LEGO & BELL’S

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It begins as a typical children’s cartoon movie: a struggle between good and evil, mildly interesting characters trying to overcome personal insecurities to ‘be all that they can be’, a love triangle of course, some witty, adult oriented repartee, and lots and lots of action.

But The Lego Movie is much, much more than this! As we shall see, this movie includes a huge twist (spoiler alert to follow), and that ‘twist’ reveals that the fundamental ontology of this film is not Classical (Euclidean/Newtonian) but Quantum Mechanical. But to appreciate this twist, we need to review the movie’s plot line.

The Story

As the film opens, we see characters existing in a world built entirely out of Legos; they are Lego pieces themselves and everything they do is done with Legos. Their tools, their weapons, all made of Legos! There is every reason to believe that this World is entirely self-contained, that it is Universe.

As the film progresses, we learn that Lego World has many realms, including Old West, Viking’s Landing, Pirates’ Cove, Middle Zealand and Cloud Cuckoo Land; but most of the action takes place in Bricksburg, a thriving metropolis dominated by a crushing culture of conformity. The dominant ethic of Bricksburg could be summed up on a bumper sticker: “Follow instructions!”

Under the influence of ‘Lord Business’, construction workers, ‘micromanagers’, robots and cops work together to nurture and, if need be, enforce the conformist ethic. But under the radar, a tiny group of Master Builders harks back to a time before Lord Business when Lego World was free and full of possibility.

In Bricksburg, everyone builds according to plans, blueprints, instructions; but not the Master Builders! They build free form. Even better, they build their creations quickly and in real time to confront immediate, real life challenges. Philosophically, they are William James Pragmatists. But they are also society’s artists and magicians. Only Master Builders are capable of introducing true novelty into the world and impacting the course of events.

But “Lord Business, who you know as President Business” has diabolical plans for Bricksburg. Lord Business plans to unleash a fully weaponized Kragle on Taco Tuesday to end the world as we know it. ‘Taco Tuesday’, a typical government program of bread and circuses designed to co-opt and distract the populace, is cover for President Business’ plan to activate the super weapon (Kragle), which will freeze Bricksburg, effectively destroying it.

The central theme of the movie is the Master Builders’ struggle to derail Lord Business’ scheme. Because of a prophesy from the blind wizard Vitruvius, they believe that their success depends on finding the “Special”, a savior foretold by Vitruvius who will locate the “Piece of Resistance” (piece de resistance), the one ‘piece’ that can disable the Kragle, and use that piece to thwart Lord Business’ plans.

When we are introduced to the Piece of Resistance, it is quite unassuming. An elongated cube, open at one end, it looks slightly out of place in Lego World…and it is (but more on that later).

The Special is simply the most important, most talented, most brilliant, most interesting, most extraordinary person in the universe…at least according to the prophesy. But surprisingly, the Piece of Resistance is found accidentally by a construction worker named Emmet who turns out to be a paradigm of the mindless conformity that dominates Bricksburg. “We all have something that makes us something and Emmet is…nothing.”

As the Master Builders learn more and more about Emmet, they trust him less and less. Even if he is the Special, he lacks the skills necessary to complete the mission. He is not even a Master Builder and he shows no hint of creativity. Something is terribly wrong but nobody knows quite what.

Nonetheless, Emmet gets a chance to plead his case at a gathering of Master Builders “in the secret realm of Cloud Cuckoo Land.” Princess UniKitty welcomes the Master Builders to Cloud Cuckoo Land and explains its unique social order to Emmet: “Well, we have no signs here, no rules, no government, no bedtimes, no baby-sitters…And there’s also NO consistency.”

Emmet introduces himself to the august assembly: “…I may not be a Master Builder…I’m not all that smart. And I’m not what you’d call a creative type. Plus I’m generally unskilled. I know what you’re thinking. He’s the least qualified person in the world to lead us. And you are right.”

Before Emmet can complete his ‘pitch’, all but a few of the Master Builders desert him. But later on, as the situation worsens and some of the Master Builders return to Emmet’s side, his experience in Cloud Cuckoo Land stands him in good stead.

