At one possible level of description, what Bennett means by 'outside' is simply 'outside of the system under consideration, the system whose process is being mapped on the enneagram'. When we use C-sharps and B-flats in the key of C, we are using notes that are 'outside' of the C-Major scale - and the equilateral triangle in the center of the Enneagram can represent the 'outside influences' of the process that is being represented by the diagram, as Bennett so eloquently illustrates in many of his examples.

But there is also another more profound sense in which the central figure of the Enneagram, the equilateral triangle comprised of points 3,6, and 9, can be taken to be 'outside' of the process represented by the 1-4-2-8-5-7 sequence. It represents, as we have been demonstrating in this series of papers, an entirely different 'order of existence', one that is indeed INCOMMENSURABLE with the order that is suggested by the 6-pointed figure. Insofar as the 1-4-2-8-5-7 sequence is understood as representing the mundane 'prevailing' order, the 369 triangle may be understood as a representation of an EXTRA-ordinary order, outside of the realm of the 'mundane' world.

What is truly remarkable about the Enneagram is that the additional 'order' is no longer represented as an undifferentiated whole, as was the case when it was represented by the dimensionless point at the center of the circle. Now it is depicted as DIFFERENTIATED (into three parts), although still 'outside' of the ordinary order. Interestingly, it is not until relatively recently that science and mathematics have provided us - via concepts like physicist David Bohm's notion of the 'implicate order' - with a model that permits differentiated information to be 'enfolded' (Bohm's word) into an order that appears to explicit awareness as undifferentiated in nature, and quite different, in this respect, from what appears in the 'explicate order'. So in this respect the Enneagram, as understood by Gurdjieff and Ouspensky, may have prefigured contemporary physics.

Another example of a fully differentiated 'hidden' order comes from mathematics - the notion of 'imaginary' numbers. Arthur Young, the inventor of the 'bell helicopter', is a contemporary theorist whose far-ranging speculations have attracted a great deal of interest. Compare the following diagram, in which Young intends to explain the relationship between imaginary numbers and the circle, to what we have been saying about the 'virtual' nature of the central triangle in the Enneagram. Needless to say, it was drawn decades after Ouspensky's work on the Enneagram.

In the figure, Young is dividing a circle into three equal parts, creating the same equilateral triangle that appears at the center of the Enneagram! The circle is drawn against the background of a coordinate system comprised of a vertical axis representing the 'real' numbers (-1 to +1) and a horizontal axis representing the 'imaginary' numbers (-i to +i). The imaginary numbers (eg, the 'square root of minus one') cannot be correlated to any number in the real number series, because there IS no real number, multiplied by itself, that results in a value of 'minus one'. Even if you are not a mathematician, it only takes a moments reflection to see this - as any real number, whether a positive or negative number, when multiplied by itself, results in a POSITIVE number. So they must be depicted as falling on an axis orthogonally related to the line representing the 'real' numbers - in other words, in another dimension or 'order of existence' incommensurable with the real numbers.

"Now the interesting thing is that all roots of unity can be shown in the SAME CIRCLE (the same plane) that displays minus one and its imaginary roots. The CUBE roots of one are the points that divide the circle in three equal parts; the fifth roots of one divide the circle in five parts, etc." (Arthur M. Young, Mathematics, Physics & Reality, Robert Briggs Associates, 1990, page 27)

As even a superficial glance at the diagram will show, what Young is doing here by plotting an equilateral triangle on the circle is very similar to what Ouspensky was trying to do with the Enneagram. For both, the equilateral triangle in the circle is the product of the intersection of 'two incommensurable orders'.

There is another interesting feature that Ouspensky ascribes to the 'octave' mapped onto the Enneagram. And it also prefigures relatively recent advances in science and math. Each note within the Enneagram 'octave' was understood by Ouspensky to contain within itself another 'octave', which he and Gurdjieff called the 'inner octave'. This, of course, gives the arrangement a FRACTAL nature. Each note 'can be regarded as an octave on another plane', he says, a world within a world. ³ As this is not true of notes in the physical world, we can only assume that he is not really talking here about music per se, but about a structural arrangement that he is LIKENING to the ordinary musical octave, but one that also has a fractal structure! Fractal structure can be classified as a specific variation of what we called, in Part I, 'liminocentric' oganization.

So in the Enneagram we see not only a heirarchical 'worlds within worlds' model that illustrates what liminocentric organization looks like and acts like, we are also specifically looking at a cross-section of this whole/part structure, one that presumably holds the key to the interface between the 'manifest' and 'unborn' orders of existence!

