I've been wondering lately why I feel like I hear more and more hints of Chopin's music in various things relating to video games.

Out the top of my head I can think of the Chopin game on iPad, starring the legendary composer resurrected by the muses to battle the corporate influences of today's music industry.

Before that, there was of course Eternal Sonata, where Chopin is the actual narrator.

Recently, I was surprised to hear the familiar melody of what was to become Chopin's own funeral music, his Prelude in e-minor, op.28 no.4, used in a tune on the Fez soundtrack.

And today I saw the trailer for Phantom Pain where, first at around the 33 second mark but most noticeably when the title card appears, a famous burst from one of Chopin's tunes is heard. I will add the title once I remember exactly which song it is.

As a little side-note: did you know that Chopin's character in Eternal Sonata actually has a special attack called Phantom Pain?

I wonder when we'll start to see more composers getting their time in the spotlight of games.

I just finished watching episode 6 of season 2 of Game of Thrones. I've really liked what's done of this season. But I've been distracted by the weird feeling of seeing all those wide shots and scenes from North of The Wall, recognizing it as the area less than two hours' away from my home, where I go hiking and running regularly. Meanwhile the characters are talking about how hostile the area is, dramatically wondering who would possibly want to defend and live there. It fits the mood and story perfectly, of course, but still funny to me.

Do you guys have any stories or experience of recognizing hometowns and familiar areas in film or television, or even video games? I imagine lots of you who live in the larger cities have seen something familiar, but any input's welcome, yo.

Peace!

A quick essay on philosophical Daoism and its self-referential nature, along with examples from painting and Japanese haiku poetry. I fully realize that this is most likely far outside the general field of interest within the community, but the few who might enjoy I hope you do.

An old pond,

a frog leaps in,

sound of water.

-Matsuo Basho, 1686

This humble sounding haiku is held as the token of the esoteric and seemingly complicated haiku art form. It is timeless and impersonal but open to anyone's enjoyment and interpretation. The reader has no need for knowledge of anything other than general awareness of nature to recognize the subject matter; the poem references nothing but itself. Although many of Basho's haikus were referential, for example autobiographical or political, this one of the old pond helps to emphasize what it is about a well made haiku that catches in the reader's memory and imagination. Furthermore to my point in this short paper, it so happens that a good haiku shares its qualities with daoist thought.

In so many words, a daoist must forget himself. Daoist texts differ in some principles, between Zhuangzi's and Laozi's teachings for example, but this self-forgetfulness is apparent in all throughout. The daoist can not literally step outside himself, but he reaches a more desirable state of mind by training himself to think less and less until he is free of thoughts or opinions of the surrounding world, for some time at least. That is, his mind stops aligning and comparing itself to exterior circumstances; he stops referencing, until there is hardly even a “he” left. This hopefully sublime state of mind could be described as Ego-less; there is no thinker, only thought. Zhuangzi's tales are rich of allegories for this. The story of the dancing cook and the ox, to mention one, has the cook describing his mastery as if his “...sense organs stop and the [inspiration] takes control”. The cook has stopped trying, lets go and simple does what he is inspired to do.

With time, the daoist's way towards the emptiness, the doing-without-doing, that Basho's haiku inspires will come more naturally to him until he will not need any inspiration or help. Like the cook in Zhuangzi's story, the daoist stops attempting and simply does, is or self-so's. This way is a “fasting of the mind”, as Zhuangzi has Confucius call it in one story. There, Confucius tells his pupil that if he merges his intentions into a singularity, he will come to hear with the mind rather than the ears. That way, he will hear with the vital energy (qi) rather than the mind. The vital energy is then an emptiness, and in this emptiness The Course (dao) will gather. (Ziporyn, Zhuangzi p.26-27)

In the haiku of the old pond and the frog, the poet has not put himself in the center of a scenery and described it, but observed and described it so that nothing more than the pond and the frog need exist for this tranquil beauty to exist and take place. He makes the poem seem completely ignorant of him. There is no chemistry between subject and object there; no viewer vs. viewed. If one observes nature without an ego, one should find poetry. If one observes poetry without an ego, one should find nature. From an observation of something like the pond and the frog in this haiku, one should experience the pond and the frog and not what the poet thinks or feels about the pond and the frog. They do not need the poet's help.

Is this a perfectly non-referential art form then? Could such a thing exist? Generally, there is always thought to be a pair of subject and object in most circumstances. Art and philosophy are no exceptions, since both heavily involve an observer and the observed. It seems like there could rarely if ever be only an observer or only the observed, since both exist in reference to the other, like left vs. right. A haiku, much like a daoist, may never be able to completely eliminate all traces of a perspective, but the art and mastery of attempting it is all the more noble for that reason. The haiku and the daoist should likely be seen as self-referential, not in the sense of repeating to themselves “Me, myself, I, Ego...” but more in the sense of being “isolated” in a way. One should take the word 'isolated' with precaution, since it is a characteristic of Daoism that everything is connected and in flux. I use the word here to mean that each haiku, just like each daoist (especially during meditation), is a specific case or occurrence experiencing itself at one specific moment.

This specified self-referential nature has its echoes in other forms or strands of art, besides the meditative Chinese and Japanese paintings and poetry. Magritte's fittingly named painting The Treachery of Images, which shows a common tobacco pipe under which is written “Ceci n'est pas une pipe.”, is one of the more famous examples. It is so mundane and minimal, yet sticks in each viewer's memory as profound and remarkable. It portrays a pipe only to deny the fact of its being a pipe, which it of course is not, seeing as it is only a painting. In other words, it only has one reference, itself, and chooses its reference to the viewer to negate it.

Others of Magritte's paintings play along the same fine, tantalizing line, such as The Pilgrim, where the viewer is met by nothing but an erect but empty gentlemanly suit and a bowler hat floating above as if perched on an invisible hat. The observer feels noticed or watched by this finely dressed person, and yet there is no one there; I (a subject) observe this painting (an object), recognizing a person (a subject) who observes me (an object) at the same time, yet there is only me there since neither is there a person in the suit nor is there anything more than a painting in front of me. The painting, or the pilgrim, is completely contained and content in his own world, disregarding me even as he theoretically faces me. There is no subject-object play that concerns him, any more than in the case of the daoist, the frog or Zhuangzi's cook.

Another way to describe what is common and remarkable about the examples I have mentioned here is to point out how free of emotion they are. The daoist comes closer to his destination the more free of emotion he becomes, the cook cuts the best slices of ox after practicing for years to free himself of emotions that get in the way of his inspiration, the frog jumps into the pond (or the pond is jumped into by the frog) without any sign of care or emotion and Magritte's pilgrim is so free of emotion he is not even there anymore!

Of course, a work of art might well display emotions without recognizing the viewer's presence, but it is close to impossible to imagine a painting, poem or any other work acknowledging the viewer without an emotion being conveyed in some manner. Even a completely indifferent gaze of the painting's subject towards its observer immediately demands attention.

This would seem similar to Denis Diderot's (French, 18 cent.) theory of painting. He claimed that for a painting to refrain from becoming un théâtre; “an artificial construction whose too obvious designs on its audience made it repugnangt to persons of taste” (Fried, Courbet's Realism p.7), the artist had to take the greatest care to make the subjects seem completely absorbed in their actions. The audience was not supposed to be able to connect or involve themselves in the painting at all, and thereby the enchantment was magnified. Coincidentally, Diderot himself wrote a story named Ceci n'est pas un conte or This is not a story (1772).

And so, as a painting or a poem can be said to achieve a certain level of beauty by not striving for beauty, a certain level of wisdom by not striving for wisdom, so can a daoist achieve a certain level of tranquility by not striving for tranquility (and indeed not striving for not striving for tranquility, ad nauseam). As a daoist wants to master his forgetfulness, he must practice not trying, to not try, and he must practice not being, to be not by his own volition and skill, but to simply be. He must be as if spontaneously there, connected to his surroundings without his surroundings getting caught within him. They must simply pass through him, and he will finally be self-so.

A daoist might then approach something like Basho's subject-object free, self-referencing haiku of the frog and the old pond (although, as a game, one may always cheat to find a subject everywhere. For example, compared to whom is the old pond old? The frog, presumably.) as Diderot approached paintings. The daoist reads the haiku, searching for inspiration, and to his surprise he is mesmerized by the complete emptiness and disregard of anything outside the poem's subject matter. Like me when I encounter Magritte's pilgrim, the daoist finds himself in a loop of recognition with the poem, and in its emptiness he does not find the old pond or the frog, but instead he finds the complete lack of anything else. It is just a simple, emotionless “plop” of water as the frog jumps in. No Ego, no emotions, only … “plop”.

Copyright 2012 Gestur H. Hilmarsson

This may well be a long shot, but I'm currently studying for a logic exam which is in three days. I'm doing pretty good, and have a high average gade so far. But I'm curious whether anyone knows of good study sites or e-books. I found the book "forall x" pretty helpful, and highly recommend it. Any suggestions, or even tips from your own logic studies?

It's good to see the /catherine/61-32367/ lore getting some use...

For anyone curious about theoretical mathematics, alternate dimensions or the quirky old novel Flatland. This essay was done with less time to spare than I would have liked, so I apologize for the confusing syntax and grammar to any native English speakers. I only hope it's understandable enough.

“To the enlargement of the imagination.”

-A. Square

A popular topic of discussion within the more science-fictional sounding part of mathematics and physics over the last decades has focused on alternative dimensions. People wonder if they are real, how many they are, how they would appear to us, if there exist unfamiliar beings there, if familiarity with a higher dimension gives us more control of the lower ones, and so the questions go on ad nauseam. In this paper I will list the classic trilogy of philosophical questions and take steps, some careful and others more adventurous, towards theorizing answers or approximations towards them. The broad, philosophical questions are, of course, ontological; “do these dimensions and the beings within exist, and in what way?”, epistemological; “can we know and learn about these dimensions and their inhabitants? Why, why not, and how?”, and ethical; “do we have duty or reason to come to conclusions regarding these dimensional matters, and, whatever the answers to the ontological and epistemological questions are, what should we do with the knowledge gained?”.

