The true star of Macbeth is the low-probability, high-consequence event. And the true story of Macbeth is the hero’s reaction to it. In this tragedy, a man is transformed by a series of low-probability, high-consequence events, in the beginning raised up by chance, and, in the end, cast down by the same power he hoped to harness. Macbeth is the story of how low-probability, high-consequence events encouraged a man to wager all-in, thinking that he was bound for glory, and of how the random element fooled him.

For the dreamers who believe that low-probability, high-consequence events could be tamed through progress, the play warns of evil’s allure and the follies of ambition and confidence. For others, whose powers of recognition are clearer, and who perceive the random element working at each existential juncture in life and in history, the hypotheses of other-worldly powers, ambition, and confidence were redundant. To them, Macbeth tells an all-too-human story of how, because of our innate predilection to scorn chance, having always satisfied our intellectual biases by seeking any other explanation than one which involved the random element, we thought ourselves lords of chance and became, instead, the fools of chance.

The definition of a low-probability, high-consequence event is one in which, before it happens, is considered improbable. Sometimes the possibility it can even happen cannot be imagined, such is its remoteness. Examples include the Gutenberg Press, the rise of the personal computer, or the Gunpowder Plot. We can know that a low-probability, high-consequence action has occurred by watching the reactions. Sometimes, it prompts the one who has seen it to alert others. “From the spring,” says the dying Captain, “whence comfort seemed to come / Discomfort swells: mark, King of Scotland, mark” (1.2.27-8). Other times it elicits disbelief. “Nothing is,” says Macbeth, “but what is not” (1.3.144). Sometimes, one takes one’s own life: this was the case of the “farmer that hanged / himself on th’expectation of plenty” (2.3.4-5). Having bet all-in on a bumper crop, when waylaid by the low-probability event, out of rent, out of food, and out of luck, he hangs himself. The danger these events present is that, though they were impossible to predict beforehand, after they happen, we retrospectively invent simplistic explanations of how they arose. In doing so, our sense of comfort is misguided, as we fail to give chance its due. This danger extends to the criticism of Macbeth.

In Macbeth, the action pivots around four low-probability, high-consequence events. The first is when, contrary to expectation, Macbeth becomes Thane of Cawdor. The second is when, against all hope, he becomes king. The third is when Birnam Wood, impossibly, comes to Dunsinane Hill. The last is when, beyond nature’s permutations, he meets a man not of woman born. That each of these events will happen is foreshadowed by the Witches—Shakespeare’s agents of improbability—to Macbeth, who, in turn, rejects each as being out of hand. By dramatizing the path from prediction to rejection to fulfillment, Shakespeare makes probability the play’s true theme: what happens when more things happen than what we thought would happen happens?

To most people, the Witches are not agents of improbability, but rather supernatural agents. Like the oracles of old in Greek tragedies, the Witches would prophecy to Macbeth his fate, fate being the antinomy of chance and probability. But, the funny thing is, to dramatize fate—to bring fate onto the stage—fate had to be cast into the play as a random event that takes place against all odds. That such an event could have taken place against overwhelming odds is then attributed back onto the powerful action of fate. The feeling of surprise that a miracle has occurred is the proof that fate exists. But really, there was no fate, only the fulfilment of a low-probability, high-consequence event that the audience appreciates to represent fate. Fate in tragedy is a literary artifact, is probability dressed up as fate. In this way, Macbeth, by exploring fate, became a venue to explore the impact of the highly improbable. Wherever there is fate, there is also chance: the way fate manifests itself in literature is by overcoming the random element. At last, fate and chance are synonymous, two sides of the same coin.

Macbeth begins with Scotland in alarm. The first crisis sees the rebel Macdonald leading Irish soldiers into Forres. King Duncan sends in Macbeth and Banquo. But, in the act of dispatching Macdonald, a second crisis strikes. Seeing Scotland convulsed by civil war, Sweno, Norway’s king, seizes the moment. He allies with another Scottish rebel, the Thane of Cawdor. With covert support from the thane and fresh Norwegian troops, they open a second front at Fife. Macbeth and Banquo remobilize to win the day. The opening action sets the scene for the first two of the four low-probability, high-consequence events.

After the battle, Macbeth and Banquo, on the road to Forres, encounter the Witches:

Macbeth. Speak, if you can: what are you?

