THE ENOCHIAN WATCHTOWERS
An Analysis of the Documentation and Mathematics
By Dana Marie Tringo
Copyrighted 1999
The history and background of Dr. John Dee is well documented by a variety of authors. However, in terms of this paper, it is important to remember that John Dee was a mathematician as well as a scholar, qabalist, linguist and magician. He was familiar with both the practical, computation aspect of mathematics and the esoteric aspect. He was searching for knowledge that could be gained through a direct link with God. Geoffrey James states in his book Angel Magic, "The notion that technological breakthroughs could result from communicating with angels seems odd to the modern mind. To Dee, however, the concept had all the force of logic. Dee, unlike a modern scientist, did not see human knowledge as something that was growing and changing as people learned more and more about the universe. Dee and his contemporaries didn’t think of human history in terms of progress, but in terms of rediscovery." (72) Dee was hoping to "rediscover" a direct link with the divine and the mechanics of the universe.
The Seals
The seals were given first. They were provided to Dee in a specific manner. The following quote was taken from A True and Faithful Relation for What Passed for Many Yeers Between Dr. John Dee and Some Spirits by Meric Casaubon, (TFR). It was delivered on June 25, 1584. It is on page 172-173.
E.K. Now he spreadeth the aire, or openeth it before him, and there appeareth before him a square table.
Now he taketh off the Table the black Carpet.
Now he taketh off a green Carpet.
Now he taketh off a white Carpet.Now he taketh off a red Cloath.
And now the Table appeareth to be made of earth, as Potters Clay, very raw earth.
Margin Note: He taketh off the coloured cloaths in order, respecting the four parts of the world. E.K. The Table hath four feet, of which two touch the ground, and two do not: The feet seem also to be of earth. The Table is square.E.K. On the left corner (farthest from E.K.) did a T appear on the Table: Out of the top of this T do four beams issue of clear collour bright.
……That part [pointing to that T] of the table of the earth of those that govern earth: that is are governed by the Seven Angels that are governed by the Seven that stand before God, that are governed by the Living God, which is found in the Seal of the Living God.(Tan with the four) which signifie the four powers of God principal in earth, &c.
……Move not, for the place is holy, and become holy.
……I said not so, he said it, that beareth witnesse of himself. Unto this obey the other three Angels of the Table.
E.K. On the farther corner of the Table (on E. K. his right hand) is a crosse like an Alphabet Crosse.
This crosse, and the other T do seem to lye upon the Table, in a dim donnish, or a sky colour. All the Table over seemeth to be scribbled and rased with new lines.
……The earth is the last, which is with the Angels, but not as the Angels, and therefore it standeth in the table of the Seven Angels, *which stand before the preference of God on the last place, without a Letter, or number, but figured by a crosse.
……It is expressed on the Angle of the Table, wherein the names of the Angels are gathered, and do appear, as of Michael and Gabriel.
i
. I remember, there is an Alphabetary Crosse.E.K. Now in the corner of the Table, on the right hand to E. K. appeareth another cross, somewhat of this fashion and appear’d these Letters and Numbers.
b |
6 |
4 |
b |
……It is in that Table, which consisteth of 4 and 8.
E.K. In the last corner of this earthly Table appeareth a little round smoke as big as a pin’s head.
E.K. Now is all covered with a mist.
It is clear from this quotation that the seals are laid out in a specific order. The arrangement is not changed at any point further in the available documentation. There were no actual elemental or directional alignments given at this point.
The T with the flames |
The Cross |
Little Round Smoke |
The Cross with theLetters & Numbers. |
The Elemental Directions
This particular vision is detailed out in TFR on pages 355-357 and occurred on January 15, 1585. Please note, that this vision was revealed approximately six months after the revelation of the seals and the watchtowers.
E.K. Here is i one with a vail afore his face, as it were, a Hair Cloath of Ash-collour: I know him not yet: I see a Garden full of fruit, of divers sorts. In the midst of it is a place higher then the rest. On that place standeth a round house, it hath four corners, [within] and 4 windows: and every Window is round, and hath 4 partitions, round also. It hath 4 doores, and at the East Door is one step, at the South 2 steps, and at the North 3, and at the West Door, 4 steps: The first door is white, like crystal, transparent: The South Door is red of an high colour, transparent. The North Door is bright black, not to be thorough seen, as the rest. The West is Green, like an Emerauld Stone: So as the South Door like a Ruby. The Doores be all plain. The house within (as it may be judged by the transparent Doores) seemeth to be white, and empty.
