Tuesday, 29 March 2011

Impenetrable Depths

Sadly I must subject you poor JOHNSPACE readers to another Kafka post, because there's a huge part of Kafka's psyche I totally ignored in the last article.

There are, ultimately, two meanings to any piece of Kafka's writing - one is about society and the dilemma of the modern man, as I explained before, and the other one is about death. Kafka, being the paranoid and intensely self-aware, was not only wary of his place in society but his place in life and the role of his life in the world around him. For him, life was not simply an endless journey, but a clear beginning-middle-end with which to spend your time wisely - if at all possible.

A few years ago I was looking up quotes for a blog post and I absent-mindedly came across a quote of Kafka's, before I had read The Metamorphosis, which was this: "The point of life is that it ends". And it's amazing that Kafka, who we often disregard as being overly pessimistic or just downright depressing, here makes his most starkly meaningful statement. The point of life is that it ends. Life leads up to death; is defined by death. Ever since seeing that quote, I've had an interest in how death should sit in life and what its purpose or meaning is, if any. Kafka was obsessed with that thought, much more than my vague interest which never failed to pop up every month or so of my 365 project last year. Because it's so intriguing, that everything we do in life is ultimately irrelevant in the face of the greatest barrier known to man: death. No man, however clever, however inventive, however healthy, can overcome death. It's a ticking body clock that starts at birth and winds down to death, and for most of our lives we ignore it. Most people simply don't think about it, out of pure ignorance of lack of deep thought. It's complicated and worrying and should therefore not be thought about.

But Kafka was plagued with death. So much so that he was overcome with paranoia, intense sensitivity and anxiety that made the later years of his life almost unbearable for him. It's no wonder his worries weakened his health and he caught TB and died at the young age of 41 in 1925, luckily before all the pain and strife he would have experienced if he had lived through World War 2. Nowadays people live for twice that age, imagine what new wonders we would have to interpret had Franz Kafka lived for twice as long. It would surely be brilliant for him to turn out something better than The Metamorphosis or The Trial, but in a way Kafka's early death is an important part of his character. In a way, a man who thought so deeply about death and respected it so honourably has no better destiny than to accept it early in his life. It's sooner or later.

On a side note, it's interesting to read that Kafka was decided on his role in life rather than being helplessly aimless. He writes in his diary in June 1913: "The tremendous world I have in my head. But how free myself and free it without being torn to pieces than retain it in me or bury it. That, indeed, is why I am here, that is clear to me." How peculiar of Kafka to be so determined of something so life-defining, but that can be explored in further posts (most likely in my head).

But, back on the topic of death, one brilliant short story of Kafka's stands out to me as being a complete, perfectly formed, clear analogy to what Kafka perceived death to be. The story is called A Dream, and explains the dream of Josef K. (an obvious pseudonym for Kafka, and obviously so), probably a dream that Kafka had himself or based on a dream he had and augmented to be more meaningful. Either way, I really love A Dream, and have read it three times now (more than I have The Metamorphosis, which to be honest takes so dedication to read).

The story goes like this: Josef K. is dreaming, and is walking along when he almost immediately comes to a cemetery. The paths are long and winding but he finds himself attracted to a grave in the distance, which "exerted fascination over him" and he "felt he could not reach it fast enough". If that's not a clear analogy for life and how Kafka sees life as a winding journey to a finite location, I don't know what is. For Kafka, he couldn't reach death fast enough - he was so amazed by the concept that it seemed almost like a state of judgement for him, judgement for the complicated life he led with complicated interactions and complicated people. Death is a singularity, a grave, an ending.

But an ironic thing for Kafka is that "his view [of the grave] was obscured by banners which veered and flapped against each other with great force; one could not see the standard-bearers but there seemed to be a very joyous celebration going on." It is only Franc Kafka who could describe the pursuits and distractions of life as banners flapping in front of his view of death. Perhaps these banners are other people, distracting him from that one definite occurrence, his death, which he can often see at the end of his life? It's brilliant how much you can interpret Kafka's stories.

