Sunday, June 5, 2011

perspectives on dimension

We live in 3-dimensions... with the added dimension of time making it four... or so it seems. Apparently, this answer is not as simple as it appears. We all can easily comprehend three dimensions. In geometry and art classes, we learned to draw cubes that replicated our experience of space on the flat plane of a paper.

Renaissance artists such as Lorenzo Ghiberti, Filippo Brunelleschi, and Donatello drew upon the optical analyses of Alhazen in order to represent a more genuine spatial (and visual) experience in paintings. Guiding the way towards a more realistic painting style, these artists also recognized the way that such spatial organization can drive the narrative of a painting. Using perspective can force the viewer's eye towards a particular part of an image. One of the most famous examples is da Vinci's The Last Supper wherein every element of the painting guides the viewer's focus towards Christ's head at the center of the composition... emphasizing his metaphorical, in addition to, his physical centrality.

Leonardo da Vinci, The Last Supper (1495-98)
Da Vinci also once said, "Perspective is the rein and rudder of painting." But back to our humanly experienced dimensions. We laymen may be satisfied living in three, even four, dimensions. However, physicists have a serious problem with only four. The problem begins with the forces that control our lives -- gravitational forces, electromagnetic forces, the weak force (radioactivity), and the strong force (prevents protons in center of atom from separating). Ok, so these forces all exist. So, what's the problem?

Well, the problem is that four dimensions are not enough to encapsulate how all these forces work together to create our reality. In his article on extra dimensions, Karl Kruszelnicki explains what happened next in order to try to resolve this dilemma:
...way back in the 1920s, Theodor Kaluza and Oskar Klein came up with the first theory that looked like it could combine the Gravity and Electromagnetic Forces. But their promising little theory assumed that the Universe had an extra dimension -- giving a total of five dimensions.

Now there's a third reason why we need a few extra dimensions. Our curiosity has been sparked because of strange results from recent experiments in accelerators where high-energy particles smash into each other. Thanks to these experiments, we have way too many sub-atomic particles. By the 1930s, the physicists had come up with a nice simple model of the atom. It looked a bit like our solar system where the planets orbit the Sun -- it had a central core with protons and neutrons, with a bunch of electrons whirling around it. This atom had only three sub-atomic particles -- the protons, the neutrons, and the electrons.

But since the 1930s, things have got way too messy. Today, we have found a few hundred sub-atomic particles. And they don't fit into a neat little system -- they're all over the place. But if you add in another seven extra space dimensions (all at right angles to each other), this mangled mess of particles gets a little neater.

Now our regular three space dimensions reach all the way to the edge of the Universe. But when the mathematicians looked at these extra dimensions, they found that some of them are 100 billion billion times smaller than the core of an atom. Even though they are space dimensions, they are as different from our regular space dimensions as is our time dimension.

With our current Physics, we have no way to get into these dimensions. In fact, it's probably a lot safer that way. Imagine if your regular walk to the corner shop was littered with extra dimensions and wormholes to Heaven Knows Where! You'd probably need more than a bus fare to get home.
Imagine indeed. And that is exactly what I asked my students one day for a journal write. "How many dimensions are there? Describe and explain them." I invited creativity and mind-expanding responses. And here is some of what I received from my 9th graders:

#1: There are two: ours -- the one we know as earth, life and society

     The other -- the exact opposite of what we know now as life.

     Everything is opposite. People's personalities; we write from right to left; life starts with death and old age and ends with youth. There are exceptions, though. People talk forward and walk forward because otherwise it would just be silly. The world is a mirror image of the opposite but what happens in it is reversed.

The only way to exit and enter them is when your opposite reaches the same age as you. For example, if you were to live to the age of 90, the only time you could cross over would be on your 45th birthday. [Student then included a little diagram.]

The only trouble is that within this year is the only time when you can switch back and forth with the help of a wormhole so BE CAREFUL! Don't stay longer than a year in the dimension you don't wish to stay in for the rest of your life, or the other half of your life. Wormholes never stay in the same spot. They are always moving! So if you wish to leave a dimension, look long and hard.

#2: In my opinion, there are 5 mathematical dimensions: length, width, height, depth, imagined dimension -- like when you think of something, there's something more to it than just the other four dimensions.

Although by definition, there are also non-mathematical dimension in which I believe... worldly dimensions:

Asgard: world of gods and heroes
Neflheim - world of ice and shadows
Hel - world of the dead
World of Fire
World of Water
World of lesser gods
World of Giants
World of the Elven people
World of Aether/Ether
Land of Control/Land of Dispersal (of Elements)
Land of Dreams
Land of Imagination
OtherLand/Negative Lands

#3: I believe there are two dimensions: one is a happy unrealistic dimension and another is a depression, bad work, no dreams dimension.

