The Sum of Creation: Squares and the Additional Mathematics of Enochian

Reflecting on the Enochian system of John Dee & Edward Kelley, the numerical component has always been of interest to me. In particular, the elements strongly reflect the meaning of squares, which can be thought of as the unfolding (as in the mathematical product of two numbers being a pure, Divine form of Creation). This is especially important with the number 19, which is the square root of 361, which seems to represent the number of degrees of a circle or a sphere, plus the center. (Note that the idea of the heavenly sphere(s) is very common in ancient and medieval thinking). As I’ve mentioned in previous posts, 19 is also the sum of the number of signs of the zodiac (itself falling along the 360° ecliptic), plus the 7 planets (whose motion around the zodiac is the subject of astrology).

A shape related to the circle in ancient and medieval thinking is the square. One question that perplexed mathematicians was how to square the circle, which is to say how to create a square with the appropriate side length such that its area would match that of a circle of a given radius. This is quite difficult because one must take the square root of pi (today, of course, is Pi Day) to do so. A square can also be thought of as a self-referential product; a side times itself creating an area (square numbers got their name from the same concept; a square of side length n has an area of n*n).

This idea can be extended to the concept of another product, which is to say all of Creation by the Divine. As we shall see, the squares are integral (heh) to Enochian, but we must consider in advance which numbers may be important, and how far this concept may go. One can make a parallel (ah, how language recapitulates mathematics again!) to the number of days of Creation in the book of Genesis, which is to say, seven, and which is explicitly blessed as holy. Seven is of course a number integral to Enochian, with its Heptarchy and its 49 by 49 (7^2 by 7^2) tables in the book of Liber Loagaeth (more properly called Amzes Naghezes Hardeh). Before continuing, I’ll make the aside that the idea of numbers as being integral to Creation is paralleled in Pythagoreanism (and, I’m sure, many other traditions which I am not aware of). I can’t claim to be an expert on Pythagoreanism, nor of course to the be-all, end-all of the esoteric traditions it’s influenced (the SHWEP is working on that difficult project!), but it’s fair to say that the idea of The One being a Creator of all numbers is important; this concept of the Unity of the Divine is common to Judaism and Islam.

Christianity has this idea but complicates it somewhat with the concept of the Trinity; (Pythagoreanism also held the number three to be very important); because Enochian is in the Christian tradition, the number three will be a guide, but also the number seven, again, as the number of days of Creation. We should also again keep in the back of our minds Matthew 20:16: “The last will be first, and the first will be last,” and consider the possibility of reversal and, by extension, doubling.

The first square integer is 1^2 = 1, the next is 2^2=4, and the next is 3^2 = 9. Together, these sum to 14 = 7 + 7, as if we have gone the length of creation, seven, and then back again. This will be of interest later.

Next three squares (16, 25, & 36) total 77 (the number of times we are to forgive our brother—that or 7*7 = 490), and here we have a palindrome of a number, and repeating the seven again. Together the first six squares total 91, which is the number of Parts of Earth in the Watchtowers, and 7 * 13 as with Christ and his apostles (and Israel and his sons) multiplied by the holy number of 7, in addition to being the reverse of 19.

We can pause here to note that adding the next square of 7^2 = 49 to this–which is to say, the sum of the first seven squares–gives us 140, reflecting the sum of the first three squares again.

Yet continuing with triads of squares, we can sum the three squares of 49, 64, & 81, which sum to 194, which is the number of pages of Liber Loagaeth (front and back), 98, plus the number of pages of the Book of Silvered Leaves, 96.

The next three squares, 100, 121, & 144 sum to 365, the number of days of the year. Finally, we come to the next two squares 13^2 (169) + 14^2 (196) = 365 again. It’s as if we’ve gone from 7 days of the week and back through the trinity, and, in following that first sum of creation, we’ve gone through the 365 days of the year and back again as well.

Summing the first 14 squares, we come to 1015, the digits of which sum to 7. Interestingly, summing the first 14 numbers themselves comes to 105, the number of letters on the last leaf of Liber Loagaeth (dwarfed by those on any of the rest of the leaves, to be sure!). It’s as if the divine unity (1) comes through as a digit via the process of Creation. Both 105 and 1015 are evenly divisible by 35, yielding 3 and 29, respectively, seeing the Trinity coming through again; 29 comes through repeatedly in a previous post.

