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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? ☺