7-pointed composite figure

Notice that point Nine, although it is part of the 'virtual' figure, the equilateral 6-9-3 triangle, is also treated by Ouspensky as part of the figure that emerges in the 'manifest' 1-4-2-8-5-7 figure, as a SEVENTH point. Point Nine 'crosses over', as it were, straddling the two figures that represent the incommensurable orders. ⁴ We should point out here that Ouspensky does indeed use the word 'incommensurable' to describe the relationship between different 'dimensions' or levels of 'cosmos', which is his term for 'orders of existence'. It is at Point Nine that 'virtual' order erupts into manifest order, and appears AS a 'real' object. It is at Point Nine that the 'extra-ordinary' overflows (in a manner that we can only describe as 'super-flous' - ie, an act of 'grace' or gratuity), thereby becoming 'ordinary' and embodied.

If 'eight' psychologically implies completion of process, Nine is something 'extra'. Interestingly, the dictionary defines the the word 'extra' not only as meaning 'in addition to the stated quantity' (ie, 'supernumerary'). There is also a more profound sense of the word, deriving from the Latin equivalent of the word 'extraordinary', which points to an 'exceptional' order - one that is 'beyond the usual', 'situated ouside', 'lying outside the assumed province or scope'. In the Enneagram, in which these two meanings are intimately connected, is an attempt to graphically illustrates this.

In 'Thus Spake Beelzebub' ^4a, Henri Tracol describes the kind of fundamental underlying organization that the Gurdjieffian 'Work' accomplishes. It is 'in keeping with the principle of the Law of Three - A RECONCILIATION OF OPPOSITES', he says. '... this underlying Order must, in that sense, include and eventually assimilate all particular order AND disorders'. Maurice Nicoll adds, 'The Work teaches that this order is connected with what is called the Law of Octaves, or law of things in order, or Law of Seven...' ^4b, and further describes the internal 'organization' achieved by the fully-developed individual in the following way -

In a fully-developed man [sic] - that is, a man possessing individuality, consciousness and will - it is not life and changing circumstances that mechanically drive him. Such a man has something ORGANIZED in him which can resist life, something from which he can act. Such a man, in short, CAN DO. And this is because he possesses more bodies than the one he received at birth. (Nicoll, 'On the Formation of a Psychological Body', in Order, Maitreya 6, 1997, Shambhala, page 25)

Nicoll quotes a transcript that Ouspensky made of a talk by Gurdjieff, who refers

pear-shaped diamond

heart-shaped diamond

The Florentine Diamond

to three 'non-physical' bodies that are achieved as a result of 'the Work'. In this talk Gurdjieff admits to having borrowed this concept of three extra-ordinary bodies from 'Eastern teaching'. In the esoteric Vajrayana Buddhist teachings of Tibet these three bodies ('kaya') are known as the dharmakaya, sambogakaya, and nirmanakaya, which are sometimes referred to by one term, the 'vajra body' (ie, 'diamond body'). We shall return to this concept further along in this series of papers. Suffice it to say here that these three 'extra' bodies are manifest only in the fully developed individual, and can thus be considered 'extra-ordinary' (in the sense of the word that we have herein connected to the meaning of the number 'nine'). When the 'Nirmanakaya' or form body of the fully enlightened being appears as the product of a 'conscious re-incarnation' process, it is referred to as a 'tulku', as the reader will recall from earlier section of this series.

What we, in this series, have been calling the relationship between 'Ego' and 'Self' is more often referred to, in the vocabulary associated with Gurdjieff's system and the Enneagram, simply by the words 'Personality' and 'Essence'. Nicoll explains the relationship between the two -

The Work speaks almost from its starting-point of the Essence in Man being undeveloped. It defines a growth of Essence as a change in the level of Being: it speaks very often about making Personality passive so that Essence can develop. Especially does it speak of False Personality or Imaginary 'I' and the necessity of observing ourselves in regard to these and separating from them. The object of this is to allow something else to grow. Essence can develop. And in connection with the development of Essence a second body can grow. But it cannot do so as long as Personality is active and controls inner life. PERSONALITY IS ACTIVE AND ESSENCE IS PASSIVE in mechanical man and this is due to the action of Life that keeps this relationship between Personality and Essence. Life is a neutralizing force that keeps Personality active and Essence passive.

There is only one force that can change this relationship of Personality and Essence - a force coming from OUTSIDE LIFE. This is the Work, or, in general, CONSCIOUS INFLUENCES, coming from the Conscious Circle of Humanity, outside mechanical life. (Nicoll, 'On the Formation of a Psychological Body', in Order, Maitreya 6, page 21)

Here, explicitly articulated, is the proposition that the fundamental 'outside force' (associated with the 369 triangle in the Enneagram) that must be brought INTO the 'process' (represented by the 142857 figure), in order to achieve the kind of order or organization that makes this a fully functional spiritual path, are the 'teachings' ('dharma', in the Buddhist vocabulary) and the presence of the lineage of those who have realized the fully-developed state (the 'sangha', or community of enlightened beings, in Buddhist terminology). The OUTCOME of the process is the development of the extraordinary 'bodies'.