E.K. He hath his face covered, openeth the East Door; and all the House seemeth to be on fire, like a furnace. The fire within doth weve, and move about in the house, and by the roofe. Now he openeth the West Door, and there appeareth, as if all the house were a fountain full of water…
……E.K. Now he openeth the Red Door. The house seemeth darkish, of the colour of the smoak of a wax candle being put out.
……By it self, it is not, but by the Sunne, it is cleare…
…E.K. Now he openeth the black bright Door; and the house there seemeth full of black dust, like Gun-powder colour, or somewhat of leadish colour.
This excerpt provides the organization of the elements very clearly. Fire in the east. Air is in the south. Water is in the west. Finally, Earth is in the North. This is not the familiar organization to most people. This organization is based on the alchemical weight of the elements. Fire is alchemically the lightest and closest to the spirit. Earth is the heaviest.
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It should also be noted that the Vision of the Round House is a heavily alchemical vision and analysis and discussion should be references from that point of view. The ancient Greek philosophers took the time to alchemically analyze the elements and their relationships to one another. Donald Tyson does an excellent interpretation and illustration to which I refer the in Appendix III—The Elements in The Three Books of Occult Philosophy. In short, this representation places the elements in the organization presented to us in the Vision of the Round House based on weight, composition and relationship to the other elements. A brief review of the Alchemical tracts and engravings of the 16th and 17th century also offers support to organization offered by consistently placing fire in the east, air in the south, water in the west and earth in the north. When all of this information is consolidated, the seals align with specific elements and directions.
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East The T with the Flames. Fire |
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North Little Round Smoke. Earth |
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South The Cross. Air |
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West The Cross with the Letters & Numbers. Water |
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Enochian Numerology
We initially began this research to better our understanding of this system. Our first question was to determine which set of tablets were correct. As we sought a definitive answer, we learned more about this nebulous and elusive system. We uncovered more questions and learned more things that are rarely or never touched upon by other researchers.
We started with a hypothesis and research watchtowers on poster board. Our hypothesis was "The Raphael tablets were the correct tablets". On the research tablets, we included all the variations of letter combinations for the tablets. We included both the Michael and Raphael tablets from Dee’s work. We also used Mather’s, Donald Tyson’s from Enochian Magic for Beginners, and David Hulse’s from Key of it All Book Two: Western Mysteries.
As we moved forward, we develop a few suppositions. First, it is clearly stated in Dee’s conversations that there should only be one letter per square. Mather’s tablets may have been incomplete research tablets that were erroneous copied exactly the way they were presented. This gives us a reason for having more than one letter in each square. He may have come up against a block in his research he could not overcome. He simply passed his papers on to another person. The history of the research within the original Golden Dawn is a series of incomplete notes from multiple members. There is a documented history that research notes were being shared and passed around within the group to one degree or the other.
Second, Tyson used Raphael’s tablets for the lettering, but his organization of the watchtowers was based on the square in the circle glyph in Dee’s Liber Scientiae:
Michael’s Tablet |
oro ibah aozpi |
mor dial hctga |
Michael’s Tablet |
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Raphael’s Tablet |
oro ibah aozpi |
mph arsl gaiol |
Raphael’s Tablet |
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Liber… Tablet |
oro ibah aozpi |
mor dial hctga |
Liber… Tablet |
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Michael’s Tablet |
oip teaa pdoce |
mph arsl gaiol |
Michael’s Tablet |
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Raphael’s Tablet |
mor dial hctga |
oip teaa pdoce |
Raphael’s Tablet |
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Liber… Tablet |
mph arsl gaiol |
oip teaa pdoce |
Liber… Tablet |
Third, Hulse created a gematria for Enochian. However, it seems too complex to be manageable in this system. The amount of work needed to extrapolate the gematria gives it a forced feeling. Also, it was developed from the calls. This in and of itself is not a problem. The issue is that the gematria cannot be consistently correlated within the text of the calls. The numbers represented in the calls all have there own unrelated names.
Fourth, we decided to adopt the paradoxical axiom, "simple in complexity, complex in simplicity". We felt it was reasonable to expect that there would be a comprehensible gematria involved, but it needed to be simplistic. A complex basic aspect would make the system too unmanageable to understand and use. We researched this extensively. No one gematria that had been applied to the system worked satisfactorily. They were either too unmanageable to be useful or not extensive enough to withstand heavy questioning. This sent us to search for a system that would work without being forced.
Finally, we decided that mathematics would be our ultimate test. Regardless of the numerical system used, one plus one always equals two. Gematria being number based can be proven ultimately by math. We felt that the tablets were similar in structure to kameas or magical squares. The basic mathematical premise of a kamea is that the horizontal and vertical totals are equal. Therefore, we could rule in or rule out a system based on how well it was able to add up. Now, all we needed to do was find a feasible system.
