I apologize in advance for doing this in 3 parts...

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PART 1

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Abstract

This theory reduces the dimensions down to a base algorithm that provides the "rules" for defining dimensions. It can be used to: predict the structure of any/all dimensions; and to help visualize how what we observe about our space and universe may be explained by that definition.

Defining the 4th Dimension and Beyond

Hypothesis and Basis for My Model

Standard Geometry tells us about the properties/rules of points, lines planes and spaces…

- A point has no form, as it is infinitely small.
- A line has only length, is comprised of at least 2 points, and is infinitely long.
- A plane has two dimensions (length and width, x,y only), a flat surface area with no thickness that extends infinitely, and its area is comprised of points and lines.
- A space has three dimensions—length, width, and height (x,y,z), and its area is comprised of points, lines, and planes.

We also know that…

- A minimum of 2 points are needed for a line to exist.
- A minimum of 2 lines (parallel or intersecting), or 1 line+1 point, are needed for a plane to exist.
- A minimum of 2 planes (intersecting or parallel) are needed for a space to exist.

So, if we had a minimum of 2 spaces, what would now exist? (And following that logic, I wondered what a “parallel” or “intersecting” space would look like.)

Since the dimensions already were defined by numbers (and to make it easier on myself so I wouldn’t have to re-program my brain when thinking this through), I used the existing numbers. However, a point didn’t have any number, but since it was infinitesimally small, and since a zero would work for the sequence, I assigned the “dimension” 0 to a point. (I did feel good when I later found out that the science field had also decided to adopt that convention. And, it makes this part of the explanation easier.)

Using the dimensional numbers to represent the elements that define each dimension, we have…

Dimension Defined by

0 ------- Point

1 ------- Line

2 ------- Plane

3 ------- Space

4 ------- ???

Trying to visualize going from one space to another...in order to do that, you would have to go through *something.* Time? Space-time?

To help visualize that part, I went back and thought about pretending I was that two-dimensional (flat) being, living on a single plane. That plane would, then, be my entire universe—any other plane would be a different universe. In order to get from one plane to another, the “something” that I would have to traverse would be a space. That is because, to get off that plane, the only direction I could go is “up” or “down”—aka 3-D. Trouble is, I would not have any knowledge about “up” or “down” because my perspective is limited within my plane-world. Likewise, in my 3-D world, it’s hard to imagine a fourth dimensional direction I would need to traverse to get to to a "different" space.

In considering how we would get between any of the other dimensions…

Going between two Points — you would have to travel along a Line.

Going between parallel Lines — you would have to travel on a Plane.

Going between parallel Planes — you would have to travel through Space.

Going between [parallel?] Spaces — you would have to travel across ????

Given that, a space could also be defined as a whole bunch of planes stacked on top of one-another. So, what is it I would need to traverse to go between spaces? It would be something that contained a bunch of spaces? That *something* would, of course, be the 4th dimension. Like the planes all stacked up to create a space…what if we were to stack a whole bunch of spaces—what would it create? What would it look like?