Friday, February 26, 2010

Cinematic Algebra, or, What I Learned from Die Hard, part IV

Though this article is officially #4 in my “What I Learned from Die Hard” series, I have decided to fold it in with a much larger, more important article I have planned for some time since both articles cover similar ground.
A few months ago I was having a heated IM conversation with a writer friend of mine. The difference between this writer and myself is that far unlike me, my friend angrily eschews any sort of analysis, theory, or critical thought when it comes to writing. He is the type who would rather shut his eyes and try to write by “The Force” or some crap like that. In fact merely mentioning the word “craft” raises his hackles and makes him plug his ears.
In our conversation, I took him to task for refusing to learn the rules that govern his chosen field, comparing it to a physicist who refuses to learn about gravity. My friend, misunderstanding my point, responded with anger, “Schock, this is nonsense! You can't approach writing like mathematics!” He then abruptly ended the conversation.
My friend, that wasn't what I was trying to say, but just for the hell of it, I will take up this argument. You are wrong. Storytelling CAN be understood in the same way. And I will prove it.
Not mathematics in general. I don't mean arithmetic where you add and multiply cold hard figures. Cinematic storytelling is more like algebra. So dust off your high school math book. We're going to learn to construct some badass cinematic scenes.

But before proceeding it is important to first establish some simple truths about our craft.
The first is that “story-telling” consists of two halves. The first is the “story.” The second is the “TELLING” – how one chooses to communicate that story to the audience. The same storyline in the hands of two different writers can have drastically different results. The first may end up with a dull, boring experience that fails to hold the audience's attention, while the second may be tense, exciting, the most thrilling movie experience ever written- even though it is the exact same story. The difference is the second writer possesses the skill and understanding necessary to communicate that story in a manner that grabs the audience's interest and appeals to their emotions.
The true art of storytelling is not in the story itself, but how that story is TOLD. When a story begins, all the cards are already out on the table. It is the storyteller's job to decide when to turn each card over and reveal to the audience the information underneath. A novice storyteller reveals his entire hand right away whether he needs to or not and ruins his game. An expert storyteller is like the cagiest of riverboat gamblers. He or she knows what card to play when, how to keep the hand hidden until the right time, and when to go all in. So with that said,
In other words, to craft an audience-pleasing story, a storyteller must always be conscious of what to allow the audience to know, and what to keep unknown. It is the art of keeping people in the dark and seeing their pleasure when you turn on a light.
(These ideas are closely related to my “Atoms of Information” theory. See the February, 2009 article.)

Now, back to the algebra.
Here is a simple algebraic equation:
6 – x = 2 (Six minus “x” equals two.)
Every algebraic equation contains two things:
  1. Constants. Constants are numbers whose values are known. The number six means exactly “six.” It can be nothing but six, never more or less. The same thing goes for the number two. Two can be nothing but “two,” and nothing else.
  2. A Variable. Variables are numbers whose value are not yet known. “x” is the variable in this equation. “x” could represent any possible number. Its currently an unknown. The whole goal behind solving an algebraic equation is to discover the value of the mystery number “x”.
In the worlds of business or sports, you sometimes hear a person or thing labeled as an “X-factor.” An X-factor refers to someone or something whose real worth or abilities are not yet known. When the Los Angeles Clippers chose the University of Oklahoma's Blake Griffin as their #1 Pick in the 2009 NBA Draft, Blake Griffin was an X-factor. Griffin was an incredible college player, but no one knew how well he would do in the NBA. He could be the next LeBron James, or he could be a disappointment. The Clippers found out their X-factor's value when Griffin became injured before the beginning of the season and had to sit out for the entire year.
Great cinematic storytelling is all about creating sequences and scenes that make ample use of an X-factor. An audience is watching a scene. There is information that they definitely know and understand about the story, the characters, and what is going on in the scene. These are constants – information that is already known. But somewhere in that scene is a big, gaping black hole of uncertainty. Something is left unknown, and all there is for the audience to confront is a big X that could be anything and everything. This unknown element is what creates the much mentioned “need to know” in the audience. The audience is presented with an unsolved equation. And they want to know the answer! As long as the question still hangs in the air, as long as X is unknown, a storyteller has the audience in the palm of their hand because the audience desperately wants to SOLVE the equation.
The thing that must be present in any great movie scene, no matter whether is a romantic comedy or horror, is DRAMATIC TENSION. Dramatic tension is created when the audience has unanswered questions. And a writer creates unanswered questions by withholding important information as X-factors.
There are three ways a storyteller can use this X-factor to his or her benefit, and each creates different results. These are: Mystery, Surprise, and Suspense.


