in a twist of fate, chance provides Iago proof.

A Handkerchief, Spotted with Strawberries

Desdemona has on her person a handkerchief, spotted with strawberries. It is of an unusual provenance. Artifact like, it was sewn by an ancient sibyl during moments of inspiration. Hallowed worms spun its threads and maiden’s hearts stained its cloth. It was given to Othello’s mother to charm his father, and damnation to her if she lost it. She, however, saw it in her safekeeping until she died, at which time she gave it to her son. He, in turn, gave the handkerchief, spotted with strawberries to Desdemona (3.4.57-77).

Halfway through the play, Desdemona takes out the kerchief to wrap Othello’s head. He has a headache. It falls off. In their haste to meet dinner guests, they forget the napkin. Emilia, having been asked by her husband many times to steal it, chances upon it. She gives it to Iago, unaware of why he should want it (3.3.288-332). Through the accident of the dropped napkin, Iago has an opportunity to bolster his flagging argument.

Once he has the handkerchief, Iago can produce the wicked proofs required by Othello. He begins by planting the handkerchief in Cassio’s bedroom. Next, he tells Othello he has seen Cassio wiping his beard with it. This, in turn, prompts Othello to ask Desdemona for the napkin. She cannot produce it, and, fatally misjudging the gravity of the situation, asks Othello to reinstate Cassio. This drives Othello into a huff, who finds it incredulous that Desdemona not only has the appetite for another man, but also has the appetite to demand from him his favour.

At this point, Othello is getting a bit run down. His epileptic attack as he visualizes the intertwined lovers is a physical analogue of his broken internal state. Even now, however, standing in his mellow-fading glory like a black Caesar, he demands proofs. As he recovers from the epileptic attack, Iago provides verbal and ocular proofs, one by cunning, and the other by another stroke of chance.

Iago arranges for Othello to overhear his conversation with Cassio. While getting Othello to believe he is questioning Cassio about Desdemona, he actually asks Cassio about Bianca, a strumpet overfond of Cassio. In hearing Cassio tell Iago of his extracurricular activities with Bianca, Othello believes Cassio refers to Desdemona. Then, in a second twist, as Othello eavesdrops, Bianca comes out of nowhere to rebuke Cassio. Cassio had found the handkerchief in his chamber, and, appreciating the design, had asked Bianca to make a copy. Bianca agreed, but, on second thought, believing the handkerchief to be a gift from a rival, now finds it beneath her dignity to do any such thing. That Bianca appears at this moment surprises Iago, who had planned many things, but not this godsend. When she rebukes Cassio, Othello draws the conclusion that, first of all, Desdemona was in Cassio’s chamber, and, second of all, Desdemona has given Cassio the handkerchief as a token of her affection. Though Bianca does not mention Desdemona, it is a short leap for Othello, a general accustomed to making snap judgements on the field of battle, to conclude that Cassio’s hobby-horse is none other than Desdemona:

BIANCA. Let the devil and his dam haunt you! What did you mean by that same handkerchief you gave me even now? I was a fine fool to take it—I must take out the work! A likely piece of work, that you should find it in your chamber and know not who left it there! This is some minx’s token, and I must take out the work? There, give it your hobby-horse; wheresoever you had it, I’ll take out no work on’t!

CASSIO. How now, my sweet Bianca, how now, how now?

OTHELLO. By heaven, that should be my handkerchief! (4.1.147-56)

Who else but Desdemona could have left the napkin there? The scene with Bianca and Cassio convinces Othello. He resolves to kill them both. He has proof. Or so he thinks.

If Emilia had—as Iago requested—stolen the napkin, the tragedy would have taken on a more ominous tone: the sound of good and evil clashing. But that is not what happens. The sound of good and evil clashing is dull. Emilia, rather, finds the napkin by chance. Chance is more interesting. That she finds it by chance leaves the audience with a sense of wonder and awe: wonder at how impartial chance should have become Iago’s partisan and awe over the extraordinary consequences that follow.

At one moment chance saves, sending a storm to drown the Turkish fleet. But in the next moment, chance casts down, putting the napkin into the wrong hands. Chance’s fantastic nature makes it a wonderful dramatic pivot. Othello himself, a crack storyteller, engages chance to woo Desdemona by telling her the stories of “battles, sieges, fortunes,” “most disastrous chances,” and of “moving accidents by flood and field” (1.3.131-6). These accidents he lives to tell, but the tale of the dropped napkin another will tell.