After a brief introduction of the issue I intend on approaching and contemplating in this paper, I will list in order the main events of Edwin Abbott Abbott's 1884 mathematical novella, Flatland; A Romance of Many Dimensions, and afterwards elaborate on how the events are relevant to the bigger picture of the matter at hand, or how they may lead us to creative hypotheses for answers.¹

The reader may be warned that I will not go deeply into practical matters of mathematics in this paper, and much of the elaborations within may seem made to complicate the matter more than help to seek solutions. I will refrain from making big claims easily disputed by elementary knowledge of mathematics and physics, but imaginative, mathematical and physical theorizing will abound. We are dealing with a still very theoretical field of science.

To better prevent confusion over seemingly repetitious phrases, concepts and terms to follow, I will go through some elementary definitions to begin with. When speaking of dimensions in the context of our issue here, I mean the axes by which points in space are drawn to generate spatial perspective and even reality.

• The first dimension is quite simply any line drawn between two points in space, except there is nowhere else in 'space' to go but further along the same line, infinitely. That line we will call axis x. For context of the further explanations, let us say that x stretches infinitely to west and east.

• The second dimension has west and east, but lines stretching north and south, along the y axes (at a 90° angle to x), can intersect that line at any angle. That way any kind of flat geometrical shapes can be formed. A square, for example, is a one-dimensional line on x of any given length, where each of its infinite amount of points are stretched along y, leaving in their wake a 'trace' until it is of equal lengths along x and y.

• The third dimension, along with lines stretching every way along x and y, has lines intersecting them outwards and inwards. A ready square, from the previous definition, could be stretched outwards in its entirety, along the z axis, leaving again a trace until it reaches as far out along z as it does x and y. Thus we would have created a cube, or even a solid.

This is of course unnecessarily complicated for anyone who has basic understanding of simple geometry. But these are the dimensions we are used to considering in our day-to-day calculations, and it goes without saying that we live within the third dimension, made of solids and traveling freely along all three axes, x, y and z. But any child will ask themselves “what comes after 'three'?” one time or another. And so have super-scientists also done, thankfully.

• The fourth dimension moves things into a more abstract sounding territory, or actually outside territory as such. The common, popular theory is that to us in the third dimension, the fourth dimension is time, to put it so simple as to amount to barbarism. What we did with the line to make a square, and the square to make a cube, was to stretch each point in the figure along a new axis lying at 90° angle from the previous axes each time. How would we stretch a cube along an entirely new axis? Somehow time seemed most plausible, to move us into 'hyperspace'. To accurately picture in one's mind's eye a four-dimensional cube, or a hypercube as it has been dubbed, is humanly impossible. But attempts have been made, and will get further explained later in the paper.

There is no doubt that any sane and willing person may think about dimensions alternative to our own, given a certain knowledge of the accepted theories on how each particular dimension likely appears and functions. We would hardly then accept that the same person is thinking in that same dimension, even though metaphorically one can be said to be thinking in one or two dimensions in certain instances.

A simple but functional comparison would be when a person is asked to imagine themselves walking across a famous plaza in a city they've never visited, but about which they have read enough to theoretically be able to navigate around. They may be wrong about certain functional or aesthetic details of the actual plaza (assuming it even exists outside the person's imagination or the information they use for this visualization) but they know enough for the imagined experience to feel possible and the thought experiment is a success. It is hopefully clear that this person has thought about this location and not, in fact, in it.

Some may argue that a plaza, full of tourists and pigeons, surrounded by charming architecture and bathed in warm sunlight is not comparable to a higher or lower alternative dimensional reality. But the fact is that in both cases we imagine ourselves entering a reality which we are able to make sense of, at least theoretically, and even exist in, however different or absurd the surroundings might seem to us. The more obviously possible space (the plaza) and the more absurd, theoretical space (alternative dimension) need to meet similar standards for us to consider them real in any relevant sense. By 'real', I mean existing and/or possible.

Equally, we may wonder whether a thought experiment involving a being from an alternative dimension visiting our own is a matter of a logically possible scenario or simply a leap of imagination. It should be no more absurd than a scenario involving extraterrestrial lifeforms or even ghosts (given we imagine the possibility of anything scientifically explicable and non-fantastic considered as a 'ghost', unlikely as that may seem).

The hypothetical situations which we might find us in as either hosts or visitors in scenarios as these may seem like the stuff of children's books, or new age brochures about ascending to higher states of consciousness and such, and have less to do with questions of mathematical and physical matters.

Luckily, in the late 19 century, an English schoolmaster, theologian and Shakespearean academic wrote a novella of mathematical fiction which paints a picture of just such an event.

In Abbott's story we accompany the protagonist A. Square (who happens to be nothing but a square) through his introduction to the third dimension by a spherical, solid visitor. On the way we also visit the one dimensional world and an imagining of what a dimensionless one would look like. Furthermore, the possibility of a fourth dimension, while only alluded to in the story, will play a larger role in the context of this paper.

One of the reasons Flatland is as intriguing and inspiring as it is may be that it asks the reader to, first, put themselves in the shoes of a two-dimensional being by describing in detail how it views its own reality, and then imagine the experience of having their world turned, quite literally, inside out. The perspective we are asked to appropriate from the beginning is completely two-dimensional. A. Square is nice enough to explain what that entails.

Envisioning Flatland as a horizontal surface, like a map, may help to prevent confusion in the following descriptions. Flatland is home to geometrical shapes of varying multitude of angles and sizes, but none of them have any height, only width and length, although they have an idea of 'up', as in 'going north', since they have the four directions and an unexplained, weak gravitational pull towards south. Despite the gravity, Flatlanders move freely along any of the north, south, east, west axes. The gravity does serve some purpose of context for them, as the roofs of their pentagonal houses always face north or 'up', and the rain falls south or 'down'.

Rain, and humidity, are actually key to their perception and understanding of their surroundings, since the fog allows a Flatlander to judge the angle of any corner he faces by how abruptly its sides fade into obscurity. This technique is necessary for them as they don't have the 'thickness' to fit two eyes on their bodies and therefore only have one, so they are not blessed with the same amount of depth perception as we are.

Just as with the unexplained gravity, the Flatlanders' thickness is a concession the author has to make for the story to be better imaginable to the reader. We can imagine a Flatlander, such as A. Square, as a royalty on a playing card with even sides and 90° angles, and a single eye on one corner. Were we to lay him on the edge of a desk and lower ourselves so that we were looking straight along the desk's surface, Square would appear to us as a thin line. In Flatland, one is thus perceived as an almost infinitely thin playing card of a sort. There are a few further matters of perception explained by Mr. Square, but they serve mainly to explain social aspects and hierarchy within Flatland's society.

Square tells of a dream or a vision he has, wherein he is transported do a place where he sees nothing but a straight line which seems to stretch on forever north and south. A segment of the line is introduced as the king of Lineland. The king and Square start arguing about matters of reality, as Square appears to the king as a voice out of thin air, seeing as his perspective is only along the line. Each of his eyes, one on each end, sees only his neighbors, one on each side. In short, all he ever sees appears as a dot to him.

We can crudely imagine Linelanders as an apparently infinite row of infinitely thin wagons in a train, each one destined to stay in the same place in the row and no windows on the sides, only back and front.

Because of their limited use of vision, Linelanders have evolved an extreme precision of hearing. By hearing, they judge the distance between and size of each other, similar to how the human ears calculate the direction of sound, where the minute time between the sound reaching each ear indicates the angle.

Square does what he can to try and explain 'left' and 'right' to the king, but is met with frustration and mounting anger. Eventually Square goes as far as to move into the king's line of sight which understandably startles the king immensely, as he has never known anything other than that same dot in front of him, with the same color and in the same distance his whole life. At that moment, the king loses his temper and attacks Square, who is startled awake back in Flatland.

At this point, the third dimension finally invades. After sending his son off to bed for supposing there might be such a thing as 3 to the power of 3 (a punishable heresy in Flatland) Square hears a voice which we would consider coming from above, but to him it seems to echo from everywhere and inside himself at once.

The voice announces that Square is wrong, and that 3³ has “an obvious Geometrical meaning”. To Square's amazement, he sees a figure forming and expanding before his eye; a dot which quickly spreads into a line, getting ever wider. What he is perceiving is Sphere, a ball shaped three-dimensional solid figure, lowering itself into the two-dimensional plane. But given the infinitely thin field of Square's vision, he only sees Sphere as an infinitely thin slice at a time; a cross section.

We can imagine pushing an inflated balloon into a body of water. A single point must first touch the surface, and the widening rest follows. What Square would see is whatever circumference of the balloon the surface of the liquid touches at each moment.

To add even further to Square's confusion, this figure has no discernible edges or angles to speak of. In Flatland, even the roundest of circles seem round simply because of their high number of angles. So, in fact, to Square the reality of the situation seems to be that a perceptible but impossibly, almost unthinkably 'beautiful' being has stepped into his reality by some way which he can not understand or imagine. Square is startled and antagonistic at first and refuses to listen to or believe Sphere's (to him) nonsensical talk of 'above'. After the realization of Sphere's pure circularity, Square's mood becomes more and more reverent.

Sphere claims that he comes from a world above and below Flatland; not from south or north, but different. He has come down into this plane after observing Square's surroundings from above, which allowed Sphere to see inside whatever Square and the other Flatlanders would consider 'solid'. Square finds this claim, understandably, absurd. To prove his point, Sphere lists the exact location of each member of Square's household around his home and even admits to having witnessed and observed Square's dreams and intimate thoughts about Lineland. Flatlander's of course have nothing covering their 'sides', and are therefore exposed from above.

After a brief but failed attempt for Square's understanding, using a Socratic interrogation about the Flatlanders' actual height, or thickness, 'infinitesimal' as it is, Sphere resorts to describing himself to reveal the truth of the matter.