mystery: n. 1. Something unexplained or secret. 2. A story involving unknown persons, facts, etc.
When something is a “mystery,” that simply means a piece of important information is missing. A big piece of the puzzle is gone, and we are unable to see the whole picture.
The natural outcome of mystery in an audience is CURIOSITY. Curiosity is defined as “a desire to learn.” Someone sees the available information, notices that they are unable to understand everything due to what is missing, and feel an urge to know more. Curiosity causes people to actively seek out information, to try to solve the mystery.
Never just GIVE your audience information. Don't just drop facts into their lap. They won't want them because they were never asked for. Have you ever dangled a string in front of a cat? The cat will be fascinated for hours by the string as long as it is just out of its grasp. But if you just give it the string, the cat will simply look at it for a moment, then walk away.
They key to a great movie experience is to turn the audience into ACTIVE participants in the story. Instead of the storyteller just giving information, and the audience passively accepting it, a storyteller must give the audience a reason to WANT the information, and motivate them to seek it out on their own.
A storyteller creates mystery by providing a bit of information to the audience- but only enough to arouse curiosity. The most important piece of this information- the thing that solves the mystery and allows everything to make sense- is purposely withheld. To use an example from Die Hard, late in the first act we are repeatedly shown a large truck approaching Nakatomi Tower accompanied with ominous music. Nothing else is explained. Each time the audience sees the truck, they wonder, what is in the truck? Why is this truck important? In terms of algebra, the truck, the tower, and the ominous music are the constants. They are what we know as facts. The X-factor, the unknown thing the audience wishes to know, is what there is inside the truck. It could be anything. Packages, exercise equipment, kangaroos. The X-factor arouses the audience's interest and makes them active viewers.
Unanswered questions create tension. If the creators of Die Hard had chosen to follow the shot of the truck with a shot of what was inside, all tension would be lost. The audience would no longer be curious, and would be robbed of the PLEASURE OF DISCOVERY when the truck's doors finally open to reveal Hans and his men armed with machine guns.
The “pleasure of discovery” is the audience's reward for their curiosity. Discovering an answer to unanswered questions gives the audience a unique self-satisfaction, a feeling just like when one solves a difficult puzzle, or gains sudden insight into a bothersome problem. When you encourage an audience to become active viewers through curiosity, the audience gains pleasure from the experience. When they finally learn important information, they subconsciously pat themselves on the back, feeling good about the fact that they were smart enough to piece together the bits of information in order to comprehend the twists and turns of the story on their own rather than having it spelled out to them like children.
Imagine a room full of schoolchildren and you as the teacher. There are two ways you could approach the lesson. The easiest, most obvious way is to simply lecture the children and expect them to sit there and pay attention. But a better way to teach is to get them involved. Ask them questions, start a dialogue, guide them to figure out the lesson on their own. By leading the students to pursue questions on their own, by guiding them bit by bit to the solution, not only will the students pay attention, not only will they enjoy the learning experience more, but they will feel proud of themselves out of the belief that they figured it out all by themselves! You will teach them without them knowing they have been taught.
In storytelling, the answer to the mystery is always right there in plain sight. It already exists, it is just kept hidden from the audience. Much of Hans' master plan is kept secret throughout Die Hard. Hans' goal is to get into the vault, but several times throughout the second act Hans' computer expert Theo tells him that it will be impossible to break through the vault's seventh lock. Hans' only reaction is a self-assured smile as he tells Theo not to worry about it. Hans' plan to get past the seventh lock already exists. He knows what he is going to do when the time comes. But it is kept hidden from the audience. This seventh lock becomes an X-factor. How does Hans' plan to get into the vault? Just why is he so confident? The audience wonders about these questions until the right moment comes and we receive the pleasure to discover how Hans' brilliant plan has fallen into place. The result is an “ah-ha!” moment where everything finally makes sense.
Die Hard's writers do an amazing job of creating mystery out of even the smallest pieces of information, often arousing curiosity with a single line of dialogue or action, and then answering it with the next:
Suddenly rifle fire sounds from the building.