I will jump to the end of the story, for though it is short it is also full of possible analogies that I have neither the time nor the patience to go through and analyse now. Suffice to say; Josef K. meets a artist at the graveside and the painter is writing the dead person's name on the grave. But before he can inscribe the name, he cannot go on. An awkward silence ensues between the two in which K. feels "deeply embarrassed and yet unable to explain himself". Finally, K. starts to cry with the horrific misunderstanding between him and the artist, so the artist reluctantly starts to write the name on the grave - "J" he starts, and finally Josef K. realises and digs away the thin layer of soil above the grave and sinks into the hole below. He wafts down the infinite hole, and "while he was already being received into impenetrable depths, his head still straining upwards on his neck, his own name raced across the stone above him in great flourishes". There really is so much to extract from this, I'll leave most of the interpretation to you but I'll leave you with this: Kafka in fact does not fear death like most people do, he in fact feels he is not complete and honourable if he has not died. Society expects him to die and it prevents pain on his and its part for him to succumb to death. And Kafka explains death as "being wafted onto [one's] back by a gentle current", into "impenetrable depths". Despite all the turmoil and anxiety in Kafka's life, it seems death is a final time to relax, to look up and see your life fading away from you, knowing your chores and your tasks and your purposes are gone and completed, your life finished and your name written on your gravestone. No more needs to be done, no more needs to be said, to be written. Kafka sees death as the ultimate ending, freeing him of all the responsibilities of the modern man - and of any man - that make life for him so unbearable.

tl;dr - Kafka loves death and thinks life is a chore. Also, he has brilliant dreams.

~John

Tuesday, 22 March 2011

Kafkaesque

Today I will attempt to talk about a man who has eluded and confused the world ever since his death. And eluded and confused his friends before his death. If you didn't understand Inception, don't bother reading his work. If you didn't understand Synecdoche, New York, have a go but you'll be fruitless. This man's name is Franz Kafka, and he was an Austrian writer and general pessimist. When asked 'is the glass half full or half empty?', he'd answer 'what's the point in a glass anyway? Every sip takes us closer to death'. He was that kind of guy.

Kafka's work is mysterious, highly symbolic and pretty much define the term 'more than meets the eye'. I often read his shorter stories - only a page or two long, but so much can possibly be taken from them that they may as well be a whole novel. Even greater than the meanings of single stories, it seems to me that Kafka's work is all related fundamentally to his mentality and the struggles he found in his life related to fitting in to society and being a modern man. Forever he is creating social stereotypes, picking out every unnecessary detail of a chance encounter with a stranger, wondering who is thinking what, who is thinking what about him, and what others' opinions of things are. He is a man constantly plagued by the existence of so many others, so many others he doesn't know, around him in such a bustling society as 1910s Prague. And yet this predicament of the modern man has changed little since then! I sometimes find myself thing Kafkaesque thoughts, the world being full of foreign souls, that can never be understood and are therefore a menace.

One story of Kafka's that shows this the most is The Bridge. In it, Kafka tells a story of a bridge spanning a small river in first person. The bridge has its feet on one side and its hands holding the other side of the river and is strong and proud of itself. It is not on any map as of yet but is happy enough waiting for its use by some unknown user. Then, the bridge encounters a man, a hiker, who tentatively taps the bridge with his stick then jumps right into the middle of it, causing the bridge to be shocked and attempted to "turn around to see him" - which in fact causes the bridge to break and fall onto the jagged rocks which had beforehand seemed so safe from when the bridge was firm.

God knows how many interpretations that story could present, but I'm going to continue the line of investigation into Kafka's fear of the modern society. The bridge is like a person, strong of itself and not fearful of another person's interference into what people would nowadays call their 'private bubble', or their personal lives. The bridge's entire purpose is that of interaction with a person, it's what it lies in wait for for so many years. It's not labelled on any map - not known, but out there to be discovered. However, when it encounters what we can assume is its first user, or first user in many years, it is immediately hurt and is affected by the appearance of someone so close to itself. Suddenly, not expecting someone to actually come along and use it, it turns in horror and is destroyed as a result of the one thing it exists for. Perhaps this is how Kafka saw himself - a man, an island, happy to be on its own but forever waiting for someone to come and interact with it, maybe romantically. The moment someone does, that hope is turned into fear and the person wants nothing to do with other people; in fact their life is ruined by having those foreign elements in it. Conclusion: your life is fine unless you interact with anyone other than yourself.

Such morals are found everywhere in Kafka's stories. For example, The Confidence Trickster, a study of a particular character you would not want to be deceived by, and The Sudden Walk - in which the protagonist suddenly walks out of his cosy home to encounter the cold, faceless streets and is distracted from himself as a result. It's a recurring theme, and also key to Kafka's masterpiece and - I believe - his best work, The Metamorphosis.