“What is the last thing Lord Business expects Master Builders to do? Follow the instructions. You’re all so imaginative and talented. You can build things out of thin air. But you can’t work together as a team. Just imagine what could happen if you work together. You could save the universe!”

And so Emmet proposes a ‘third way’. In contrast to mindless conformity or anarchic creativity, he suggests a middle course: conscious, intentional, voluntary cooperation. For the remainder of our adventure, this is the strategy that Emmet and the Master Builders adopt in their crusade against Lord Business.

But even that is not enough! Nothing the Master Builders do can derail Lord Business’ plan to end the world. To make matters worse we learn that Vitruvius made up the prophesy in the first place “because I knew that whoever found the piece could become the Special, because the only thing anyone needs to be special is to believe that you can be.”

Perhaps Vitruvius was right after all. In the course of leading the Master Builders against Lord Business, Emmet does indeed become a Master Builder himself. A Master Builder “sees everything”; he understands that every piece has the potential (actually, is the potential) to participate in the creation of more complex structures. Master Builders share the vision of Aristotle (matter is pure potentiality) and Alfred North Whitehead (every being is potential for a new becoming).

So far, we have a good story with some interesting philosophical and sociological insights but nothing more…yet. Then something amazing happens.

Spoiler Alert!

Separated from the Special by Lord Business, the Piece of Resistance falls out of Lego World entirely. Who knew that was even a possibility? Who knew Lego World had borders, that there was anything beyond Lego World?

The Piece of Resistance is gone…and now all is certainly lost! But the transformed Emmet refuses to give up. He follows the Piece of Resistance right out of Lego World. He falls freely toward all but certain annihilation; but amazingly, he instead lands in another world, a world entirely beyond his wildest imagination, a world far removed from any of the realms of Lego World. He finds himself in the basement of a house where a boy named Finn is playing with a gigantic Lego set that nearly fills the room.

Then we hear Finn’s father’s footsteps ominously descending the cellar stairs. Finn’s father is “the man upstairs” we’ve heard references to throughout the movie; we discover that he is using these Legos to create a model for a major real estate development project. He has repeatedly instructed his son not to play with these Legos. Yet that is exactly what Finn is doing.

At the beginning of the movie, perhaps before Finn was even born, Vitruvius issued another prophesy, “He is coming. Cover your butt.” It seems likely that ‘ancient’ prophesy referred to just this moment. A confrontation between the boy and his father ensues and in the process the movie is decoded.

It’s Tuesday night and Tuesday night is Taco night in Finn’s family (‘Taco Tuesday’). But Dad (aka Lord Business) has a tube of Krazy Glue (Kragle: Kra Gl e) and tonight is the night when he plans to superglue all the Lego pieces together to solidify his model. Once the superglue takes hold, Lego World will be frozen solid.

Throughout the movie, we are told that Lord Business plans to “end the world”. Now we understand what that means. According to Alfred North Whitehead, “…it belongs to the nature of a ‘being’ that it is a potential for every ‘becoming’.” By that standard (as we saw above), Lego pieces are paradigmatic ‘actual entities’ (beings). What is a Lego piece but the potentiality to participate in the formation of novel, complex structures? But once Lord Business ‘freezes’ Lego World with his weapon of mass destruction (Krazy Glue), all potentiality will vanish. The Lego pieces will no longer be actual entities (beings) and Lego World will effectively cease to exist.

Until now, we have assumed that the Special must overcome Lord Business by force and use the Piece of Resistance to destroy the Kragle. But now we realize that we, and our Lego characters, have misunderstood the true mission of the Special. It is not to overcome Lord Business by force of arms; it is to persuade him by force of argument to abandon his plans to freeze the world. The Piece of Resistance turns out to be the cap to the Krazy Glue tube and it must be voluntarily re-attached by Lord Business himself if Lego World is to be saved.

Finn argues that it is totally unreasonable to expect a boy his age not to play with a huge Lego set in his basement. “We bought it at a toy store,” and he points out that the instructions on the box read, “Ages 8 to 14”. But Dad is less than impressed by Finn’s legalistic argument. For a moment it looks as though Vitruvius’ initial prophesy may be fulfilled.