It’s here that the pattern of triads seems to end, yet we have another sum of squares through 21. 21^2 = 441 is already important on its own in Enochian as both the sum of the numbers in the cells around the Sigillum Dei Aemeth (440 plus 1 for the unity of the Divine as explained by the Archangel Michael) and the number of cells with individual letters on Leaf 1b (9 rows * 49 columns). The sums of squares 1^2 + 2^2 + … 20^2 + 21^ 2 = 1202, which is 1 or 2 more letters than the (main) letters on later leaves of Liber Loagaeth (e.g., Leaf 30b, Glonz alnoptd, & 31a, Gemnarv Hvncol). Or, if one doubles this number to 2404, then it is 3 more than the letters from a table on one of the earlier pages.

Looking again to the sum of squares through 28, we see the total is 7714; through 35, we come to 14910. The patterns seem to end approximately here, but, of course, the reader is encouraged to reach out if they find additional robust patterns.

A Solution to Liber Loagaeth: Part 2

This post follows on to this post, and is edited from a Discord discussion about my thinking about the ring nature of the leaves of Loagaeth. Thanks to Jon Ciel of Uizelian magic and Argus for their feedback and input, some of which I have incorporated.

So here’s the outlines of an approach to unlocking Liber Loagaeth that I’ve been thinking about; the Great Table in Enochian is 25 letters wide by 27 letters high. This is divided into four quadrants, typically thought of as elemental in nature, but also includes the names of all 91 (or 92) governors.

There are 94 Liber Loagaeth half-leaves of 49×49 grids (more on this in a moment). So the idea here is you place a reduced Great Table (24×24) by eliminating the names of God (the 12-letter names, e.g., ORO IBAH AOZPI–they are holy, after all) in the four quadrants corners as well as the entire Black cross. Then, overlay four Great Tables in the onto a 49×49 leaf. This leaves (heh) each 49×49 table with its own central cross, possibly as the key to try to solve it.

Another possibility (let’s call it Approach 2) is removing only two of the rows, leaving a 24×25 and overlaying this version four times (two of them would be rotated 90 degrees). This would leave a single letter in the center as the possible key to solving it.

There are some advantages to each approach. Approach 1 leaves a nice parallel to the Great Table. Furthermore, this Central Cross is more evenly balanced than the Great Table’s Black Cross, and could be folded three dimensionally into two rings, like so:

Which would look similar to this diagram by Johannes Dryander:

Annulorum trium diversi generis

In fact, this suggests that a third ring should be added, such as at the 13th and 37th rows or columns. I would stick with rows, though, because this would continue the parallel to the Great Table. Ultimately there would be 9 letters in all, and this parallels not only the bottom of Leaf 1b (which is a 9×49 table) as well as the sum of the numbers in the SDA (which totals 441: “Truth” in Gematria).

Approach 2 has its own merits. Not only does respect the placements of the central names of God (after all, these are the names on the Tablet of Union!), it leaves each of them four times, not twice (if this sounds tricky, consider we could instead have a 25×24 modified Great Table by leaving the column of the Black Cross as-is and instead deleting its row along with the rows for the four 12-letter names of God. Why would this matter? This means that you get 16 names–a perfect parallel to the Great Table–as well as a Gematrially-sound 1 + 6 = 7, matching the septuple nature underlying the entire system. On a personal note, 16^2 = 256, and I was specifically asked to calculate the ratio of a 5D-volume of a 5-sphere circumscribed about a 5-simplex vs one inscribed…it was 256:1. Took me a while to find the formulae, (thank you Google Books), but I did.

Both approaches include deleting the names of God in the Great Table. Note that this leaves 77 governors, which adds both the septuple nature and also appears in the 2nd Book of Chronicles, the Gospel of Matthew (and, via an alternative interpretation of that passage as 70 times 7, the Book of Daniel.

We’ll come back to another Bible verse in a moment, but here is a sequential summary of what constitutes the leaves of Liber Loagaeth:

1. One half-leaf, which actually is 49 long lines of text;
2. One half-leaf which is a hybrid of 40 lines of text with a 9×49 table at the end to complete it;
3. 54 straight-up 49×49 tables of letters (and with one exception, numbers), each of them uniquely titled;
4. 40 titled tables of 49×49 with every other letter missing (i.e., tables to be completed/solved).
5. One table of five 21-letter triangles (side length 6).