They're shooting at them!

It's panic fire...they can't see anything.

(under breath)
They're shooting at the lights.

More shots ring out from the building going over the SWAT officers' heads. Suddenly the huge dome of one of the spotlights shatters behind Mitchell and Robinson's head.

They're going after the lights!
But, the more important a piece of information is, the longer you can, and should, withhold it from the audience. The final phase of Hans' plan is to blow up the roof of the building, killing all the hostages and the FBI helicopter with it in order to escape in the ensuing chaos. This is a bombshell of information that is kept hidden until very late in the film. But if one backtracks, you will find that small pieces of this information has been scattered throughout the story from the very beginning. Soon after the terrorists first arrive, we see them doing some sort of work on the top floor. We have no idea what they are doing, only that they are doing something mysterious. Hans and his men make several mentions of “the roof” as they speak among themselves. John finds a bag full of detonators- something Hans wants to kill John in order to get back- which begs the question, what does Hans need all those detonators for? Little by little, small pieces of information are added to the story, just like a jigsaw puzzle where you begin with the edges and slowly add more and more as you move closer to discovering the whole picture. Yet the biggest piece that makes the picture all clear, the X-factor is still unknown. The longer the audience is allowed to wonder, the bigger the payoff will be when it is finally revealed. The audience gets the maximum pleasure of discovery, a big “ah-ha” as they look back and find that all the clues before made sense.
(Just make sure that this big, important piece of information really is big and important enough to be worth the wait. Anything less will come off as a letdown. There seems to be a direct relationship between the importance of a piece of information and the length of time you're allowed to keep the audience waiting before giving it to them.)
Well-crafted mystery can drive an audience crazy with anxiety. But the good type of anxiety. The immensely pleasurable anxiety that you felt as a kid at Christmastime when you looked at those presents under the tree. You were dying to rip them open and see what was inside – but you couldn't. Not just yet. A storyteller pleasures the audience by teasing them. By chanting, “I got a secret! I got a secret!” and then making the audience twitch in their seats with the need to know.


surprise: n. 1. to come on suddenly or unexpectedly. 2. to attack without warning.
Where mystery fosters an audience's interest by giving small clues and keeping important information hidden, surprise abruptly seizes the audience's interest by doing the near opposite.
Surprise withholds ALL clues from the audience. Something important is occurring, but the audience is given no indication of its existence. Then, without warning, information is shoved in their faces, a big important piece of information is thrown at them, and they never saw it coming.
The audience reaction to surprise is SHOCK. They are thrown aback, momentarily disorientated, as their minds scramble to understand the sudden onslaught of action on screen. Surprise, like mystery forces the audience to ask questions. But whereas mystery makes the audience wonder “What is going to happen?”, surprise hits the audience like a panic attack and makes them ask “Why did that happen just now?” Surprise is like a backwards-mystery. Mystery gives clues and leaves the important info unknown, but surprise gives the important info up front and keeps the clues unknown. Without the clues, the audience is left scrambling after the initial shock to put together an explanation. This is why after the dead body has fallen onto Powell's police car, after the initial shock and confusion, after Powell's fear and the cacophony of gunfire, it was necessary for the audience to see the shot of John McClane through the broken window. This piece of additional information answered the audience's questions and solved the backwards-mystery. The body landed on the car because Jon threw it out the window. This information was the scene's X-factor.
A great surprise is like an explosion. Extremely powerful, but short-lived. If someone jumps out of your closet and yells “boo!” you receive intense emotional excitement – but your heart continues to race for only as long as it takes discover there is nothing to be afraid of. A shock given to an audience lasts only a few seconds as well – the amount of time it takes for the audience to understand what just happened and regain their senses. For this reason, surprise should not be used as the writer's primary storytelling tool. Surprises should be used sparingly, and only in moments where the writer feels that a sudden shocking reveal of information will be the most dramatically effective. The problem with surprise is that once the shock has worn off, the dramatic tension will soon go dead. A story with nothing but surprising moments will be one that constantly alternates between heart attack and boredom. As the story continues onward, each surprise will become less and less shocking as the audience becomes desensitized to the device and will eventually start to expect surprises to happen. Another thing that makes surprise weaker than the other two dramatic devices is that unlike mystery and suspense, there is no slow build of tension that proceeds the device's payoff. Instead, surprise gives its payoff immediately. This means that moments before surprise can sometimes be dramatically dead, allowing the audience an opportunity to slip back into becoming passive, disinterested viewers. Alfred Hitchcock famously spoke of his preference for suspense over surprise. He would rather see the time bomb hidden beneath the desk, silently ticking down, than the shock of an uneventful scene interrupted by a shocking explosion.
Surprise definitely has its place in the storyteller's arsenal. When well used, it can be the atomic bomb of storytelling. But use it wisely. It is always far less fun to throw something in the audience's face than to make them squirm as you hold it out of their reach.