Chance fascinates because every eventuality lays within its grasp, given enough time. But even given its myriad combinations and permutations, some eventualities are more probable, some, less so, and others implausible unto impossible. This feature of chance—that some probabilities are more likely and others less so—allows Othello to draw fatal proofs.

Five Sigma Events, Significance Tests, Moral Certainty, and Iago’s Gambit

In the character Othello, Shakespeare has created a sceptic to rival Sextus Empiricus. For Othello, it was not enough that Iago was the most honest of Venetians. Nor was it enough that Iago had stood shoulder to shoulder with him, comrades-in-arms on the front lines. It was not even enough that Desdemona’s own father warned him to be wary. Othello, after all, had heard the wise Duke rebuking Brabantio for acting on circumstantial evidence:

DUKE. To vouch this is no proof,
Without more certain and more overt test
Than these thin habits and poor likelihoods
Of modern seeming do prefer against him. (1.3.107-10)

Othello will not be a brash Brabantio. He will demand a certain and more overt test:

OTHELLO. Make me to see’t, or at the least so prove it
That the probation bear no hinge nor loop
To hang a doubt on, or woe upon thy life! (3.3.367-9)

Now Iago is in a jam. Othello demands proof, or his life. Iago cannot make Othello see it, as there is nothing to see. Othello himself, likewise, is in a jam. He must judge a covert crime, and, having judged, kill. He can count on neither Desdemona nor Cassio to fess up: unchaste eyes must never name the things unchaste hearts cannot do without. When Iago proposes the test of the napkin, however, Othello has a path forward:

IAGO. But if I give my wife a handkerchief—

OTHELLO. What then?

IAGO. Why, then ’tis hers, my lord, and being hers
She may, I think, bestow’t on any man.

OTHELLO. She is protectress of her honour too:
May she give that ? (4.1.10-5)

In Iago’s gambit, the napkin will stand in for her honour. Since Desdemona is honourable, the likelihood that she gives away the token of her honour is low. Because it would be an outlier event to see the napkin in the hands of another man, if it is seen, the likelihood is high that the observation is significant. The test of the napkin—coupled with both Iago and Brabantio’s warnings—may constitute, therefore, a sort of proof that, while not absolute, demonstrates infidelity beyond a reasonable doubt. This probabilistic proof that “the probation bear no hinge nor loop / To hang a doubt on” is the best proof available in the indeterminate world of the play. The idea that random chance may—or may not—engender absolute truth is the powerful idea Shakespeare plays with.

Though it was not until 1668 that philosopher and mathematician Gottfried Wilhelm Leibniz formally associated probability with certainty by arguing that, given a sufficient probability, a degree of moral certainty could be achieved, it is clear that Shakespeare was already thinking along these lines in the opening years of the seventeenth century. Probability is in the air. Mathematician Jacob Bernoulli in the late seventeenth century would quantify these thresholds: something possessing 1/1000 a fraction of certainty (0.1%) would be morally impossible, whereas something possessing 999/1000 a portion of certainty (99.9%) would be morally certainty. The standard is flexible. Modern statisticians use anywhere from one to five percent significance tests to establish certainty. Different fields likewise require different levels of certainty. When physicists used a sensitivity of three sigma to validate discoveries (corresponding to a 99.7% chance that the result is real and not by the action of chance), they found that, because their work involved a multitude of data points, they would arrive at many discoveries which would be later proved spurious. Accordingly, when searching for the Higgs boson, they adapted a five sigma threshold. This threshold translates to a 99.99994% confidence level: the chance that the discovery is an anomaly is roughly 1 in 3.5 million. Even with a five sigma sensitivity, however, the chance that the observation is a fluke and not the real thing remains. Moral certainty is a subjective and pragmatic standard. Too low a threshold results in false discoveries and too high a threshold results in no discoveries. The question is: does Othello achieve moral certainty and, if so, to what degree?

The first great critic of Othello, Thomas Rymer, found the proof of the handkerchief so implausible as to be risible. To Rymer, Othello was acting without any kind of certainty, let alone moral certainty. In 1693, he voiced his misgivings in a jingling couplet: “Before their Jealousie be Tragical, the proof may be Mathematical.” Everyone knows that Michael Cassio is the great arithmetician of the play, not Othello. Perhaps Othello had miscalculated the odds?