Due to Dee’s background, extensive education and knowledge, his passion for linguistics and as a bibliophile, we felt he had access and familiarity with a multitude of approaches to numerology and gematria. We widen our circle of research. We came across the tract entitled "The Alchemical Marriage of Christian Rosenkruetz". This tract presents us with a simple, all-encompassing numerology in the form of a riddle. This particular system is known as Pythagorean numerology.
Pythagorean numerology sets up the numerical correspondences with groups of letters:
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A |
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Each letter is substituted for a number. Then, the numbers are totaled. This system makes use single numbers. The word or letter combinations being totaled are added down to a single digit. For example,
DANA
D = 4 A = 1 N = 5 A = 1
4 + 1 + 5 + 1 = 11
1 + 1 = 2
DANA = 2
Also, through our research we came across the transcription of one of the 49 tablets of the good angels. These tablets were used to derive the calls. There are numbers on the tablet. The numbers are 1 through 9. There are no 0’s and nothing higher than a single digit. This discovery further strengthened our belief that the Pythagorean system was correct. These are the only numbers used is the system beyond those found on the Sigillum Dei Aemeth. The numbers on the Sigillum are used as instruction for reading it.
We applied this system to both the Michael and Raphael tablets. The feeling was that if the tablets function similar to kameas, they should total out. However, this was unsatisfactory. Neither tablet could be corresponded fully. This returned us to the transcriptions available of Dee’s work. Michael originally revealed the tablets. However, errors were made in the transcription. Raphael then provided some correction to the tablets.
We proposed that human error might have occurred both times. The communication between Divine Light and human comprehension is limited by our ability to comprehend the abstract. Ultimately, we thought it might be a combination of the tablets that was correct. We used Pythagorean numerology. We addressed only those squares that were different from the Michael to the Raphael tablets. We were able to come up with a set of tablets that stood up to the ultimate test, MATH. This was a long and tedious process and required a combination of both tablets. Ultimately, we found that not only did each tablet added up similar to a kamea, so do each subquadrant. We also found that the total of each banner name was equal to the total of the respective tablet itself.
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oro ibAh aozpi
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Mor dial hctGa
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The Great Cross
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The math of the great cross demonstrates some interesting results when Pythagorean numerology is applied.
Horizontal axis = 2
Vertical axis = 1
Half the horizontal axis = 1
Half the vertical axis = 5
EXARP = 1
HCOMA = 4
BITOM = 5
NANTA = 5
The GREAT CROSS = 3
The combined total of the watchtowers and the great cross:
9 + 3 + 2 + 5 + 3 = 22 = 4
The Great Cross represents the Trinity via the correspondence of the number three. The Angels called the complete tablet with the cross the Watchtower of the Earth. The number four represents manifestation and the elements.
The Geometry of the Watchtowers
The last discussion is the placement of the watchtowers. This has always been a source of confusion and debate. There were three organizations noted from the text of Dee’s various diaries. The issue lies in determining the correct organization of the tablets. The answer may be found in the mathematics of the watchtowers.
The first organization is from the original revelation of the tablets by Michael in June 1584. The second occurs in Dee’s Liber Scientiae… dated May 1585. Finally, the third is the correction by Raphael in April 1587.
Order of Revelation |
|
Michael |
Liber Scientiae |
Raphael |
oro |
East |
oro |
oro |
oro |
mor |
South |
mor |
mor |
mph |
oip |
West |
mph |
oip |
oip |
mph |
North |
oip |
mph |
mor |
It should be noted that the oro ibah aozpi tablet is the only one specifically given a placement from the documentation. "…out of that line cometh the three names of God, from the East gate, being of 3, 4, and 5 letters…oro ibah aozpi…" (Casaubon 177) It is also the only one that is not moved in any of the arrangements. In the Vision of the Round House, the doors were revealed with numbers: East 1; South 2; North 3; and West 4. This, however, does not answer the question directly, but interesting patterns are noted when all this is brought together.
Order of Revelation |
Michael |
Liber Scientiae… |
Raphael |
||||||
oro = 9 |
oro = 9 |
mor = 2 |
oro = 9 |
mor = 2 |
oro = 9 |
mph = 5 |
|||
mor = 2 |
oip = 3 |
mph = 5 |
mph = 5 |
oip = 3 |
mor = 2 |
oip = 3 |
|||
oip = 3 |
|||||||||
mph = 5 |
There are three interesting patterns that develop when the organizations created are compared to the order of revelation. The Michael tablet organization reads from right to left. This is reminiscent of the numerical organization in the Vision of the Round House. The Liber Scientiae tablets are organized clockwise as compared to the order of revelation. Finally, the Raphael tablets are organized in a counter clockwise organization as compared to the order in which they were revealed. This analysis still does not provide us with an obvious answer. A deeper analysis is required.
