Fazacaş Iudita
Babeş-Bolyai University, Cluj-Napoca, România
iuditafazacas@yahoo.com

 

 

Diabolic Geometry

Cube-Rubik- Hypercube

 

 

Abstract: The cube, known as a representation of spatial stability and human perfection, can sometimes have negative sides, thus even leading to a self-destroying system. It can be also seen as the crisis point of modern human being (modern human is homo sapiens) confronted with high speed development and the birth of a new world that he cannot yet manage. According to theoreticians like Hannah Arendt or Françoise Choay this crisis is just beginning. This paper will focus on the possible manifestations of a chaotic world and man’s place in it.

Keywords: Cube movie series; Hyperspace; Cube; Labyrinth; Captivity; Anthropocentrism.

 

 

We are all used with spatial patterns, certain spaces designed for certain kinds of activities, in real and/or fantastic worlds. Some of them are already established, or emblematic, being considered (we evoke them when we are talking about) a certain type of world. Neverland, for example, is a nice, cosy place, full of light and coloured flowers, where a rainbow becomes a ‘must’.

Thinking of imaginary places, the first thing that comes to mind is usually a better, even perfect world. However, this is not the case, as there can be a lot of negative influences around the characters, including the surroundings and a dream can turn into a nightmare.

In the following we deal with a different type of spaces: cubes. Four movies will be discussed: The Cube, a 1969 American teleplay, and the Canadian Cube series: Cube (1997), Cube 2: Hypercube (2002) and Cube 3: Cube Zero (2004). These are mostly Science Fiction movies with a strong psychological dimension.

The Cube (1969) is the most spectacular of them. The chamber in which the character wakes up is similar to the well-known Holodeck^[1] of the Star Trek – series. The idea of a special room that can place people in different realities started with Enterprise (2001-2005), where the Holodeck is presented as a brilliant invention borrowed from an advanced civilization from the 22^nd century.

This kind of holographic room is somehow opposite to the one presented in The Cube. The first striking difference is colour-related: while the Holodeck can be grey (Voyager) or black (The Next Generation), the environment from The Cube is all white. Squares, on the other hand, are a resemblance for these places. Only on the Xyrillian ship, it looks totally different, and quite psychedelic. There is a lot of colour and the entrance is the starting point of a spider-web.

Another difference that needs to be considered is the presence/absence of the door. While the Holodeck clearly has a functional door and people can get in and out, the cube seems to be a one-way place: it is hermetically closed and has no visible door. This lack of control is an important aspect of The Cube, along with the fact that we do not know much about the white room. Compared to this, the Holodeck has a history of its own and can be seen as a character.

Xyrillians used the room to recreate different places where they have been. It is a place that enlarges the universe and that can be used to develop the perspective on the world, to add more colour to it. It could be named a living travel diary. Humans used the Holodeck for recreation or trainings.

The recreational side of the Holodeck is used to keep the mental health of the crew, and prepare them for different scenarios. The personal life of the crew mostly takes place here more than in any other part of the ship, all of their dreams and expectations can be met here. Once you step outside of the room, none of these constructs survives. After a program is finished, it can be erased or saved on record for future use. It is, after all, a computer system.

In Star Trek (Next Generation, episode: Encounter at Far point) we also find out about the existence of an energy-based life form capable of recreating environments exactly like the Holodeck. This being was captured on a planet and it has the power to bring to life any wish. It forms a weird, unseen structure, similar to a spaceship. This special place has many galleries, resembling a labyrinth (quite a common structure when talking about cubes), as it will be shown in the following pages.

The character from The Cube – whose name is never mentioned – isn’t able to find a way out. The Holodeck can perform similar pranks to the people who are using it. Worth mentioning would be TNG: “Elementary, Dear Data”: a holographic advanced version of the Sherlock Holmes story is brought to life, but it becomes too strong. Professor James Moriarty, nothing more than a character, starts to gain self-consciousness and claims his right to become real. For this, he starts by taking hostage the people from the real world, including Data, the android for whom he was actually created in order to have an equal enemy.

Reality versus illusion is one of the things questioned in The Cube. At the very end, the character faces a huge disappointment when he comes to realise that he didn’t actually get out of the cube, that the escape was just another illusion.  By cutting himself accidentally while talking to the director of the show, he realises that his blood is in fact strawberry jam. In this crucial moment everything disappears and we see him back in the white empty cube. It can be inferred here that the character could be a holographic projection, just like Professor Moriarty, but he is not aware of this. While on the Holodeck the illusion is always kept and the environment doesn’t change, in the cube you can see its actual structure.

Another difference between the two is the fact that while on the Holodeck the problems tend to get solved in a positive manner, the cube enjoys torturing the hostage. It resembles a room in a mental institution, which leads to a more psychological interpretation.  Actually, the place is a mixture between the Holodeck and a room from a sanatorium, as it allows both the characters and the bystanders to speculate about reality and psychological issues.

In these conditions, the door remains a central problem of the whole construction.  Where two worlds are the case, the passageway is one of the most important elements. It should be the link between them, a source of communication. It has to be present in Science Fiction productions as well, as the connection must be made. The Cube, however, doesn’t seem to have a door, at least not for the character. He just wakes up already there, just like in the latest Cube series. The difference is that in these series the characters are given the opportunity to find a way out. This is not an easy task, maybe it is just luck, but we know that there is a border. In the teleplay we simply don’t know if there is a reality.

What is strange in The Cube and only here is that a bunch of people are passing by, saying “hello” or having a word or two with the character. After this, they get out as easily as they got in, nothing is stopping them. They make small talk, but no one says anything about the way out, not even when asked. There are some characters, like the manager and Arnie, the maintenance man, that get in the main character’s room and refuse to let him use their door, as they claim he should find his own.

All these characters can be considered a simple projection of the main character’s sick mind, if we would rather prefer a psychologically oriented interpretation. As mentioned above, the room seems quite similar to a sanatorium cell. However, the possibility of it being a sort of Holodeck cannot be ruled out, as we are told, at a certain point, the cube might be the product of a machine. One cannot possibly know if there’s someone watching (the Big Brother) or if there’s no one out there. All the characters and the events that are going on seem to be just a diversion meant to stop him from reaching his goal (getting out). This method is very stressful, and he is not allowed to pull himself together and find a solution. Even if the main character can obtain whatever he wants, he cannot have one moment of silence.