1 Witch. All hail Macbeth, hail to thee, Thane of Glamis.

2 Witch. All hail Macbeth, hail to thee, Thane of Cawdor.

3 Witch. All hail Macbeth, that shalt be king hereafter. (1.3.47-50)

The first Witch accosts Macbeth by name and title. This draws his attention: when his father died, he had become Thane of Glamis. The second Witch teases him with a present tense pronouncement, calling him Thane of Cawdor. Macbeth finds this both disturbing and unlikely. The news that Duncan has executed the traitor and given his title to Macbeth is still in transit. Then, the third Witch goes in hook, line, and sinker, hailing Macbeth as tomorrow’s king. Macbeth finds this impossible:

Macbeth. Stay, you imperfect speakers, tell me more.
By Finel’s death, I know I am Thane of Glamis,
But how of Cawdor? The Thane of Cawdor lives
A prosperous gentleman: and to be king
Stands not within the prospect of belief,
No more than to be Cawdor. Say from whence
You owe this strange intelligence, or why
Upon this blasted heath you stop our way
With such prophetic greeting? Speak, I charge you. (1.3.70-8)

The Witches vanish. At that moment, Angus and Ross enter. Acting as though the mouthpiece of chance, Ross hails Macbeth the Thane of Cawdor:

Angus. We are sent
To give thee from our royal master thanks,
Only to herald thee into his sight
Not pay thee.

Ross. And for an earnest of a greater honour,
He bade me, from him, call thee Thane of Cawdor:
In which addition, hail most worthy thane,
For it is thine.

Banquo. What, can the devil speak true?

Macbeth. The Thane of Cawdor lives. Why do you dress me
In borrowed robes?

Angus. Who was the Thane lives yet,
But under heavy judgement bears that life
Which he deserves to lose.
Whether he was combined with those of Norway,
Or did line the rebel with hidden help
And vantage, or that with both he laboured
In his country’s wrack, I know not,
But treasons capital, confessed and proved,
Have overthrown him. (1.3.101-118)

Macbeth’s surprise—“Why do you dress me in borrowed robes?”—relays to the audience the improbability of what is happening. Banquo too, stunned, says: “What, can devil speak true?” a little too loud.

As the true star of the show, not only do low-probability events change our perceptions of how many things there are in heaven and earth, they also change the plot’s trajectory. Macbeth, previously fighting traitors, turns traitor. With the low-probability event, Shakespeare boldly pivots the trajectory of the play. The imperial theme begins.

Shakespeare’s Swans

Part of the good interpreter’s task is to sound out yesterday’s iambs on today’s instruments. For yesterday’s plays to jingle and jangle to modern ears, new approaches are required, approaches which resonate with today’s preoccupations. Today, there is a preoccupation with low-probability, high-consequence events: 9/11, the Great Recession, the fall of the Berlin Wall, Deepwater Horizon, and other events give us reason to reflect on how nothing is impossible, once it happens. In the last decade, a new term has arisen to describe these events: today, we call them “black swans.”

The term “black swan” comes from Roman antiquity, and its journey to the present day has been itself swan buffeted. In the beginning, it meant something entirely different. The Roman poet Juvenal coined the term in the Satires where he likened a wife, perfect in all her virtues, to “a prodigy as rare upon the earth as a black swan (6.165).” Since it was believed that the perfect wife does not exist, the black swan became a byword for the impossible. This was the term’s first meaning.

In 1697, European explorers sighted black swans off the coast of Australia. With one sighting, the improbable overcame the probable and a belief system—that all swans are white—fell. As a result, the term was orphaned. In 1843, however, John Stuart Mill reinvented it. In A System of Logic, Mill transformed the term from an expression of impossibility (which it could no longer denote) into a visual representation of the power of the unexpected. In Mill, the black swan is the empiricists’ bogeyman. It symbolizes the philosophers’ horror of how one observation can wreck any number of inferences based on any number of observations made over any immemorial period of time. In philosophical circles, the black swan came to symbolize the danger of formulating general principles from particular observations, otherwise known as the problem of induction. Another swan event, however,  was required for the term to enter the public consciousness.

In 2007, mathematician, options trader, and philosopher Nassim Nicholas Taleb released The Black Swan. He argued that Wall Street’s risk management models, far from containing risk, exacerbated risk and endangered the financial system. Being rooted in the idea of past as prologue, these models gave traders false assurances that they could wager all-in: every swan will be white and events progress forwards, inexorably, quiescently, in a predictable steady state. But, if time were a punctuated equilibrium and arrived in fits and starts like ketchup out a glass bottle, full of revolution, a world of hurt awaits. Taking the cue from Mill, Taleb called these unforeseen, unexpected, and catastrophic events black swans. Mainstream financial pundits, busy riding the boom, disregarded Taleb, whom they regarded as an eccentric voice crying out in the wilderness. But, without warning, the Great Recession broke out in 2008 to break each one of the world’s oldest and most decorated financial institutions. The timing of Taleb’s book—having come out the previous year— seemed prescient.