suspense: n. 1. a state of uncertainty.
Out of the three storytelling devices discussed in this article, suspense is by far the most effective when it comes to seizing and holding the audience's attentions. Suspense uniquely combines the curiosity of mystery with the shock and fear of surprise. The audience has a question that they are dying to know, but they are afraid of what will happen when it is answered.
The primary differences between mystery, surprise, and suspense is easy to understand. In mystery, important information is withheld from the audience, to be revealed at a later time. Usually a character or characters already know what the audience does not. The characters have a position of advantage on the audience.
In surprise, the important information is suddenly revealed right as it happens with no clue beforehand. Characters learn this information at the same time the audience does. Character and audience are on equal footing.
Suspense, on the other hand, gives the audience story information in advance. Suspense clues the audience in on something unwanted that is sure to happen in the immediate future that will have a negative effect on the story situation. Suspense gets its power from the audience's feeling of anticipation- and fearful anticipation at that. Disaster is waiting to strike, and the audience both knows and fears it. The X-factor of suspense, that one piece of unknown information that the audience is dying to know, it not WHAT will happen, but WHEN it will happen and WHAT will be the outcome. For example, early in the Third Act both John McClane and the audience discover that Hans plans to blow up the roof with the hostages on it. At this point, the mystery over Han's final plan turns into suspense. The question is no longer, “What is Hans' plan?”, it is “When will Hans do it, and can John save everyone in time?” The audience is on the edges of their seats for the rest of this sequence for an answer to this question.
Suspense can be broken down into two types: standard suspense, and heightened suspense.
Standard suspense occurs when both the audience and the protagonist know about the impending disaster at the same time. Audience and character are on equal ground. The audience is with them every step of the way, getting information as soon as the character does. The unwanted event could be something waiting to happen in the immediate future, such as in a classic ticking clock scenario, or it could be happening in the present moment. Whenever John McClane is engaged in battle with Hans and his henchmen, standard suspense is at play. The audience's question is not “What is going on?” it is “What will be the result?” - will John McClane escape this fight alive?
Heightened suspense occurs when the audience is given information on an impending unwanted event, but the character is NOT. The audience is informed that danger or misfortune is rushing the protagonist's way, but the character is ignorant of this, a sitting duck waiting to get ambushed. In heightened suspense, the audience has a position of advantage over the characters. Early in the second act, John McClane goes to the rooftop to radio the police for help. But what John doesn't know, and what the audience does, is that Hans has heard his transmission and has sent Karl and two others to kill him. We see Karl and the two others riding to the roof in the elevator, readying their weapons. Then cut to John continuing to argue with the police dispatcher, completely obvious to the danger he is in. Likewise, in the third act, the audience is allowed to know that the FBI agents Johnson & Johnson plan to land their helicopter on the roof with guns blazing, killing anyone suspicious- something that comes as a complete surprise to John when he must suddenly run for his life. These scenarios of heightened suspense create a slow build of tension with each second that passes between the moment the audience learns the information to the time when the protagonist has this information thrust upon him, ending in a climax of audience anxiety.
