In geometry, an enneagram is a nine-pointed plane figure.
Its prefix, ennea- is Greek for 9. It can be created by three equilateral triangles shifted 40°.
It is interesting that the Enneagram shown here:
has become the symbol of Gurdjieff, similar to the Jesus and the cross and yet Gurdjieff made no mention of it in his trilogy:
The Enneagram comes originally from P. D. Ouspensky's "In Search of the Miraculous", Chapter 14 where Gurdjieff gave a lecture showing this symbol. This was before the founding of the Institute for the Harmonious Development of Man in Fontainebleau and the writing of Beelzebub's Tales. Since then it has been expanded upon by millions of people as a tool of spiritual advancement. A huge industry has evolved from the study of its intersecting lines, specifically in the mapping of nine personality types (arbitrarily chosen) and their interactions. Many have become rich giving presentations, drawing diagrams, and acting as therapists in these studies that have become synonymous with the enneagram, called the Enneagram_of_Personality by Wikipedia, which was lifted from Gurdjieff by Oscar Ichazo and Helen Palmer. The Fourth Way Enneagram in Wikipedia plays second fiddle to it now. It is the Ouspensky and John G. Bennett followers who use this term, but it should be correctly called the Gurdjieff Enneagram. The so-called 'scientific' studies of the "Fourth Way Enneagram" that try to predict events by using the six vectors of the repeating decimal seem to be no more useful than games of chance.
Astrology already has twelve types, but they are of the essence, whereas these nine types in the Enneagram_of_Personality seek to map the personality. The personality is merely the artificial structure that we create to shield our essence from the world. Ultimately, this study of personalities is a complete waste of time in the building of a Soul, which is built upon essence. It is possible that this knowledge could be useful in the manipulation of others who do not have a clue that they have an essence, but clearly serves no purpose to one's spiritual growth.
When I read this excerpt, I said to myself, this must be a mistake and it should be "Sevenfoldness" as in the "Law of Heptaparaparshinokh", especially in the context of the seven notes in the octave. If it was meant to be the one and only reference to the nine points of the Enneagram, it is strange, since the unique figure really consists of seven lines that directly relate to the repeating decimal being the division by 7. The other two points are from the inner triangle which is often left out.
It is more likely that the mentioned 'Law of Ninefoldness' refers to something more complex than the Enneagram and was not known by Gurdjieff at the time of his writing. This "Law of Ninefoldness" most likely refers to the recently discovered (or shall I say remembered) Vortex Math that will be demonstrated in this lecture. In Vortex Math the number nine has a unique relationship, for example, one of the properties of nine is that when it is added to any number, it gives that same base number:
It is important to note that the process of "reduction", as used throughout this presentation, is to add all digits greater than nine together to demonstrate their essence as 1-9. This is a common practice in Numerology.
The number is also written in the cosmos: diameter of the earth: 7920 miles (7+9+2+0 = 18 = 9), square foot = 144 inches, cubic foot 1728 inches, square yard=1296 inches, (multiply by 10 is 12960 and 12960 years (one half of the precession of the equinoxes 25,920 years), circle 360 degrees, square 90 degrees x 4 = 360 degrees, equilateral triangle 60 degrees x 3 =180 degrees, pentagon= 108 x 5= 540 degrees (silver atomic weight 108), pyramid truncation 4 x 180 degrees = 720 degrees, cube 6 x 360 = 2160 degrees
, octahedron 8x180 degrees=1440 degrees. There are many more.
This 'Law of Ninefoldness' has many other amazing features such as perpetual motion as I will show. Disappointingly, "Beelzebub's Tales to His Grandson" Chapter 6 Perpetual Motion does not reveal this secret, except to describe the spaceship that they are traveling in as an analogy of being-Partkdolg duty. In the Chapter 41, the excerpt of Gurdjieff as Beelzebub mentioning the 'Law of Ninefoldness' is, unfortunately lost in a tangential story on the effect of sound vibrations on the physical body that is clearly about his failure to prevent his wife's death from cancer.
If Gurdjieff had had access to the concepts of Vortex Math as presented by Marko Rodin (1911 - 2007), he could have elaborated further on the Enneagram and even shown the mathematical derivation by Vortex Math of "The Nirioonossian-World-Sound" as described in The Law of Heptaparaparshinokh, Ch 40: "being just that sound, the vibrations of which have been taken from ancient times - and even at the present time there, is still taken, it is true, for a very small number of your favorites, of course, of this same China - for their sound-producing instruments as the 'absolute vibrations' of the note 'do'."