Though experts disavowed that such a catastrophe could be ascribed to as fleeting a notion as chance, Taleb’s ideas were backed by a badass image (a sinister swan) and hardcore math (attacking the venerable bell curve). When the media suggested that the Great Recession could be understood as a swan event, a low-probability, high-consequence event precipitated by, of all things, chance, a firestorm of controversy ensued. It was at this time that the term “black swan” to denote the impact of the highly improbable entered the popular consciousness.

Before there was Taleb, there was Shakespeare. Only Macbeth was not taken as a warning of the highly improbable, but rather, a warning of the dangers of confidence, ambition, and evil. Perhaps that was because people did not associate Shakespeare with probability theory, which, having been recently founded in the sixteenth century, was still in its infancy. Shakespeare, however, grasped with his playwright’s intuition the inordinate impact the highly improbable. Consider his use of the improbable elsewhere to generate fantastic outcomes: Desdemona, in Othello, dropping the handkerchief, spotted with strawberries or the letter-carrier, in Romeo and Juliet, being caught in the wrong house at the wrong time. Hamlet’s injunction to Horatio—“There are more things in heaven and earth, / Than are dreamt of in your philosophy”—also warns of the impact of the highly improbable (Hamlet 1.5.167-8). Shakespeare’s tragedies are full of curious improbabilities and now, when they are all the rage, is the time to talk about Shakespeare’s swans.

The Imperial Theme

Shakespeare’s understanding of the highly improbable and its dramatic applications can be illustrated through Macbeth’s interaction with Angus and Ross. Macbeth’s question: “Why do you dress me / In borrowed robes?” is spoken from the viewpoint of his initial reality. In this reality, Duncan is his cousin and king. He will lay his life on the line fighting foreign kings and native rebels to defend this reality. In this reality, all swans are white. But the moment Angus and Ross confirm the second Witch’s pronouncement, Macbeth sights the black swan. A new reality opens, one in which he is king. It is the improbable that draws him to the existential fulcrum. In this reality, having seen the swan, he knows the impossible is possible. The plot pivots into the imperial theme.

Finding himself, unexpectedly, Thane of Cawdor, Macbeth muses: “Glamis and Thane of Cawdor: / The greatest is behind” (1.3.118-9). The greatest that lies behind is to be king. Not only have the Witches prophesied thus, Ross, in his fruitfully ambiguous phrase that the new thaneship is “an earnest of greater honour,” intimates that Macbeth could be named heir apparent, a declaration consonant with the system of tanistry used in medieval Scotland where the crown, not yet bound by primogeniture, would revolve between collateral branches of the leading families.

Why would the greatest lie behind? We perceive the past, not the future, as that which lies behind. “Leave the past behind,” we say. We perceive the future as that which lies ahead. “Look to the future,” we say. The future is something we see approaching. Our expressions reflect our biases. Since we fear uncertainty, we disarm it by putting it in plain view. To highlight the role of the unexpected, Shakespeare turns convention on its head by placing the future behind, rather than before Macbeth. The future now steals up to Macbeth with the result that, when it catches him, it takes him by surprise. The image highlights the elusiveness of chance: not only does it lie in the future, sometimes we cannot even see it coming.

The improbable event has so unseated Macbeth that he allows himself to consider murder. But the thought of murder is so abhorrent to his previous beliefs that his hair stands on end and his heart knocks against his chest (1.3.137-44). His last recourse to preserve his previous reality is, ironically, to trust chance: “If chance will have me king, why chance may crown me, / Without my stir” (1.3.146.7). As soon as he considers it, however, Duncan names his son heir. Crushed by having the prospect of the crown presented and ripped away, Macbeth moves further towards murder with his “Stars, hide your fires” soliloquy (1.4.50). Within a day, Duncan will be dead, clearing the path for Macbeth to be invested at Scone. The imperial theme is complete.

The Engine of Suspense

After the first two swan events take place, two remain: Birnam Wood and the man not of woman born. When Macbeth faces his first setbacks, he seeks a fresh start and goes back to where it all began. He will seek the Witches. All they presaged has come to pass. They said he is Thane of Cawdor, and it was confirmed. They said he will be king, and he became king. They said Fleance would found the Stuart line, and Fleance proved hard to kill.

