Dec 082012

Before Iago planted in him the seed of doubt, Othello was absolutely certain about Desdemona’s loyalty:

My life upon her faith. (Act 1, Scene 3)

 In other words: BR=0. But as soon as the seed settled in, Faith gave way to sober reflection (Act 3, Scene 3):

Othello:  I do not think but Desdemona’s honest.
Iago:      Long live she so, and long live you to think so!
Othello:  And yet how nature, erring from itself –
Iago:      Ay, there’s the point;

 Infidelity may be unlikely, but is not impossible: BR>0.

Iago starts in a low key. He describes himself as a rather poor forecaster, prone to calling too many False Positives:

Though I perchance am vicious in my guess – 
As I confess it is my nature’s plague
To spy into abuses, and oft my jealousy
Shapes faults that are not –  

 He knows Othello is starting from a very low BR, and that he will require very accurate evidence to be moved away from it. Othello is very clear about this:

 No, Iago,
I’ll see before I doubt; when I doubt, prove;
And on the proof, there is no more but this:
Away at once with love or jealousy.

 Othello is willing to change his mind, but only if he sees full-proof evidence: TPR=1 and FPR=0. Iago knows this will be impossible. But he also knows that, if he manages to increase Othello’s priors, imperfect evidence may suffice. So he gets to work:

 I speak not yet of proof.
Look to your wife. Observe her well with Cassio.
Wear your eyes thus: not jealous, nor secure.
I would not have your free and noble nature
Out of self-bounty be abused. Look to ’t.
I know our country disposition well.
In Venice they do let God see the pranks
They dare not show their husbands; their best conscience
Is not to leave ’t undone, but keep ’t unknown.

 Forget about this BR=0 nonsense – says Iago. Open your mind and face reality: the probability that a Venetian woman is unfaithful is higher than you like to think.

Othello trusts Iago, and thinks he is an expert:

This fellow’s of exceeding honesty,
And knows all quantities, with a learnèd spirit
Of human dealings.

 But he is desperately trying to hang on to his Faith:

If she be false, O then heaven mocks itself!
I’ll not believe ’t.

 Then Iago gets hold of the handkerchief, and orchestrates his plot by planting it in Cassio’s lodging. He knows the evidence is far from perfect, but he is counting on Othello’s expanded BR:

I will in Cassio’s lodging lose this napkin,
And let him find it. Trifles light as air
Are to the jealous confirmations strong
As proofs of holy writ. This may do something.
The Moor already changes with my poison.
Dangerous conceits are in their natures poisons,
Which at the first are scarce found to distaste,
But with a little act upon the blood,
Burn like the mines of sulphur.

 Othello is in pain. He feels his BR expanding. What he would love to see is a Perfect Alibi: evidence that is logically inconsistent with the hypothesis of infidelity: TPR=0. This would imply PP=0, irrespective of BR. He could ask Desdemona, or Cassio, or Iago’s wife Emilia, Desdemona’s confidant. But he doesn’t trust them. Instead, he asks Iago for a Smoking Gun: evidence that is logically inconsistent with the hypothesis of fidelity: FPR=0. He hopes Iago is wrong, of course. But in case he is right, he will at least end the torment of an expanding BR. If that’s the only way, so be it, even if it implies PP=1.

Othello threatens Iago to provide no less than a Smoking Gun:

Othello:  Villain, be sure thou prove my love a whore.
Be sure of it. Give me the ocular proof,
Or, by the worth of mine eternal soul,
Thou hadst been better have been born a dog
Than answer my waked wrath.
Iago:  Is’t come to this?
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.

 But it’s too late. Othello’s BR has already expanded to the 50% indifference level:

By the world,
I think my wife be honest, and think she is not.
I think that thou art just, and think thou art not.
I’ll have some proof.

 This is the Prior Indifference Fallacy precisely. Othello is done: PP=TPR/(TPR+FPR). He doesn’t need FPR=0. Some proof will do. He just wants to be satisfied:

 Iago:  And may. But how, how satisfied, my lord?
Would you, the supervisor, grossly gape on,
Behold her topped?
Othello:  Death and damnation! O!
Iago:  It were a tedious difficulty, I think,
To bring them to that prospect. Damn them then
If ever mortal eyes do see them bolster
More than their own! What then? How then?
What shall I say? Where’s satisfaction?
It is impossible you should see this,
Were they as prime as goats, as hot as monkeys,
As salt as wolves in pride, and fools as gross
As ignorance made drunk. But yet, I say,
If imputation, and strong circumstances
Which lead directly to the door of truth,
Will give you satisfaction, you may ha’t.
Othello:  Give me a living reason she’s disloyal.

 By now Iago is teasing Othello. Sure – he says – you should try to surprise your wife in bed with Cassio – that would be a perfect proof! Unfortunately, it is rather tricky. So you’d better be happy with circumstantial evidence. Othello is beaten. He no longer requires a perfect proof – barely a ‘living reason’ will be enough. Iago obliges, by telling him that he heard Cassio talking in his sleep about his affair with Desdemona, and that Cassio has the handkerchief. So what? – Othello would have said, had he kept a small BR. Instead:

O that the slave had forty thousand lives!
One is too poor, too weak for my revenge.
Now do I see ’tis true. Look here, Iago,
All my fond love thus do I blow to heaven – ‘tis gone.
Arise, black vengeance, from the hollow hell.
Yield up, O love, thy crown and hearted throne
To tyrannous hate! Swell, bosom, with thy freight,
For ’tis of aspics’ tongues.

 To Othello’s prior indifference, Iago’s evidence is virtually as conclusive as a Smoking Gun. He is blinded by evidence.

By Act 4, Iago has turned the poor Othello into the hapless victim of his perfidious irony:

Iago:  Will you think so?
Othello:  Think so, Iago?
Iago:  What, to kiss in private?
Othello:  An unauthorized kiss.
Iago:  Or to be naked with her friend in bed
An hour or more, not meaning any harm?
Othello: Naked in bed, Iago, and not mean harm?
It is hypocrisy against the devil.
They that mean virtuously and yet do so,
The devil their virtue tempts, and they tempt heaven.
Iago:  So they do nothing, ’tis a venial slip.
But if I give my wife a handkerchief—

 Finally, the coup de grace. Othello had started with BR=0; then he admitted BR>0; then Iago manoeuvred him into prior indifference: BR=50%. What next?

Othello: Dost thou mock me?
Iago:  I mock you not, by heaven.
Would you would bear your fortune like a man.
Othello:  A hornèd man’s a monster and a beast.
Iago:  There’s many a beast then in a populous city,
And many a civil monster.
Othello:  Did he confess it?
Iago:   Good sir, be a man.
Think every bearded fellow that’s but yoked
May draw with you. There’s millions now alive
That nightly lie in those unproper beds
Which they dare swear peculiar. Your case is better.
Oh, ’tis the spite of hell, the fiend’s arch-mock,
To lip a wanton in a secure couch,
And to suppose her chaste! No, let me know,
And knowing what I am, I know what she shall be.

 Face reality – says Iago. Being cheated by their wives is the plight of most married men: BR≈1. You might as well start with that assumption. In fact, worse than the small risk of a False Positive – a wrong belief of being betrayed by a faithful wife – is the much larger risk of a False Negative: to sleep unknowingly with an unfaithful one. So cheer up: now that you know you’ve been cheated, you are no longer at risk. You are the lucky one.

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