The Metamorphosis is the most accessible of Kafka's stories because it is so unusually formally structured and begins with such a simple and understandable idea - that you wake up from sleeping in your bed to find yourself transformed into something horrific. Right at the start we have the concept of deceit from something you trusted - your simple humble bed, your home, your family, your shelter. And, due to no fault of your own, you become something that sets you out from society in the worst way possible - being a giant insect. Suddenly your family is turned against you, the entire city is against you because you are different. A totally respectable man - Gregor Samsa, I believe - is a public humiliation and object of hatred the moment he wakes up. Social embarrassment is another theme Kafka loves experimenting with. Then, poor Mr. Samsa, confined in his room and listening to his distraught family discussing him outside the door (specifically, how he should get to work on time), also struggling to come to terms with his many new limbs, finds a friend of sorts in the cleaner sent to clean out his room. She and him are brought together by being two social outsiders. Then, naturally, Samsa is hit by an apple and dies a slow and painful death, still inside his bedroom.

Suffice to say, Franz Kafka was a very pessimistic guy but also a very clever guy. On the back of my Kafka short story book it says 'Kafka's predicament is that of the modern man', and I think if we're going to take anything from this post, it's got to be that. Kafka experienced social life as an outsider, fearful of anything that wasn't him and fearful of the community itself. It's not a bad thing most of his stories are about him; he's not conceited - rather, afraid of having any sort of self-confidence taken from him by the dangerous free radicals that are other people. Because he knows that, someday, one of those free radicals will get too close and he'll come crashing down - and that peaceful stream he felt so safe from beforehand turns out to be his greatest foe.

And in every one of Kafka's stories, whether society-related or not, based on characters from dozens of cultures and settings, we see a little more of the frightened, sensitive man behind the pessimism. It's like Kafka's mind is a plateau and each story offers a hole punched through to reveal the true personality beneath. The Metamorphosis offers a large, very accessible hole, so if you're going to attempt to understand Kafka I recommend you read that. Or even if you don't care for the man himself, I recommend you read The Metamorphosis. There is a lot to be interpreted from such a short read, and since it's a bit more to-the-point than FK's other work, it's a damn good start on a whole range of Kafkaesque wonders.

~John

Sunday, 20 March 2011

Portraits

Well hey guys, it's been ages. Many apologies. Today I bring you something a little more mainstream (Argh! I burns my hispter eyes!) in the form of a bunch of photos from my recent photo-taking sessions. After that bunch of black-and-white photos, I've returned to the usual, more flexible format of colour film. And, even better, I've found a developer who won't fuck up every roll I give them - Bonusprint - who may take a while to send your films back to you but it's cheaper than Jessops and the results are perfect. Thanks, Bonusprint people!

Before we get onto two colour rolls of pure awesomeness, I have one final black and white to show you. I don't think I showed you the others, but never mind - you can find them all on my photostream a page or so back. This photo is the second in a long-running photography project of mine, Skylines. It's basically just Intersections, but in the sky. The idea is that grounded and flying objects interact with each other and with the frame, creating unique and unusual compositions with telegraph wires, planes and birds. The first photo was simple some pylons and a moody cloudy sky, and now I've started interacting the pylons with planes:


It may seem empty and basic, but it's a simple composition and that's what I wanted to achieve. The two lines (pylon wires) give the idea of a runway, something extending out and creating thrust to the top-left of the frame. The plane accentuates this and gives it purpose and a vague meaning (runway? The aim of the plane? Something along those lines). That's the general idea. I hope to extend and continue the series in further rolls, but all in good time! It's a long-scale project.

Next up is the first of my portraits. For my current GCSE art project (which sadly fuels most of my photography nowadays), I have decided to take a break from grungy urban architecture and Skylines. I'm moving into a much more emotive artform, the portrait. Unlike blocks of flats, people give off distinct, passionate and sometimes disturbingly clear emotions in their expressions and poses, and we can use photography to enhance that. I read somewhere that in Tess of the D'Urbervilles, Thomas Hardy uses the descriptions of the background, setting and other people as a sort of mirror for Tess' emotions. What she feels and what she thinks echoes in the world around her, for she is the centre of the whole novel and everything eventually leads back to her. This is an idea I really want to explore in my photography over the course of this gosh-darned art project - reflecting emotions of the subject in the background so that the emotion is both clear and deeply set into the photo.

But, before I get into that, I need to get used to taking portraits. The only portraits I've taken of any note were a bunch of cast photographs for my youth theatre group's production of Alice in Wonderland back in the Summer, a bunch of digital photos against a shitty backdrop with shitty lighting and me not doing much work to make it look less shitty. I'm not including those in my portfolio; they're behind me now and portraits with film is a whole new start.