To show Macbeth the path forward, the Witches conjure three Apparitions. The first Apparition tells Macbeth to beware Macduff. Even without the Apparition, Macbeth knew Macduff would be trouble: Macduff had declined to attend both the coronation and the state dinner. The second and third Apparitions prove more helpful, setting in motion the last two low-probability, high-consequence events:

2 Apparition. Be bloody, bold and resolute: laugh to scorn
The power of man, for none of woman born
Shall harm Macbeth. Descends.

Macbeth. Then live, Macduff: what need I fear of thee?
But yet I’ll make assurance double sure,
And take a bond of fate: thou shalt not live,
That I may tell pale-hearted fear it lies
And sleep in spite of thunder. Thunder

[Enter] : a child crowned, with a tree in his hand.

What is this,
That rises like the issue of a king
And wears upon his baby-brow the round
And top of sovereignty?

All.                               Listen, but speak not to’t.

3 Apparition. Be lion-mettled, proud, and take no care
Who chafes, who frets, or where conspirers are.
Macbeth shall never vanquished be, until
Great Birnam Wood to high Dunsinane Hill
Shall come against him. Descend[s].

Macbeth.                       That will never be.
Who can impress the forest, bid the tree
Unfix his earth-bound root? Sweet bodements, good.
Rebellious dead, rise never till the Wood
Of Birnam rise, and our high-placed Macbeth
Shall live the lease of nature, pay his breath
To time, and mortal custom. (4.1.78-99)

Like the prospects of becoming thane and king, Macbeth finds the likelihood of either eventuality so low as to approach nil. His courage swells with apodictic certainty:

Macbeth. Bring me no more reports, let them fly all;
Till Birnam Wood remove to Dunsinane,
I cannot taint with fear. What’s the boy Malcolm?
Was he not born of woman? (5.3.1-4)

Exactly as Hecate predicts, Macbeth, consumed by certainty, begins reciting the Apparitions’ words like a novel mantra:

Hecate. He shall spurn fate, scorn death, and bear
His hopes ’bove wisdom, grace and fear;
And you all know, security
Is mortals’ chiefest enemy. (3.5.30-4)

He repeats it to the Doctor: “I will not be afraid of death and bane,” he says, “Till Birnam forest come to Dunsinane” (5.3.59-60). “Thou wast born of woman,” he says, gloating over Young Siward’s corpse (5.7.12). He becomes another of chance’s fools.

In addition to all the functions mentioned earlier—driving the action forwards, exploding and reshaping worldviews, and pivoting the plot—black swan events also fire drama’s engine of suspense. They are part of a metatheatrical game played between dramatists and audiences.

A funny thing is that low-probability events, while low-probability to the characters (who are invariably blindsided by them), are, from the audience’s perspective, high-probability events. When the second Apparition tells Macbeth that “none of woman born / Shall harm Macbeth,” Macbeth understands that, chances are, it will not happen. The audience, however, is of the opposing belief. They understand that a man not of woman born will certainly strike Macbeth down.

Similarly, when the third Apparition tells Macbeth that “until / Great Birnam Wood to Dunsinane Hill /Shall come against him,” Macbeth understand that, chances are, it will not happen. The audience, however, is of another belief. They understand that, like a Houdini or a David Copperfield—Shakespeare will wow them by pulling off the impossible in plain sight. The moment the Apparitions speak, the theatregoers start trying to figure out how Shakespeare will accomplish the impossible. On the one hand, the playwright telegraphs cues to the audience, and, on the other hand, the audience tries to figure out these cues. This metatheatrical game between playwrights and audiences is drama’s engine of suspense. With a few cues, the dramatist stokes the fires of a thousand imaginations.

When the Apparition tells Macbeth that he will never be vanquished until Birnam Wood comes to Dunsinane Hill, Shakespeare is telegraphing to the theatregoers that it will happen. Since it is not immediately obvious how Shakespeare can accomplish this, the theatregoers try to figure it out. As they try to figure it out, they feel the thrill of suspense. “Am I on the right track?” thinks one. “This is how he will do it,” thinks another. In these thoughts is the magic of suspense, and its magic increases with improbability. To bring about a probable event only requires the skills of a probable dramatist. To bring about the improbable event requires the skills of a most improbable dramatist. In this way, when Macbeth responds to the Apparition by saying, incredulous: “That will never be,” the audience understands it two ways. On the one hand, Macbeth is saying that it cannot happen. On the other hand, it is Shakespeare saying to the audience through Macbeth: “If I pull this off, you will admit I am a dramatist of the most improbable skill.” And so, this game of suspense between dramatist and audience plays out.

