Normally, I am not that interested in connecting my system to other systems or beliefs. But there are a few ideas out there whose patterns are interesting enough to consider. The Pythagorean pattern of a Tetractys is one good example. I don't really know much about how the Pythagoreans saw and used this simple pattern of 10 dots, and it is not my intent to give a history lesson. I would encourage everyone to acquire that knowledge on their own. What I do know, however, is that the Tetractys was considered to be very sacred. Unfortunately, with me, nothing is sacred! So with no attempt to assimilate Pythagorean ideology whatsoever, I decided to look at how a pyramidal arrangement of 10 dots might be used to explain my own ideas. If any of my ideas match that of the Pythagoreans, great! If they don't, too bad. I am not here to explain Pythagorean philosophy.

The Tetractys is a pyramidal arrangement of dots. In pyramid lore, the capstone, or pinnacle is considered special, even divine, as it alone touches the heavens. So I decided to view my Tetractys that way, with the top dot as the one of unity with the divine.

Actually, this study doesn't really need to borrow the Pythagorean Tetractys, because... as seen in the essay The Tree Unitites, we've already established good reasons for inventing our own Tetractys. In the essay The Tree Unitites, our tetractys was born as the result of a reflection from what we came to call a Fourfold Trinity of Binary Unity! When we are done with this essay, it would probably be a good idea for us to exmine the mandala presented in that essay. In the mean time...

-----

The Tetractys is a pyramidal arrangement of dots. In pyramid lore, the capstone, or pinnacle is considered special, even Divine, as it alone touches the heavens. So I decided to view my Tetractys that way, with the top dot as the one of Unity with the Divine. Most of the ways in which I see these 10 dots numbered (when they are numbered) is with a 1 at the top. That's probably because, to many, the number 1 equals unity, as the word itself implies. But to me, the number 1 indicates the concept of identity, more than unity (see The Three Unities elsewhere on this site). To me, the number 1 says "I am here, I am one, ready to begin... and/or beginning." To me, the number 1 emerges as an entity, from the uniform unity of nothingness that surrounds and contains all manifest entities. So to me, nothingness is where the real concept of Unity lies (at least within the "knowable" universe we are describing with these 10 dots, as opposed to the "unknowable" realm of The Absentia). Thus, in my opinion, the wholistic, uniform sameness of nothingness, as opposed to the diversity of manifest things (whether described with a 1, or a 2, or whatever) is where we find true Unity... within any knowable universe.

If we number the 10 points of the Tetractys the way people number the 10 pins in a bowling alley, we see different things. I decided to number them with the nine equidistantly related numbers of manifestation and a zero at the top.

If we number the 10 points of the Tetractys the way people number the 10 pins in a bowling alley, we see different things. I decided to number them with the nine equidistantly related numbers of manifestation and a zero at the top. I then decided that, rather than number them from top down, left to right, in a very linear, left-brained, book-reading fashion, I would number them top down as equidistant pairs of numbers sequentially removed from nothingness, with the 5 in the middle. Given that 5 is the middle of the number line, and represents the center of our spherically equivalent model (which can be seen elsewhere on this site) it made sense for it to be at the center of this model.

Unity above.. the Material World below. By numbering the Tetractys with nine numbers and a zero, instead of 1 through 10, the idea of a Spiritual world being separate from a Material world below, is visually conveyed.

Unity above.. the Material World below. By numbering the Tetractys with nine numbers and a zero, instead of 1 through 10, the idea of a Spiritual world being above, and in some ways separate from a Material world below, is visually conveyed. In the essay Why Only Nine, I try to explain why I see nine numbers and a zero as superior to that of thinking in terms of 1 through 10. I point out how zero can be viewed like bookends to any number line, and how, when multiple number lines are juxtaposed together, the zero that resides between them are thus counted. In this way 10 is just the first (1) zero (0) to be counted, and twenty the second (2) zero (0). By placing zero at the top of my Tetractys, and arranging the other nine numbers in such a way as to circulate around the base and back up, we can see how zero becomes analogous to the "GO" square on a Monopoly board! Every time you pass, collect $200 dollars, and place a number in front of the zero... 10, 20, 30, 40, etc. around and around. This is how we count.

The Unity of the continuum of nothingness that surrounds and contain any manifest entity divides into duality. Duality leads to Diversity. Diversity leads to Complexity. This compounding departure from the divine is visually displayed by the ever widening base of the Tetractys.

In the essay Fun with Fibonacci, the Fibonacci Sequence was used as a pattern to describe a proposed Law of Sequence, and describe how a universe, and each entity born into that universe, evolve from simplicity to complexity. In that essay, it was shown how the Unity of the continuum of nothingness that surrounds and contain any manifest entity divides into duality, and how duality then leads to diversity, and diversity to complexity. In this modified Tetractys, this compounding departure from the divine is visually displayed by the ever widening base of the triangle shape. By arranging my Tetractys with equidistant number pairs, we can traverse down to the base, and thereby replicate the idea of coagulation (seen elsewhere on this site) and the idea of something emerging from nothing into greater and greater complexity. Things don't line up in exact concentric circular, or spherical layers, like they do with the spherical model and its concentric circles of Circumsphere (1/9), Atmosphere (2/8), Surface (3/7) and Core (4/6) (seen elsewhere on this site), but it's pretty close.