#4: There are 4 dimensions. The first dimension is a flat object: for instance a piece of paper. The second dimension in my eyes is just regular things, for example a water bottle. The third dimension is the dimension of things like a cube. I may be wrong but I think there are four dimensions. The fourth dimension is unknown. I believe that there are an unlimited amount of dimensions because we don't know what exists beyond Earth and where we have traveled in space. Then there is the question of the after-life. If there is a life in the afterworld, maybe that is its own dimension. This is something I have never really thought about or learned about. If you relate dimensions to the novel, Of Mice and Men, there are two emotional dimensions. One is where they are dreaming about future lives. The other is the true reality of their hard lives.

#5: In the world, there are four dimensions. With each dimension, things become closer to actual life and living things. The first dimension is flat, nothing, not real. It is just a picture on a piece of paper. The second dimension is still flat, but made to resemble something which is not. The third dimension has actual height and shape, but no life. In the third dimension, things are very simple; you can touch them at times, but there is still no life. We are in the fourth dimension. We are real living, moving, breathing things. We can reach out and touch something. We can feel the spray of water at the ocean's edge. The fourth dimension is real life and it is what we live and move in.

#6: Creatively, in terms of inception, there are so many dimensions. To me, a dimension is a way you look at something, like a point of view. So we have our own dimension -- our perceived reality and what we think of what we see. There are other dimensions besides our own, like another person's reality based on what they have learned, past experiences, and what they believe. Everyone has his own dimension, his own way of looking at the world and making sense of what he's seeing. Then there is actual reality, what is really happening which no one person can determine on his own. Reality is the truest, non-deluded dimension, though no one can see it. All people are biased with reality, even if they don't know it. It would take a group of people with different values and beliefs to try to find what is really happening, because a mixture of perceived reality might make the real reality. Everyone has his own dimension, a perceived reality, but there is one dimension that we are all a part of, even if no one can actually understand the actual reality.

#7: There are an infinite number of dimensions -- since we can only comprehend three, everyone assumes that time is the fourth. However, this is untrue. The first dimension is a line which only has length, not width. Then comes a geometric plane which has length and width but no depth. The third dimension is where we get depth, and the fourth is difficult to explain. [diagram follows] Basically, each dimension adds a sort of 'bridge' between two of the same dimension which is what causes that extra layer. Since we live in a world without a fourth dimension, it's difficult to imagine this sort of 'bridge,' but I like to think of it as playing a game of chess and turning over the chessboard to find a separate game of chess being played on the other side. Or like the front door of your house leading to someone else's living room instead of outside. Going by this theory, by 'attaching' the two fourth dimensions, you would get the fifth dimension, and so on. Therefore, you could go on infinitely discovering more and more dimensions until you either run out of paper, life, or sanity. [Another diagram... captioned with "The fifth dimension: Don't get me started on the sixth.]

#8: Realistic: I feel that there are four dimensions, like in math (point, line, shape (cube), time.)

Creative: I feel that there are dimensions to everything. A story has dimension. A story has an obvious plot-line; then there are characters' emotions, and then there is a deeper meaning to the plot that carries an idea, a concept, or parallels a real event (or a made-up one.) That especially happens in creative writing because the author has space to change and add and remove parts, people, or ideas. In non-fiction writing, it is much more difficult to do so because the author has to stick to facts.

I feel like humans have dimensions as well. The most basic being their appearance, then the physical emotions they portray, then their 'external' emotion (the emotion or tone they give off), and then even more complex is the emotion they feel inside that only a few outsiders know of, and the even more complex dimension of humans is the emotion that we don't know what it is caused by... the type of emotion and feeling that builds up for no reason or when we "get/feel/" a vibe from someone else, when we feel uncomfortable for no apparent reason. Lastly, the most complex is the emotion in humans that is so deep down in us, underneath all our other layers, hidden from ourselves, so that we don't even know if it exists.

#9: 1. dot
     2. a line, has length, no height
     3. our dimension: height, length, depth
     4. time
     5. Narnia
     6. Star Wars
     7. Fight Club
     8. Jurassic Park
     9. Halo universe
    10. The Matrix

[5-10 are parenthesized with a comment: "seems legit"]

#10: I think there are 9 dimensions: nothing, length, width, depth, linear on a timeline, different possibilities on that timeline, different timelines, backwards toward within those possibilities in those timelines, difference universes, multiples

#11: There are many dimensions that we can use. Some dimensions are width, height, volume, length, area, perimeter, circumference, etc. Dimensions are hard to describe but they are important too in that they help humans live and play a huge role in how much humans and technology have developed. Without dimensions, life would be much harder for the living things on Earth and we probably wouldn't be as developed as we are without these dimensions.