As the endgame approaches, Malcolm closes on Inverness with the English forces to revenge his father. Shakespeare has a chance to locate the action. The English, being unfamiliar with the terrain, request a bearing:

Siward. What wood is this before us?

Menteith.                                  The Wood of Birnam.

Malcolm. Let every soldier hew him down a bough
And bear’t before him; thereby shall we shadow
The number of our host, and make discovery
Err in report of us. (5.4.4-7)

In the cat and mouse game of suspense, this is the moment the audience has been anticipating. Shakespeare satisfies the audience in the following scene where the Messenger arrives, breathless:

Macbeth. Thou com’st to use thy tongue: thy story, quickly.

Messenger. Gracious my lord,
I should report that which I say I saw,
But know not how to do’t.

Macbeth.                       Well, say, sir.

Messenger. As I did stand my watch upon the hill,
I looked toward Birnam, and anon methought
The wood began to move.

Macbeth.                       Liar and slave.

Messenger. Let me endure your wrath, if’t be not so.
Within this three mile may you see it coming.
I say, a moving grove. (5.5.28-37)

From two scenes earlier, they know that ten thousand march on Inverness. In any other play, the Messenger would have simply reported that troops approach under camouflage. In this play, however, Shakespeare plays up the improbability of the commonest of tactics to place the audience in check. He has brought Birnam Wood to Dunsinane Hill.

Though the improbable has, once again, happened, Shakespeare reminds the audience through Macbeth that their game is not done. The man not of woman born still lurks, undiscovered:

Macbeth. They have tied me to a stake; I cannot fly,
But bear-like I must fight the course. What’s he
That was not born of woman? Such a one
Am I to fear, or none. (5.7.11-14)

The probable, most of the time, prevails over the improbable. The improbable, however, has one decisive advantage. The probable can occur many times, and that is all that it can be: probable. The improbable, however, only needs to happen once. So it was with the black swan and so it is with Macbeth. As the end approaches, Macduff finds Macbeth:

Macduff.                      Turn, hell-hound, turn.

Macbeth. Of all men else I have avoided thee.
But get back, my soul is too much charged
With blood of thine already.

Macduff.                      I have no words.
My voice is in my sword, thou bloodier villain
Than terms can give thee out. Fight. Alarum.

Macbeth.                       Thou losest labour;
As easy mayst thou the intrenchant air
With thy keen sword impress, as make me bleed.
Let fall thy blade on vulnerable crests;
I bear a charmed life, which must not yield
To one of woman born.

Macduff.                      Despair thy charm,
And let the angel whom thou still hast served
Tell thee, Macduff was from his mother’s womb
Untimely ripped. (5.8.3-16)

Checkmate. The improbable man is the man born from caesarean section. The suspense, building since the second sabbath, resolves. The audience feels entertained, having seen how Shakespeare brings to pass the highly improbable, and many times.

Tragedy is a compact between dramatist and playwright. Its structure consists of a series of low-probability, high-consequence events, foreshadowed and fulfilled. Tragedy showcases the playwright’s ingenuity in bringing about the highly improbable. Minor feats of improbability for minor playwrights and major feats of improbability for major playwrights. Such a reading interests us, who are today most interested in finding new ways to explore the unexpected, as more and more, we see that in life as in tragedy, the more improbable it is, the harder it hits.

Not Intended Consequences, but Unintended Consequences

Tragedy dramatizes low-probability, high-consequence events to remind us how good actions can have bad consequences. Unintended consequences arise when the swan event happens because the world has been changed: though no one knows what to do, everyone must act quickly. When Sweno and the Thane of Cawdor see Macdonald revolting, they must act at once, risking all: there is a tide in the affairs of men. This all-in risk, in turn, further antagonizes the unintended consequences: the greater the risk, the further the risk taker’s resources are stretched beyond what the risk taker can cover. The risk taker stands naked in the rain. Actions made in the new world, made in haste and multiplied by risk, tend towards unintended consequences.

Macbeth’s quest for the crown is set against the backdrop of all the failed attempts on the crown. Macdonald and the Thane of Cawdor dared, and lost their lives. Sweno dared, and was out ten thousand dollars. The opening action establishes that, in the world of this play, the highest risk enterprise is to reach for the crown. Despite the risks, however, the play also establishes Macbeth’s competency to fulfil the task. He was the one who thwarted the ingrates and upstarts, who, by all accounts, had been within a hair’s breadth. If they had been close, Macbeth, who was by far greater than them, could entertain higher hopes. Duncan, an armchair king, hardly stands in his way. From the outset, to kill a king is, paradoxically, presented as both the riskiest and the most assured task: riskiest because the others had failed and most assured because Macbeth is like no other. The deed needs to be fraught with risk to cement Macbeth’s daring. But the deed also needs to be most assured so that when the unintended consequences occur, the audience is surprised. This is the pleasure of tragedy.

