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Connections Beyond Words

If you have read the material on this website about Vortex-Based Mathematics (such as this article), then you might have already noticed the similarity between the Enneagram of System 4 and The Fingerprint of God. This is not a coincidence. They are definitely connected to the same archetypes. Let's explore some of these connections...

The hexad within the Enneagram is the sequence of numbers 1, 4, 2, 8, 5, 7, repeat. This is the same as the repeating decimals that we get from dividing by 7:

1 ÷ 7 = 0.142857...
2 ÷ 7 = 0.285714...
3 ÷ 7 = 0.428571...
4 ÷ 7 = 0.571428...
5 ÷ 7 = 0.714285...
6 ÷ 7 = 0.857142...
7 ÷ 7 = 1
8 ÷ 7 = 1.142857...
9 ÷ 7 = 1.285714...
etc.

Notice that these are the same numbers within The Doubling-Halving Cirucit, but in a slightly different order (i.e.: 1, 5, 7, 8, 4, 2, repeat). We can also see that the Structural Regions and Process Regions of System 4 are the same as Family Number Group 1 and Family Number Group 2 within The Binary Triplet:

Family Number Group 1 is shown here in red, and Family Number Group 2 is shown here in blue. The Structural Regions are Terms 7, 1, and 4, while the Process Regions are Terms 2, 8, and 5.

In other words, the Particular Sets of System 4 and The Doubling-Halving Circuit of The Fingerprint of God are definitely equivalent in some way...but how? We can actually transform the hexad inside the Enneagram (representing division by 7) directly into The Doubling-Halving Circuit (based on division by 2), or the other way around:

This is a remake of the wonderful animation at PiALOGUE.

In the context of The System of Cosmic Order, we are interchanging the positions of Term 1: Perception of Field and Term 8: Balanced Response.

We might think of the Enneagram of System 4 and The Fingerprint of God as two different views of the same thing, one looking at reality from the "inside" and the other looking at reality from the "outside":

Vortex-Based Mathematics seems to be a mathematical way of describing The System of Cosmic Order! Like All things, on the most fundamental level they are One. This relationship is incredibly useful because it can allow us to use the patterns and processes demonstrated within one context in the other, and vice versa. Let's see if we can tease out a few more correspondences...

Systems "Higher" Than 4

The layers of the System quickly increase in complexity. For example, here is a general representation of System 5 through System 8:

Again, the Active Perspective of the Terms, and how Sets of those Terms interact, is an emergent property. We cannot predict them, but we can get experiential glimpses of them. However, even if we may not be able to go into full detail in each layer of the System, there are useful self-similar patterns throughout. Notice how the Enneagrams keep nesting within each other in the above diagram.

We know that The ABHA Torus is self-similar as well! The Nested Vortices along its surface are also tori:

So, it is a ring made of rings!

We also know that The Fingerprint of God is a highly simplified representation of The ABHA Torus as a whole:

...and that each Nested Vortice has a pattern of 1-9 in it like The Fingerprint of God:

Therefore, we can think of The ABHA Torus like a "Fingerprint of Fingerprints", much like how The System starts to make "Enneagrams of Enneagrams". Wow!

...Is The ABHA Torus an incredibly "deep" layer of The System? And can the Terms that we are already familiar with give us a fuller understanding of the dynamics going on inside of it? ☺