“You are living on a Plane. What you style Flatland is the vast level surface of what I may call a fluid, on, or in, the top of which you and your countrymen move about, without rising above it or falling below it.

I am not a plane Figure, but a Solid. You may call me a Circle; but in reality I am not a Circle, but an infinite number of Circles, of size varying from a Point to a Circle of thirteen inches in diameter, one placed on top of the other. When I cut through your plane as I am now doing, I make in your plane a section which you, very rightly, call a Circle. For even a Sphere – which is my proper name in my own country – if he manifest himself at all to an inhabitant of Flatland – must needs manifest himself as a Circle.”

Square is still unable to fathom this information, so Sphere appeals to Square's love of geometry and arithmetic to lead him towards understanding, going through the evolution from point to line to square and beyond. But this is, of course, blasphemous talk in Flatland, and Square attacks the heretic alien.

Sphere slips up and disappears to dive into the family's safe and bring Square valuables from within, without the safe being opened. A simple transaction from Sphere's perspective, but unimaginable to Square unless by some trickery. Tired and disappointed by this square he chose as the messiah of the second dimension, Sphere pokes at Squares insides and finally whips him up into the third dimension.

Square experiences something of a religious revelation:

“There was a darkness; then a dizzy, sickening sensation of sight that was not like seeing; I saw a Line that was no Line; Space that was not Space: I was myself, and not myself.”

“I looked, and, behold, a new world! There stood before me, visibly incorporate, all that I had before inferred, conjectured, dreamed, of perfect Circular beauty.“

Square considers himself now blessed with a divine gift, since only God should be able to see all, but Sphere comments that if that is indeed the only requirement, then every petty soul of his own world is a god in Flatland. After this forced and shocking progress of Square's awareness, the education continues.

To further explain solids, Sphere builds a cube out of fabricated squares, similar to Square himself. He lays one on top of another until they form a shape with six equal sides and eight corners, like a deck of square playing cards. Square is amazed that he himself can be considered an originator of such a complicated object.

But, after all this, a strange idea has formed with Square. He begins asking about dimensions of beings even more perfect than Sphere; beings which might easily look within Sphere and all other solids; the home of a some figure like a cube but with sixteen terminal points rather than the 'divine' eight. Sphere brushes his ideas off as 'inconceivable', even though there were indeed reports within the third dimension of figures appearing and disappearing, and whoever claimed the existence of such beings was considered a heretic. Square pushes on and is eventually cast back down into Flatland by an infuriated Sphere.

Saddened by his punishment, but still intrigued by what he has learned, Square goes to bed in his home, and dreams yet again. Now of moving through blank space, next to Sphere, towards a “bright but infinitesimally small Point”. Sphere calls this place Pointland, “the lowest depth of existence, […] the Abyss of No dimensions”. This point exist in total solipsism; not only ignorant and unaware of the surrounding world, but incapable of understanding any experience as different than his own. Whatever is said to him, he assumes to be his own clever, creative thought. There is nothing else to learn from this non-dimension.

Square awakes in his bed, excited about the prospect of delivering the prophecy and message revealed to him. But, sadly, he is dismissed as a lunatic by the flat society and imprisoned for life, and the story ends there.

This has been a rather elongated summary of a short story, but I have saved any serious thoughts and questions which rise during the reading, until now. I hope to approach the more significant ones in order with as little confusion or chaos as possible.

A general question to pose might be; what do we talk about when we talk about alternative dimensions? This would be the ontological consideration, that is, whether they can be said to exist. I fully admit that within the context of Flatland, a metaphor for the dimensional issue, we presume more than should be allowed in serious mathematical thought, including sentient yet infinitely thin beings with language common to beings of every other dimension, allowing for communication.

But, however possible or not it would be to communicate with a square, a line, a point and so on, the question of the level of their existence must be a valid one, just as with beings or the possible experiences exclusive to higher dimensions than ours. It feels easy enough to imagine beings of lower dimensions and consider oneself aware that of course they wouldn't speak our language, and that this is only an experiment; the beings would still be able to exist in some basic manner of the way we imagine them. But being able to picture something before our mind's eye is of course no sign that there must be a possibility involved. Famous enough are the examples of a candle staying lit in vacuum, or a bar of gold floating in regular water.

Said candle, the vacuum, the gold and the water can indeed be said to exist, but where would we find the square we seek to communicate with? Is it enough for me to draw a sequence of a dot (to signify an infinitely small point), a line, a square and a cube for all of these to be considered as existing? Is there some sort of Platonic existence I allude to by presenting these constructions?

One common, if a bit playful point made in discussions of dimensions is one of shadows. We can observe that a cube may be held and oriented so that it casts a completely square shadow. A square may be held so that its shadow is nothing but a thin line. A line, if pointed straight towards a light source will simply cast a dot. What could it be, then, that casts a cube as a shadow? It is absurd to think about in the same context as looking at shadows cast on flat surfaces.

That may be because we are still trying to picture it within our own capabilities. Although Abbott most likely did not have time in mind as the imagined fourth dimension, long before anything like the theory of relativity was put forth. But it is a common enough idea today. It is then proposed that an object in the fourth dimension appears as its own entire lifespan as a whole. A person would appear as herself from conception until death in one and the same moment. A construction perceptible to us might look like a long sausage, with a person's life extending through it. Rather than talking about shadows, we might imagine that a cross section of an object of each dimension looks like an object from the next dimension beneath. So, a person in our three-dimensional space appears to us as a cross section of her entire four-dimensional lifespan. You cut the sausage anywhere, and the person appears in the wound at the appropriate age depending on where along the sausage it was cut.

The way for us to imagine and talk about these dimensions seems to always require some dose of absurdity, but is that not the necessary evil until science can present further proof or definitions? To move past theses and guesses, and towards the possibility of actual experience and empirical evidence, we will have to devise ways of perceiving other dimensions. But how might that be possible?

The question moves us towards epistemological considerations; can we ever know these things? Would it come down to some external, technological equipment? We can imagine some sort of complex spectacles. Or is it possible that the human being could evolve the ability to perceive higher dimensions? Perhaps something along the lines of how we advanced in cognitive abilities through evolution; from cells to primitive lifeforms all the way to primates and now (but not 'at last', since we may have a long way to go still) to human beings.² A subtext of this is the mind/body problem. If we can at all experience other dimensions, the possibility should lie in either matter or cognition, or both, whether that means that here are different ways to achieve the goal on the side of mind vs. body or it is fallacious to consider them as separate paths. I will not delve into the mind/body problem too deeply, but touch on it if needed.

First, the physical matter, which we would utilize to help the human body to achieve perception of the fourth dimension. (I will, humbly, only attempt to theorize higher dimensions one at a time.) There would need to be a way to develop and construct some sort of technology by which we would see through to the fourth dimension. However that is to be done, it would practically work as a looking glass. With it we see. Without we do not, even though we feel aware of what we know to exist beyond our senses.

Second, the case of purely cognitive advances. In this case the human body would evolve to a stage where perception of the fourth dimension is actually a natural part of the senses. Strict training could perhaps help to push the process along over a stretch of generations, given that the right kind of focus and training had been discovered and developed. Some might even argue for the case of meditation or some sort of medication to alter the state of the brain's chemistry, and hence the mind. That does indeed involve matter, as the first option did, but the matter of the human body and brain itself. The prior option needed technology and equipment alien to the body to allow for the perception to take place.

Notice that I do not speak of 'going to' other dimensions, since they do not exist in different, unreachable locations where different rules apply. They are here, around us, at all times. I do not have the ability to notice shifts of sub-atomic structures in my hands as I type, or the radio waves passing around and through me, and I would have no reason to suppose either were real if I were not familiar with the supporting scientific evidence. Likewise, I can not perceive higher dimensions 'happening' around me, or interact with lower dimensions, even though I can easily construct and abstract the relevant geometrical forms on any piece of paper.

An overarching problem between the characters in Flatland is that varying dimensions are homes to creatures of varying perspectives and conceptions of space and reality, but again, they share a common language to illustrate these problems even further. Can we find a similar situation within our own present reality? That is, could we communicate with a being whose personal library of experiential concepts are remarkably different from ours? We could come at least theoretically close to it by researching human beings able to communicate perfectly despite always having been blind.

No matter how long I would discuss matters of experience which I have gathered by sight, whether it be painting, natural scenery, cinema, geometry or what have you, I could never be certain that I and the blind person are visualizing similar things. In general, one can not really be certain of shared thoughts or opinions with other people, but it is damn likely that two people looking with perfect eyesight at the same painting can describe at least similar colors. With the blind person, on the other hand; even though they can have experience of everything I mentioned, by smell, hearing and touch; whatever they create within their mind's eye must only be a cross section, a 'shadow', of what I try and describe to them.³

The difference between this case and the situation in Flatland, though, is that a blind person most likely has an idea of what they are missing since they regularly communicate with fellow seeing humans. They don't have the idea pushed on them that there is in fact nothing to see. To do so would be a cruel prank, indeed.

If the blind are missing out on the full experience of three dimensions, what of those who might claim to see glimpses beyond it? Since the science of dimensions has not been blessed with much concrete evidence yet, it is easy for many to claim 'dimensional interference' to explain their superstitious believes or pseudo-scientific ventures. However, only the disingenuous swindlers should be dismissed, since there is ever the slightest possibility that some individuals genuinely experience events which we can only describe as 'supernatural', and use terms such as 'ghosts'. A genuine 'ghostly apparition' might be at last explained as a higher dimensional being appearing as a three dimensional, humanly perceptible object, for a split second. Remember Sphere's phrasing in the story, where he explains to Square how he reveals a two dimensional part of himself for Square to be able to comprehend him. Those people, who happen to have these experiences are, in our times and reality, doomed to suffer ridicule from any skeptic, simply because of how easy it is to point out dozens of fakers for each possibly true case. Further advances might, if nothing more, help us to finally tell the liars from the sincere.