Having seen what happened to Macdonald and the Thane of Cawdor, Macbeth knows the risk of “Vaulting ambition, which o’er-leaps itself, / And falls on th’other” (1.7.27-8). In awe of risk, he changes his mind, telling Lady Macbeth they will go no further. “I dare do all that may become a man, he says, “Who dares do more is none” (1.7.38-9). Despite his ample resources and insider knowledge, Macbeth remains circumspect. He refuses to act unless every question mark is removed.

At this point, Lady Macbeth offers the failsafe of failsafes. In addition to the assurances they already possess, she proposes to frame Duncan’s chamberlains for the murder. She will ply them with wine so that they can access Duncan. Once murdered, she will smear them with royal blood and set their weapons—now the instruments of murder—next to them. Everyone will be in a deep sleep after the long day. When the murder is discovered, Macbeth will, in a fit of rage, murder the chamberlains. The truth will die with them. None will know. Her plan, being foolproof, convinces Macbeth. Every question mark disappears. “I am settled, “ he says, “and bend up / Each corporal agent to this terrible feat” (2.1.80-1).

They put the plan into action. As expected, it works perfectly. Macbeth become king. Duncan’s sons, Malcolm and Donalbain flee, drawing suspicion of murder on themselves. No one knows better. The play shows them controlling, taming, and mitigating the foreseen risks. But then play turns to the unseen risks in the unintended consequences of their actions, cascading one after another in a beautiful sequence of mischance.

Macbeth had wanted to become king. But he cannot become the type of king he had expected. The best he can do is to become a tyrant, a degraded form of a king. This is the first of the unintended consequences. Now he begins consorting with murderers. Friends must die, and Fleance too. But when he marks them with death, further unintended consequences result. To be sure, ghosts can be found in Shakespeare’s other plays. In the world of this play, however, ghosts are like Juvenal’s black swans: they do not exist. Now, for the first time, the undead rise:

Macbeth. Blood hath been shed ere now, i’th’olden time,
Ere humane statute purged the gentle weal;
Ay, and since too, murders have been performed
Too terrible for the ear. The times have been
That when the brains were out, the man would die,
And there an end. But now they rise again
With twenty mortal murders on their crowns,
And push us from our stools. This is more strange
Than such a murder is. (3.4.73-81)

Macbeth, too, could not have foreseen how Lady Macbeth, entrenched within her iron will, would crack under pressure. Nor could he have foreseen that the moment he masters stoicism, hardening himself to all perils, is the moment Seyton breaks the news:

Macbeth. I have supped full of horrors;
Direness familiar to my slaughterous thoughts
Cannot once start me. Wherefore was that cry?

Seyton. The Queen, my lord, is dead. (5.5.13-6)

Lady Macbeth, too, generates unintended consequences. She had wanted to become queen. But she can only be a posthumous queen, a degraded form of queen: Seyton, as she dies, first addresses her thus.

How did Macbeth fall, Macbeth who removed every last question mark? Some say he fell because of overconfidence. If you believe he was overconfident, ask yourself if Shakespeare could have done any more than what he did to justify Macbeth’s confidence. He gave Macbeth the competence. He gave him insider knowledge. He gave him the best-laid plan. Why should Macbeth not have been confident? His confidence is grounded. He was confident, but did not fall as a result of confidence.

Others say Macbeth fell through uxoriousness. He should not have listened to Lady Macbeth. Lady Macbeth, however, had the foolproof plan. Her plan is shown to be successful. The suspicion of the murder falls on Malcolm and Donalbain. He was swayed by Lady Macbeth, but did not fall through uxoriousness.

Then, there are those who say he fell because of his ambition. The world of the play, however, encourages ambition. The throne is ready for a shaking. Macdonald, the Thane of Cawdor, and Sweno all sense a changing of the guard. Later Banquo—and perhaps Donalbain—entertain their own imperial themes. The king is a poor judge of character, easily deceived, and cannot take it to the field. God had already deserted him: he can only send his wounded to the surgeons, other kings heal their subjects by a divine touch. Macbeth was ambitious, but his ambition was justified.