Ancient and Renaissance scholars viewed geometry as the discussion and study of the relationship of man, the universe and the divine. This study included the spatial relations between simple two-dimensional objects up to and including harmonics. "The laws of simple harmonics were considered to be universals which defined the relationship and interchange between the temporal movements and events of the heavens and the spatial order and development on the earth. The implicit goal of this education was to enable the mind to become a channel through which the ‘earth’ (the level of manifested form) could receive the abstract, cosmic life of the heavens." (Lawlor 6) Geometry was a sacred science. It allowed for a tangible explanation of the universe and the divine.
Enochian seems to be like a key to comprehensible communication between the Divine and the manifest universe. The universe is multi-layered and multi-dimensional. Communication and access to the Divine is limited by the restrictions of the manifest universe. Mathematics and geometry serves as a jumping off point for understanding the relationship by aiding in the ability to comprehend it.
1 + 1 = 2
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 5 = 13 and so on.
1, 1, 2, 3, 5, 8, 13, 21, 34…
NOTE: This progression is not the only Fibonacci series. There are several others.
Finally, the numbers 2, 3 and 5 are sacred roots. They represent different aspects of life and creation. The square roots of these numbers are irrational. There values continue on infinitely. They represent the Divine connection between Assiah and the other worlds.
The square root of 2 represents the division of unity. It is representative of the Divine initiating the force needed to manifest. As in the meiosis of an egg, a geometric progression occurs when unity is divided: the 1 becomes 2; the 2 becomes 4; the 4 becomes 8; and so on. The square represents manifestation. When a square is divided in half by a diagonal, the diagonal is equal to the square root of 2. This pattern is maintained no matter how many successive squares are divided by a diagonal. They always equal the square root of 2. It "represents the universal metaphor of the root." (Lawlor 30) The square root of two is the generative root from which life begins.
Just as the diagonal divides the area of a square, the diagonal of a cube divides its volume. The diagonal of the cube is equal to the square root of 3. It is called the formative root. It is representative of the Vesica Pisces. It represents the process of growth. The Vesica Pisces is the universal mouth from which emanates the vibration that created and maintains the universe. "The overlapping circles – an excellent representation of a cell, or any unity in the midst of becoming dual – form a fish-shaped central area which is one source of the symbolic reference to Christ as a fish. Christ, as a universal function, is symbolically this region which joins together heaven and earth, above and below, creator and creation." (Lawlor 33)
The square root of five is known as the regenerative root. It is the diagonal that divides the rectangle. "The square root of 5 transverses two worlds, indicated by the upper and lower squares, the world of spirit and the world of the body." (Lawlor 37) It is reminiscent of the symbology of the double cubical altar. It represents the possibility of all other forms. The pentagon and pentagram become apparent through the square root of 5. The pentagon is segmented and symbolizes the flowering of life that expresses itself through the elements. The pentagram is symbolic of the elements themselves present in man.
Mathematically, the combination of the square roots of 2, 3 and 5 represent the necessary ingredients for the creation of the Platonic solids and the mystic spiral. The Platonic solids encompass three dimensional representations of the familiar polygons which can be metaphysically corresponded. The mystic spiral is created by the ratios of the square roots of 2 and 3. The difference between the ratios of the square root of 3 to the square root of 2 approaches the square root of 5. As this process is mathematically produced, the difference found oscillates above and below the square root of five. (Lawlor 67)
1:3 |
1 |
3 |
4 |
7 |
11 |
18 |
29 |
47 |
76 |
123 |
1:2 |
1 |
1 |
2 |
3 |
5 |
8 |
13 |
21 |
34 |
55 |
3 |
2.3 |
2.25 |
2.2380952 |
|||||||||
Square Root of |
||||||||||||
5 |
= |
2.2360679 |
||||||||||
1 |
2 |
2.2 |
2.2307692 |
2.2352941 |
This creates a spiral with a radius that increases geometrically and a radial angle that increases arithmetically. (Lawlor 71) This spiral represents both the mathematical and spiritual processes present in the universe. This pattern also leads into the mathematics of harmonics, the musical scale and sound waves. This in turn leads to multidimensional discussion of the system.
