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Note: a few minor updates were made to this page in March 2006 including this note! What the page is about is introducing the so-called Celtic Glyph of the Enneagram and showing how this glyph sheds light on the relationship of the enneagram to other systems. It thus aids in the "joining the dots" project so much needed, it is intended to help lead to material for useful work on oneself not to substitute for such work.

Introducing the Celtic Enneagram

One question which has puzzled many people is why the enneagram has remained hidden for so long, given that it is such a powerful tool. Some will tell you that it was invented by the Sarmoun Brotherhood 2500 years ago....but the "Sarmoun Brotherhood" as described in Gurdjieff's extremely unreliable memoirs is a body of doubtful locality and literalness...I have always supected it was much the same as Gurdjieff's friends the "Seekers After Truth". "Sarmoun" is supposed to mean "Bee", perhaps Gurdjieff was saying something about how knowledge is gathered. Maybe, just a guess, something about it being gathered from scattered sources and transmuted through ones body as part of a collective effort. (And then, maybe it has to do with flowers and hexagons...Alternative spellings are 'Sarmoung','Sarman'.)

If one burrows into the history of Western occultism, one can find an enneagram or two, if not exactly the form used by Gurdjieff. Ramon Lull's Great Art used an enneagram, not of the Fourth Way form, but relatable to it. The points were each connected by lines to every other point, one might argue that Lull's enneagram contains the Fourth Way enneagram. (Lull's Figure A, see link below) And Lull and others also used a "three triangle" enneagram (Figure T); see Webb's book The Harmonious Circle for a brief discussion of this. Especially Lull's Great Art or Ars Magna, though, is very much worth looking up. He used a circle divided into nine with each division associated (among much else) with one or another of the Nine Deadly Sins which are still stressed as the basis of the Personality Enneagram especially in Jesuit usage. The Nine Sins are the familiar Seven plus Inconstancy and Deceit...and we can safely assume that Lull is one source of, at least, the modern Personality Enneagram. He is also referred to as (general Lull link here)Raymond or Raimon or Raimundus Lully or Llul or Lullus .(Here isanother Lull link worth listing separately)

However, on this page I want to look at another form in which the Fourth Way enneagram seems to have been known to (at least) Western occultists. I have called it the "Celtic Enneagram" or more accurately (as it has eight external points) "Celtic Glyph of the Enneagram", because it is among Druids and their friends that it is most publicly found.(You can find it in at least one published source on modern Druidism, although not to my knowledge the insight that it is a version of the Fourth Way enneagram. I got that from oral sources.) I should also mention that the Naqshbandi Idries Shah, in The Commanding Self , 1994 Octagon Press, remarked that the enneagram appeared in "coded form" in European tradition as "two superimposed squares"; which is to say as an eight-pointed or sided figure; with the ninth point represented as a "space in the middle". I take this as confirmation of material I first encountered before Shah's brief remarks on this head were published.

In internal structure the Celtic Enneagram is the same as the Fourth Way enneagram, although it emphasises different relationships.

No pictures again! Never mind the Celtic Enneagram is fully described below.

The Celtic Enneagram is a circle of 8 points with the ninth in the centre. The points are numbered not 1-8 but in the following sequence around the rim of the circle: 1 2 3 4 8 7 6 5. It will be seen that if the points are joined together in the order 1-9 and back to 1 that a roughly drawn lemniscate or "infinity symbol" results. There is an internal line connecting the points in the following sequence: 1-4-2-8-5-7-1-. (The same sequence as used in the Fourth Way "normal" enneagram, but of course it looks different mapped onto the Celtic sequence.). The points 3-6-9 are connected also.

If one looks at the Inner Hexagram (ie the numbers apart from 369) you will see that their order around the rim of the circle can be derived from the powers of two, reduced to one digit form by what Gurdjieff called Theosophical Addition. The powers of two go: 1, 2, 4, 8, 16, 32, 64, 128, 256 etc.
By Theosophical Addition this creates a repeating series like so:1,2,4,8,7(ie 1+6=7),5 (ie 3+2=5), 1 (ie 6+4=10, 1+0=1), 2 (1+2+8=11, 1+1=2), 4 (from 256) etc.
In other words, the Inner Hexagram numbers are arranged in Octave Order or Doubling Order around the rim of the circle.