Thus behold, my friend Rob. In our school hall. In front of a projector. With the focus a bit off and a bit wobbly. Imperfect but perfectly so. Or something like that. I like the imperfection of it, despite my perfectionist ways. Sure, the motion blur doesn't help, but the softness of the photo and warmness of its colours seems to make this a good pic for me. Not a proper portrait - none of these are - but more a photo-of-a-person portrait.


Also on my second roll is this photo of Tim, a guy in my art class, sitting in my art classroom and generally looking moody and very cool. I reiterate what I said earlier; these photos don't necessarily show the personalities of the person in them. They're just emotions, not the genuine people. Because though Tim may have one heck of a badass fringe, he's a really nice guy and is rarely moody. And Rob doesn't always have a rainbow on his hair.



In the half term I did my first photoshoot, with my photography friend Olly, my not-so-photography-but-she's-actually-very-good-at-it friend Zoë, and her friend Maria. Yes, it was freezing cold, and it rained half the time, and my jeans got muddy (ooh sissy me). But I got some goddamn good shots out of it, if I don't say so myself. Here are the four best ones that I put on my Flickr:

Zoë, the first location thingy we did.
Maria, Zoë, bokeh.
Same angle, better pose, better light. Mmmm, glowy.
Maria by a tree
I'm only two rolls into this project (will probably be six by the end), but it's already had a dramatic effect on my photography. I see photo opportunities that I would beforehand have loved, but in the absence of someone to pose for me in front of it, it seems lifeless and emotionless. Sure, there are still good personless photos, but photos such as a nice shot of the blossom on a tree on my road don't entice me like they used to. Have I moved up? No, probably not, I've just moved away. Into a different field of photography. And I really love it. All I need is more people to pose for me, but there seems to be no shortage of that, whether it's people who want to model like Zoë or Maria or people who get told to stand, whether they like it or not, in my photos, like Rob and Tim. Thanks to you all.

And, before we go, here's a non-portrait, a shot of Zoë's awesomely retro suitcase:


Mmmmm, short DoF. How I love you. I'm just perfecting my portfolio right now, kids, so expect more posts about my creative projects very soon - including furniture! Proper furniture! Oh the exictement!

~John

ps. It's been so long. I hope you didn't all judge me on that dimensions post; I had to indulge.

pps. Dammit, I'm reading Kafka again. I'm formulating a Kafka post in my mind, I'll try and get that done for you guys.

Sunday, 13 March 2011

Cartesian what now?

OK guys, for today's post (jeez I need to post more often, jeez), I have a little bit of maths for you to comprehend. OK, it's not that maths-y, it's the sort of thing that I would have put up on Dimensionality back when it was alive. Let it be known before I start my multi-dimensional ramblings that this is something that I worked out a few weeks ago, but it has actually been worked out differently and 'properly' by mathematicians decades ago. Sure, maybe I'm wrong in some places because I'm not au fait with the proper notation and I'm not going into tesseracts and shit like that, here's the theory. And just the theory.

Before we begin, I need to inform you we'll be talking a lot about dimensions. You know, those planes of existence in which we live. The four dimensions we can perceive with our human eyes are 0, 1, 2, and 3. Below you can see these represented graphically. You see we can graphically show a 0-dimensional object, a point. Then we can extend that point into a new dimension, the first dimension, created a line from point A to point B. We can extend that line and thus points A and B again, creating a square, and a third point, C. That's the second dimension; like this screen. We can then pull points A, B and C out of their two dimensions and into a third, creating a cube. This offers us point D. Like the other points, D can be represented in any of the lower dimensions, but it's only when we open those dimensions up that we see the true placement of D. For example, squash that cube back down into a 2D shape and it goes right on top of one of the other points, so in a 2D plane we see it as being the same as that other point. It's only in a higher dimension that we realise just how far away certain points are.

Similarly, you could be right next to someone else in the first 3 dimensions, but maybe in the fourth or fifth dimensions, you're aeons away. It's a scary thought.

Some display schtuff: 1D coordinates (x-variables) are brown, 2D coordinates (y-variables) are blue, and 3D coordinates (z-variables) are yellow.
OK. Let's get started.

Science is based on comparing different variables, right? For every variable, one value in that variable corresponds to a different value in a different variable. This was the starting point for me. We compare two variables together and we can display them in a table; much like the times table you know so well from primary school. That grid with numbers on one side (1 to 10, say) and numbers on another side (1 to 10 again), and then meeting to create different numbers in the table space. This is a 2D variable comparison space.

