What is the hexatheron

The Hexateron is a fifth dimensional triangle or pyramid. The dimensions are as follows:

0 Dimension

The zero dimension is a simple point with no directions.

 

1st Dimension

The first dimension connects two or more points in a single line. That line is the single dimension called length.

 

2nd Dimension

Things start to get interesting in the second dimension, where two or more lines can connect to each other to form a plane. The two dimensions here are length and width. Connecting points aligned differently than two identical lines allows for the creation of all types of shapes, including the triangle, below.

 

3rd Dimension

The third dimension is the one we live in(?), allowing two or more planes to connect to add the third dimension of depth to length and width. Above is a representation of a three dimensional cube, or what we recognize as a box. Below is the three dimensional represenation of a tetrahedrom, more commonly known as a pyramid.

   

 

4th Dimension

          

Because we are limited to the third dimension, it is impossible for us to see or step into any dimension above (for a full explaination, see Carl Sagan's brilliant Flatland video), however, in addition to length, width and depth, the fourth dimension adds time to what we think of as the physical experience.

In the third dimension, we are able to walk back and forth across space, such as a room or yard. In the fourth dimension, we are able to walk back and forth across time, not unlike our ability to start a video from any point and go back or forth inside of the movie.

Above is a tesseract, which is a representation of a fourth dimensional cube. Below is a pentachoron, or 5-cell, which is a representation of a fourth dimensional triangle. Each are shown in a few different representations in order to faciliate conceptualization, but, again, we cannot see a fourth dimensional object. 

           

Each stacked layer is not a new plane of width or depth, but of time.

 

5th Dimension

With it's 4th dimensional addition as a physical property, one can travel back and fourth across time. Such a feat, however intriguing for us stuck in the third dimension, contains a fatal limitation: it assumes there is only one 'plane' of time. That means all the decisions for us as individuals and societies are already made and, therefore, we can simply travel back and forth to view what already happened and what definitely will happen, because there are no other options. 

In some respects, the fifth dimension can probably be described as the dimension of choice, although the more formal defintion is that of additional or alternative time lines. Similar to the 2nd dimension, which allows one to select any one of multiple parrallel lines, the fifth dimension allows for multiple parrallel lines of time/choice.

In the fifth dimension, noone has to choose between two vacation spots. Simply go to vacation on time line 1 and then go back and see what vaction would have looked like on time line 2. 

 

We cannot see the fourth or fifth dimensions from the third, but above are represenations of a Hexateron, or 5-simplex, also known as a fifth dimensional pyramid.

          

     

 

In the physical sciences, the hexateron represents a complex and fascinating theoretical concept with many implications for this universe and dimension (are we actually living in a hologram?). In the social sciences, the hexateron represents the alternative societies based on different economic systems, social orders, historic outcomes and collective decision making. Individually, the hexateron represents choices made and how those choices led us to the place and person where we find ourselves.

TheHexataron.com examines the possibilities and alternative realities of doing things differently.

In the fifth dimension, of course, because there exists multiple time-lines, there is no such thing as "the" anything, because there are unlimited possibilities for each thing, based on the time-line. So, if you think about, The Hexateron is also a joke. Ok, stop thinking about it.