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}

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

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