An Existence of Six Dimensions - an exercise in Geometry by Ithamar Eshpar
Let's define a dot as our theoretical atom: We'll
select a dot which we'll name "the Zero Dot"
To define a line, we'll put another dot on one side
of the Zero Dot, and another one on it's other side. We have defined a
DIRECTION which we'll call "Length". Each dot on the line can be accessed
by measuring the number of dots between itself and the Zero Dot, and expressing
it's direction relative to the Zero Dot: one side will be called "Plus" and the
other will be called "Minus".
To define a dot on the line we will be needing one measurement, and thus we can
say that the length in one-dimensional. We can point the location of
the dot with one coordinate: Y, that can be any number - positive or negative.
We shall now define another line, using the same method and under the following rule: the new line will cross the first one at the Zero Dot exactly, and will be perpendicular to it. We have defined another direction, which we will call "Width". Each dot on the Width line can be accessed using one coordinate, just like on the "Length" line - but actually we now have access to an infinite number of dots not on any of the lines. To access any of these dots we need to measure TWO distances: the shortest distance between the dot and the Length line - i.e. its location on the Width line (X), and the shortest distance between the dot and the Width line - i.e. it's location on the Length line (Y).
We have now defined an infinite number of dots, that have one thing in common: they all belong to the same PLANE, which is defined by the Length line and the Width line. Each of these dots can be defined by measuring TWO distances, so we can say that the plane is two-dimensional.
We shall now define a third axis according to the same rule: an axis that crosses the previous two at the zero dot, and is perpendicular to both. There is exactly one such line, that we shall call "Height". Once again, we have access to an infinite number of additional dots - only this time we'd have to specify the dot's distance from the original plane that holds the two previous lines - i.e. their "Height".
The group of new dots will be called "Space". Each dot can be referenced using three coordinates - X,Y and Z - and that is why we say "Space" is three-dimensional.
So far we have defined three dimensions, but what is the FOURTH dimension?
If we try to continue with our basic rule, and try to draw a fourth line that would cross all previous three and would be perpendicular to them, we'll soon discover that we cannot draw such a line.
However, if we have drawn our three-axis system, than it has been existing for a while. We have drawn our "Zero Dot" at a certain time, and added lines that crossed it. We can say that there is another line, the TIME-LINE, that crosses the Zero Dot and is perpendicular to all other lines. We shall call the time coordinate T for now, and so we can access any dot within this four-dimensional structure by providing four coordinates: T to represent time, and X,Y,Z to represent the location within Space. Just like we measure space with equal units called "centimeters", we measure time with equal units called "seconds".
The size of a four dimensional object is the amount of time that has elapsed since its creation to its disappearance. For example:
A four dimensional box is a box that appears at a certain time, and disappears after a certain amount of time. If we define one minute as "one meter of time", then a box sized 1 meter by 1 meter by 1 meter, that exists for one minute, is actually a four dimensional CUBE.
It's true, we can't add the time axis to our drawing - but if we reduce the three-dimensional space to a single dot, which will represent the whole three-dimensional universe at a certain time coordinate, than we will be able to draw an adjacent dot which will represent the same universe at a different time coordinate. We can thus make a drawing that we all know from our history books: the time-line. As our perception of time is similar to our perception of a single dimension - Length - we will, from now on, use Y1 as a representation of the time coordinate.
If the three-dimensional universe is reduced to a dot, than the fourth dimension creates a line. What is, then, the PLANE - the fifth dimension?
We must continue according to the same rule: add yet another line, that crosses the time line at the Zero Dot and is perpendicular to it. Now we have access to yet another collection of "dots" (I remind you that each "dot" is an infinite three-dimensional universe) that exist "besides" our time line. We can assume that these dots define universes that are parallel to ours - universes and time-lines that do not "really exist" (from our point of view, as we live within a certain time-line) but hold all kinds of alternative histories. This five-dimensional structure will be called "The Plane of Possibilities". Each dot on this plane must be accessed using five coordinates - X1 to define the time-line we're in, Y1 to define the exact moment on that time line, and X,Y,Z to define the three-dimensional location of the dot.
Until now, each time we have added an axis to our system (thus adding a dimension), we have encountered an infinity of new dots, that we could not access with the previous system. These new dots always had something in common - all are on the same plane, within the same space, existing on the same time-line. What's common to all the new dots on the "Plane of Possibilities"?
Let me ask you, the reader of this article, to raise one arm in the air. Assuming you comply, we have two options: you might raise your right arm, or you might raise your left arm. We can say that there is a time line in which you have chosen the first option, and there is another time line in which you have chosen the second option. As far as we're concerned, the possibility of you growing a third arm on your forehead and choosing to raise it - does not exist. This option does not exist within the physical reality that we know - thus it is NOT on our Plane of Possibilities.
There must exist yet another dimension, a sixth one, that holds all the possibilities that we do not regard as "real". Just like this moment is a dot on an infinite time line, which is one of an infinity of alternative time-lines, our whole reality is one of an infinity of alternative realities - all of which have physical existence, and all of which hold an infinity of dots that we can access by using six coordinates: Z1 to represent the reality (set of rules), X1 to represent a certain time line within that reality, Y1 to represent the moment in time and X,Y,Z to represent the three-dimensional location of the dot.
We have defined a coordinate-system that holds all possible realities, all possible histories of those realities and all physical universes within that history. I call this coordinate-system, that holds everything that exists and that COULD exist, "Existence". Theoretically, we can go on, reduce this six-dimensional "Space" to a single dot and add more dimensions, but I didn't find any meaning in going beyond the seventh dimension (which I would discuss later, after I have established the content of the 6-D existence, and the connection of this structure to Fractal Mathematics).
* An elaboration about the fifth and sixth dimension
COMING SOON:
* The Fractal Connection