But remember that those variables, such as in that times table (though they're not scientific variables) are discrete - as in, they only have certain values, such as 1, 2, 3, 4, etc. We can link our tables to what is known as Cartesian space. Cartesian space is the xy plane in which we deal with most graphs. And the only difference between a two-way table and Cartesian space is that in the xy plane, the variables (x and y) are continuous, whereas in a table, the variables are discrete. In a table, the values are simply '1,2,3' but in xy space the variables could use values '1,2,3' or go deeper and use '0.00001, 0.00002', etc. There are an infinite number of values in Cartesian space.

You can see the comparison here, and it's also clear to see that variables are compared to each other in both systems as being a simple 2D shape - extending that 1D line outwards to form two sides of a square.


Now, if you were doing proper science, you'd perhaps want to compare three variables. And just as comparing two variables requires a 2D table space, comparing three requires a 3D space. You extend that grid of values out into a third dimension, creating a grid cube of sorts. Imagine you had ten values in Variable A, ten values in Variable B and ten values in Variable C. Plotting A against B will give you a table of 100 values, and plotting those two against C will multiply that number by the number of values in Variable C, ie. 100x10 = 1,000.

Knowing this simple maths, we can easily plot our first three variables - A, B and C - against a fourth, D. If D also has 10 values, then clearly we have 1,000x10 = 10,000 values in our grid space. We can't represent it graphically in a 2D space like we can a 3D table, but it's still possibly to work out - as we just did - how many values would be in it according to how many values our fourth variable has.


Similarly, we can plot the first four variables against a fifth, E. If E has ten values, then we know that the resulting 5D grid space has 10,000x10 = 100,000 resulting values. The five variables intersect at 100,000 points, and it's simple to find out what those are. Say A=1, B=2, C=3, D=4 and E=5. Therefore the resulting value is 1x2x3x4x5 = 120, and the highest possible value is when all five equal 10, so 10x10x10x10x10 = 100,000. See? Not so complicated stuff after all.

Plotting a 3D ABC table against a 2D DE table
So now let's return to Cartesian space. Descartes, who was the dude who created Cartesian space, originally accommodated it for three variables. In our previous example, we had Variables A, B and C creating a 3D table space. In Cartesian space, we have x, y and z. xy is the 2D space you see to your left, plotting x against y. Just like in the table, we can then plot that 2D space against a third variable, z. This gives us a 3D space to work in, where people can place and manipulate cubes, spheres and other things. However, the genius of it is that we can also place one- and two-dimensional shapes in 3D space, such as lines and squares. The only difference is that instead of a point being defined by (x,y), its coordinates include a third variable: (x,y,z).

Side note: It's ironic to think that we have an infinite number of values in the xy space, then when we plot them against a third, infinite variable (z), we are left with ∞x∞ values. Which turns out just to be infinity again.

But, just as 1D and 2D objects can be displayed in a 3D space, that same 3D space, full of complex 3D objects, can be displayed accurately in 2D spaces. The only problem is, 2D spaces only plot two variables against each other. We need three. So we plot x against y on one 2D graph, then y against z on another 2D graph, therefore showing the value and location of all the points in all three dimensions. This solution needs two graphs as opposed to one, and it's much harder to understand the location and size of shapes, but it could mean the difference between thinking two points as the same and realising that they are incredibly far away in the z plane.


You can see there I'm using the point (2,2,2) as an example. Luckily for us, the xy coordinate (2,2) has a z coordinate of 2. That's not too hard to comprehend. Take a point at 2 on a 1D plane, extend it into a 2D plane by 2, then extend it out again into another, 3D plane, creating a (2,2,2) coordinate.

But what if we want to show a line in this 3D space? I'm not going to try showing it in the xyz space in a 2D format as above, because it's hard to tell where the points are, so I'll use two 2D graphs to show one 3D graph. Here we can see a line that runs from (2,2) to (3,3). Quite a basic line, right? Well, we may misinterpret it! If we then show that line in another graph, plotting y against z, then we see that it runs from (2,2,2) to (3,3,17). It's longer than we thought. NB. we could also have plotted x against z, the line runs from one point to another in that plane too. It's just a different way of showing where the point lies. However, for future developments (it gets complicated later on), we will follow a rule to plot the last variable against the next one, ie. in xyz, plot xy and yz, not xz. You'll see why later.