Quantum physics has notoriously suffered a kind of occult abuse, spawning a sub-strata of new age science called 'quantum mysticism', and even post-modernist schools of philosophy have had their reputation smudged by careless, amateur misuse of scientific concepts. Dimensional science is indeed in danger of becoming familiar enough to exploit long before any proper proof surfaces and spreads among the misinformed public. The rollback of misinformation related to quantum physics has only recently begun, as the risks have materialized over the last decade. The reader may wonder, how is this in any way relevant to the question of the possibility of alternative dimensions? For the answer I will turn at last towards ethics; a field most people seem to think the mathematician does not have to worry about at any stage in his profession. What is or could be our ethical duty when it comes to alternative dimensions?

Two perspectives of this ethical part come to mind at first; how would it be best for us to handle this knowledge vis-a-vis going after discoveries and keeping misinformation at bay, and later, should the reality of extra-dimensional beings become clear, what would be our ethical (or even civic) duty towards them? The first question relates to our duty towards ourselves, and the latter to our duty towards these dimensions or rather the mutual duty between us and them.

Regarding our own duties within, let us say, the third dimension, it must be said that most likely information will be misused however carefully and clearly it is distributed amongst the public, academic circles and those in between hoping to gain from new ways of selling their ideas or beliefs as plausible to the public by seeming more academic than they in fact are. Astrology's prosperity even in recent years despite progresses within astronomy being made constantly is one example that comes to mind. Not everyone will be persuaded, no matter the amount or clarity of the evidence put forth. As a quote often appropriated to Abraham Lincoln states: "You can fool all the people some of the time and some of the people all of the time, but you cannot fool all the people all the time".

Still, I do find comfort in my suspicion that those fooled, by snake-oil promises of higher dimensions professionally covered in scientific jargon, will veer far enough into mysticism to stay out of the way of actual scientific progress. They may congregate and attempt to reach dimensions through mystic means at their own expense and comfort. I am not aware of cases where astronomy or physics have in modern times been held back by popular beliefs ingrained by gurus and life coaches.

The duty to still chase after further progress and confirmation of the existence or non-existence of these other planes of reality, by proper means, should still be seriously considered, since there is at least strong enough suspicion and theories to warrant investigation. No one can yet say for sure what knowledge may lie within, and how it might benefit us. This field may not be fully comparable to the investigation and research done by NASA and others to mine space for information, since the planets are of course already perceivable by any seeing person, but there was a time when even the skies were believed to hold nothing but gods and fire.

When it comes to our duty towards these possible higher dimensional inhabitants, the matter is more complicated, seeing as if they exist, they exist around and amongst us already. Higher or lower dimensions are, again, not alternative places, any more than the 'possible worlds' we may mention in talk of alternative, possible timelines exist somewhere far out of reach. These dimensions are our own world seen with better or at least different sense organs, capable or perceiving what we may only theorize about, for now.

I doubt that any serious mathematician considers himself obligated to respect two-dimensional geometrical shapes as persons, but at most as aesthetically pleasant characters in the context of his passion, maybe as an artist respects and admires the different characteristic hues his paints create on the canvas.

But would we not expect respect from creatures of higher dimensions, who have likely been aware of us, or at least our theoretical existence around them? Maybe they have never been directly aware of us, but only abstractions and constructions of us, used in formulas and examples such as squares, triangles and such do for us on paper. A four dimensional person might find it weird but curious to think that a cross-section of her would look like a thirteen year old Nigerian boy, or a middle-aged investment banker, without ever touching on the reality of the dimensional matter. I can not begin to speculate what sort of calculations would involve constructions of 'simple' three dimensional beings, but a square might think the same about himself when theorizing about the existence of us.

However, if we assume that we have been an integral part of the world of the four-dimensional beings, and them fully aware of us, it would be curious to find out if they have some more control over our surroundings than we might have thought. We pretend to alter lines and squares, and maybe we actually are doing so and not only abstracting. Could it then be that events that we find chaotic and uncontrollable are in fact controlled or at least touched on by these higher beings, for their own comfort or survival? Weather, disease and aging, for example, are things we try our best to figure out and even fight, but time makes it difficult.

Would we then ask that they consider and respect us enough to trouble themselves and save us? Perhaps it would be as unlikely as human beings lending a sympathetic ear after suddenly getting a distress call from the society of rodents to stop lab experimentation, now that they had finally found the way to make themselves understood to us.

Should communications and relations be established between the third and fourth dimensions, nothing in our livelihood would necessarily change, but only our perspective towards how we have already been living. Like realizing that your pillow is full of bed mites, or that there is or is not a God, nothing in your behavior needs to change if you were not bothering either the mites or God before. But you can easily find ways to change your perspective and better your behavior with either knowledge at hand. In the case of us coming to terms with being aware of higher beings, some might even choose to consider them as divine beings, and would of course be free to do so within safe limits.

Whatever ethical duties would seem appropriate would entirely depend on the reality of the situation. The fourth dimension may well be empty of any extra conscious being. In that case, it will then be completely up to us to decide what to do with the gained knowledge and opportunities, and the ethical questions involved will be elaborated on our already established ethical code to take care that discoveries and technologies are used for good and gain of all.

All in all, this has been a matter of interdimensional communication; whether we theorize talking to a sentient geometrical shape, a ghost, our own dog or even our own god. Without appealing to religion and faith, there should at least be a plausible scientific explanation to how this might be possible. Dimensions may just be where to look for these opportunities, even if only to decide where an actual, genuine case for extra dimensions can be made. Furthermore, we would be able to recognize arguments which use less than properly explained scientific phenomenon to account for imagined objects of faith or even superstition. Just as the terms and concepts of quantum physics have been better introduced to the common knowledge and education of the public, arming people better against misinformation used for ill gains, interdimensional sciences must not fall prey to disingenuous gurus but be saved and used for all the progress it has potential for.

So far I have elaborated on the issue of dimensions, more specifically the second and fourth, since they are 'closest' to us. Without any concrete answers, since the field has not moved so far as to sincerely prove much, I attempted to highlight questions regarding the existence of these dimensions (ontology), how we might know or perceive them (epistemology), and how we might have to consider behaving towards them or their inhabitants, should they be proven real (ethics). There is no solid conclusion to this paper, but my hope is to have the reader realize that there is something more to consider there than simply thought experiments and mind games, although they, too, can be an integral part of coming up with theories on how to progress towards any discoveries. Edwin A. Abbott was just such a thinker, who, through playful imagination, sparked ideas and theories within mathematicians of each generation to come.

Notes

1. Edwin Abbott Abbott (20 December 1838 – 12 October 1926), an English theologian and schoolmaster, originally wrote this novella (under the pseudonym 'A Square') as a satire, ridiculing the hierarchy of Victorian England. In the story, Flatlanders are judged and placed in society according to the number of their angles, the more the supposedly wiser, and anyone found with irregularities is deemed inhuman and unworthy. Each individual's aspiration is to have a healthy child, since each child is born with one more angle than it's father, and hope for their child to succeed. Women are completely without angles. They are lines, and therefore with no room for thought. They are emotional and dangerous for that reason.

2. One is reminded of Kant's talk of space and time. To him, time and space were as tools for us to perceive and understand the world outside ourselves. We judged distances by space, and duration between events by time, for example. Space and time are therefore a kind of a filter, or spectacles, which we observe and make sense of the world through. Thus, and upgrade to those Kantian spectacles is in some sense what might be needed to reach the fourth dimension.

3. The reader is hopefully familiar with the famous Molyneux's problem. It is a thought experiment which Molyneux (an Irish philosopher in the 17 century) proposed to John Locke (English, 17 century), wherein a blind person is asked to lay their hands on a sphere and a cube, and when he suddenly gains sight is asked to distinguish between the two objects by sight alone. This was to raise the question of how ideas were formed in the mind, through the senses or any other way.

Bibliography

Abbott, Edwin Abbott. Flatland: A Romance of Many Dimensions. New York: Dover Publications, 1992.

Crilly, Tony. "Why Are Three Dimensions Not Enough?" The Big Questions. London: Quercus Plc, 2011. 114-23.

Copyright; Gestur H. Hilmarsson, 2012

For anyone interested in film theory, philosophy or both. A recent essay comparing the 2003 film The Dreamers, which I suspect too few have seen, and the existentialist philosophy of Sartre. Hope you endure and enjoy, and are intrigued enough to decide to see the film if you haven't already.

The question of whether one is justified in making connections between certain films (the problem does of course apply to other art forms as well) and particular philosophical ideas is an interesting one and not easily done away with. A loose definition of the opinions of two different kinds of philosophers, admittedly polarizing, might shed a light on the problem.

• This tendency is a step in sound, logical thinking which pushes the imagination to form theories to further test and hopefully lead to better understanding. (Positive towards the relevance of film, P from now on)

• It is simply an imaginative flight of fancy, a sort of poetic escapism, to be dismissed for posing as an acceptable way of progressive philosophical thinking. (Negative towards the relevance of film, N from now on)

Although I will not try and conclude either hypothesis in this short essay, I will point out and elaborate on the connection I find between The Dreamers (Bernardo Bertolucci, 2003) and a simplified, popular version of Jean-Paul Sartre's philosophy of existentialism. Different readers of different opinions of film's relevance to philosophy may not be moved in their persuasion by this short essay, but I will show that the possibility of relevance is indeed there.

After some elaboration on the difference of opinions P and N, and a short outlining of the film, I intend to single out the most important of Sartre's concepts and show how scenes and characters in The Dreamers can be viewed and, indeed, read as examples of those concepts and ideas, although varying in subtlety. Whatever connections I make may well be far from the intention and inspiration of Bertolucci, which makes one of the protagonists lines sound especially fitting in the light of this essay: “I didn't know I was being philosophical”.

Both the film and Sartre's ideas have a reputation for being obscure and even pretentious. My aim is to utilize each to hopefully shed a light on how the film can be said to, in fact, show or act out philosophy by vivid Sartre-like examples that engage any open-minded viewer.