 He is constantly being put in shocking situations by the characters that are passing by and by the objects found there (the bed, a non-functional call button, or a bar). He is stressed by the new telephone (every time he tries to call, the person that answers is Arnie), the manager’s visit and his tips, the designer, a pretended wife and in-laws, and many others. The most amazing “appearance” is another prisoner – that seems to be trapped in the cube for a long time – who gets in his cell by removing a block, near the floor. He quickly becomes anxious and tries to start an argument, as he doesn’t like the main character’s room. He claims that his own room is formed by perfect squares, unlike this one, that is based on rectangles, according to him. The visitor wants to return to the safety of his own cell. Later we find out that he was just an actor.

To sum up, it’s all about illusion, acting, projection, things that only a really upset Holodeck could do to its hostages. It could be all explained also as a reflexion on an overwhelming society and consumerism, a well-known problem of the 70’s. This kind of society seems to resemble a broken Holodeck.

The other three movies treat the same issues; the background is a little changed. A small spatial transformation can be noticed in the Cube series. From a single cube with no door we face a multiplication process: many cubes (a huge Rubik-cube) and too many doors (a manhole on each side of the cube – including on the floor and ceiling of each cube). From a static, closed environment, we move to a dynamic one, still closed. If we want to name this place, we can simply call it a labyrinth. This evolution is actually a change for the worse, a decline that reflects the modern man’s crisis.  From a simple confinement he develops a way of life. Getting out is just a reflex, or a lack of comfort, not the character’s will. He doesn’t really seem to have a purpose in the outside world and he’s in a conflict with his own environment (except for a few characters in Cube Zero).

According to Hannah Arendt, Françoise Choay, and Erick Fromm, it could all be related to modern man not being able to adapt to a world that he created and that he can no longer control, hence the crisis. He refuses the old values, even the Earth as his home, preferring something new, which he can’t handle it yet. He cannot find his own place and this is the starting point of a strange, hostile environment (mechanical or holographic world).

In the first Cube movie (1997) there’s a very strange place, a macro Rubik-cube where people are trapped. This is actually the spatial pattern for all three movies. Unlike the two already mentioned spaces (the Holodeck and The Cube), this one is a mixture between a cube and a labyrinth. Some of the cubes that are forming this system are safe and some are death-traps out of which the characters try to escape.

A sort of evolution can be noticed from the first version to the third movie from the Cube series. Cube (1997) and Cube Zero (2004) are quite similar, at a first glance there seems to be just a difference in design: while the first one is made of coloured cubes and geometrical shapes on the walls, the second one, smaller (25 rooms), resembles a sewer. The crucial difference is actually the exit. The first one had a single entrance-exit door, which had to be found by going through the maze. The other one has two exits and one entrance. To get in, one has to use an elevator that can go either up or down. There are two ways out of the cube: one that can actually get you to the outside world passing through a lake, and another one, a dead-end.

Cube Zero, although it is the movie with the most mythological elements, it is also the easiest one, all the explanations are given to the viewer. The cube is actually an exterminating machinery, situated deep underground, being guarded by two men. They are in charge of making sure things go smoothly. They sometimes play chess, the connection of the game with the whole idea of the movie being obvious: two teams (the humans and the system) are constantly fighting.

Unlike humans, the system has high performance weapons to fight and he is cheathing to. One of the prisoners, a young woman doesn’t have the pink contract (the agreement of being subject in the experiment) which used to be in each file.[2] The senior employees of the system are diabolical. The boss is a cyborg, half machine (the right part) and half human, thus becoming the embedded image of the devil. One of his eyes is mechanical, he’s limping and uses a crutch for thid. He seems to be a real gentleman, but he is worse than a serial killer. His servants have gadgets and they are computer experts, their arrival transforms the old dusty office into a high tech center. Under the same category of hybrids falls one of the prisoners, a soldier with a microchip that ends up being used as a weapon by the system.

The idea of hell is also supported by the exit- mechanism  of the cube. There’s a device with two huge No and Yes buttons, which the guards push according to the prisoner’s answer to a quite strange question: Do you believe in God? If the answer is no, the victim is burned alive. No one knows what’s happening if someone gives an affirmative reply, as no one did so. That means, according to H. Arendt, that the contemporary man has simply broke any connection to divinity, there is no certainty, just doubt. „(God) created a being who bears within a clue about Truth, only to grant it afterwards such abilities to never be able to reach any truth, never be able to have any certainty”^[3]. He is the prisoner of the hell made by himself.

In Hypercube and in Cube Zero, besides the whole construction, is showed the background where the cube is placed. In both can be found elements of an oppressive system, but we can never figure out who’s in charge. The ruler’s presence is shown through a black phone. His employees give him simple answers, for example.: Yes, Sir! Right away, Sir!

In Cube Zero we can see the administrative office and also the file department. Hypercube has a big hall where the bad guys meet for transactions, resembling an old mafia movie. The only strange element is the floor, which seems to be a lake, the remainders after the implosion of the hypercube.

This is also the only cube where almost everything is possible. If the other two cubes are just labyrinthine, this is the most spectacular one. First of all, it seems to be all holographic, an energy field capable to create the illusion of real space, revealed at the end of the story. Before the final moment, all we can see is a multi-dimensional quantum environment (parallel timelines, multiple realities that can communicate with each other). Characters are terrified by seeing themselves dying or already dead. Simon, for example, gets out of control and becomes a serial killer. One of his victims is a character named Jerry, killed a few times in different realities. The killer, Simon, take his watch each time, without knowing the reason of this collecting process. There are also other strange things: gravity-shifting rooms, variable timelines, moving walls, rooms moving at hyper speed, a chopping motion-sensitive hypercube that appears from nowhere and vanishes after killing Jerry (his first death).

In Hypercube, everything is black and white (quite similar to The Cube) and the walls have a discreet drawing of a tesseract on them (cubic prism, four-dimensional cube, or just simply hypercube), but the characters notice this quite late. The whole place is actually a fourth spatial dimension, something considered to be impossible. Although it’s mentioned several times that finding the exit is a matter of time, no one except Keith can figure out the code. The whole construction collapses at 6:06:59, the number (almost diabolical one) which is following them all the way. In this case, solving a spatial problem (finding an exit) is actually a time question.