But after some further give and take, the ‘man upstairs’ decides to give his son another chance to present his side of the story and to argue for the future of Lego World. This time, however, he invites Finn to present his case through Emmet, the Special. Using Emmet as a less vulnerable intermediary, Finn is empowered to take a different approach:

“You don’t have to be the bad guy. You are the most talented, intelligent, extraordinary person, capable of amazing things. You are the Special…and so am I. The prophesy was made up…but it’s still true. You still can change everything.”

At that moment Lord Business walks toward Emmet and gives him a hug…just as Dad walks toward Finn and hugs him. Finn and Emmet succeed and Dad/Lord Business decides to use the Piece of Resistance for its intended function, to cap the tube of superglue. Lego World is saved.

The Ontology

Thanks to this surprise ending, a good story becomes great. But how are we to understand the ontology that makes this outcome possible? What is the relationship between Finn’s World and Lego World?

One is tempted to say, “Simple! There is no ‘Lego World’ per se. It is just a part of Finn’s world. Lego World has no independent reality. Thoughts, words, actions ascribed to the Lego characters are really just Finn’s thoughts, words, actions.”

This is certainly the Classical view…but it is not the position of the film itself!

According to the Classical view, events in Lego World are entirely dependent on events in Finn’s world. There can be no conflict between the worlds because there really is only one world, Finn’s world, and Lego World is just part of it. In the language of pre-20th century philosophy, we would say that events in Lego World are completely determined by events in Finn’s World. In the language of mathematics, we would say that Lego World is a proper subset of Finn’s World.

According to the Classical hypothesis, all consciousness, all awareness resides in Finn (and his dad). The Lego characters have no independent mental activity. Therefore, there can be no displacement between Finn’s consciousness and the consciousness of the characters he creates and directs.

For the most part, the movie does not contradict this view. In most scenes, the apparent consciousness of the Lego characters can be understood merely as a projection of Finn’s consciousness. But unfortunately for the Classical view, there are exceptions to this generalization…more than enough exceptions to invalidate the hypothesis.

For example, looking back through the movie, we see that there were several early clues that Lego World might be embedded in some larger reality. But because these clues pointed to things far beyond the experience of the Lego characters, and because at that point we were experiencing events solely through the eyes and ears of those Lego characters, we missed those clues.

There was Vitruvius’ initial prophesy: “He is coming, cover your butt!” A warning undoubtedly intended for Finn (sometime in the future) but the Lego character who overhears the warning, a guard, merely says, “Cover what?”…and looks around, confused. The warning has no meaning in the context of the guard’s own experience (Lego characters apparently don’t get spanked).

At various times in the movie, President Business (Finn’s dad) speaks in a manner that seems intended to resonate in both worlds…but with slight differences of meaning for each. For example, he says, “Let’s take extra care to follow the (my?) instructions or you’ll be put to sleep (bed?).” Emmet hears (or mishears) the warning and reacts: “Wait, did he say ‘put to sleep’?” But he gives it no further thought; the warning makes no sense in Emmet’s world. (Lego characters apparently don’t get sent to bed early either.)

According to the Classical model, warnings directed at Finn would be perceived by Finn and only by Finn and he would have understood them. But that is not what happens here. Instead, we see that the information is spread between Finn’s World and Lego World and is understood differently, and incompletely, in each world. The two worlds share information but in the process of sharing, its meaning is diluted.

Bricksburg includes a collection of odd items that belong to Lord Business, items that seem out of place in Lego World. The Lego characters understand them as purposeless ‘relics’ but we later come to understand that they are really human artifacts, detritus of the organic world (Band-Aids, golf balls, etc.), that have somehow made their way into the Lego complex.

The ultimate relic is the Piece of Resistance itself, a superglue cap that is certainly out of place in Lego World (as we noted earlier); but the anomaly is unappreciated by the Lego characters.

The Lego characters have an awareness of these relics but because the relics are completely foreign to the Lego characters’ experience, they cannot appreciate their significance or understand their purpose or their origin. For example, they mistake the Krazy Glue cap for some kind of explosive weapon.