A familiar example from the culture of film will hopefully show the reality of these simplified opinions and the difference in philosophers it makes for.

Paul, a P-thinking person, and Ned, his N-thinking friend, exit the theater after seeing the film The Thin Red Line (Terrence Malick, 1998). Paul is filled with thoughts on the significance of the events and dialogue of the film and how they may relate to his own and others' lives; questions about the existence and nature of God, ethics of war and so on. Ned enjoyed the film as a piece of art, found it superbly directed if a bit long and would recommend it to anyone interested in films on war. He is, however, not willing to go to the same lengths as Paul to analyze the film's undercurrents. To him this was a well crafted, partly historical film about men at war and, at most, the different psychological impact it had on each of them. He is not interested in reading between the lines.

Paul and Ned happen to be philosophers, and the film will likely leave very different impressions on each of them. Paul is inspired to watch the film again to catch dialogue and situations which may resonate with something he has previously studied, and this in due time may just bring him to a breakthrough in his way of thinking and working philosophically. Ned on the other hand is merely intrigued by the film as a form of social commentary which will not help him in his search for logical truths or solutions to tricky problems.

To Paul the characters in the film are at least something like human beings like himself. To Ned, they are at most something like himself and not to be empathized with too much (except perhaps as a deterrent to going to war). The difference between them is then one of ability or openness to perceive and accept analogy; to make connections between things and events outside their own private experience and use those as examples to get a different perspective on their own reality.¹ It is not a question of different tastes, but of different mindsets.

Of course it should be pointed out that Paul might not be the optimal philosopher if to him just about any film begs to be analyzed and taken as philosophically significant. He would be better off with a touch of logic on his side. As for Ned, it seems his philosophical thought lacks something if there isn't room for anything but superficial evidence. Insight and lateral thinking might add some spark to his thought. Most people are likely somewhere in the more moderate range between P and N.

So now we may turn to the film at hand. The Dreamers tells the story of Matt (Michael Pitt), an impressionable, young film buff and American exchange student in Paris, France in 1968. There he spends most of his free time in the famous movie-houses, watching some of the most influential and progressive cinema of the time.

Through this he meets a pair of bohemian twins; Theo (Louis Garrel), a rebellious young man familiar enough with the radical ideas of the time to pose as a proper, worldly intellectual, and Isabelle (Eva Green), a colorful girl with a penchant for drama and theatrics, always ready with a quote from a memorable scene to recite even in the most ordinary conversation. When asked about her birthday, she answers, with an inspired look in her eyes: “I entered this world on the Champs-Elysées. 1959. [...] And you know what my very first words were? […] “New York Herald-Tribune!”” This would make her nine years old, yet nothing is said of the matter.

Meanwhile tempers are rising among students and followers of the cinema out on the streets of Paris (which will eventually lead to the famous riots of May 1968). The twins' parents leave town for some time and Matt moves in. Fun and games ensue, but soon turn sinister and more perverted. Matt's values and morals are shaken and even mocked by the twins, which they claim to do out of love. He in turn manages to unveil each of their own insecurities and tries to push them towards maturity, out of his own love, until the world literally crashes in through their window. Matt, refusing to resort to violence, loses the twins as they rush into the student riots that have been raging outside their nest for the past weeks.

A summary of most films doesn't have to take more than a single page of text, but a sufficient summary of a single philosophy will take more. In the case of existentialism, understanding might have less to do with the length of the summary and more to do with being met with an open mind. For the sake of clarity I will explain a few of Sartre's concepts to have in mind on the way through the main body of the essay.

Primarily I will focus on the issue of bad faith. By what Sartre calls 'bad faith' he means a certain form of inauthenticity. It is a refusal to take responsibility for actions or situations. In his own jargon, the many different forms and instances of bad faith will always be constituted of a person's inversion or separation of their facticity and their transcendence.

'Facticity' means, simply put, the concrete reality of a person and the world she inhabits. A person's choices and actions are in response to her own facticity. By doing that, the person exercises the freedom to choose her own future in response to her own past. This freedom is a necessary aspect of any person since it is each person's own decision how she sees herself in her concrete, physical situation. This freedom is in fact an obligation. A widower's facticity is his sudden solitude, but he is necessarily free to choose his interpretation and meaning of it.

A person's existence in this flight from the facticity of her past is called 'transcendence' for the fact that the person realizes her worldly surroundings and exercises her freedom to choose the next step, placing her outside or above the state of less aware beings of the world. The transcendent consciousness sees itself as more than a mere object in the world.

This person is what Sartre calls 'being-for-itself' (BFI) (as opposed to 'being-in-itself' which simply is and can not be fully explained but can be crudely compared to Kant's idea of 'noumena' as things-in-themselves which I will not dwell on here). The BFI is aware of and acts upon the world but is trapped in a complicated relationship with it. BFI constantly wishes to surpass the physical and its complications to become something like an idea of God. It follows then that BFI lives in perpetual anxiety over its necessary options and possibilities, that is, responsibilities.

The ones who try and deny this reality of facticity and transcendence, to avoid responsibilities, are in bad faith. They think themselves unable to choose, and thus in fact choose not to choose. It is important to distinguish bad faith from self-deception, since one and the same consciousness can not seriously lie to and deceive itself. Bad faith is more akin to self-distraction. This self-distraction is not all bad, since a person can and will utilize it in difficult circumstances to stave off the anxiety or 'vertigo of possibility' she feels in the face of unlimited freedom. A person in bad faith might tell herself that the option of pushing the man next to her in front of the oncoming train is not open to her, and thus she doesn't feel anxious over the realization that she is free to do so. She sees herself as a transcendence-less object, purely in facticity.

On the contrary, when a person deliberately accepts her freedom without regret for her past or present facticity, and realizes that she must choose her actions and reactions at each moment and by that transcend, she is living in authenticity, opposed to bad faith. Again, being in bad faith would not be bad in all cases, but neither is BFI necessarily the best or most right way to be at all times (Sartre does away with most value concepts, so there are few if any definite rights and wrongs, goods and evils in his worldview, similar to Nietzsche's).

Generally, BFI can still be said to be better than being-for-others (BFO) where the person lets herself become an object whose role is defined by the Other. A person never stays BFO for long in usual circumstances, but in human interaction two or more consciousnesses play this game of transcending each other, choosing for each other. Imagine the interplay between a head-waiter and his chef, a prisoner and his warden, or teacher and student: each individual is free to choose the meaning of their own role, but also that of their antagonist. Each is aware of the benefits of playing the role that the Other expects of them and choose to do so temporarily before turning back to their own transcendence.

'The Other' in this context is simply consciousnesses other than our own, from whose perspective we can not help but see ourselves occasionally. Still, those who are more prone to bad faith than most may tell themselves they are transcending when in fact they choose their attitude and actions based mostly on other people's judgments and expectations, that is their transcendence. That way, a person BFO is essentially a transcendence-transcended.

Now that the relevant concepts (bad faith, transcendence, facticity, being-for-itself, being-for-others, the Other, authenticity) and their chemistry have been touched upon I will list scenes from The Dreamers and explain how Sartre's philosophy can be seen manifesting on screen. Hopefully these examples will in turn fill what gaps of understanding my previous, brief explanations have left with the reader.

Matt, when introduced, feels relatable to many viewers who remember being impression-able and awkward yet adventurous in their adolescence. His narration sounds cocksure and experienced, but is told after the events of the film with an 'if I knew then what I know now' attitude. A boy living in exciting times with plenty opportunity to search for and come into his own, it is ironic then that he is halfway across the world but spends all his time in the cinema. “I was one of the insatiables, the ones you'd always find sitting closest to the screen” he states early on. Far from being alone, every night the theaters are full of adolescents in search for escape, inspiration or even guidance.

When Matt meets the twins he is instantly struck with admiration. To him they seem cool, experienced and completely sure of themselves and their surroundings. He recognizes in them what he has seen and admired in movie stars. To him they are what we would, in the context of this essay, call BFI. He wants to become like them. He wants to transcend. In a letter Matt writes home to his mother, he talks about “getting in with the right kind of people”.

Early on, the twins' father points out that Matt has more to offer than they may realize, after Matt shares some analyzing and insightful thoughts with the rest of them. This becomes more apparent through the film, as Matt appears to step ever closer to BFI, but not by becoming more like the twins. On the contrary, as Matt and the viewer see more and more evidence of the twins' inauthenticity, he realizes ways to practice his own freedom of choice. His realization is strengthened by how hard it is for the twins to join him in his growth, as their immaturity is exposed each time. It is no coincidence that the scenes where Matt is pushed the most towards actualizing his BFI are the ones with the most conflict between him and one or both of the twins.

From the moment Isabelle is introduced, to most viewers, she comes across as pretentious. Her theatrics are apparent from the beginning and we wait for her mask to come off. She is first seen (except for a brief glimpse in the film's opening) where she stands against the gates of the closed theater, wrapped in chains and wearing a bright red beret, a cigarette hanging of her lip, with a somber, defiant look on her face. She exhibits herself as a martyr of the cause only to playfully toss the chains off as soon as the curious and awkward Matt is sufficiently intrigued. She is practically flaunting her BFI, her self-diagnosed authenticity.

The unveiling however seems to begin only when Isabelle is put under extreme pressure, knocking hard against her comfortable 'bubble'. She is most notably shaken just after making love to Matt for the first time, again when she hears Theo having sex with a girl in the adjacent room while Isabelle is at her most vulnerable in her private and up until then hidden room with Matt, and at last when she realizes her parents' discovery of the kids' debauchery and attempts to go through with her promise of suicide should they ever be found out.