So that's alright to understand. Coolio. But, when we were dealing with tables way back at the start of the post, we extended our 3D table space by presenting another variable, D, and plotting A, B and C against D. ie., the space was called ABCD. It turns out that you could do this pretty easily in Cartesian space too, though I don't think Cartesian space was designed to deal with a fourth variable. Our fourth variable is the value of a point, or line, or whatever, in a fourth dimension. 'Fourth dimension!?' you say, 'that's crazy talk! How can we ever interpret or understand that?'. Well my little non-believer, we can. We can't display a 3D graph on a 2D screen (such as the one you are reading from), because each point would correspond to an infinite number of points if that 3D graph were real. That's why I said it was bad form to keep using that '3D' graph to show xyz spaces. So I used two 2D graphs to = a 3D graph instead.

And we can do just the same with a 4D graph. Only, because we now have four variables, we have to show three variables on one graph and two variables on another. We use a common variable that appears on both graphs to link them together. So, let's take a look at this:

This is a 2D (just about) representation of a 4D space. The first graph is easy; it's a simple 3D graph (yes, in a 2D format, but just ignore that for now). We're plotting x against y (as per usual) against z. That gives us a three-dimensional space. But what if that point, (2,2,2), had another value? A value in a fourth dimension? Well, just as we took the y from xy and plotted it against the new variable, z, we're gonna take the z from xyz and plot it against our new fourth variable, w. (Wikipedia uses w, BTW, it's no personal thing). So we plot a second, 2D, graph of zw. And from that we can see that the point (2,2,2) has a value of w=2. Therefore its xyzw coordinate is (2,2,2,2). It's quite simple, really.


And, just as before, we can use multiple graphs of the same multidimensional space to show the true values of lines. Just as before, I'm going to switch back to only using 2D graphs when I'm representing lines in higher dimensions, because otherwise it's really hard to display it properly. So, I've used three 2D graphs here. We need to show an xyzw space, so we plot xy (you'll be sick of that by now), yz (remember that?) and zw. Once again, we see that the first few dimensions are very deceptive. In the xy plane, we see the points on the line are (2,2) and (3,3). In the xyz plane very little changes as we see their coordinates are (2,2,2) and (3,3,3). However, extend that line into a fourth plane, a fourth dimension, and we see that the points are (2,2,2,2) and (3,3,3,20). That second point is in fact further away than we thought.

But does that make the line longer ? We can still measure it in cm, it's still a 1D shape, but in a 4D plane. Perhaps. There's a bit too much mindfuckery there for me.

So now we reach the final throes of this horrendously long post. But before we go, I have one final thing to show you. We've seen how easy it is too understand and graphically represent 4D space, whether they exist physically or not. So, using our advanced understanding of simple 2D and 3D graphs, we can therefore represent even higher dimensions. Be prepared to be confused.


So now we're plotting five variables against each other. Remember we need to display all five, but repeat one to link the two graphs together. That means we need a series of graphs to display six variables. Therefore, we need two 3D graphs. One one graph, we plot our usual 3D space of xyz. On the second graph, we continue z from the first to link the two. We plot z against w (the fourth dimension) against our newbie, ŵ. The first graph tells us the point is at (2,2,2), and the second graph tells us it's at (x,y,2,2,2). Combine the xyz and zwŵ spaces together and we can produce a (x,y,z,w,ŵ) coordinate of (2,2,2,2,2). It's surprisingly simple to do!

I won't go on, because from now on it's all boring and samey. Need to display an eighth-dimensional point? Sure thing! Eight dimensions means (theoretically, just choosing symbols now) (x,y,z,w,ŵ,ŵ',ŵ'',ŵ'''). That means plotting graphs xyz, zwŵŵŵ'ŵ'', and ŵ''ŵ'''. And that's all there is to it, for an infinite number of dimensions, forever and ever. Of course, this is all purely mathematical, and hypothetical, so that means that there may not be a 58th dimension, however many shapes you can represent in it. Different theories give us different values as to how many dimensions actually exist (ignoring time, which isn't representable in Cartesian form, haha); some say 16, some say 20. If you ask me, the nature of the universe seems infer that there would be an infinite number of dimensions, partially because we can work with an infinite number of dimensions graphically (as shown above). I also think that something so key to the being of the universe shouldn't be so finite, so human-defines as simply 16. To me, it seems crazy to put a cap on the number of planes in which matter - and antimatter and presumably dark matter - exists and is perceived.

But that's a rant for another day.

~John