The most fascinating thing about heightened suspense is that its immense power, the great emotional pleasure it can give an audience, comes directly from a feeling of helplessness! The helplessness of the audience is what heightened suspense is all about. Have you ever been in a movie theater and have heard someone literally yell at the characters on on screen? “Don't go in there!” or, “Look out behind you!” Of course, it seems silly to do this. The people on screen obviously can't hear you. But these people in the audience have been led to feel so burdened by their privileged information that they cannot stand to see the characters stumble into danger. Despite all common sense, are compelled to try and help them! The audience cares about the character. The audience knows that the character is in danger. The audience knows information that could save the character's life. If they could only tell it to them the character would be safe. But they can't! They can only sit there in fear as they watch the character do something they KNOW they shouldn't do.
There is something known as the “Cassandra complex”. The idea originates from Roman mythology. Cassandra was the beautiful daughter of Priam, the king of Troy. The sun god Apollo became smitten with her and gave her the gift of prophesy to convince her to be his bride. However, Cassandra rejected his proposal. Angry, Apollo allowed her to continue to prophesy, but cursed her so that no one would ever believe her visions. Cassandra continued to foresee disasters, accidents, death and destruction, but she could never do anything to prevent them from happening. Cassandra eventually went mad from her helplessness, from the thousands of horrible events she saw coming, but could do nothing to stop. This in a nutshell is what heightened suspense is all about. The storyteller-god is giving the audience their own little Cassandra complexes, driving them just a little nuts, one scene at a time.
Heightened suspense sequences usually operate under a sort of hunter/hunted dynamic. John McClane is usually the one who is being hunted, and he is usually the one in the dark. But a heightened suspense sequence can work just as well if the dynamic is reversed with the hunter as the one who is deprived of information rather than the character who is hunted. Just before the mid-point there is a scene sequence that finds John McClane hiding in a ventilation duct. John wound up there in order to escape from the homicidal Karl. However, Karl has figured out that John is hiding in the ducts. He just doesn't know where. So we have John stuck in the duct, unable to escape, unable to move without giving away his location, and Karl down below poking around with his machine gun. The audience knows where John is and where Karl is. John knows where Karl is. Karl is the one in the dark. We see Karl getting closer, and closer to discovering John. The audience wishes to help John out of this situation, but they are just as helpless as he is. The question, the X-factor that winds the tension of this scene so very tight is “Will Karl find John? What will happen when he does?”
The audience feels this sensation of helplessness because the audience cares about the characters and does not want to see them come to harm. This shows a direct connection between good suspense and empathetic, identifiable characters. Character identification is a prerequisite for good suspense. If the audience does not yet care about your characters, if they don't like them, or cannot at least care whether the character lives or dies, any attempt at suspense will fall flat. Suspense, especially heightened suspense works by creating a DILEMMA in the mind of the audience. The audience WANTS to see what is going to happen when the danger strikes, yet at the same time they FEAR what will happen to the character when it happens. They are torn between their curiosity and their compassion – in an emotional panic where they proceed forward with one eye open and one closed. If the audience does not care about the characters in the first place, that dilemma never happens and the feeling of suspense will fail to materialize.

Mystery, surprise, and suspense work well on their own, but they work even better when combined. Watch this clip from Die Hard and try to count how many times mystery, surprise, and suspense are used in a single scene.

Mix. Match. Every moment has the potential to engage its audience by the creative giving and withholding of information through our cinematic algebra. Become its master and you can easily turn this:
2x + 3 = 8
Into this:
I don't know what the hell this equation is supposed to be, but it looks like it would make a great movie scene.

Next month: Part V: Info Plants - The Writer's Time Machine