In the other two cubes, the key was directly related to the space. It’s something expected when talking about coordinates of mechanic constructions. In Cube, the doors were marked with numbers, which had two meanings: they could either show if the room is safe or unsafe and could also indicate its position in the big cube. Cube Zero has a letter code which hides a numerical code. Using the alphabet, they figure out how many rooms the system has; calculate their position using the coordinates.

In these two movies, the characters are walking up and down searching for an exit, just like in a classic labyrinth. According to Eco’s classification of labyrinths there are three types: the classical linear one, with one entrance and one exit, the mannerist one, with multiple ways out, but just one functional, and the rhizomatic labyrinth, where every point which forms the whole construction can be an exit. Each of the movies can be linked with one of the types mentioned above.

Cube (1997), for example, finds its pattern in the mannerist labyrinth, although this assumption could be contested at a first look. The misleading elements are the cubes themselves, which form the entire construction. So many cubes with so many doors can easily lead to a rhizomatic construction, but this fails, as there’s only one bridge that gets activated for a short time (when the cube is in its initial position, which happens periodically). This cube is the only one with the same element as entrance and exit. The entire labyrinth is constructed through the characters movement; they are the ones making its existence real by trying to find the way out. Although it is a mechanical system about which no one could tell how and why it was built, this cube is an anthropocentric place. People are creating paths by moving around and thus making the labyrinth come true. It couldn’t exist without elements like: paths, traps, key-codes for finding the way out. If they stood there, just like Leaven said, the labyrinth couldn’t exist. The characters wouldn’t have had any clue about what’s really going on. Similarly to the character from Cube, they wouldn’t know which door is leading out.

According to Chevalier and Gheerbrant’s Dictionary of Mythology, a trip in a labyrinth is a ritual of initiation. Also, according to the labyrinth types mentioned earlier, Cube has no centre and no monster, besides each character’s dark side. Throughout the movie, the prisoners are fighting their own weaknesses and show hidden parts of themselves. The meaning of the whole trip is that the real world is just like the labyrinth they have just passed:” What is out there? Boundless human stupidity”.^[4] It could also be there is no outside, since there is no difference between in and out (another reason to compare it with The Cube).

Cube Zero is constructed on the same labyrinth pattern like its older version. If Cube had numerous dead ends (some doors could lead to dark gaps), Cube Zero has two exits, out of which only one gets you out in the real world, the other one sends you inside the prison (the equivalent of the dark gap). This is the cube where prisoners are questioned about believing in God and executed. There is no reward for getting so far (just one step to the exit) but death.

The other door is a bit secret, no one really knows about it, but it’s the only way out. Wynn, knowing the place and being helped out from the outside by Dodd (saboteur of the system), succeeds in finding the door and getting out. He is caught and sent back to the cube. However, the balance is restored by the escape of the woman or at least this is what we are led to believe – the classical battle between nature and the system. Cube Zero, unlike Cube, keeps the idea of an outside world, opposite to a diabolical system. From all the movies we discussed, this one is the most optimistic.

Cube Zero is also based on anthropocentricism: we have the pattern of the superhero and values shared by human beings (empathy, commitment, justice, etc). Wynn, named Brain Mann in his own comics, is smart enough to find out what is truly going on and to escape from the cube, even without markers (deleted by Jax). The machines aren’t yet capable of self-support; they need the humans in order to have power. Even Jax, the cyborg devil sent from upstairs, says at a certain point: “Mr Finn, I don’t trust machines. I have a machine to thank for this and this (eye and leg). I need to see them, with my own God-given eye.”^[5] Jax is able to have full view on all the prisoners by activating Haskell’s biochip. By connecting the chip to the computers, the former squad soldier is killed.

These machines and surgeries are nothing more than extensions of the human brain and will, as men leave space for the artificial. At the end we can see Wynn in surgery, tied to a bed. He takes part as subject, by his own will (Jax shows him the signed pink contract), to a scientific experiment. This is most likely a lobotomy, because in the final scene he is mentally handicapped. If we pay attention to the background of the operating room we’ll see a string of hanged corpses behind a veil.  We talk about an exterminating system created by the human brain. Men seem to refuse their own bodies and try to create an artificial, obedient body – the cyborg. All that doesn’t fit or disobeys is sent to vanish in the cube, the perfect killing machine. There is no need to clean after these murders. Once reset, the cube burns everything. “It’s gone into reset mode. The system will restart itself in 10 minutes, the first routine that runs on restart, is a clean sweep. […] flash-incinerates anything still living in all the rooms.”^[6]

If space is the dominant part so far, time becomes the essence in Hypercube. A certain time pressure was also noticed in the other two films: the reset mode from Cube Zero mentioned earlier and how much the human body can last in Cube.

Hypercube seems to be more complicated than the two mechanical-cubes.  Here the prisoners are just moving around without figuring out their position. Jerry, one of them, marks the rooms they’ve been passing by, but this is useless due to the on-going collapse. In the other cubes, even if all the sides of the cube were the same, characters had gravity to establish the first landmark, verticality. The same does the character from The Cube too, even those from the Holodeck in their artificial worlds. In Hypercube everything is relative; to be more specific, they have nothing to grab on to, except their knowledge. With these, they can recognise: parallel time-lines, multiple realities, gravity-shifting rooms, variable time-speed rooms, moving walls, rooms moving with hyper-speed. Also, they recognise the tesseract, a theoretical, impossible object:

 

A hypercube – a four-dimensional cube./ Four dimensions? /All the elements are there. Rooms repeating. Rooms folding in on themselves. Teleportation. It could all very well add up. […] /I thought time was considered to be the fourth dimension./ Sure. That’s one idea. But what if you have a fourth spatial dimension?^[7]

 

Like in the Greek tragedies, everything is in front of them, but they just can’t see it. They are not able to see the clues and understand the solutions.

The fourth special dimension is linked to one of the characters, the greatest hacker of the outside world, Alex Trusk. She is considered to be a myth by some people the group, but proves to be real: she is the innocent blind girl named Sasha. She got in the cube while running from the people from IZON (weapons factory). This leads us back to Cube Zero and their experimenting and exterminating system. Sasha seems to actually be part of the system:  “You forgot the one about Alex Trusk being the first genetically engineered superhuman, bred in a test tube, who now lives and walks amongst us.”^[8] Other characters seems to have connections to the system as well: colonel Maguire (who kills himself), Nobel prize candidate Dr. Rosenzweig (found dead) with his Quantum chaos theory, Ms. Pealy, an insane great theoretical mathematician at IZON (refused the creation of the hypercube: “General, I will not be party to this insanity! […]I don’t care what Alex Trusk says. It’s impossible. And what’s more, it’s inhuman.”^[9], Julia, the lawyer of IZON. Even Kate is part of the system, a kind of agent, she is the only one who gets out and delivers Alex’s device.