In regard to Enochian, these concepts present us with an interesting theory. All three patterns presented could be correct. The mathematical correspondences of the Watchtowers lead us to a mystic spiral and multidimensional aspect of Enochian that allows the system to be dynamic. This would allow the organization of the Watchtowers to be based on the frequency needed to complete the ritual. The Michael organization would correspond to the formative root and affect the mundane. The Liber Scientiae… organization would correspond to the generative root and function to drawn energy into manifestation. The Raphael organization would correspond to the regenerative root and function to aid in the process of transformation and transcendence.
All three organizations function together to demonstrate the laws of harmonics. These laws focus on the actions of sound in relation to the universe. Sound is vibration. Vibration is the basis of creation. Everything in the universe has its own vibrational frequency. Harmonics mathematically utilizes all three sacred roots to create each vibrational frequency. Geometric and arithmetic progressions are simultaneously present in a harmonic progression. This particular combination of mathematical progressions creates a vibratory spiral.
The symbolism of the mystic spiral is multi-leveled and related to sacred geometry. The mystic spiral is an ever-present pattern in our universe. "This cyclic becoming appears in mythology as the protecting serpent or dragon which coils around the World Tree or Mountain—the central axis, the Axis Mundi. This dragon is also the world of illusion, the coils of manifestation, which the hero must destroy on his quest for truth, for the treasure, the incorruptible diamond of the Self at the still point in the midst of things." (Purce 11) This can be likened to the constellation of Draco that passes through all twelve of the zodiacal constellations. Its influence affects multiple aspects of our lives all at the same time.
On a physical level, it is apparent in the whirling of the sub-atomic patterns of our simplest building blocks to the double helix strands of DNA to the theory of how the big bang occurred in a spiral. The beauty of this pattern is that it allows for expansion and restriction. It also allows movement in all directions simultaneously. The mystical spiral taken to its furthest degree creates a vortex. Present in the vortex, is the spiraling up and down in an eternal circle. In a two-dimensional representation, this is a zigzag pattern. There is also the presence of both clock-wise and counter clockwise movements.
This vortex could allow us contact with another dimension. "Any circular movement carried into the fourth dimension (of space-time) becomes a spiral; which is why apparently cyclic processes in time never repeat themselves. Even the earth’s orbit round the sun is a spiral in time, and every year is different from the last." (Purce 13) The spiral allows movement from the 3rd dimensional to the multi-dimensional and back to the 3rd dimension. It can be likened to the process of ascending and descending the Tree of Life. As we spiral upwards, we return to the unity of the Light in Kether. As the Light spirals downward, it moves into manifestation in Malkuth. Each restriction of the spiral to a point can be likened to the connection of Malkuth on one Tree of Life and Kether of the next.
One of the most important glyphs for the mathematical scholar of the esoteric is the squaring of the circle. This process is the melding of geometry and metaphysics. The circle represents the divine and infinite. The square represents the manifest and mundane. The process of squaring the circle in terms of geometry is the attempt to create a square with a perimeter that equals that of a circle. In metaphysical terms, it is an attempt at uniting with the divine. Geometrically, the closest a square’s perimeter can get to the perimeter of the circle is 0.0095548. It requires the mathematical use of the square roots of 2, 3, and 5, and Pi and Phi. The latter two are irrational numbers and geometric constants that spiritually represent the Divine.
The final result of this process is a glyph that looks similar to the Sigillum and the watchtowers overlaid on one another. This glyph is the squaring of the circle. All the components necessary for manifestation and knowledge of the divine are present in one glyph. It includes the ability to connect with dimensions beyond our own. It allows for the infinite, timeless and endless expression of the divine. It encompasses the finite and mundane world of the physical. Overall, it expresses the presence of the Divine in man and the man in the Divine. It demonstrates the interplay and the points of connection.
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SPECIAL THANKS TO:
Callisto Radiant for being so kind as to host this paper here on this site.
Poke Runyon for taking the chance on publishing this article.
Clay Holden for his time and effort in looking over the tablets.
Zack Ramsey, for his patience and understanding while I was consumed with writing this paper.
Lance Walker for pissing me off by saying I am not ready for Enochian, but then being willing to research it with me anyway.
Mamdouhl Al-Daye for all the scholarly, and occasionally heated, discussions.
My dear friend SH for the late night discussions about men, magick, the divine and everything else in between.
John Brawl for reminding me there was more than a hallway to talk about.
Jayson King for finding the typographical errors right before the presentation to our research group. ;-p
I would like to also thank the members of our research group for listening to me babble on and on about this:
Dorris Behr, Larry Smith, Todd Hendrickson, Mike Durnell, Tracy, Mace Smallwood, Ken and Becky Hyde, and Alexandria Cooley