Throughout the plot Isabelle keeps up an air of maturity which still seems borrowed from her role-models in films. She addresses the boys with phrases such as “...my little Matthew...” and “Oh, yes you do, my pet”. Isabelle holds up the appearance of being in control of the unconventional situations they find themselves in. During Theo's forfeit, she seems completely unsurprised that he is actually going through with the humiliating task. Later, when Theo has Matt in a hold after hunting him across the apartment, Isabelle asks, stark naked: “...you aren't being very gallant. Is the prospect of making love to me so hateful?” A few scenes later, when Matt and Isabelle have grown comfortable with the unabashed and frequent lovemaking, he professes that at first impression he thought she had had many lovers before him: “...you looked so cool. So sophisticated. Like a movie star.” and she replies, proudly: “I was. I was acting, Matthew”. Without any sense of irony or doubt, she admits her inauthenticity.

On the surface, Theo is not unlike any other rebellious teenager. His manner can easily be excused by pointing towards his immediate surroundings. At that time and place, Paris in 1968, there were plenty more people at Theo's age who were swept along with ideals and ideas of change and rebellion, influenced by larger-than-life characters on the movie screen and on the streets.

It is not until after closer inspection in more intimate enclosure that Theo is exposed as someone going through more than just a phase. Theo considers himself an embodiment of the radical, rebellious spirit, in a complete mode of BFI. Matt, as well as the viewer, meets Theo outside the theater where he arrives with a following of his peers while reciting names of famous directors. Theo has his peers' attention, and catches Matt's just as easily, while keeping a constant air of coolness about himself. His coolness stays throughout the film (except for some excitement during a few arguments which all revolve around matters of culture and nothing deeper) until near the end when Matt finally exposes a chink in Theo's radicalist armor and hits too close to home, pushing Theo to violence. Up until then, he had kept his cool during his forfeit after losing Isabelle's movie challenge, even going as far as to assure Matt a moment later that he had performed the forfeit willingly and thus negating the humiliation. “Why don't you admit you were thrilled? […] You think Isabelle forced me, do you?” Even when he is hunting after Matt through the apartment to force him to have sex with Isabelle, Theo's own sister, he is levelheaded. “This is silly. Come out of there”. When he finally has his way and Matt makes love to Isabelle on the kitchen floor, he calmly makes an omelet while the moans of the pair blend in with the excited yells of the rioters running in the streets outside.

Theo has by then proved his influence and power over Matt. Soon, Theo thinks Matt is getting too comfortable with the situation, so he starts staking his claim over Isabelle again. At one point he takes Matt's place next to sleeping Isabelle while Matt takes a short trip to the kitchen. “Let's get something straight, okay? […] but no. It wasn't always meant to be the three of us.”

The relevance of Sartre's concepts manifests best in the scenes where the kids' various existential states clash. The plot might be boiled down to the suggestion that the twins have thrived on their mutual recognition of each of their own fragile state of BFI, hiding away the fact of their bad faith for however long until Matt comes into the picture unwittingly in the role of the Other. In exercising their transcendence over Matt, they push him towards maturity while fighting against the realization of their own inauthenticity, digging themselves ever deeper into a state of bad faith.

In the beginning, Matt is infatuated with the twins. Through painful steps of embarrassment they at last get him under their spell, their forced transcendence, during the sex-scene in the kitchen.² Later, in a scene in the bathroom, Matt professes his love of Isabelle. She answers him casually, unemotionally, and even answers for both her and Theo as if it is a joint decision to accept Matt's love. “Oh, poor Matthew. We do love you very much”. Matt, irritated, pushes for a direct answer from Isabelle alone. Isabelle grabs the chance for yet another of her games and proposes a way for Matt to prove his love. She toys with his hope of transcending to their level, of becoming their equal, which Matt thinks must have already occurred. When it becomes clear that this is yet another embarrassing task, to shave Matt's pubic hair, he finally takes the reins and rebels. Theo retreats uninterested, but Isabelle is visibly shaken. Matt, at last in control of an embarrassing situation, calls on the twins, and especially Isabelle, to let the mask drop and join him on a regular date. “Don't look at Theo. Isabelle, you don't need his permission”. After their date, Isabelle has a breakdown and it becomes obvious to Matt that she is unchanged.

Later, it is Theo's turn to have his authenticity seriously questioned. The boys discuss matter of rebellion. Theo tries to convince Matt of the beauty and truth of Mao's socialism and how justified the revolution is. Matt speaks out in doubt: “...if you really believed what you were saying, you'd be out there”. Theo becomes upset, angry, and starts choking Matt, only to stop when he discovers Isabelle standing behind them. Matt mumbles: “I think you prefer when the word 'together' means not 'a million', but just two”. Theo remains unchanged in his bad faith.

At last, when the twins have had their authenticity seriously doubted, they grab the chance to run into the streets when it finally seems like the whole city has poured out to protest. Matt begs them to reconsider, to think and see that violence isn't the answer. Matt has realized his freedom to choose and act on his own accord, when the whole city seems to go against his believes around him. He is finally BFI, transcending above his facticity. Theo reclaims Isabelle, grabbing her in one hand and a Molotov cocktail in the other, and runs into the oncoming lines of police in one last desperate attempt to choose and be free, to defiantly transcend.

Sadly, yet hopefully encouraging for the reader to explore the film further, there is a plethora of topics concerning the film and its relevance to philosophy, psychology, sociology and so on which the length of this essay simply will not suffice to cover, and that just from one particular film. Some of the further investigation may be used to fight the suggestion of film's philosophical relevance I have argued for here. But I, like many lovers of film, would welcome the opportunity of enlightening arguments rather than settling for the notion of film being no more than film.

In the end I hope that the reader can see how even a seemingly pretentious film and a philosophy notorious for being unnecessarily obscure can combine to form a mind-expanding, eye-opening experience. Together they may be enjoyed and explored, but also mined and used to possibly reflect on one's own existence for new perspectives. Some films can supply the viewer with that on their own, and few if any philosophies have accompanying films to their credit.

Many philosophies have a soulful message to bring the regular everyman (or cinemagoer), especially ones to do with some form of psychology, but may have a hard time getting that message across due to, for example, technical or obscure language. A film may have a lot to say to its viewer but would suffer for putting its message too bluntly. Film's advantage lies in the fact that it gets more and quicker exposure to more people. These people are bound to read the films differently, P- or N-minded as they may be, but anyone with a sufficiently open mind is bound to find a film which speaks to them on a personal level, as so many philosophies are meant to do.

It may take a conversation after a film with a more philosophically acquainted friend to make some of the connections, but that should not subtract from the relevance and relation one feels to a film and its message, whether fully intended or no. One of the film's reviewers put it well enough when he said that “living in and through movies is not a solitary neurosis but a mode of communion” (Scott, 2004).

Notes

1. There are of course varying levels of analogy, so to speak. It is hard to imagine a sensible adult incapable of reading between the lines in stories such as Aesop's fables. Analysing more complex stories as those in films with multiple interwoven plots, variously relatable characters and veiled messages is a different, bigger task, but not too taxing.

2. The use of the word 'spell' feels especially appropriate since Sartre himself, in Sketch for a Theory of the Emotions, speaks of the 'magical'. When consciousness is faced with an extreme or dangerous situation which it can not deal with or overcome, it tries to change it's own perspective of the situation. It transforms the experience almost as if by magic. Some may, for example, “choose” to faint in such circumstance to escape from what goes on and evade the danger or humiliation.

Bibliography

Cox, Gary. The Sartre Dictionary. London: Continuum, 2008.

Sartre, Jean-Paul, trans. Hazel E. Barnes. Being and Nothingness: an Essay on Phenomenological Ontology. London: Routledge, 2005.

Sartre, Jean-Paul, trans. Philip Mairet. Sketch for a Theory of the Emotions. London: Routledge, 2004.

Scott, A.O. "When to Be Young Was Very Sexy." Review. The New York Times. http://www.nytimes.com/2004/02/06/movies/film-review-when-to-be-young-was-very-sexy.html?src=pm. Accessed 22/11/2011.

Copyright; Gestur H. Hilmarsson, 2011

For no specific reason I decided to put up here a recent essay of mine regarding philosophy of computers and mathematics. I don't expect many or any readers, but those curious enough are welcome to it. The text and paragraph format is a bit messed up, but nothing serious.

In the early years of computers, around the middle of the 20th century, there was much excitement within academic circles over questions of the nature and possibilities of these new machines; their potential for good (and, to a greater extent with science fiction authors, bad) and whether further developments and investigations might shed a new light on man and his mind.

While imagination was often a ruling factor in projections for this technology, where some prophesied much smaller and slower advances than we are familiar with today and others saw no objections to the possibility of outlandish science fiction coming true in the near future, there were those who took a different, more logical and systematic approach.1

What they did was ask a simple, 'binary' question: Are minds machines?2 If so, the possibilities of advances in computer technology would seem without boundaries, aided by the progress in knowledge of the functions of the human mind, each progressing field feeding of the other. But if not, there would appear to be at least some recognizable boundaries; we can not say what a computer might be able to do in the future, but we can say what it can not do no matter the technological breakthroughs: be human.

The arguments for either answer have found new support with each step up in computers' complexity, so what evidence one finds depends largely on the date of each argument. The same is true for most sciences, but computers are in a unique position due to the speed and near instant applicability of its advances. Still, there is a general consensus that primary logical and mathematical truths will not be affected by your everyday, regular technological revolution.

This is what allowed logically thinking and computer curious academics the smart move of viewing computers of their day purely as systems and by clever application of logical advances, made in the decades before them, define the nature of the thinking computer and its limitations.3

In this paper I will make clear one of the more famous and elementary theories or explanations for the difference of computer and man, the one made using Gödel's theorems. It was made quite long ago, before the biggest leaps in computers' evolution had been even foreseen, so many may and do use the argument's age against it. But consideration of a few definitions, which I will begin with to regulate our concepts, should help the reader to recognize the missteps, the fallacies, the category mistakes in those counter-arguments, as the argument shows quite convincingly that ignoring it leads to contradictions and inconsistencies right out of the gate.4

After explaining some basic terms and concepts, I will explain briefly how Gödel's theorems apply to the problem at hand, along with propositions to keep in mind when it comes to further objections. Then , to approach each main problem posed by the mechanistic view of the mind.