If not confidence, uxoriousness, or ambition, why did he fall? I think he fell through chance, the unexpected, more things happening than what he thought would happen, black swans, uncertainty, unknown unknowns, and low-probability, high-consequence events, the effects of all of which were compounded by risk. While indiscriminate evil cannot explain why Malcolm should ask the troops to cut down the boughs of Birnam Wood, chance multiplied by risk can. By chance, Macbeth meets a man not of woman born. By risk, he dies. Had he not put so much on the line by killing Macduff’s wife, babes, and lord, the encounter may have been less grievous.

Chance and the unexpected appear to the mind as a gap in nature, as a vacuum where there should have been knowledge. The intellect is poorly designed to comprehend the dark night of chance: though the math to comprehend chance was available from antiquity, it was not until the Italian Renaissance that probability theory laid down its footings. The intellect strives at all times to prove that everything happens for a reason. Thought finds a world where the random element runs amok false and impenetrable. Thought abhors empty space, rails against wild things.

When the world confronts timid natures with accident and uncertainty, they feel pity and fear. Pity for the tolling of the bell and fear that they too are exposed. These natures, who needed to reassure themselves from chance, sought to contain it, some by devising simplistic explanations (overconfidence, uxoriousness, ambition, etc.,) and others by devising complex metaphysics (the forces of darkness and evil). With these objectively questionable and subjectively comforting explanations, they allayed their fears, saying to one another: “Be more modest in your ambitions,” “Do good,” and other like refrains, thinking that with a change in behavior, next time they could stop Birnam Wood. Their explanations are from the point of view that the mischance of men’s ambitions are caused by man, and not by chance.

When the world, however, confronts more ambitious and confident natures with accident and uncertainty, far from pity and fear, they feel wonder and awe, wonder at how an individual, so full of fire and the seed of greatness, could be struck down by chance, and awe for the smallness of man in the boundlessness of randomness. They see that the killing risks are not the risks they see, but the ones that cannot be seen until after. They see that greatness is not without risk, and that there is a price to live dangerously. These fiery natures Macbeth marshals forwards, into the unknown, into risk, into the dark night of thought, as though saying to them: “Friend, dare to live dangerously, and you too shall die. Why the fuss? I also died, who was better by far than you.”

To these souls on fire, the highest honour is to join Macbeth and the pageant of tragic heroes who, having climbed past every ladder, found a way to climb on top of their heads, ever higher, higher than Ida’s peaks and Icarus’ flight. For them, to live is to dare. But it may be that there are other readings, and that there are as many truths to Macbeth as there are hearts, some circumspect, some like fire, some obsequious, some firing out their chests like cannons, some lily-livered, some cold as iron, hard as rock.

Littlewood’s Law

Some find the concatenation of low-probability, high-consequence events in Macbeth beyond belief. How could one individual become thane, then king, fall into tyranny, lose his lady to madness, see the wood come up the hill, and then meet a man not of woman born? That this too is part of an all-too-human heuristic that shuns chance and uncertainty can be demonstrated through Littlewood’s Law.

J. E. Littlewood, a twentieth century Cambridge mathematician, believed that exceedingly improbable events happen more often than we anticipate. To demonstrate his hypothesis, he devised a thought experiment. First, he called these unanticipated events miracles. Next, he defined miracles as events a million to one against. Through the observation that we experience many events each day, he demonstrated that we encounter the highly improbable monthly:

Littlewood’s Law of Miracles states that in the course of any normal person’s life, miracles happen at a rate of roughly one per month. The proof of the law is simple. During the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of about one per second. So the total number of events that happen to us is about thirty-thousand per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect one miracle to happen, on the average, every month.

In life, it is thought that we experience a handful of defining moments, moments full of miracle and wonder such as comings of age, marriage, and convalescence. The implication of Littlewood’s Law, however, is that these existential fulcra whereon life hangs in balance happen more often than we anticipate. Life, far from being a steady state with gradual change, is in a constant state of revolution. The moments of respite are as infrequent as the major upheavals are frequent. In this probabilistic existence, we find ourselves often standing, like Macbeth, outside the safety of circumscribed beliefs.

Macbeth, in dramatizing the crossroad between probability and life, not only illustrates that more things can happen than what we think will happen, but also that these more things happen more frequently than we allow. These strange concatenations of events in the play may be more emblematic of life than critics have allowed. Even in a world of pure good, and one in which the drives of ambition and confidence are constantly held in check, we should expect to see a Birnam Wood event, by chance alone, on the average, every month.