Although it is considered perfect, the hypercube is steel uncontrollable:„This place is out of control. It’s not stable.”  Sasha says. Only Sasha’s super-human brain was able to think and design such a place: “I gave them the key to build it – better than they wanted. I gave them a real hypercube.” As mentioned earlier, machines are included in human beings lives and cyborgs were created through experiments. It’s also the case of Sasha, created in vitro and programmed to be a brilliant mind in a disabled body, as she is blind. This transformation is more subtle and interesting than in the case of the cyborgs or of the mechanical killing machines, because both Sasha and the hypercube are more than ordinary machines. It’s even more interesting if we consider the fact that the super-brain is more human than those who created it, even if she can’t see the world which she should destroy by creating weapons against it. That super-brain is actually defeated by this super construction, the hypercube. Sasha is the only one who entered there by her own will, the only place where her enemies (IZON) wouldn’t dare to follow her. That hyperreality slips from the human hands and it starts to self-manage. Even Sasha, the superhuman, isn’t able to control it.

It’s been mentioned earlier that Cube Zero and Cube are anthropocentrical mannerist labyrinths. Hypercube seems to be the newest labyrinth type, the ryzomathic one, where the human being loses its control; man is no longer the centre of the universe, although a brilliant mind started all of this. The point situated in the fourth dimension is really able to displace the Earth, like Archimedes said. The same thing happens with the human beings too. Kafka, one of the well-known novelists who created similar spaces, said in his Journal: “He found the Archimedean point, but used it against himself; it is clear that he was allowed to discover it only under this condition.”^[10] The multiplying point actually evades the human understanding, which can be considered the same with his control. The tesseract is the perfect labyrinth which is not centered on the human being, but on itself. A strange perspective, since we know that labyrinths’ meaning is to initiate the novice. The only thing that they’ve found is “No time to spare.” as Kate said, but it’s not enough to understand that new-born world, which rejects humans. By collapsing and imploding, it refuses everything, it is destroying everything which refuses to leave, or is unable to do so. To be a bit clearer, the hypercube is forcing the prisoners to go to its beginning point, it just wants to throw them out. Opposite to the other cubes already mentioned, this labyrinth is based on a point, and not on a geometrical figure: the square, or the cube, it seems to be pure geometry just by its shape. As fourth dimension is more than that. Pure thinking is surpassing geometry, our three-dimensional well known world, just like Hannah Arendt said in Human Condition: “Modern Mathematics freed man from terrestrial chains, freed his knowledge from the bondage of its limits. (…) Geometry is replaced with algebra, a symbolic, non-spatial language”^[11] Once started, it’s moving along, without any reason or purpose.

The man trapped in The Cube can experience the same thing like those from Hypercube. It may sound weird, but it would fit in the hyperreality. Even if we can’t talk about labyrinths, complicated shapes and all those strange things happening in Hypercube, there still are some elements which can lead to this conclusion. First of all, there is no door and a lot of things appear from the middle of nowhere, just like in the hypercube. Also, The Cube can be a stabilized hyper-space, which is just playing with his hostage. All of this is possible because the human mind is trying to force its boundaries and ends up turning against its own self. The result is a loss of control, consciousness and centrality. The artificial wins. „He was pushed back to life, closed in inner introspection, where the highlight of the experience is the calculation processes of the mind emptied of any content, the mind’s game with itself”^[12]

Holodeck (Star Trek), the holographic room, doesn’t simply create schematic or empty spaces, but surrogate realities. A person could live in one of these realities, without knowing it is not real, just like Professor James Moriarty, who claimed his right to become real when he figured out that he is a simple computer projection. After this long discussion regarding mechanical traps, killing machines and hyperspace, the Holodeck seems to be a happy ending to all those stories about human versus machines. Here, everything is settled, control is established again: humans control the computer, which controls the hyperreality. It is a micro-space, if we consider the whole Universe. The moment of crisis represented by the tear between the human being and its environment discussed by Arendt and others, clearly represented in The Cube and Cube series, is overcome in Star Trek. In these series, humans seem to have found their place in Space, and they also managed to accept that they aren’t the most important part of the system, they moved on from the idea of anthropocentrism. However, we don’t have all the pieces of the puzzle here. We can talk about the beginning of the crisis and we can see the world after it gained its balance, but we cannot know how the human beings managed to restore it. We are still at the beginning of fighting these cubes and the labyrinths within.

 

 

 

Bibliography

 

Henson, Jim, The cube (1969), pinchyawhoasnarm, Web, 05.05.2013

Natali, Vincenzo, Cube (1997), pinchyawhoasnarm, Web, 25.05.2013

Hood, Sean, Cube 2: Hypercube (2002), pinchyawhoasnarm, Web, 26.05.2013

Barbarash, Ernie Cube Zero (2004), pinchyawhoasnarm, Web, 27.05.2013

Cube Script – Dialogue Transcriptscript-o-rama.com , nd. Web 30.01.2014

Cube 2: Hypercube (2002) Movie Script, Springfield! Springfield! database, UK, nd. Web 30.01.2014

Cube Zero (2004) Movie Script,Springfield! Springfield! database, UK, nd. Web 30.01.2014

Kafka, Franz, Jurnal, trad. Radu Gabriel Pârvu, Bucureşti, Ed. RAO, 2006

Arendt, Hannah Condiţia umană, trad. Claudiu Vereş şi Gabriela Chindea, Cluj, Ed. Casa Cărţii de Ştiinţă (Ideea Design & Print), 2007

Chevalier, Jean, Gheerbrant, Alain, Dicţionar de simboluri: mituri, vise, obiceiuri, gesturi, forme, figuri, culori, numere, trad Micaela Slăvescu, Laurenţiu Zoicaş et alii, Iaşi, Polirom, 2009 (1969)

Eco, Umberto, De la arbore sprelabirint. Studiiistoricedespresemnşi interpretare, trad. Ştefania Mincu, Iaşi, Ed. Polirom, 2009

Choay, Françoise, Pentru o antropologie a spaţiului, trad. Kázmér Kovács, Bucureşti, Ed. Revista Urbanismului, 2011

 

 

Notes

Fazacaş Iudita
Babeş-Bolyai University, Cluj-Napoca, România
iuditafazacas@yahoo.com

 

 

Diabolic Geometry

Cube-Rubik- Hypercube

 

 

Abstract: The cube, known as a representation of spatial stability and human perfection, can sometimes have negative sides, thus even leading to a self-destroying system. It can be also seen as the crisis point of modern human being (modern human is homo sapiens) confronted with high speed development and the birth of a new world that he cannot yet manage. According to theoreticians like Hannah Arendt or Françoise Choay this crisis is just beginning. This paper will focus on the possible manifestations of a chaotic world and man’s place in it.