Mainly they include matters of a mind's deductive abilities, consistency and whether it is to be considered a formal system or not. Finally I hope to shed some light on the significance of this question and topic, and in what way its conclusion may affect philosophical thinking.

To begin with we should be clear on the terms with which the arguments are made. First and foremost, when we talk about computers in the case of our question, we mean any functional Turing-machine (TM). In Turing's own words, a TM consisted of:

“...an infinite memory capacity obtained in the form of an infinite tape marked out into squares, on each of which a symbol could be printed. At any moment there is one symbol in the machine; it is called the scanned symbol. The machine can alter the scanned symbol and its behavior is in part determined by that symbol, but the symbols on the tape elsewhere do not affect the behaviour of the machine. However, the tape can be moved back and forth through the machine, this being one of the elementary operations of the machine. Any symbol on the tape may therefore eventually have an innings.”

His use of the word 'infinite' may give a clue that this is indeed only an allegory for what an algorithm in fact does, since infinite things are of little help in a construction such as this. Each TM goes through a computable sequence of commands according to its state at each time.

In addition to this is the Universal Turing-machine (UTM) which is capable of simulating the functions of any other TM or collection of them and will be the concept by which we define the machines we discuss and compare to mind in this paper. The common computer we know and love today is (most likely) the closest approximation to this UTM yet. Now it may seem easy to point to the brain as an extremely complex UTM, but familiarity with computing's background in logic may make the comparison more difficult.

On that note that we turn to Gödel's theorems, or more specifically, his two incompleteness theorems. A quick, borrowed definition from the mathematician Stephen Cole Kleene of the first theorem might look something like:

“Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”

In short, in a formal system, which is without contradictions and able to solve basic mathematical problems, one can build a statement which is recognizably true, but out of the system's powers to be proven as such. From that follows the second incompleteness theorem:

For any formal properly generated theory F, which includes basic arithmetical truths and certain truths on formal provability, if F states its own consistency then F is inconsistent.

That is, should said system manage to state its own consistency, something must be wrong and the system therefore inconsistent.

So, each consistent system can state a truth which it can not prove, and neither can it prove its own consistency. A convenient truth-statement for the issue at hand here would be along the lines of “This formula is unprovable-in-the-system”. This is a type of statement which we, from Gödel's work, suppose any consistent system can make. But obviously it is quite loaded, since if the system would manage to prove it, it would completely contradict itself, and therefore reveal itself as inconsistent. We, however, can recognize its truth value within the system. We accept it and move on.

Although the matter of fully proving and solidifying the preceding definitions would take a lot more effort and space than this paper allows, along with fitting and impressive formulas, the basic understanding presented here will do for us to move towards the main arguments for and against the proposed identity of computers and minds.

I will refer to those who deny the difference of computers and minds as 'mechanists', since to say that a mind or brain works like a computer, although a remarkably complex one, is to say that it obeys the same laws as computers and machines, and therefore mechanically deterministic, or mechanistic. For the mechanist to prove his theory, above simply pointing out similarities, he would need to be able to build a computer not only comparable but equal to a mind. We would even accept his argument if it were only demonstrable in principle, and not practice, within our imagination or lifetime.

The strong mechanistic view holds, in short, that minds are nothing more than complex machines, UTM, whose only call to mystery is the lack of human understanding of such complicated neural systems. With further advances in science and knowledge of the brain, it would be within human might to explain how sensory experience works on the brain just as computational input does on computers, how the brain stores it like a computer would, and how the person's actions and reactions may be explained as output. As with a computer, the mechanist would explain human behavior (internal as well as external) as obedience to programming which declares how the system should react to each current state. Turing's imaginary, infinite ribbons would thus belong to the mind as well.

What would follow is the fact that should we know as much as would be needed, for this analysation of the mind, every action of a person should be entirely predictable. Although an interesting and important point to keep in mind, we're still focusing on what a, let us call it a computer-mind (CM), would do if it existed. But more to our point, we must consider what a CM could do. In other words, we will take care of 'practice' by tackling 'principle', and since near- infinitely complex computers may be capable of fantastic things, for brevity's and convenience's sake our question might thus be: What demonstrable human qualities could a CM not have? Note that I choose not to ask what it could 'simulate', since surely we are not looking for the possibility of a computer seeming human, but actually becoming human (as far as 'human' can be used as an adjective about anything that is in every aspect like a human being).

Since predictability was mentioned already, we may do away with that option first so not to complicate the string of arguments too much. Since I can not hope to prove the idea of free will in this paper, I will make a concession and mark human decisions down as acts of randomization. We can easily imagine granting a computer advanced randomizing elements. So advanced, in fact, that they are humanly and practically unpredictable. A computer might be free to add or subtract any number to each side of an equation. Imagine that its decision is determined by how many radiated atoms of a certain sort in a certain led box have deteriorated in the last millisecond, or whether the amount of leaves of a certain weight the computer can hear rustling in the wind outside its office is a prime number or not.

The results would seem entirely unpredictable, but the fact remains that the computer would make the calculations with the purpose of choosing between determined options. It can not choose just anything to add or subtract in the equation we put before it, since it must choose from a selection of numbers that make sense. Anything else would cause a contradiction with following inconsistencies. A machine is programmed, and would thus always be picking out of its designated bag of tricks when faced with mathematical problems, no matter how random its eventual choices might seem.

From this it seems granted that however complex and intricate a computer and its possible actions would be, a human mind could observe it for long enough to collect and write down its various states, decisions and resulting states to finally have a complete, formal explanation of that computer's system. Even if we assume that the computer might go on to surprise the human mind infinitely, we will also assume an infinite presence of human minds with infinite amounts of pens and paper to achieve this formal account.

Furthermore, we would only be interested in the system's sorts of operations, which must be finite in number, each one adding to our understanding of its various underlying axioms. Imagining a machine with infinite sorts of operations would be imagining something else and more than a machine and no longer relevant to the issue at hand. When all of the system's states and actions would finally be accounted for, we humans could proceed to 'Gödelizing' it by producing the infamous truth-statement which could not be proved within that system. We would expose its Achilles' heel which the system itself was incapable of recognizing as such.

In summary, a computer in so far as it is a machine, however complex, will always follow a formal system which is liable to being Gödelized by a competent human mind. The fact is, as J.R. Lucas put it, that

“[w]e are trying to produce a model of the mind which is mechanical – which is essentially “dead” – but the mind, being in fact “alive”, can always go one better than any formal, ossified, dead, system can. Thanks to Gödel's theorem, the mind always has the last word.”

A common mechanistic objection applies, in some way, to most of the points I have made so far. I mean the suggestion that a more complex computer might always be built after a previous one has been trumped by a Gödelian formula. Obviously there are immediately two faults with that suggestion. First, constantly building another system is only to admit the deficiencies of all earlier systems. And second, the same would still hold, that each renewed system would have its own chink in the armor to be exploited by Gödel's theorem, rendering all the mechanists' hard work unnecessary. Could we then not instead integrate some fail-safe in the system which would allow it to resolve each Gödelian truth-statement as soon as it was made, and thereby prove itself consistent in an infinite sequence of 'leveling up'? Would we allow such an infinite process, the computer would be above and beyond any definition of a 'machine' relevant to us, so the possibility is dismissed without much consideration.

The point here is not entirely to argue for the mind's superiority over computers. After all, it is easy to find relatively simple computers which can answer mathematical questions which, in practice, no one human's lifetime would last to solve. Turing himself commented that a human being's 'victory' over a computer can only be a petty one, since there can always be so many other computers far more capable.

But again, the aim for the mechanist must be to prove that a single computer could exist which could do everything that a mind could do, not just any thing. It may be easy to find a question which a computer gets wrong, but even easier to find one for a human. But isn't there a fundamental difference in what actually happens when computers make mistakes, as opposed to humans? I will argue for my answers to that question further down.

Before I get further off track, the point must be made again, in answer to the above discussed objections, that we are not looking for superiority of mind or machine, but identity. So the slightest difference, even if discovered through petty victories, is enough to lay ruins to the mechanistic argument.

Now we can face and move to a series of more radical and fundamental objections raised by the mechanist against a difference of machine and mind. Gödel's theorems apply to systems which are (i) deductive, (ii) consistent and (iii) formal. We may ask ourselves whether human beings can be said to truly have any of these three qualities, and if they can then be treated as systems comparable to computers. It may probably be safely assumed that a human mind is at least not completely deductive, consistent and formal. So, will the mechanists then propose their computer be built to be equal to humans in their lack of these qualities? I will now approach the possibility and relevance of each in an orderly fashion.

Deduction

In order to free a computer from totally relying on deduction, one might imagine giving it a feature similar to creativity or original thought. In addition to its built-in axioms, which dictate all of the system's inferences and actions, the computer would ponder various propositions not generated by its own axioms. By some standard, it would then decide whether to add this new proposition to its collection of axioms or discard it.

The computer would consider keeping the proposition at least as long as the it did not cause a contradiction with the preexisting axioms. In that case the negation would be added instead. So, this computer would then have axioms and propositions not approachable through its system's axioms and native rules of inference. This would make this particular computer more similar to a human mind, the mechanists hope.

However, problems follow. A system like this might end up in odd circumstance, like having both accepted a Gödelian formula and its negation, since both are unprovable in the system. It might also choose to accept a yet undecidable formula, and ignore its negation from then on, when in fact the opposite would be right. In any case, even if the system would not appear inconsistent immediately, it would be unsound. This would disqualify it from being considered a model for a mind.

The argument would actually not even have to go that far. Consider what we have already argued earlier. We will say that since the system is not random, and thus still deterministic, and we grant the imagined possibility of observing it infinitely, there would come a time when a formal schematic of the system had been drawn up and a Gödelian formula then constructed.

Consistency

Possibly the weakest point in the defense of a mind's superiority over machine is the fact that we can never fully, absolutely, categorically state that a system is consistent. The truth of the matter is that we can only examine a system and tell if it seems consistent as far as we can tell. This is because, as Gödel showed, a system can not prove its own consistency.