Notice that in the mandala that is the Enneagram, there is a six-pointed figure, a seven-pointed figure, and a nine-pointed double mandala. But there is no 'eight pointed' figure. The eight pointed figure, although implied by Ouspensky's analysis, which utilizes the word 'octave', does not actually exist in this figure. Where we would expect the eight-pointed 'double-mandala' figure normally to occur, we find the nine-pointed figure - with the extra point, the 'Superflous Ninth', making a surprise appearance in the sequence. As if to say, as does the I Ching (a system which is also based on a nine-pointed double mandala system, as we shall see) - that real 'completion' NECESSARILY entails a new beginning; the last step is simultaneously the first step into a new process.

As we shall see in the next paper, 'The Enneagram as Double-Mandala', the number Nine is also psychologically associated with 'synchronicity' - which is a 'process' that involves an 'acausal' element connected with 'divination' AND 'incarnation', both of which are associated, in particular, with 'double-mandala' representations.

Section Two - Seven and Nine, Identical Twins in Magic

skip to footnotes

Eliade, in his book, Shamanism, identifies 7 and 9 as the 'mystical' numbers. The Yurak-Samoyed initiate, he tells us, is carried to the Nine Seas associated with the Land of the Shamanesses, where there grow nine herbs which are the ancestors of all the plants on earth. The voyage serves the Shamaness well in her promethean quest to utilize the healing properties of plants to serve humankind.

And according to Buryat beliefs, 'nine sons of the Boshintoi, the celestial smith, came down to earth to teach men metallurgy; their first pupils were the ancestors of the families of smiths'. In a related Buryat smith ritual, 'nine youths play the parts of Boshintoi's nine sons, and a man, who incarnates the celestial smith himself, falls into ecstasy and recites a long monologue in which he tells how, IN ILLO TEMPORE, he sent his nine sons to earth to help manking, and so on. Then he touches the fire with his tongue'. Their power over fire and the magic of metals 'have everywhere given smiths the reputation of redoubtable sorcerers, according to Eliade. 'The Tibetans', he adds in a footnote, 'likewise have a divine protector of the smith and his nine brothers'. ⁶

Notice in this passage the return of many of the themes that we explored in Part II - tongues of fire, the embodiment of holy spirit in spiritual alchemy, the promethean gift delivered by virtue of an individual's capacity to 'draw down' particular types of 'spirit'. What is of special interest in the context of our current discussion, however, is the fact that Eliade seems to consider the two numbers - 7 and 9 - as nearly SYNONYMOUS in the Central Asian cultures that he is investigating. There are seven OR nine notches on the tree or post used by the Altaic shaman ⁷; seven OR nine celestial levels, with seven OR nine gods; seven OR nine hells; seven OR nine branches of the Cosmic Tree; and seven OR nine sons of the celestial god.

Eliade gives no explanation for this curious conflation of the two numbers, nor does he explain the tacit omission of the number 8 in these mystical schemes. But in an interesting passage in which he describes the initiation of the shaman

Mandalas are sometimes used for healing purposes. Interested in seeing if any of the contemporary propopents of this art utilize the seven-nine combination/ambivalence that plays such an important role in shamanism and in the Enneagram, we searched the web. We found only one clear example of this phenomenon. It is a mandala purported to have healing properties, which utilizes a nine-pointed circle at the bottom of which there is an opening, precisely where the opening is in the Enneagram - between points '4' and '5'. Extending downward from that opening is a column on which the seven chakras are depicted. When we asked Ralph Henninger, the artist, why he used a nine-pointed circle in combination with the seven chakras, he said, "The seven chakras are the key to personal enlightenment. Nine is the number that represents the highest level of that state." By clicking on the thumbnail above (which pictures only the upper half of the painting), a much larger version can be found at Ralph's site.

amongst the Ostyak of the Yenisei, Eliade offers us a description of a ritual that is reminiscent of how Ouspensky deals with the numbers 7, 8, and 9 in his analysis of the Enneagram. It helps to explain why 7 is often identified with 9 in this way, and why an 'eightfold' figure appears to be 'missing' in diagram that we know as the Enneagram.