Keywords: Cube movie series; Hyperspace; Cube; Labyrinth; Captivity; Anthropocentrism.

 

 

We are all used with spatial patterns, certain spaces designed for certain kinds of activities, in real and/or fantastic worlds. Some of them are already established, or emblematic, being considered (we evoke them when we are talking about) a certain type of world. Neverland, for example, is a nice, cosy place, full of light and coloured flowers, where a rainbow becomes a ‘must’.

Thinking of imaginary places, the first thing that comes to mind is usually a better, even perfect world. However, this is not the case, as there can be a lot of negative influences around the characters, including the surroundings and a dream can turn into a nightmare.

In the following we deal with a different type of spaces: cubes. Four movies will be discussed: The Cube, a 1969 American teleplay, and the Canadian Cube series: Cube (1997), Cube 2: Hypercube (2002) and Cube 3: Cube Zero (2004). These are mostly Science Fiction movies with a strong psychological dimension.

The Cube (1969) is the most spectacular of them. The chamber in which the character wakes up is similar to the well-known Holodeck^[1] of the Star Trek – series. The idea of a special room that can place people in different realities started with Enterprise (2001-2005), where the Holodeck is presented as a brilliant invention borrowed from an advanced civilization from the 22^nd century.

This kind of holographic room is somehow opposite to the one presented in The Cube. The first striking difference is colour-related: while the Holodeck can be grey (Voyager) or black (The Next Generation), the environment from The Cube is all white. Squares, on the other hand, are a resemblance for these places. Only on the Xyrillian ship, it looks totally different, and quite psychedelic. There is a lot of colour and the entrance is the starting point of a spider-web.

Another difference that needs to be considered is the presence/absence of the door. While the Holodeck clearly has a functional door and people can get in and out, the cube seems to be a one-way place: it is hermetically closed and has no visible door. This lack of control is an important aspect of The Cube, along with the fact that we do not know much about the white room. Compared to this, the Holodeck has a history of its own and can be seen as a character.

Xyrillians used the room to recreate different places where they have been. It is a place that enlarges the universe and that can be used to develop the perspective on the world, to add more colour to it. It could be named a living travel diary. Humans used the Holodeck for recreation or trainings.

The recreational side of the Holodeck is used to keep the mental health of the crew, and prepare them for different scenarios. The personal life of the crew mostly takes place here more than in any other part of the ship, all of their dreams and expectations can be met here. Once you step outside of the room, none of these constructs survives. After a program is finished, it can be erased or saved on record for future use. It is, after all, a computer system.

In Star Trek (Next Generation, episode: Encounter at Far point) we also find out about the existence of an energy-based life form capable of recreating environments exactly like the Holodeck. This being was captured on a planet and it has the power to bring to life any wish. It forms a weird, unseen structure, similar to a spaceship. This special place has many galleries, resembling a labyrinth (quite a common structure when talking about cubes), as it will be shown in the following pages.

The character from The Cube – whose name is never mentioned – isn’t able to find a way out. The Holodeck can perform similar pranks to the people who are using it. Worth mentioning would be TNG: “Elementary, Dear Data”: a holographic advanced version of the Sherlock Holmes story is brought to life, but it becomes too strong. Professor James Moriarty, nothing more than a character, starts to gain self-consciousness and claims his right to become real. For this, he starts by taking hostage the people from the real world, including Data, the android for whom he was actually created in order to have an equal enemy.

Reality versus illusion is one of the things questioned in The Cube. At the very end, the character faces a huge disappointment when he comes to realise that he didn’t actually get out of the cube, that the escape was just another illusion.  By cutting himself accidentally while talking to the director of the show, he realises that his blood is in fact strawberry jam. In this crucial moment everything disappears and we see him back in the white empty cube. It can be inferred here that the character could be a holographic projection, just like Professor Moriarty, but he is not aware of this. While on the Holodeck the illusion is always kept and the environment doesn’t change, in the cube you can see its actual structure.

Another difference between the two is the fact that while on the Holodeck the problems tend to get solved in a positive manner, the cube enjoys torturing the hostage. It resembles a room in a mental institution, which leads to a more psychological interpretation.  Actually, the place is a mixture between the Holodeck and a room from a sanatorium, as it allows both the characters and the bystanders to speculate about reality and psychological issues.

In these conditions, the door remains a central problem of the whole construction.  Where two worlds are the case, the passageway is one of the most important elements. It should be the link between them, a source of communication. It has to be present in Science Fiction productions as well, as the connection must be made. The Cube, however, doesn’t seem to have a door, at least not for the character. He just wakes up already there, just like in the latest Cube series. The difference is that in these series the characters are given the opportunity to find a way out. This is not an easy task, maybe it is just luck, but we know that there is a border. In the teleplay we simply don’t know if there is a reality.

What is strange in The Cube and only here is that a bunch of people are passing by, saying “hello” or having a word or two with the character. After this, they get out as easily as they got in, nothing is stopping them. They make small talk, but no one says anything about the way out, not even when asked. There are some characters, like the manager and Arnie, the maintenance man, that get in the main character’s room and refuse to let him use their door, as they claim he should find his own.

All these characters can be considered a simple projection of the main character’s sick mind, if we would rather prefer a psychologically oriented interpretation. As mentioned above, the room seems quite similar to a sanatorium cell. However, the possibility of it being a sort of Holodeck cannot be ruled out, as we are told, at a certain point, the cube might be the product of a machine. One cannot possibly know if there’s someone watching (the Big Brother) or if there’s no one out there. All the characters and the events that are going on seem to be just a diversion meant to stop him from reaching his goal (getting out). This method is very stressful, and he is not allowed to pull himself together and find a solution. Even if the main character can obtain whatever he wants, he cannot have one moment of silence.