What Iago wants is for Othello to assemble all the information—the warning from Brabantio, the accusations from Iago, Cassio’s frequent associations with Desdemona, Desdemona’s importuning, and so on—so that the napkin “speaks against her with the other proofs” (3.3.444, emphasis added). Probability theory in the time of Shakespeare and Rymer was in its infancy. That is not to say, however, that Othello could not intuit conditional odds: that is, in effect, what he does. So too, without formal probability theory, Iago well knows that many less plausible proofs may add up into one great proof, saying: “This may help to thicken other proofs / That do demonstrate thinly” (3.3.432-3).

The formal calculation of conditional probabilities lay in the future. That future arrived in 1763 when Bayes’ theorem was posthumously published. Thomas Bayes was a mathematician and Presbyterian minister. His contribution to probability theory was a formula to calculate conditional probabilities, a way to revise probability estimates as new information comes to light. With Bayes’ theorem, it is possible to test Iago’s hypothesis that many lesser proofs constitute one great proof. With Bayes’ theorem, it is possible to test Rymer’s couplet, to see whether Othello’s proof be mathematical, and, if so, to what extent.

To determine the posterior probability—that is to say, the revised probability that Othello has been cuckolded after the test of the napkin—we require four probability values. The first two values are P(C), the initial or prior probability that he has been cuckolded, and P(~C), the initial or prior probability that he has not been cuckolded. Before Iago’s gambit, Othello’s opinion on whether he has been cuckolded appears evenly divided:

OTHELLO. By the world,
I think my wife be honest, and think she is not,
I think that thou [Iago] art just, and think thou art not. (3.386-8)

Given what he says, we can assign a value of 0.50 (with 0 representing an impossibility and 1 representing a certainty) to P(C)and a similar value, 0.50, to P(~C). The odds he has been cuckolded are 50:50.

The third probability value is P(H C), and it represents the chance that Cassio should have his handkerchief given that Othello has been cuckolded. The dialogue suggests Othello believes that, next to catching the lovers in the act, the test of the handkerchief is a great proof. The value of P(H C), while not 1 (which is an absolute certainty), must approach 1: perhaps 0.90, representing a 90% chance, is reasonable.

The final probability value is P(H ∣ ~C), and it represents the chance that Cassio should have his handkerchief given that Othello has not been cuckolded. Although Iago suggests true hearts give away telltale tokens all the time, Othello’s reaction suggests he strongly disagrees. As a result, the likelihood of P(H ∣ ~C) is quite low, having an order of magnitude of 0.01, or a 1% chance.

Here is what Bayes’ theorem looks like when solving for P(C H) or the posterior probability that Othello is a cuckold, should he see his napkin with Cassio. The formula takes into account his initial, or prior belief, and revises it to take into account the test of the napkin:

                                                               P(H ∣ C)
P(C H) = P(C) * _____________________________________________________________

                                          {P(H ∣ C) * P(C)} + {P(H ∣ ~C) * P(~C)}

Putting it all together yields this result:

                                                               0.90
0.989 = (0.50) * _____________________________________________________________

                                          {0.90 * 0.50} + {0.01 * 0.50}

Othello can be now 98.9% certain that he has been cuckolded. While this falls short of the five sigma standard (99.99994%) used in high energy physics, its significance falls within the one to five percent tests used by modern statisticians. The napkin brings him to a point of moral certainty, the degree of probability one must attain to act. The jealousy was tragical because the proof was mathematical.

Is Othello correct to believe that he has caught the lovers in his mousetrap? That, I think, is the question Shakespeare invites us to ask. The answer—like many answers in the great plays—is fluid. Some may argue that P(H ∣ ~C)—the odds that Desdemona gives away the napkin and is true—is too low at 1%. People with the truest hearts, may, some of the time, give away treasured tokens as though trifles. Changing P(H ∣ ~C) from 0.01 to 0.10 (from 1% to 10%) would decrease Othello’s confidence level from 98.9% to 90%. There is now a 10% probability that what he sees is a pageant of chance rather than a proof of infidelity. Others, however, would argue that starting from a 50% prior probability of being a cuckold is egregiously low. Given the constant goings-on between Cassio and Desdemona as well as warnings from both Desdemona’s father himself and the most honest person in the room, Othello’s initial belief, or the prior probability P(C), that he has been cuckolded should be much higher, perhaps closer to 80%. Now, even with P(H ∣ ~C) at 0.10, Othello can still be 97.3% certain he is a cuckold. If P(H ∣ ~C) stays at the original 0.01 and the prior probability Othello is cuckold rises from 50% to 80%, the posterior probability of being a cuckold after a positive napkin test rises to a confidence-inspiring 99.7%, equivalent to the three sigma threshold used by physicists until rather recently.