Toward the end of the movie, when he falls out of Lego World into Finn’s cellar, Emmet is genuinely startled. He sees Finn but does not understand his relationship to the boy: “What in the world is that? It’s adorable.” Later Emmet refers to Finn (in contrast to his dad) as “smaller creature”. Finn, of course, recognizes Emmet immediately and welcomes him by name, completely bewildering Emmet. There is an imbalance in their relationship caused by an asymmetrical distribution of information between the two heroes.

Most convincingly, Emmet remains completely conscious even though he is outside Lego World and, initially at least, outside of Finn’s awareness. In fact, Finn is so totally unaware of Emmet’s presence in his basement that he actually steps on him. There is no way to account for this if Lego World is merely a proper subset of Finn’s World. Emmet’s independent consciousness clearly falls outside of Finn’s World.

In fact, it is now Emmet who takes control of events in Finn’s world. Emmet endeavors to get Finn’s attention and direct that attention toward the Piece of Resistance that is lying, previously unnoticed on the basement floor. The asymmetrical distribution of information between the two heroes now favors Emmet. There is no way to account for this if Lego World is merely a projection of Finn’s consciousness.

Finn notices Emmet’s gesture, reunites Emmet with the Piece of Resistance and inserts Emmet back into Lego World: “It’s up to you now Emmet.”

So we have two worlds, related to one another yet independent of one another. Clearly, some information is shared by both worlds; just as clearly, each world has information that the other world lacks.

The two worlds share a common timeline but their event narratives are quite different. Yet in the end, when the story line demands that they produce a single result, they both arrive at exactly the same conclusion at exactly the same moment in time. What kind of universe can account for these strange features? Certainly not the Classical universe presupposed in the orthodox hypothesis!

Bell’s Theorem

In 1964, the great Irish mathematician, John Bell, asked about the information content of a simple system consisting of 2 ‘entangled’ quantum particles (e.g. two quantum particles with a common origin). He already knew that measuring the state of one entangled quantum would give us reliable information about the state of the other quantum. But if the particles are distinct and independent, why should this be and how could it be?

Bell considered various classical explanations for this phenomenon but found that they did not precisely account for the phenomenon he sought to model. He then developed an alternative, non-classical theory that did account for the phenomenon in question.

He reasoned that a pair of entangled particles must possess a finite amount of information. While that could be any amount, for our purposes let’s ‘normalize’ the quantity and call it 1.

So let “1” be the total information content of the system, denoted as “T” in the equations below:

T = A + B (where A and B represent the two quanta)

Now, if T = 1, then A and B must add up to 1. So, for example, A could equal 0.5 and B could equal 0.5, and that would be a perfectly valid model so long as A and B are entirely independent of one another.

But that model doesn’t fit the data for entangled particles. The model allows for no sharing of information and therefore there should be no significant correlation between measurements on A and measurements on B. But in fact such a correlation exists so this model contradicts the demonstrated facts of Quantum Mechanics.

So Bell constructed an alternative model (Bell’s Theorem) that he believed would better model the theoretical and experimental results. For that model, he turned to a very simple formula called the “Sum of Squares”. (Most of us first encountered the Sum of Squares as the “Pythagorean Theorem”.)

T² = A² + B²

Now if T = 1, T² = 1 as well. Then A² + B² must also equal 1. Suppose A² = 0.5 and B² = 0.5. What does that mean for A and B?

A = .7 and B = .7 (approximately). Now if we add A + B we find a combined information content of 1.4 (i.e. the square root of 2). But that’s also a problem because how can the information content of the parts exceed the information content of the whole? That would contradict the principle that information is always conserved.

So Bell came to the only possible conclusion. The extra 0.4 quantity of information is actually shared by the two particles; it exists in two places at once. So A has its own information content equal to 0.3 and B has its own information content equal to 0.3 and A and B share information content equal to 0.4.

0.3 + 0.3 + 0.4 = 1

Each particle has 70% of the total information content of the system but because 40% of the total information content of the system is shared information, the total information content of the system remains equal to 1.

Because information is shared by two particles separated by an indefinite distance, the universe modeled by Bell’s Theorem is called non-local. Events in such a universe do not happen in one place at a time. Instead, events happen in at least two places at a time and those two places can be as far apart in space as you wish (that’s why it’s a non-local model of Universe).