 He is constantly being put in shocking situations by the characters that are passing by and by the objects found there (the bed, a non-functional call button, or a bar). He is stressed by the new telephone (every time he tries to call, the person that answers is Arnie), the manager’s visit and his tips, the designer, a pretended wife and in-laws, and many others. The most amazing “appearance” is another prisoner – that seems to be trapped in the cube for a long time – who gets in his cell by removing a block, near the floor. He quickly becomes anxious and tries to start an argument, as he doesn’t like the main character’s room. He claims that his own room is formed by perfect squares, unlike this one, that is based on rectangles, according to him. The visitor wants to return to the safety of his own cell. Later we find out that he was just an actor.

To sum up, it’s all about illusion, acting, projection, things that only a really upset Holodeck could do to its hostages. It could be all explained also as a reflexion on an overwhelming society and consumerism, a well-known problem of the 70’s. This kind of society seems to resemble a broken Holodeck.

The other three movies treat the same issues; the background is a little changed. A small spatial transformation can be noticed in the Cube series. From a single cube with no door we face a multiplication process: many cubes (a huge Rubik-cube) and too many doors (a manhole on each side of the cube – including on the floor and ceiling of each cube). From a static, closed environment, we move to a dynamic one, still closed. If we want to name this place, we can simply call it a labyrinth. This evolution is actually a change for the worse, a decline that reflects the modern man’s crisis.  From a simple confinement he develops a way of life. Getting out is just a reflex, or a lack of comfort, not the character’s will. He doesn’t really seem to have a purpose in the outside world and he’s in a conflict with his own environment (except for a few characters in Cube Zero).

According to Hannah Arendt, Françoise Choay, and Erick Fromm, it could all be related to modern man not being able to adapt to a world that he created and that he can no longer control, hence the crisis. He refuses the old values, even the Earth as his home, preferring something new, which he can’t handle it yet. He cannot find his own place and this is the starting point of a strange, hostile environment (mechanical or holographic world).

In the first Cube movie (1997) there’s a very strange place, a macro Rubik-cube where people are trapped. This is actually the spatial pattern for all three movies. Unlike the two already mentioned spaces (the Holodeck and The Cube), this one is a mixture between a cube and a labyrinth. Some of the cubes that are forming this system are safe and some are death-traps out of which the characters try to escape.

A sort of evolution can be noticed from the first version to the third movie from the Cube series. Cube (1997) and Cube Zero (2004) are quite similar, at a first glance there seems to be just a difference in design: while the first one is made of coloured cubes and geometrical shapes on the walls, the second one, smaller (25 rooms), resembles a sewer. The crucial difference is actually the exit. The first one had a single entrance-exit door, which had to be found by going through the maze. The other one has two exits and one entrance. To get in, one has to use an elevator that can go either up or down. There are two ways out of the cube: one that can actually get you to the outside world passing through a lake, and another one, a dead-end.

Cube Zero, although it is the movie with the most mythological elements, it is also the easiest one, all the explanations are given to the viewer. The cube is actually an exterminating machinery, situated deep underground, being guarded by two men. They are in charge of making sure things go smoothly. They sometimes play chess, the connection of the game with the whole idea of the movie being obvious: two teams (the humans and the system) are constantly fighting.

Unlike humans, the system has high performance weapons to fight and he is cheathing to. One of the prisoners, a young woman doesn’t have the pink contract (the agreement of being subject in the experiment) which used to be in each file.[2] The senior employees of the system are diabolical. The boss is a cyborg, half machine (the right part) and half human, thus becoming the embedded image of the devil. One of his eyes is mechanical, he’s limping and uses a crutch for thid. He seems to be a real gentleman, but he is worse than a serial killer. His servants have gadgets and they are computer experts, their arrival transforms the old dusty office into a high tech center. Under the same category of hybrids falls one of the prisoners, a soldier with a microchip that ends up being used as a weapon by the system.

The idea of hell is also supported by the exit- mechanism  of the cube. There’s a device with two huge No and Yes buttons, which the guards push according to the prisoner’s answer to a quite strange question: Do you believe in God? If the answer is no, the victim is burned alive. No one knows what’s happening if someone gives an affirmative reply, as no one did so. That means, according to H. Arendt, that the contemporary man has simply broke any connection to divinity, there is no certainty, just doubt. „(God) created a being who bears within a clue about Truth, only to grant it afterwards such abilities to never be able to reach any truth, never be able to have any certainty”^[3]. He is the prisoner of the hell made by himself.

In Hypercube and in Cube Zero, besides the whole construction, is showed the background where the cube is placed. In both can be found elements of an oppressive system, but we can never figure out who’s in charge. The ruler’s presence is shown through a black phone. His employees give him simple answers, for example.: Yes, Sir! Right away, Sir!

In Cube Zero we can see the administrative office and also the file department. Hypercube has a big hall where the bad guys meet for transactions, resembling an old mafia movie. The only strange element is the floor, which seems to be a lake, the remainders after the implosion of the hypercube.

This is also the only cube where almost everything is possible. If the other two cubes are just labyrinthine, this is the most spectacular one. First of all, it seems to be all holographic, an energy field capable to create the illusion of real space, revealed at the end of the story. Before the final moment, all we can see is a multi-dimensional quantum environment (parallel timelines, multiple realities that can communicate with each other). Characters are terrified by seeing themselves dying or already dead. Simon, for example, gets out of control and becomes a serial killer. One of his victims is a character named Jerry, killed a few times in different realities. The killer, Simon, take his watch each time, without knowing the reason of this collecting process. There are also other strange things: gravity-shifting rooms, variable timelines, moving walls, rooms moving at hyper speed, a chopping motion-sensitive hypercube that appears from nowhere and vanishes after killing Jerry (his first death).

In Hypercube, everything is black and white (quite similar to The Cube) and the walls have a discreet drawing of a tesseract on them (cubic prism, four-dimensional cube, or just simply hypercube), but the characters notice this quite late. The whole place is actually a fourth spatial dimension, something considered to be impossible. Although it’s mentioned several times that finding the exit is a matter of time, no one except Keith can figure out the code. The whole construction collapses at 6:06:59, the number (almost diabolical one) which is following them all the way. In this case, solving a spatial problem (finding an exit) is actually a time question.