By cleaving seeming and being in twain, Shakespeare invites the audience to explore probability and its ramifications. Would different ages, ethnicities, and sexes input different values into Bayes’ theorem? How high a degree of confidence must we have to act? Those who contend Othello achieved moral certainty must also contend that, in the final examination, he was wrong. Those who contend Othello failed to achieve moral certainty would do well to wonder how yesterday and today’s insurance, medical, and consumer safety industries—not to mention courts—often hang matters of life and death on less stringent significance tests. Othello makes us wonder: should graver actions demand higher levels of certainty? Not only that, it also makes us wonder if our interpretations of Othello reveal something about ourselves. Do we allow Othello to judge after receiving a tip from an honest source and catching the culprit in the mousetrap? And would these same people who say no to Othello allow Hamlet to judge after receiving a tip from a possibly dishonest (and diabolical) source and catching the culprit in another sort of a mousetrap?

The intersection between probability theory and theatre is the one of the richest crossroads in interpretation today. Through a twist of chance, Shakespeare takes Othello from good to great: since chance is indeterminate, interpreters of the play will forever debate whether Othello achieves moral certainty, and to what degree. Othello makes us think on the role of chance in theatre and in life.

Whether Heads of Tails, Chance always Prevails

In this essay, I have argued that chance and probability form a basis of interpretation. In Othello, Shakespeare represents chance in the form of a handkerchief, spotted with strawberries. The action pivots around the errant handkerchief because its journey gives Othello the proof that Iago could not provide. Chance supplies the proof because it is made up of probabilities, some common, some uncommon, and others so uncommon as to stand outside the prospect of belief. For Othello, it stood outside the prospect of belief that the handkerchief could have went from Desdemona, to Cassio, and then to Bianca, unless Desdemona were untrue. To Othello, Iago’s extraordinary claim required extraordinary evidence, and, through chance, he witnessed an extraordinary proof. Whether or not this proof achieves a point of moral certainty, however, will be a point of debate forever, as chance is, in the last examination, subject to uncertainty. Othello, read through the lens of chance, makes for great reading for pollsters, jurors, insurers, high energy physicists, ethicists, medical researchers, and anyone else corroborating theories based on many observations: there is always a risk that what appears certain is only a statistical anomaly that has the seeming of truth.

From the page to the stage, tragedy is a theatre of risk. And what better for today’s days of risk than to look at tragedy as a theatre of risk? When life gives you lemons, make all of theatre a theatre of risk and you will see not only the play, but all of life, through new eyes. “O vain boast, / Who can control his fate? ’Tis not so now,” says the one who has seen the power of chance in all its guises, sometimes raising up, and other times casting down (Othello 5.2.262-3).

In Othello, Shakespeare has drawn a moving portrait of the empire of chance in its limitless power. When want, will, and intention collide with accident, chance, and fortune, no matter how strong want, will, and intention are and how unlikely accident, chance, and fortune were, chance finds a way. Some thought that the gods were fate. Others thought that politics or character was fate. But, really, chance is the rebel fate. Certain proof of this lies in the great mystery of tragedy, the mystery of how, whether heads or tails, chance always prevails.

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If you have enjoyed this reading of Othello, here is a link to a reading of Macbeth from the perspective of chance. Those interested in the role of chance in ancient drama may want to click here. These “risk theatre” readings are derived from arguments in my book presenting a new theory of tragedy: The Risk Theatre Model of Tragedy: Gambling, Drama, and the Unexpected. Ask your local library to carry a copy! Risk theatre is more than theory. It is also the basis of the largest playwriting competition in the world for the writing of tragedy, now in its third year. The competition brings together playwrights, writers, dramaturgs, directors, actors, and audiences to explore the many guises of chance and uncertainty. Click here for more info on the competition. Thank you for reading.

Don’t forget me, I’m Edwin Wong and I do Melpomene’s work
sine memoria nihil