The future shaman, Eliade tells us,

... withdraws into solitude, cooks a flying squirrel, divides it into eight parts, eats seven, and throws away the eighth'. After seven days he returns to the same place and receives a sign that determines his vocation. (Eliade, Shamanism, page 278)

Indeed, in the living traditions in which mandalas as tools on the spiritual path, the word 'mandala' is more often associated with this practice than with the mere visual diagram that represents it. The 'body', in the form of food, is sacrificed to the spirit - made receptive to it. Released from attachment to its previous owner, it is free to be occupied by the invoked spirits/energies.

In the ritual that Eliade describes, immediately after the Seventh (day), comes not the Eighth (which has been 'offered', in a way that is sometimes associated with 'dismemberment' - ie, deconstruction), but what we have been calling the 'Superflous Ninth', the 'sign'. This simple initiatory ritual actually PREFIGURES the entire career of the shaman, since the 'sign' that appears on this occasion is identical to the appearance of the initiate's 'tutelary spirit' - as the Yakut word 'amagat', which means both 'sign' and 'tutelary spirt', indicates. Often the tutelary deity is the soul of a dead shaman - ie, an ancestor in the shamanic lineage, who becomes 'incarnate' in the body of the initiate. ⁸ In the Nyingma School of Tibetan Buddhism a similar situation is described, in which the individual's teacher ('guru' or 'lama', who may be living or dead) is believed to appear in the manifest world in various symbolic forms - as an old woman, a fishmonger, or a disease, for example - in order to provide profound tutelary instruction to the student. The term for this, in Tibetan, is 'Dayi Lama' (ie, 'Sign Lama').

What Jung called 'synchronicities', are in these systems interpreted as 'signs' bearing guidance from tutelary deities. Synchronicities are associated with 'double mandalas', in which the number 9 plays a key role, as we shall see in the next paper in this series.

Last week we mentioned Jung's hunch that a 'competition' sometimes seemed to occur between 'four' and 'five', and how this was associated with the issue of symmetry and asymmetry and also with the meaning of the number nine. We are now in a position to recognize one of Eliade's observations as further confirmation for this view. 'Among the Buryat, he explains, there are 'ninety nine gods, divided into good and evil and distributed by regions - fifty-five gods in the southwestern regions and forty-four evil ones in the northeastern. These two groups of gods have been fighting each other for a very long time'. ⁹ The conflict that Jung observed taking place between 'four' and 'five' (which add up, as Eliade's example explicitly reveals, to 'nine') may actually represent a dilemma taking place between eight and nine, and integral to the symbolic meaning of the latter number. The dilemma is this one - is the individual who succeeds in attaining the 'enlightened' state that is achieved in the first half of the spiritual path (marked by the insight into the 'empty' quality of 'form') to remain in a self-contained individual 'completeness' or will he or she SACRIFICE that completeness in order to descend back into embodied form, for the purpose of helping others? In the Buddhist tradition, the individual who chooses to return is considered the embodiment of the religious ideal, and is known as the 'Bodhisattva'.

Conclusions

We may choose to take the statements that Gurdjieff and Ouspensky made about certain physical processes that they associated with the Enneagram as literal truths about real-world phenomena. Or we can take them in the same spirit in which Jung proceeded in his analysis of the work of the medieval alchemists - as suggestive of deeper psychological truths. But even if we choose the latter path, is it not possible that we might actually find, somewhere in the physical world (even if not in the ordinary musical octave), structures of the type that they described? For if, as we propose, mandalas reflect the structure of consciousness, and, as human beings, we are limited to viewing our world through the lens of consciousness, are we not likely to see things that fit that structure?

Because the mandala that Ouspensky presents us with - the Enneagram - deals with the hitherto unexplored region in analytic psychology associated with the number Nine, it is likely that by exploring it in depth we can bring into relief truths that could not be gleened from previous analyses based on the lower-level fourfold and eightfold mandalas of the type in which Jung showed primary interest.

Hopefully, in this and the previous part, we have demonstrated not only that the form that the Enneagram has taken as a 'mandala' is the product of minds that were absorbed in a spiritual quest, but also that the issues that were thereby addressed were ones associated with advanced stages of that path.

Despite the fact that 'The symbol is not an allegory and not a sign, but an image of a content that largely transcends consciousness', Jolande Jacobe remarked, '... symbols can 'degenerate' into signs and become 'dead symbols' ...' ¹⁰ Nevertheless, as Eliade pointed out, 'A religious symbol conveys its message even if it is not longer CONSCIOUSLY understood in every part' ¹¹. This provides us with hope that even it it turns out to be the case that the Enneagram is a symbol the deeper meaning of which has been lost, this meaning can once again be recovered, and used to infuse the personality typology with which it is connected with a more profound base.