The Lego Movie

What does Bell’s Theorem have to do with The Lego Movie? Everything! Bell’s phenomenon is exactly what we experience when we watch the film. The total information content is distributed between Finn’s World and Lego World. But it is not neatly divided in half like a candy bar. Instead, some resides in Finn’s World and some resides in Lego World and some resides in both places at once.

In our example, here’s how it works: of the total information content (1), 30% resides solely in Finn’s World (F) and 30% resides solely in Lego World (L) but 40% resides both in Finn’s World and in Lego World. It’s no wonder that both Finn and the Lego characters misunderstand so much of the information they are given; each sees only 70% of the total picture.

Bell’s Theorem, derived from the science of Quantum Mechanics, is the best approach to understanding The Lego Movie. What confirms this use of the Bell Model is what happens at the end of the film. Both Finn and Emmet attempt to influence Dad/Lord Business. Initially, their efforts are independent and in fact quite different. Gradually, however, the two approaches converge and ultimately they merge completely. There is no way to be certain what the outcome will be…but it is absolutely certain that it will be definite and the same in both worlds.

In Quantum Mechanics, when it is no longer possible to maintain several possible outcomes at the same time, we say that “the wave function collapses”. That is exactly what happens in The Lego Movie. Finn’s World and Lego World offer radically different accounts of the same events and, so long as that persists, the outcome is undetermined. But once an outcome is required (whether by external measurement or observation…or by the story line itself), the wave function collapses and the two worlds become one with a single, definite outcome.

The predictions made by Quantum Mechanics (QM) are more accurate than those of any other theory in the history of science. That QM works is virtually beyond dispute; but why and how QM works is still a bit of a mystery. As a result, there are many different “interpretations of Quantum Mechanics”; here, we will deal with just three.

Early Quantum Mechanics interpreted the data using probability theory. Just as there is a probability that a craps player will roll a 7 and a reciprocal probability that she will roll some other number, so there is probability of finding an electron at point A and a reciprocal probability of finding it someplace else. This interpretation gave us the paradox of Schrödinger’s Cat. The cat is locked in a box inside a hermetically sealed room; no contact with the outside world is possible. The cat’s life (or death) is dependent on a subatomic event that has a finite probability.

Is the cat alive or dead? We can’t know without opening the box and according to this interpretation of Quantum Mechanics, the cat is both alive and dead until such an observation is made.

Hugh Everett suggested an alternative possibility. His “Many Worlds Interpretation of Quantum Mechanics” suggested that the cat was alive in one world and dead in another. At every quantum junction, the world bifurcates into two (or more) worlds corresponding to the different possible outcomes. The bumper sticker for this view reads, “Whatever can happen does happen..somewhere!”

The third interpretation comes from Richard Feynman. His “Sum over Histories” interpretation bridges the gap between Schrödinger and Everett. Feynman proposes that the electron does indeed follow all possible paths simultaneously but that the final result is the sum of all such paths weighted by the relative probability of each. With Feynman, we keep ‘one world’ but that one world reflects contributions from all possible path or outcomes.

Which of these interpretations underlies our film? In The Lego Movie, there were two possible outcomes, either one of which might have occurred, but only one of which actually did occur. Finn’s and Emmet’s pleas could not have led to inconsistent results. Lord Business could not have acceded to Emmet at the same time Dad was denying Finn, or vice-a-versa. Dad and Lord Business could only come to one and the same conclusion regarding the fate of Bricksburg, whatever that conclusion might be. Bricksburg could not be both glued and unglued. So Schrödinger’s model doesn’t work.

Likewise, we have already seen that Lego World and Finn’s World, while different, and not totally independent; throughout the movie they influence one another, however subtly. Ultimately, the two worlds actually merge, so Everett’s interpretation doesn’t work either.

Feynman’s Sum over Histories is the QM model that The Lego Movie demonstrates. Separate but related events occur in the two worlds but the outcome is simply the sum of the histories of these two worlds. If there were only one world, Lego or Finn’s, the end result would probably have been different that it was. Neither Emmet nor Finn could have swayed Lord Business/Dad alone. It is because the unique histories of both worlds converge that we get the happy finale.