The Gurdjieff Enneagram, as shown to Ouspensky, is formed by this mathematically elegant process:
Here is the Gurdjieff Enneagram with all possible lines shown within it in yellow and green with the notes assigned:
The Marko Rodin Vortex claims to describe all energy processes and
The Marko Rodin Vortex begins like the Enneagram with a circle with numbers 1-9. It is built by doubling and reducing and by adding the digits of the number over 9. A series of 1, 2, 4, 8, 16 (7), 32 (5), 64 (10 = 1) is formed in a different way than the the Gurdjieff Enneagram.
|The Gurdjieff Enneagram can be derived from the Vortex figure |
1-2-4-8-7-5-1 not 1-4-2-8-5-7-1
This derivation shows that the two systems are related, except for having opposite circular motions.
The Marko Rodin Vortex also works by halving. In this case the circular direction is reversed which clears up the conflicting lines 4-2 and 5-7.
The are certainly critics of the Vortex Math presented by Marko Rodin. They claim that it is the obvious result of the base-Ten mathematical system and point out that it will not work for other base number systems. This is, however an absurd complaint as we have ten fingers and toes and we count by ten! Also, there have been experiments performed that appear to show that free energy or at least enhanced energy can be produced using a "Rodin Coil".
Nikola Tesla (1856-1943), the famous inventor, is known for the quote “If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.”
Tesla observes that:
Vortex Math uses doubling and its inner triangle, like the Gurdjieff Enneagram, is 9-3-6.
Vortex Math also works for the Fibonacci Series as shown
by Maff Math:
yielding forward and backwards spirals:
In the next table of Vortex numbers, all numbers are multiplied and then reduced (RED), showing each number has its reversed twin. (See the linked statements in the top row.)
Thus the Vortex diagram can be divided into right and left, positive is on the right and the negative on the left.
Since the Enneagram has similar mirror image, we can surmise that it also has a positive and negative side. The action of the Enneagram can be considered to be of the spiritual realm and the Vortex to be of the material realm because the crossing point of the Enneagram is closer to God ('do') at the top than the Vortex which serves the physical body and is lower down. Also, the Vortex follows the side tracks and the Enneagram takes shortcuts and the returns back like the peaks and troughs of a wave which allows it to cross at a higher point.
The influence of the triangle points at 3 and 6 are similar in both systems. In the Vortex Math, 6 and 3 swap places continuously. In the Enneagram, the triangle influence is important to help bridge the two discontinuities of 'mi' and 'fa' and 'sol' and 'la' as both system lines of each are in opposition. (Incidentally, this supports the symmetrical action at 'sol' and 'la' instead of the expected discontinuity between 'ti' and 'do' - further discussed in the in the Food Octave in Talk 1.)
The next figure shows the Enneagram's mirrored nature. (What is amazing is the affinity of mi' and 'la' to the triangle at 6 and 3.)
Next, let us study the relationships of the notes using Vortex Math.
The first column of the table below:
derived from the table above (showing exact digits)
All these triads are suspended chords, but their relationships reveal other influences:|
'do' (9) influences 'sol' (6&3); which influences 're', which influences 'la'; which influences 'mi'; which influences 'ti'
'ti' influences the space between 'sol' and 'fa'; which influences the space between 'do' and 're';
which influences the space between 'sol' and 'la'; which influences the space between 're' and 'mi';
which influences the space between 'la' and 'ti'.
Note that 'ti' is the joining point of the positive and negative energies on it return back through 'fa' on it's return to 'do' (9).
Here we can see some notes that are opposite to the direction of the Enneagram and some places they enforce the direction of the Enneagram. And the two places actually where they are opposed and supported will be the laurels of the devil and the angel in our final diagram.
The line E ('mi') to B('ti') from seven natural notes of the Twelve Note diagram (above) reinforces one line of the Enneagram while line D ('re') to A ('la') is being opposed by the Enneagram line. These are the two laurels of the angel and the devil. Comparing the functions to the corrected Food Octave in lecture 1:
In Food octave 're' was Digestive System (stomach), 'mi' was Circulatory System (liver), 'fa' was Nervous System (cerebellum), 'sol' was Thinking Center (cerebrum) (These were swapped from what Gurdjieff has shown.), and 'la' was the Endocrine System (hormones, "heart") (that was the vibration that was left out of the Food Octave by Gurdjieff), and then the final one was the Reproductive System (the sex organs).
Here is the triumph of our study