In the other two cubes, the key was directly related to the space. It’s something expected when talking about coordinates of mechanic constructions. In Cube, the doors were marked with numbers, which had two meanings: they could either show if the room is safe or unsafe and could also indicate its position in the big cube. Cube Zero has a letter code which hides a numerical code. Using the alphabet, they figure out how many rooms the system has; calculate their position using the coordinates.

In these two movies, the characters are walking up and down searching for an exit, just like in a classic labyrinth. According to Eco’s classification of labyrinths there are three types: the classical linear one, with one entrance and one exit, the mannerist one, with multiple ways out, but just one functional, and the rhizomatic labyrinth, where every point which forms the whole construction can be an exit. Each of the movies can be linked with one of the types mentioned above.

Cube (1997), for example, finds its pattern in the mannerist labyrinth, although this assumption could be contested at a first look. The misleading elements are the cubes themselves, which form the entire construction. So many cubes with so many doors can easily lead to a rhizomatic construction, but this fails, as there’s only one bridge that gets activated for a short time (when the cube is in its initial position, which happens periodically). This cube is the only one with the same element as entrance and exit. The entire labyrinth is constructed through the characters movement; they are the ones making its existence real by trying to find the way out. Although it is a mechanical system about which no one could tell how and why it was built, this cube is an anthropocentric place. People are creating paths by moving around and thus making the labyrinth come true. It couldn’t exist without elements like: paths, traps, key-codes for finding the way out. If they stood there, just like Leaven said, the labyrinth couldn’t exist. The characters wouldn’t have had any clue about what’s really going on. Similarly to the character from Cube, they wouldn’t know which door is leading out.

According to Chevalier and Gheerbrant’s Dictionary of Mythology, a trip in a labyrinth is a ritual of initiation. Also, according to the labyrinth types mentioned earlier, Cube has no centre and no monster, besides each character’s dark side. Throughout the movie, the prisoners are fighting their own weaknesses and show hidden parts of themselves. The meaning of the whole trip is that the real world is just like the labyrinth they have just passed:” What is out there? Boundless human stupidity”.^[4] It could also be there is no outside, since there is no difference between in and out (another reason to compare it with The Cube).

Cube Zero is constructed on the same labyrinth pattern like its older version. If Cube had numerous dead ends (some doors could lead to dark gaps), Cube Zero has two exits, out of which only one gets you out in the real world, the other one sends you inside the prison (the equivalent of the dark gap). This is the cube where prisoners are questioned about believing in God and executed. There is no reward for getting so far (just one step to the exit) but death.

The other door is a bit secret, no one really knows about it, but it’s the only way out. Wynn, knowing the place and being helped out from the outside by Dodd (saboteur of the system), succeeds in finding the door and getting out. He is caught and sent back to the cube. However, the balance is restored by the escape of the woman or at least this is what we are led to believe – the classical battle between nature and the system. Cube Zero, unlike Cube, keeps the idea of an outside world, opposite to a diabolical system. From all the movies we discussed, this one is the most optimistic.

Cube Zero is also based on anthropocentricism: we have the pattern of the superhero and values shared by human beings (empathy, commitment, justice, etc). Wynn, named Brain Mann in his own comics, is smart enough to find out what is truly going on and to escape from the cube, even without markers (deleted by Jax). The machines aren’t yet capable of self-support; they need the humans in order to have power. Even Jax, the cyborg devil sent from upstairs, says at a certain point: “Mr Finn, I don’t trust machines. I have a machine to thank for this and this (eye and leg). I need to see them, with my own God-given eye.”^[5] Jax is able to have full view on all the prisoners by activating Haskell’s biochip. By connecting the chip to the computers, the former squad soldier is killed.

These machines and surgeries are nothing more than extensions of the human brain and will, as men leave space for the artificial. At the end we can see Wynn in surgery, tied to a bed. He takes part as subject, by his own will (Jax shows him the signed pink contract), to a scientific experiment. This is most likely a lobotomy, because in the final scene he is mentally handicapped. If we pay attention to the background of the operating room we’ll see a string of hanged corpses behind a veil.  We talk about an exterminating system created by the human brain. Men seem to refuse their own bodies and try to create an artificial, obedient body – the cyborg. All that doesn’t fit or disobeys is sent to vanish in the cube, the perfect killing machine. There is no need to clean after these murders. Once reset, the cube burns everything. “It’s gone into reset mode. The system will restart itself in 10 minutes, the first routine that runs on restart, is a clean sweep. […] flash-incinerates anything still living in all the rooms.”^[6]

If space is the dominant part so far, time becomes the essence in Hypercube. A certain time pressure was also noticed in the other two films: the reset mode from Cube Zero mentioned earlier and how much the human body can last in Cube.

Hypercube seems to be more complicated than the two mechanical-cubes.  Here the prisoners are just moving around without figuring out their position. Jerry, one of them, marks the rooms they’ve been passing by, but this is useless due to the on-going collapse. In the other cubes, even if all the sides of the cube were the same, characters had gravity to establish the first landmark, verticality. The same does the character from The Cube too, even those from the Holodeck in their artificial worlds. In Hypercube everything is relative; to be more specific, they have nothing to grab on to, except their knowledge. With these, they can recognise: parallel time-lines, multiple realities, gravity-shifting rooms, variable time-speed rooms, moving walls, rooms moving with hyper-speed. Also, they recognise the tesseract, a theoretical, impossible object:

 

A hypercube – a four-dimensional cube./ Four dimensions? /All the elements are there. Rooms repeating. Rooms folding in on themselves. Teleportation. It could all very well add up. […] /I thought time was considered to be the fourth dimension./ Sure. That’s one idea. But what if you have a fourth spatial dimension?^[7]

 

Like in the Greek tragedies, everything is in front of them, but they just can’t see it. They are not able to see the clues and understand the solutions.

The fourth special dimension is linked to one of the characters, the greatest hacker of the outside world, Alex Trusk. She is considered to be a myth by some people the group, but proves to be real: she is the innocent blind girl named Sasha. She got in the cube while running from the people from IZON (weapons factory). This leads us back to Cube Zero and their experimenting and exterminating system. Sasha seems to actually be part of the system:  “You forgot the one about Alex Trusk being the first genetically engineered superhuman, bred in a test tube, who now lives and walks amongst us.”^[8] Other characters seems to have connections to the system as well: colonel Maguire (who kills himself), Nobel prize candidate Dr. Rosenzweig (found dead) with his Quantum chaos theory, Ms. Pealy, an insane great theoretical mathematician at IZON (refused the creation of the hypercube: “General, I will not be party to this insanity! […]I don’t care what Alex Trusk says. It’s impossible. And what’s more, it’s inhuman.”^[9], Julia, the lawyer of IZON. Even Kate is part of the system, a kind of agent, she is the only one who gets out and delivers Alex’s device.