Devotees of Renaissance magic will find symbols reminiscent of the Celtic Enneagram in the grimoires, most notably the so-called "Sigil of Saturn" which is formed from the number sequences 1-2-3, 4-5-6 and 7-8-9 (ie a straight line and two tent-shaped lines), but drawn on a 3x3 Magic Square. You get a mirror pattern to the Sigil of Saturn if you join the three sets of numbers which comprise the "three triangle" enneagram as: 1-4-7, 2-5-8, 3-6-9.

Join the Numbers for the Sigil of Saturn

4 3 8
9 5 1
2 7 6

The ancients were very interested in the properties of magic squares, the 3x3 one has a special place as the simplest, there is no 2x2 magic square. (Other magic squares are associated with other planets, following the number-planet correspondences of the sefira. For example the Moon is associated with the 9x9 magic square. You can find all this in Barrat's 18th century compendium The Magus, available from occult booksellers on and off.)

Another distinguishing feature of the 3x3 square is that it includes the complete set of numbers 1-9. It is very widespread, the 3x3 Magic Square for example relates to the Later Heaven arrangement of the trigrams.

Moon Symbol

Then again, look at the following "Moon goddess" symbol taken from wikipedia's Triple Goddess page:

When I was first shown the "Celtic enneagram" the similarity of its inner lines to the Minoan double-axe associated with goddess worship was pointed out to me. I don't think it is stretching the point to claim a like similarity with this symbol. It is intersting to note that in conventional Western magic, Golden Dawn etc, the nine-pointed star is regarded as a moon symbol.

The Chinese Connection

One should also compare the Celtic Enneagram with the Chinese Early Heaven arrangement of trigrams, like so:

This symbol, like the Later Heaven arrangement, is often shown as set of nine, icluding the middle as an additional point. The key is to regard the trigrams as binary numbers, so that for example the symbol here shown at the top (traditionally meaning Heaven)of three unbroken or firm lines is equivalent to the binary numeral 111, ie (4+2+1=7)seven; while the symbol to the viewers left of two firm and one broken line is equivalent to the binary numeral 110 or six (ie outer firm line counts as 4, middle firm line counts as 2 inner broken line counts as zero, would count as one if it was firm) . If one translates all the figures so one obtains a sequence around the circle of the numbers 7 6 5 4 0 1 2 3; or starting from the bottom trigram Earth: 0 1 2 3 7 6 5 4. That is, the same sequence as the Celtic Enneagram sequence (which, remember, is: 1 2 3 4 8 7 6 5) except that each number is less one. (I've just, July 2005, found a stand-out website on the Early Heaven arrangement which is a required visit for anyone interested in this subject. It appears to solve the old question of relationship between the Early Heaven and Later Heaven arangements) In Gurdjieff's Beelzebub's Tales the source of the "law of ninefoldedness", which is to say the enneagram, is stated to be China (Chapter 40....or was it 39?).

To see some of these connections explored see The Enneagram as Classic 'Double Mandala' . For a vast array of connections see Tony Smith's pages on the Early Heaven arrangement and much (much) else. This link has now (2006)been updated.

Relationship Between the Enneagram and the 3x3 Magic Square

It will be seen that the sides of the Celtic Enneagram can be straightened out to make a diamond shape like so:

Enneagram as Not Very Magic Square


We can turn it on its side for typing convenience like so:

6 5 1
7 9 2
8 4 3

This presents the Celtic Enneagram in outline ; (as a Not Very Magic Square !) internal lines (1-4-2-8-5-7-1- and 3-9-6-3) not drawn. However if you flip the 3 and 6 (which by general enneagram theory are, um, flippable) you will discover an Almost Magic Square, every line adds to 9 or 18 (which can be reduced 1 + 8 =9). So:

Flipped Enneagram as Almost Magic Square


or, conveniently
3 5 1
7 9 2
8 4 6

Furthermore, if you circulate the numbers around the infinity symbol or lemniscate so that the next Not Very Magic Square is:
Not Very Magic Square With 8 In Middle:


you will find that you can again create an Almost Magic Square by flipping the corner points, so:
Almost Magic Square With 8 in Middle:


If you continues the process until 5 is in the middle and then flip the corner points then of course the Magic Square proper is generated, and there are a few other interesting features that I have noticed so far...

