The Theoretical Exploration of Dimensions 0-5

Following is my personal interpretation of dimensions 0-5 of our physical existence, as well as descriptions of the shapes that inhabit such existences and the process by which I envisioned them. I arrived at these conclusions by observing the differences between points, lines, squares etc. and studying the nature of their relationships. I am sure there are many who would disagree with my conclusions.
Lastly, before I begin it is important to state that in my view, we are not living exclusively in the third dimension. Rather, dimensions should be used as lenses with which to view our spatial, chronological and theoretical existence. With that in mind, let us begin.

Dimension 0 is best described as a singular, all-inclusive point. Everything that occurs in dimension 0 exists within a space exactly the size of the intersection of two lines. A being that exists on such a dimension would by necessity occupy the entirety of such a space, as the 0 dimension is the smallest possible space imaginable.

The process of moving between the 0 and first dimensions is the basis for all inter-dimensional transition. In order to take a 0D object (a point) and create a 1D object (a line) you must move the original point parallel to itself while simultaneously allowing it to occupy every “space” from start to finish. The two points are, in a sense, connected by an infinite number of points (that unit which occupies the initial dimension), ultimately creating a first dimensional shape–known as a line segment–between them. Moving from the 0 dimension to the first is much the same, except in that neither the concept of “start” nor “finish” exist. Naturally, this is the difference between a line segment and a line. This process will become clearer when demonstrated on more advanced objects.
The first dimension is best thought of as a line, and indeed, many of us know it as such. However, it resembles a line in a way that is truly different from any we might experience in any non-theoretical sense. A line drawn on paper with a pencil may appear flat, but it has some minute measure of height, not to mention a width corresponding to that of the tip of the pencil used to create it. A true first dimensional line has neither width nor depth. It is a perfect line on which there are infinite points.
The only “shapes” possible on a first dimensional line are line segments. Two beings located within the same first dimensional space could only see each other as points, and if they were looking at each other, could see nothing else. Only an outside observer who did not inhabit such a dimension would be capable of viewing such creatures as line segments.
When an object occupies first dimensional space, it can only exist as a line segment on that particular line of existence. The first dimensional representation of a third dimensional object could be thought of as the intersection of two perpendicular cross sections within that object. For example, the cross section of a cube would be a square. A perpendicular cross section of that square would result in one specific line wherein all points would fall on both the first and secondary cross sections of the original cube. In a first dimensional perspective, the cube would appear to be a line segment within an infinite line.

Plane perpendicularly intersecting with cube, creating the cross-section of a square.
Plane perpendicularly intersecting with cube, creating the cross-section of a square.
Two 2D planes perpendicularly intersecting a cube, creating a 1D overlap.
Two 2D planes perpendicularly intersecting a cube, creating a 1D overlap.

Because a “point” would represent the smallest possible unit of measurement and there are an infinite number of numbers between integers, it should go without saying that there are an unlimited number of places within the cube in question that either perpendicular cross-sectional plane could occupy, and therefore an infinite number of places for those cross sections to intersect. As such, at any given time such a cube could be said to exist on an infinite number of independent first dimensions simultaneously. If you were to move that cube in a third dimensional sense, it would cease to exist on some or all of the first dimensional lines it had previously inhabited. Similarly, if you were to angle it differently, so that where the line that had previously been occupied by an entire edge of the cube was now inhabited by a corner, it would appear as a smaller line segment within the same 1D line of existence.

As in the example of creating a 1D line through the “movement” of a 0D point, a second dimensional plane is realized by moving a first dimensional line parallel to itself while allowing that same line to occupy every space in between at the same instant. This could be thought of as an infinite number of lines of infinite length laid parallel to each other. It could be tempting to think of this as a giant square, but the truth is that no shape is really a suitable description for a plane that expands infinitely.

A plane differs from a line in that it has width as well as length, yet it still has no depth. In the same way that there are an unlimited number of lines within a plane, there are an unlimited number of planes within a three dimensional space. If a singular point is the depth of a plane, which is to say it has no depth at all, then there are an infinite number of planes that can be said to fit into any prism.

The diversity of figures that can be expressed on a 2D plane is infinitely greater than the singular possibility of a line segment. We are all intimately familiar with many of these shapes-triangles, rectangles, pentagons etc. It is common to see representations of these in our daily lives, however it should be noted that no one has ever held a polygon.
Two second-dimensional beings of the same plane looking at each other would see only line segments, as pointed out by Edwin Abbott Abbott in his book Flatland, Romance of Many Dimensions. As two first dimensional line segments can only regard each other as points, polygons existing on the same plane are limited by their dimensional inhabitance. In this case, it is their inability to experience depth that causes them to view each other straight on, resulting in a line segment appearance. In Flatland, a third dimensional sphere visits the second dimension. To a square, he appears to be a circle whose diameter changes as he alters the depth at which he is cross-sectioned by the planar second dimension. Interestingly (and logically) the sphere is able to view the square in his full 2D form, due to his ability to alter his depth and regard the square from above-a concept completely foreign to the square. In the book, both one and two-dimensional beings are able to infer each others’ shapes or lengths through the use of information other than sight.