The Old Master

Part of the reason so few have based their readings of Macbeth around low-probability, high-consequence events is that such readings are inherently paradoxical. The low-probability event is only improbable to Macbeth. To the audience, it is a high-probability event. This paradox drives critics to look elsewhere for the play’s keys. Many have done exactly this, basing their reading around ambition, hubris, error, uxoriousness, or the insidious action of evil. It need not be so, as the paradox is easily resolved: it exists to generate suspense. Another reason, however, why so few have tried this reading is that it flies in the face of the old master, Aristotle.

Just as the intellect abjures the role of chance as a causal factor in life, it is perhaps fitting that the greatest of intellects would abjure the role of chance from the construction of the best of plots. Aristotle declares in the Poetics that tragedy dramatizes the sorts of thing that could happen. Tragedy deals with probable events:

It is also evident from what has been said that it is not the poet’s function to relate actual events, but the kindsof things that might occur and are possible in terms of probability or necessity. (1451a)

Not only should tragedy deal with the probable, he goes on to say that chance events, being signs of inferior plot construction, are to be avoided (1454a-b). The net effect of his condoning the probable and condemning the improbable was to preclude chance and the highly improbable from the discussion of tragedy. It is a shame.

Aristotle had reasons for banishing the improbable. He was trying to rehabilitate tragedy. His teacher, Plato, had found tragedy to be degenerate and unceremoniously banned it from his ideal city-state (Laws 817a-e, Republic 607b). To rehabilitate tragedy, Aristotle gave it a social function. To Aristotle, theatregoers seeing the consequences of characters’ actions onstage would better understand the consequences of their own actions offstage. For this stage to street transference to work, however, actions had to be repeatable. For actions to be repeatable, they had to be probable. If a flaw onstage would lead to a similar fall offstage, nine or ten times out of ten, then tragedy could fulfil its social function.

In rehabilitating tragedy, Aristotle turned tragedy into a distant early warning of poor character. For the next two thousand years we would talk about how irascibility led to the fall. The fall was precipitated by confidence, stubbornness, ambition, and other behavioral factors that the agent could change, and by changing, escape tragedy. By neutering the improbable, Aristotle rehabilitated tragedy.

Aristotle has ruled the roost for two thousand years. In new millenniums, however, we seek new truths. In this age of the unexpected, we seek and find, through Macbeth, a new truth for tragedy that speaks to the pervasiveness of the random element. From its dramatization of black swans, Macbeth gains its overwhelming impetus. By affirming how the unthinkable happens again and again, Macbeth touches all the themes of our day. What is more, tragedy is once more dangerous. When it is dangerous, it is exciting and fit entertainment for the highest natures.

The Great Race

In this reading of Macbeth, I have shown how the action pivots around the fulcrum of the low-probability, high-consequence event. By the advantage conferred by this force multiplying machine, with the lightest touch the dramatist can provoke characters to abandon belief systems and risk certain comfort on uncertain hopes. Risk unbound, in turn, leaves characters susceptible to the unintended consequences of their actions: the more risk they assume, the more susceptible they become to each tremor. All the meanwhile, the dramatist plays a metatheatrical game with the audience, creating suspense by dangling before the audience the prospect that he will bring about an event so rare and wild that any lesser dramatist would cringe at the attempt. From the page to the stage, tragedy is a theatre of risk.

This concludes my study of probability in Macbeth. I needed to write this, because, to me, this play was like a great race in which runners would compete, and, in the course of the running, they would run across banana peels. Some of them they would see, and jump over in great leaps. Some of them they would not see, or see too late, and slip. The runner, who led by an overwhelming margin in the final stretch, slips by accident and is unable to cross the line. This same runner, while jockeying for position earlier, had also pushed last year’s winner into the ditch.

Now, listening to the commentators, I was surprised because they would never declare these falls as accidents. Instead they would say that this runner slipped because he ran too ambitiously or that that runner slipped because he ran with too much gusto. As for the frontrunner who never crosses, this, according to them, was to show that cheaters never prosper. If you saw the play as I do, would you not yourself have needed to say this, that it was not error, hubris, confidence, or justice that causes the fall, but that the fall results from something much simpler, namely that, in a course full of banana peels, more things may happen than what we think will happen?

This reading is based on my new theory of tragedy, which is laid out in my book: The Risk Theatre Model of Tragedy: Gambling, Drama, and the Unexpected. The book has launched the world’s largest competition for the writing of tragedy, The Risk Theatre Modern Tragedy Competition, now in its third year. Thank you for reading.

Don’t forget me. I’m Edwin Wong, and I do Melpomene’s work.