We use another system to prove the former's consistency, but that latter system then requires another to prove its own, ad nauseam. Furthermore, wherever we are placed in this infinite regress, it is the human system which judges whichever other system's consistency, and we have only ourselves to state our consistency. The problem is obvious and awkward, and academics like Putnam have indeed stated that man is a machine, and an inconsistent one. Gödel's second theorem would forbid us to state our own consistency.

The only way to save the mind would seem to be to discover some distinctive attribute which allowed the mind to bypass this last hindrance and state its own consistency.

However, this pigeonhole which the mind is squeezed into under the banner of not having the right to judge about consistency assumes that a machine and mind would be inconsistent in the same way. After all, only one inconsistency need be exposed for a system to be deemed inconsistent. But common sense will show us that there is distinct difference. A machine's inconsistency comes about when it believes both a statement and its negation, and tries to work through its processes and computations unaware of this illness. A person will not believe a contradiction in the same way, but may be mistaken for a while until encountering circumstances where the misunderstanding will be cleared, hopefully without much effort.

The mind isn't functioning while a blaring logical inconsistency thrives within its system in the same way a machine could be said to. In an inconsistent, formal system anything can be proved. An inconsistent (yet sane) person will however not believe anything and everything. She chooses between beliefs at various points, and may change her mind when confronted with evidence. She is fallible. After all, errare humanum est.

The mechanist must be allowed a proposal here, and most likely he would suggest a moderately inconsistent machine, to simulate humanity. It would have to be self-correcting, as humans are selective; fundamentally inconsistent, so as not to be entirely deterministic; impervious to Gödel's theorem and yet entirely credible as a thinking mind.

There are various ways of going about this, but most seem to involve severing the system's strings of deductions and inferences so as not to arrive at any troubling inconsistencies. What we would need to introduce is some kind of a stop-rule. It would allow/force the machine to choose between deductions based on convenience, it would seem. That is hardly comparable to a human mind, although it may serve a purpose in the odd occasion for a human to suspend an inconvenient truth at least temporarily.

But to have each case of modus ponens (MP), to take an example of a simple enough deduction, subject to this treatment does not fill one with trust in the system. In an argument with another mind, the computer could use MP for its own evidence, but dismiss the mind's use of the same method simply because of the prospect of a contradiction. A similar argument between equally capable minds works in a way that each mind can follow through with each case of MP, weight and measure the relevance and soundness of the evidence, and finally come to some agreement or conclusion.

In the larger scope of things, human beings indeed live under the threat of discovering their belief systems and even logical truths to be inconsistent and contradictory. While a computer would in that case, presumably, come to a standstill or break down, the human race has the potential to rearrange and adapt to the new situation. We would recognize our opposition, the contradictions, and mend them. Again, J.R. Lucas phrases the conclusion well:

“We may be consistent; indeed we have every reason to hope that we are: but a necessary modesty forbids us from saying so.”

Formality

It now may seem like the human mind is stuck under the mechanist's heel, because of the insurmountable doubt whether minds are to be considered above machines, since we are unable to state our own consistency. Gödel's second theorem, which we meant to use against the mechanists, has turned in our hands. That is, if we keep consenting to being considered formal systems for the sake of the issue at hand.

The theorem, in fact, would state that a mind, if it was in fact a machine, could not conclude to be consistent. If the mind is not a machine, however, the theorem does not apply. Even though a mind can not construct a proof of consistency of a system within that same system, the possibility of what the mind is in fact doing, stepping outside the system, is not excluded. We are able to stand back from each system and construct arguments, both formal and not, for systems, both formal and not.

The result is what we can not completely formalize our argument about the system, but that is the point of Gödel's theorems after all. In the end, we simply decide that we are consistent, since we are capable of thought and function. A mind built out of an inconsistent system would not function, since it could hold and believe anything and everything.

Now to mention the proverbial elephant in the room: self-reference. The gist of a Gödelian formula is, almost ironically, its implicit self-reference. It is constructed and tailored to a particular system in each case, so the system is being asked to consider its own processes. We ask of the system to tell us what it is and is not capable of doing, and should it actually try and answer it would inescapably end in a paradox.

A similar process is involved when a human mind asks itself how and whether if actually knows what it thinks that it knows that is knows. It leads inevitably to an annoying, puzzling regress before the mind simply drops the question as pointless. Were a computer asked to consider the same question it would check internal states and processes as something it holds to be true, and not as something it finds interesting to analyze and mull over. It would do this step by step, going through deduction after deduction. A person, rather than going through a systematized sequence of thought-processes, looks at itself and its thoughts as a whole before realizing the pointlessness and may choose to give up.

In summary, for a machine to be able to consider itself as a person does, it would have to be have a way to step back, with the help of some added part, like the proposed infinite Gödelizing additions mentioned earlier. That would, as explained, make it a different machine than the one asked to consider itself, and the regress goes on. A mind needs no extra part or help to metaphorically step back and consider itself. It considers itself, other things, and itself as other things (figuratively speaking), yet always remaining a complete entity. This paradox of the human consciousness has more to do with the question of divisibility of parts of thought, body, personality and so on, and is beyond the scope of this paper.

A very interesting point raised by Turing has found a growing number of supporters as computer technology advances. He realized how early in the computer's infancy many of the arguments I have touched on here were made, and implored his critics to consider the future. The computers available for testing back then were fairly simple, so a machine's consciousness might lie in its eventual super-complexity. After all, were a computer to be compared to even the simplest of human brain, it would have to be astronomically complex. He imagined some critical level of complexity which would have to be reached before original thought sparked into existence. He described the “qualitative difference” between simple and more complex entities.5 Today these are described as “emergent properties”, such as water's wetness in spite of each atom not being anything we would call 'wet'.6

There are even currents within phenomenology today which deal with the same questions and terms. These debate what collection and degree of psychological and phenomenological characteristics an entity needs before a mind/personality emerges, and whether this self is a part of natural evolution or something external, secular and independent.7 But that is again beyond our scope.

Still, the communal quest is after the definition of what is needed for a consciousness to thrive. Is it complexity, or some unfamiliar element without which we can only hope to make more complex but never quite human machines? From what we have covered here I feel comfortable in concluding that, whatever turns out to be needed when this artificed consciousness sparks to life, what we will be dealing with is no longer a machine in the relevant sense and thus outside the mechanist's view. It will be unpredictable, and not only due to randomness or inconsistency. It will act outside the rules of any analyzable programs and axioms. It will no longer be determined by its internal states and the rules of inferences therein. And, of course, it will escape the clutches of the Gödelian formula, since it is not a machine. This creation will be the equivalent of the conception of a human being, even though this person is made up of mechanical parts.

What may we now have gained from dismissing the mechanistic view? A debate like this may seem to belong among philosophy-minded computer enthusiasts, and in some ways epistemology (What are thought and knowledge?) and metaphysics (When is an entity human?) but not have much relevance to more critical fields of philosophy such as ethics.

Closer consideration will reveal to us more severe implications, though. If people are mechanistic, determined vessels, they are anything but free, autonomous beings able to act morally according to their own convictions. Without probable explanations, like Gödel's theorems have allowed us to make, morality often ends up being tucked under semi-mystical or religious agendas, looking away from advances in fields of science to do with neurophysiology and others that give insights into functions of us as thinking beings. We no more find ourselves as torn between cold science or leaps of faith. There are fantastical advances in store for computer sciences still, but so long as the human mind is hovering over the circuit boards there will be an added element in the mixture.

Notes

1. I am reminded of an anecdote from 1969, year of the Moon-landing, about NASA's fantasy of one day fitting their computers into a single room, while I type this essay using a comfortably sized laptop computer capable of far more complex calculations than NASA's in those days.

2. The reader should keep in mind that throughout the paper I will use the words 'computer', 'machine' and to a lesser extent 'system' almost interchangeably. A machine is any mechanistic contraption, and with an added formal system we have a computer. For all intents and purposes of this paper this should not cause too much confusion.

3. We are, of course, discussing only binary computation here, where computations and processes follow rules of 1 and 0, Yes and No. The mentioned, curious academics might perhaps specifically be called 'bi-curious'.

4. The term 'category mistake' was termed by the philosopher Gilbert Ryle in his 1949 book The Concept of Mind. It describes an error where “things of one kind are presented as if they belong to another”.

5. One of the more famous thought experiments to do with complexity is the China brain experiment, originally introduced by Lawrence Davis in 1974. It proposes that every person in China were given a role similar to a neuron in a brain, made to interact with each other, and then asks whether something like a consciousness might emerge.

6. This particular example comes from Kristinn R. Þórisson's paper Machine Consciousness, Consciousness and Self-Consciousness in Meat Computers and Robots (authors transl. of Vélvitund, meðvitund og sjálfsvitund í kjötvélum og vélmennum) from the collection Is Matter familiar with the Mental? (author's trans. of Veit efnið af andanum?) where he wonders where the 'wetness' is stored in a waterfall, discussing the significance of complexity in artificial intelligence.

7. A very prominent thinker on this subject is Thomas Metzinger whose book, Being No One. The Self-Model Theory of Subjectivity (MIT Press, 2003) has stirred many in the phenomenological field, as he claims there is in fact no such thing as the popular understanding of a self.

Sources

Penrose, Roger. Shadows of the Mind: a Search for the Missing Science of Consciousness. London: Vintage, 2005.

Lucas, John Randolph. "Minds, Machines and Gödel." Oxford Philosophical Society. 30 Oct. 1959. Lecture.

Kleene, Stephen Cole. Mathematical Logic. New York: John Wiley & Sons, 1967. Turing, Alan. "Intelligent Machinery." Cybernetics: Key Papers. (1968).

Steinar Örn Atlason and Þórdís Helgadóttir (edit.), Is Matter familiar with the Mental? (Icel. Veit efnið af andanum?). Reykjavík: Heimspekistofnun, 2009.

Copyright; Gestur H. Hilmarsson, 2011

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