-----

The Four Suit Mandala

Here is a mandala you can use to meditate on the ideas presented with this modified Tetractys. This mandala uses the idea of a pyramidal Tetractys as one of many reasons to view a tarot deck with four suits. The separation of the capstone from the base gives rise to the idea of Unity being separate from the manifestations of the material world below. The square is the material world. The circle is the infinity of Unity.

The Tetractys as a pyramid gives rise to the idea of four suits in a deck. The separation of the capstone from the base gives rise to the idea of unity being separate from the manifestations of the material world below.

As number lines, the pips are bookended with the four symbols of manifestation: Frame, Flow, Form and Force. The sum of all is seen in the array of nine pips, at the center. The seasons decorate the corners of the square, and run round the circle: An Oak leaf in the Force corner, leading to Spring, flowers and tulips. An Elm leaf in the Form corner, leading to Summer, greenery and corn. A Maple leaf in the Flow corner, leading to Autumn, seeds and weeds. A Pine cone in the Frame corner, leading to Winter, snow and icicles.

-----

A Trinity of Unity

A Trinity of Unity! Elsewhere on this site, there can be found explanations that demonstrate exactly how it is we come to view the numbers 3 and 7 as points of spiritual contact with the Divine from within the material world. By landing on the two corners of the Tetractys that lie opposite to the Unity of the zero, this connection to unity is accurately portrayed in a visual way. In the essay A Significant Signature of Nature, the 3 and 7 landed at the trough and crest of a sine wave, indicating important points of pause within the action of a temporal progression of ideas. So, in a similar manner, as we progress around this modified Tetractys, the corner points can stand as a similar representation of critical pause.

A Trinity of Unity! Elsewhere on this site, there can be found explanations that demonstrate exactly how it is we come to view the numbers 3 and 7 as points of contact with the Divine, from within the material world. By landing on the two corners of the Tetractys that lie opposite to the zero, this connection to unity is accurately portrayed in a visual way.

By isolating the corners of the Tetractys we reveal another interesting pattern, as the remaining dots can now be viewed as the corner points of a cube. Thus the cube represents manifest existence, residing within spiritual corners of three triangular unitites (see the essay The Three Unities elsewhere on this site).

By inverting or rotating the whole Tetractys triangle, we can consider how the nine numbers of the material section describe life and death cycles. Such an arrangement also replicates the idea of zero on the outside and 5 in the center - the custodians of the split absentia that lies eternally outside and inside our universe.

Lastly, by inverting or rotating the whole Tetractys triangle, we can consider how the nine numbers of the material section describe life and death, or light and dark cycles. I'm not going to speculate on which is better, inverting or rotating. Different numbers get replaced differently with either method, I don't see any significant advantage to either way. The idea is simply that one triangle points up to a positive result, and one points down to a negative result. Thus, we duplicate the Major Trumps of The Numerical Tarot. And, if once again visualized as a three dimensional pyramid, we also duplicate the four Minor Suits as seen in the Four Suit Mandala above!

Such a two dimensional arrangement also replicates the idea of zero being on the outside, and 5 in the center - the custodians of the split absentia (seen elsewhere on this site) that lies eternally outside our universe and at the same time, deep within every manifest entity that coagulates out of the unity of nothingness.

But these are all just romantic notions of coincidence. There are many ways to image a number line divided, or a deck organized. They are all pretty much arbitrary, and are only offered as a means of getting across certain critical ideas. One can take their pick, as to which patterns make the most sense to each individual. The only pattern that is superior to them all is the pattern of concentric spherical ideas coagulating to a point of recursion from a source of absentia. All these other patterns are just attempts to replicate those ideas in one way or another.

-----

The Tetractys Mandala

Here is another mandala that you can use to meditate on these modified Tetractys ideas. Notice, there is no 5 in this Tetractys Mandala! The 5 has been replaced with an optical illusion known as Neckar's Cube. Stare at the cube, and try to decide which way it faces. Is the face on the left defining the front of the cube, or the back of the cube? Keep looking and notice it change back and forth endlessly. Thus it is a perfect representation for the endless unresolveable back and forth alternation of a 5, being the midpoint of a number line, or the center of a mandala where opposites converge, blend and alternate without resolution.

This mandala also shows how the 3 and 7 create a trinity of unity, and how we might invert or rotate the Tetractys as a representation of opposite light or dark, life or death, Yang or Yin concepts. Stars represent the nothingness of zero and its connection to the idea of spirituality. While the outer ring has a motif with parallel and twisted lines to represent the paradox of a Mobius strip and how it describes the paradox of what this system calls The Absentia. Beyond that, are the Alchemistic symbols for the four elements which some suggest are derived from alchemistic marriage of a male and female, symbolized by one triangle penetrating another.

There is no 5 in this Tetractys Mandala! The 5 has been replaced with an optical illusion known as Neckar's Cube. Stare at the cube, and try to decide which way it faces. Is the face on the left defining the front of the cube, or the back of the cube? Keep looking and you will notice it change back and forth endlessly. Thus it is a perfect representation for the endless unresolvable back and forth alternation of a 5, being the midpoint of a number line, or the center of a mandala.