Per my former logic, a 3D space is created by moving a 2D plane in a direction parallel to itself while allowing said plane to occupy the entirety of the area simultaneously. The third dimension should be the one most familiar to anyone reading this, as it is the one we tend to think of ourselves as living in. However, as I have previously theorized, we are constantly existing on huge numbers of points, lines and planes, as well as in space.

2D plane moving parallel to itself. If it could occupy all spaces between start and finish simultaneously, it would appear as a cube.
2D plane moving parallel to itself. If it could occupy all spaces between start and finish simultaneously, it would appear as a cube.

As one 2D shape observing another would be capable of seeing only a line, beings existing in the third dimension must regard each other in second dimensional representations of our “true” forms. This may sound foolish or irrational at first, but if you take a minute to observe your surroundings you will find that you are capable only of viewing certain sides of them at the same time, depending on your physical (third dimensional) perspective in relation to them. In the case of a cube, one might observe three square planes at the same time. Due to depth perception and the fact that these planar figures do not exist on the same plane, we can tell which is furthest from us and ultimately infer the that the figure in front of us is a cube. However, this is not the same as viewing a cube in its entirety. Such a cube could be an irregular prism that happens to have three square sides exposed. It would be impossible to tell the difference between both objects if they were placed correctly according to the position of the observer.

The reason for this is simple. From a third dimensional perspective, one is capable only of occupying one physical space at the same time. For the most part, this is the way we perceive our lives.

Zero through third dimensional existence is more or less easy to grasp. The more conceptually tricky-and thus fun- part is trying to envision 4D figures and above. From here on out, this is more about my own opinion and conceptualization, which I will attempt to back up with established logic.

A fourth dimensional existence is created by a parallel move of a 3D space. The fourth dimension is what keeps an object from occupying two spaces at the same instant. We most commonly refer to this phenomenon as time. Allow me to explain:

Imagine a cube occupying some space on a table. Now, imagine that you move the cube to the other side of the table. This cannot be accomplished timelessly, or rather the cube cannot occupy both sides of the table simultaneously. Say this movement occurred over the course of two seconds. At the various time intervals within those two seconds, the cube occupied an infinite number of spaces between the start and end of its movement. If we could see all this at once, it would be the fourth dimensional shape of the cube, within the time limit of the two seconds between the start and stop of the movement.

4D rendering of a cube over a finite course of movement.
“4D” rendering of a cube over a finite course of movement.

The true fourth dimensional shape of such a cube would include its every spatial occupation for the duration of its existence. In such a way, the entire fourth dimensional shape of a human reading this would be include an ever increasing shape, occupying every space that person has ever been in from conception to the reading of this very sentence. I think they would resemble very odd-looking snakes, not unlike the images created by playing with shutter speed settings on a camera. I think that a 4D being would be able to see a 3D object in its entirety, as it could freely occupy multiple spaces at the same time.
A cube may be thought of as a three-dimensional object, but as we have covered it contains an infinite number of planes, lines and points within itself. The fourth dimensional representation of a cube would include, in addition, an unlimited number of cubes within itself. Or if you prefer, a cross-section of a 4D shape created by a cube’s movement would be a cube.
Even when an object appears to us to be stationary, it is moving constantly in space. Our planet rotates and revolves around the Sun, which itself revolves around the center of the Milky Way which is constantly traveling through the universe. To an earthly observer, it may appear that his house has a fourth dimensional shape that is identical to its current shape (if we disregard the building process during which the house took different forms. Let us stipulate that the house has never changed form.) The reality, however, is that the house—because it is fixed on Earth—is subject to the rotation of our planet, its revolution around the Sun, the Sun’s revolution around the center of our galaxy, and our galaxy’s movement through the universe. To us, this house appears a stationary object. A celestial observer, however, would be aware that the house is constantly hurtling through space at a great speed, and thus occupying different space constantly.