Although it is considered perfect, the hypercube is steel uncontrollable:„This place is out of control. It’s not stable.”  Sasha says. Only Sasha’s super-human brain was able to think and design such a place: “I gave them the key to build it – better than they wanted. I gave them a real hypercube.” As mentioned earlier, machines are included in human beings lives and cyborgs were created through experiments. It’s also the case of Sasha, created in vitro and programmed to be a brilliant mind in a disabled body, as she is blind. This transformation is more subtle and interesting than in the case of the cyborgs or of the mechanical killing machines, because both Sasha and the hypercube are more than ordinary machines. It’s even more interesting if we consider the fact that the super-brain is more human than those who created it, even if she can’t see the world which she should destroy by creating weapons against it. That super-brain is actually defeated by this super construction, the hypercube. Sasha is the only one who entered there by her own will, the only place where her enemies (IZON) wouldn’t dare to follow her. That hyperreality slips from the human hands and it starts to self-manage. Even Sasha, the superhuman, isn’t able to control it.

It’s been mentioned earlier that Cube Zero and Cube are anthropocentrical mannerist labyrinths. Hypercube seems to be the newest labyrinth type, the ryzomathic one, where the human being loses its control; man is no longer the centre of the universe, although a brilliant mind started all of this. The point situated in the fourth dimension is really able to displace the Earth, like Archimedes said. The same thing happens with the human beings too. Kafka, one of the well-known novelists who created similar spaces, said in his Journal: “He found the Archimedean point, but used it against himself; it is clear that he was allowed to discover it only under this condition.”^[10] The multiplying point actually evades the human understanding, which can be considered the same with his control. The tesseract is the perfect labyrinth which is not centered on the human being, but on itself. A strange perspective, since we know that labyrinths’ meaning is to initiate the novice. The only thing that they’ve found is “No time to spare.” as Kate said, but it’s not enough to understand that new-born world, which rejects humans. By collapsing and imploding, it refuses everything, it is destroying everything which refuses to leave, or is unable to do so. To be a bit clearer, the hypercube is forcing the prisoners to go to its beginning point, it just wants to throw them out. Opposite to the other cubes already mentioned, this labyrinth is based on a point, and not on a geometrical figure: the square, or the cube, it seems to be pure geometry just by its shape. As fourth dimension is more than that. Pure thinking is surpassing geometry, our three-dimensional well known world, just like Hannah Arendt said in Human Condition: “Modern Mathematics freed man from terrestrial chains, freed his knowledge from the bondage of its limits. (…) Geometry is replaced with algebra, a symbolic, non-spatial language”^[11] Once started, it’s moving along, without any reason or purpose.

The man trapped in The Cube can experience the same thing like those from Hypercube. It may sound weird, but it would fit in the hyperreality. Even if we can’t talk about labyrinths, complicated shapes and all those strange things happening in Hypercube, there still are some elements which can lead to this conclusion. First of all, there is no door and a lot of things appear from the middle of nowhere, just like in the hypercube. Also, The Cube can be a stabilized hyper-space, which is just playing with his hostage. All of this is possible because the human mind is trying to force its boundaries and ends up turning against its own self. The result is a loss of control, consciousness and centrality. The artificial wins. „He was pushed back to life, closed in inner introspection, where the highlight of the experience is the calculation processes of the mind emptied of any content, the mind’s game with itself”^[12]

Holodeck (Star Trek), the holographic room, doesn’t simply create schematic or empty spaces, but surrogate realities. A person could live in one of these realities, without knowing it is not real, just like Professor James Moriarty, who claimed his right to become real when he figured out that he is a simple computer projection. After this long discussion regarding mechanical traps, killing machines and hyperspace, the Holodeck seems to be a happy ending to all those stories about human versus machines. Here, everything is settled, control is established again: humans control the computer, which controls the hyperreality. It is a micro-space, if we consider the whole Universe. The moment of crisis represented by the tear between the human being and its environment discussed by Arendt and others, clearly represented in The Cube and Cube series, is overcome in Star Trek. In these series, humans seem to have found their place in Space, and they also managed to accept that they aren’t the most important part of the system, they moved on from the idea of anthropocentrism. However, we don’t have all the pieces of the puzzle here. We can talk about the beginning of the crisis and we can see the world after it gained its balance, but we cannot know how the human beings managed to restore it. We are still at the beginning of fighting these cubes and the labyrinths within.

 

 

 

Bibliography

 

Henson, Jim, The cube (1969), pinchyawhoasnarm, Web, 05.05.2013

Natali, Vincenzo, Cube (1997), pinchyawhoasnarm, Web, 25.05.2013

Hood, Sean, Cube 2: Hypercube (2002), pinchyawhoasnarm, Web, 26.05.2013

Barbarash, Ernie Cube Zero (2004), pinchyawhoasnarm, Web, 27.05.2013

Cube Script – Dialogue Transcriptscript-o-rama.com , nd. Web 30.01.2014

Cube 2: Hypercube (2002) Movie Script, Springfield! Springfield! database, UK, nd. Web 30.01.2014

Cube Zero (2004) Movie Script,Springfield! Springfield! database, UK, nd. Web 30.01.2014

Kafka, Franz, Jurnal, trad. Radu Gabriel Pârvu, Bucureşti, Ed. RAO, 2006

Arendt, Hannah Condiţia umană, trad. Claudiu Vereş şi Gabriela Chindea, Cluj, Ed. Casa Cărţii de Ştiinţă (Ideea Design & Print), 2007

Chevalier, Jean, Gheerbrant, Alain, Dicţionar de simboluri: mituri, vise, obiceiuri, gesturi, forme, figuri, culori, numere, trad Micaela Slăvescu, Laurenţiu Zoicaş et alii, Iaşi, Polirom, 2009 (1969)

Eco, Umberto, De la arbore sprelabirint. Studiiistoricedespresemnşi interpretare, trad. Ştefania Mincu, Iaşi, Ed. Polirom, 2009

Choay, Françoise, Pentru o antropologie a spaţiului, trad. Kázmér Kovács, Bucureşti, Ed. Revista Urbanismului, 2011

 

 

Notes