The Masonic Square and Compass symbol may be a disguised reference to the internal lines of the Celtic Enneagram (The connection between the origins of speculative masonry and seventeenth century British Druidism is, erm, well-speculated. Also see for example K Paul Johnson's scholarly work for the emerging picture connecting theosophy, the more heterodox forms of Islamic mysticism, the teachings of Gurdjieff and Masonry)


I believe a good argument can be made that this Celtic Enneagram was used in the construction of the Tarot.Just for a start please not that there are 13 points on the Celtic Enneagram (ie the 9 plus four un-numbered points where lines cross). There are 78 Tarot cards, and 78 lines that can be drawn between 13 points. Furthermore the groups of lines when drawn on the Celtic Enneagram fall into natural divisions which relate to the divisions of the Tarot pack very closely, more closely than is at all likely to be coincidence.

One can consider the Celtic Enneagram as composed of three parts, two halves of an outer shell (1-4 and 5-8) and a core consisting of the 9 point plus the four un-numbered crossover points (which I'll mark as #). Thus:

1 2 3 4 1Shell layer
# # 9 # # Core layer
5 6 7 8 2Shell layer

You will find that 22 lines can be drawn between points within a single layer, 10 in the core and 12 in the shells (six in each of 1Shell and 2Shell) The 22 corresponds to the trumps of the Tarot, which (at least in the Golden dawn usage) can be divided into the 12 trumps which relate to the signs of the zodiac and the 10 which don't (they are related to planets and elements). The zodiacal signs can in turn be broken down into 6 male and 6 female as of course the 12 Shell lines can be divided between 6 in the first and 6 in the second Shell layer.

That leaves 56 lines that can be drawn between layers, and 56 minor arcana. 16 of those lines can be drawn between the Shell layers, corresponding to the court cards. In the Golden Dawn usage the court cards were defined in elemental terms; the Queen of Rods being defined as "Water of Fire" for example; Queens being Water and Rods being Fire. (So; Queen of Cups would be Water of Water etc). That leaves the forty simple number cards to be generated by lines between the Core layer and the Shells. I would suggest that probably the idea is that each of the Core layer points stands for two numbers, (the 9 relating to perhaps the Ace and Ten cards for example.) The Shell numbers refer to elements (with, just as a speculative example 1 and 8 referring to masculine and feminine fire respectively) and therefore also Tarot suits. So, again I am speculatively illustrating the proposed structure, a line between 9 and 8 might represent 10 of Rods while between 9 and 1 might represent Ace of Rods.

While the details especially of this proposal are (wait for it)speculative it must be said that the numbers work out very well, especially when compared to the conceptualization of the Tarot structure used by the Golden Dawn.

And speaking of the Golden Dawn...Aleister Crowley remarks Magick in Theory and Practice that the numerical structure of the I Ching and the Kabbalah (and thus necessarily also in Crowley's scheme the Tarot) turn out on close investigation to be identical. An odd comment, but an intriguing one. I suspect that the remarks above take us some distance towards what Crowley meant. For those interested who are familiar with the Changes I offer the following comment: One might analyse the hexagrams of the I Ching as in terms of a set of basic hexagons which can generate a variety of the known hexagrams. For example consider the 52nd hexagram which can be represented 001001 and the 29th which can be represented 010010. Each of these can be thought of as an example of an endless hexagon which might be represented numerically as ....100100100100100.... etc. If you treat all of the hexagrams that way there turn out to be 13 basic hexagons. And again, 13x6=78, and I'll stop there. This may well not throw much light on what the orginators of either the Tarot or the Changes had in mind .... or it may .... but in either case I'm suggesting here that it throws light on the real beliefs of the Golden Dawn . More may have been kept secret than is often imagined.

Elsewhere on this site....

Using the Celtic or "Compass" Enneagram opens up some interesting lines of enquiry, the surface has barely been scratched so far. For one example see the Fibonacci page on this site. (Elsewhere see more recent discussion by Gonsowski dealing in part with the Celtic Enneagram.)

Another interesting aspect of this glyph of the enneagram is its application to "reifed" or "static" applications of the enneagram. The Personality Enneagram is just such an application, being based on a "reified" or "static" form of the Lifestage Octave . When a static application is displayed on the Celtic Glyph of the Enneagram then it becomes possible to analyse it in an interesting way. An example is the easiest way to explain this, see the Enneagram of Social Order on this site. The Personality Enneagram can be analysed using the Celtic Glyph in a similar, and I suppose for most people that will be the main point. But again, the surface is barely touched here.

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