A crude rendering of the celestial movement of my house, within our solar system alone.
A crude rendering of the celestial movement of my house, within our solar system alone.
The involuntary celestial movement of a stationary, terrestrial object. The Earth rotates while orbiting the Sun, which orbits the center of the Milky Way. The Milky Way itself is moving.
The involuntary celestial movement of a stationary, terrestrial object. The Earth rotates while orbiting the Sun, which orbits the center of the Milky Way. The Milky Way itself is moving.

So, when I previously stated that 4D objects would appear as “snakes” I was oversimplifying a bit. They would appear that way, yes, but they would be much longer than one would initially believe. The aforementioned cube that I moved across the table actually traveled a much greater distance than the space between point A and B within those two seconds, because it is subject to constant celestial movement.

Let us consider a simple example of the relative nature of movement: For a moment, let us neglect celestial movement and think of the Earth as a stationary object. A car is traveling at 60 mph. A young girl in the backseat flips a coin straight into the air that returns to her hand in exactly one second. To the girl in the car, it appears that the coin traveled straight into the air and has returned to its initial position. Its movement could be drawn as a straight line up and down.

However, an observer on the road with a view of the coin toss would chart a very different path of the coin’s movement. He would see the coin launched at an initial position we will call x, travel at a constant speed of 60 mph, and land in the girl’s hand 88 feet away from point x.

The two different perspectives on movement drastically affect the mental image each observer has on the fourth dimensional shape of the coin over the duration of that one-second interval. (Imagine how this would look from the perspective of the Sun, etc.?) When celestial movement is considered, it becomes even more complicated to contemplate the “true” space that an object has occupied/traversed over a given duration and thus, the 4D shape that would present itself.

The fifth dimension is, for me at this point, the highest conceptual interpretation of our existence. Using consistent logic, the fifth dimension is created by the parallel movement of a fourth dimensional shape. What that means is that the fifth dimension is that which keeps separate realities from coinciding.

To exemplify this, let us examine my current reality. I am writing this at 1:56 PM on January 31, 2015 while sitting in my mom’s dining room. I am sitting here for a variety of reasons which include my choice, the temperature of this room, my mood at the time I woke up, the fact that I didn’t have work today etc. The list is infinite and each of these reasons is the result of consequences of past occurrences. For example, if I had drank more last night, I might not have gotten out of bed when my sister was making breakfast, and thus might not have sat down at the table. If I were taking a trip tomorrow I might be packing right now. If my parents didn’t go to college, they might make less money and the downstairs might not have any heat in it, so I might have just stayed upstairs. Past and current actions as well as future expectations have created the possibility for me to sit in this room and type on a laptop. Chaotic expressions of free will and consequence have altered my prerogative so that I choose to sit here writing this.
It is not hard to imagine a reality alternative to this one where I sit here writing this paper. These alternatives are very real and possible, and that reality corresponds to a theoretical 4D shape. Not only would my personal 4D shape be altered, but so would the shape of anything that I might have influenced in the process of sitting here and writing this piece. In addition, the unseen influences that I did not have (but might have had) on other 4D shapes are also affected by my choice to sit here. I could have woken up this morning in a terrible mood and punched the wall, breaking my hand. I could have gone for a run instead of writing. The consequences of these actions will never be known to us in this timeline, but they are just as possible as the one in which I write this article. Thus, as long as we do not believe in predestination, we must accept that there is an infinite possibility of 4D shapes we might take in the future. If we accept that our present is determined by our past, then it seems reasonable to state that were the past altered, our present would be different.
To say that it is choice that separates different hypothetical realities is to assume that everything that occurs in the universe happens either by choice or is preordained. The truth is much more complicated. It is circumstance, randomness and choice that separate realities. In truth, it is chaos that keeps realities apart from each other. This is the nature of the fifth dimension, the dimension of possibility.
If the fourth dimensional shape of an object looks like a long snake that ends at the present, then that object’s fifth dimensional shape (from that point in reality/time) could be thought of as that same snake with an infinite number heads that have an infinite number of infinitely-headed snakes crawling out of their mouths.
In considering the fifth dimensional shape of our universe and reality, we might imagine a snake that grows instead of moves among an infinite number of similar snakes, representing the current reality among all the conceivable current realities. These might be referred to as parallel universes. Each snake is capable of moving in an infinite number of fashions. Perhaps each snake’s tail would intersect and end at a point that we might call the beginning of the universe.

The expansion of these realities is infinite because changing circumstances necessarily create new possibilities. In such a sense, the fates of the victims of the September 11th terror attacks were affected by the Wright brothers’ inventions. There is no way to imagine all the consequences an action may have in the future. Even two seemingly identical scenarios cannot be guaranteed to play out the same, because there is no way to account for 100% of the variables that may occur. From my perspective, this exemplifies the infinite possibility of the fifth dimension.