#12: There are many different concepts about dimensions and their existence. Some people, in a mathematical sense, believe that the three dimensions are x, y, and z. Other people believe there are four dimensions that are represented by a point, line, cube, and time. In a literary sense, time and space are the two main dimensions, though some people branch off into other areas like the mind. My point is that a dimension can be something that measures length or something that represents space. It all depends on what you want to believe. Dimensions aren't something proven; you can't create the 4th dimension in math and you can't physically prove time or space. They aren't facts, just concepts that we believe in. Dimensions are almost like a trick of the mind. We exist in space; we live in space, but other than that it is just present in our lives. Space needs us like we need it to survive. In order to be space, something or someone must exist in it and bring it to reality. It is like this with all the dimensions, even the mathematical concepts. The so-called '4th dimension' is a common idea. However, we've never seen it and no term of it can exist on Earth. Dimensions are playing with our minds. If we wanted to we could just say everything significant is a dimension. It is all up to us and our imagination. Dimensions are objects we cannot prove; they are something that we can create and destroy in our minds; however, most of all dimensions are something that impact us. They may be a trick of the mind but we can only exist if they do. Dimensions are a part of our lives and we can't change that concept, just alter it till we feel satisfied.

#13: I could really take this in any direction and choose any answer. However, I'm going to totally choose something that probably won't make any sense. I'm going to say that there is only one dimension. That dimension is size. Size includes everything in its category. It has width, length, height, surface area, perimeter, area... and so on.

#14: Dimensions are never-ending. There are countless things that could be in a dimension. The way I think of dimensions is that they are basically universes that are similar to ours, but certain things in the dimension we live in are different or there are more things or less in a different one. Dimensions are very complicated: something like gravity is in ours and not in numerous others.

#15: Dimension is a relative term. It could be something far off in outer space, like an ultra-dimension, or something used commonly by many mathematicians. I think in the math world, there are 4 dimensions. The first describes a line that can extend infinitely in its 2 directions. The second is a plane. It has an infinite area which is made up of its length and width. The third dimension consists of length, height, and width. It is something solid and tangible. The so-called 4th dimension consists of time. Time governs over life, causing us to wake up the time we do, sleep the time we do, and die. In the 4th dimension, time changes things. It transforms a cube into something else. On the other hand, dimension can be referred to something that exists as we do, maybe even in the same space, but is not known to us because our dimension does not correspond with theirs.

#16: There are 4 dimensions and they describe where you or something else is. The first is length, the second is width, and the third is height. That's why 3D movies are called 3D because you can see length, width, and height. But two people can be in the same spot, but just not at the same time...which is why the 4th dimension is time. If you have a description of all of these put together, you know exactly where something is.

#17: For us, in our world, there are three dimensions that are described by the x, y, and z axes in space. Everything in space can be described by one or more ordered triples (x, y, z) which determine its location. A "dimension" is how many times a point is replicated and all of the corresponding points are connected like so.

However, since we have never encountered the fourth (or more) dimensions, we say that is does not exist because we cannot perceive or imagine how the figure would behave.

Flatland is a book that illustrates this point, because it involves a two-dimensional square living on a plane with other polygons and is visited by a sphere from the 3-D world who pulls him out of the plane and shows him what the next dimension is, and when the square is disbelieving, he is shown a point in its own world, unable to recognize the existence of anyone else since the world has no dimensions, and a line with people on it that cannot imagine the plane world that the square lives in. When the square tells his people about the third dimension, he is considered insane and is locked away for life. This shows how we have been conditioned to be unable to imagine a 4-D world, and even reject the idea because it does not make sense to us. However, if we look at figures in other (fewer) dimensions, we think it would be logical to explain the third, second, or first dimension to them, but in reality, it would be like someone trying to explain the 4-D world to us -- since we really do not know its properties and how it behaves, it would be futile.

It would be possible for there to be infinite dimensions, each looking down on those with fewer, and believing that they are so narrow-minded not to be able to see the simpleness... if their dimension was n, the n + 1th dimension's geometry... but, in reality, they are also being just as narrow-minded for not realizing the n + 2th dimension. It is easy to understand the world with fewer dimensions than yours, but it is difficult to understand, or even verify the existence of a dimension past yours.

Kids are fantastic thinkers and their imaginations are boundless. Would that we all think as creatively. There will be a part II with more of these entries to come tomorrow... a double the dimension, double the pleasure tomorrow's and tomorrow's tomorrow's theme. :)

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