Another bible passage that is used by the angels in their transmission to Dee & Kelley, and seems very apt, is The Gospel of Luke (here I use the King James Version): “And, behold, there are last which shall be first, and there are first which shall be last.” This suggests that the last table should at least be considered first; I have yet to write it but it can be found at the end of this version attributed to Donald Correll. Perhaps the sequence of all of the chapters of the book is to be reversed.

Some of what I have realized about this last table is that it was originally transmitted via Galvah (whose is described as “the end of wisdom”–suggesting the path of Aleph (or Heh, depending on the source) connecting Chokmah to Kether), and in that transmission, there is an additional word, “LOAGAETH,” which of course itself means “Speech of God.” This leaves 5×21 =105 letters (or 113 letters if we include Loagaeth). This once again leaves two approaches to understanding ways to unlock and use this table.

Both approaches have the five triangles together suggest inner and outer 4-simplexes (AKA a 5-cell), which is a 4-dimensional regular polytope made of tetrahedra (just as the 5-simplex is made of 4-simplexes). Galvah says of this table: “In them is the Divinity of the Trinity. The Mysterie of our Creation. The age of many years. And the conclusion of the World. Of me they are honoured, but of me, not to be uttered: Neither did I disclose them my self: For, they are the beams of my understanding, and the Fountain from whence I water.”

Any correct understanding of this must include a mystery of the Trinity (i.e., look for triangles of words), the mystery of our Creation, and the conclusion of the world. Since this is coming via Dee, we can expect a mathematical bent to this, but let’s first look at one of the triangles (using English letters; sorry if the formatting comes through weird, essentially it’s an equilateral triangle with side-length six (keep that number in mind) and 21 letters arranged from top to bottom in a 1-2-3-4-5-6 format):

S
EG
LOX
IBRI
NCCLA
RZEDDO

The “middle triangle” of 3 that one could make from this would be OBR (Med-Pa/Peh-Don). Thus the mystery of the trinity would be to create one of each of these creating 5 three-letter words in all. This would match the 15-nature of Saturn and, with 105 letters across these five tables, would also be 15*7. This would be the first approach. Keep, 15, 3 and 5 (the factors of 15) and 7 in mind, they’ll come up again.

Taken as-is, the 105 letters of the final table are divisible by 7, 15, yet we see that 15 is the mystery of the trinity, for it means that humanity) long associated with the number 5) is in production with God and with creation (7 planets suggesting the three Kabbalistic worlds of Formation, Creation, and Emanation). Remember that in mathematics, products are definitionally the result of multiplication. The implications of this are that God’s work on earth is something He produced with/through humanity to bear witness to his Creation (105 in Gematria: “God is Witness”/ALAD; “Yah is omniscient”/YHVYDA). Finally, note that Galvah says it is “the conclusion of the world.” Another word for conclusion is “end” and thus “purpose.” This suggests that the end of wisdom is to understand the purpose of the world, and here we see that this purpose is to understand ourselves to be in constant co-working with the trinity (at Binah/Understanding) and the creation. Regardless, we have a strong case for this approach.

The next approach is to note the glaringly absent word LOAGAETH from these equilateral pyramids. Why would happen if we put this at the bottom? The 8-letters would be imbalanced, but if we omit the name of God eL/L (again, too holy to be included), we get 7 letters, and a 1-2-3 triangle (six letters–I told you this number would come up again!) of OBRCCL, which is of side-length three and also a divisible in number by 3.

Well, I admit I had to put something back in to get this interesting take, but let’s step back a minute and look at 113 (the number of letters if you include LOAGAETH). Turns out, this is an interesting number for various reasons. In Gematria, it suggests gems & glowing. Mathematically, it’s prime, and a centered square number, the sum of 49 & 64 (these numbers have a difference of 15!), and is part of a Pythagorean triple of 15(!), 112, and 113. Speaking of triples, 49 (7^2) + 24^2 (576) = 25^2 (625)–now we have our friendly 24×25 returning.

Sticking with the 15/112/113 triple, let’s look at this kabbalistically: 15 squared, which is 225 (“Worthy gift”), which comes to 9 in Gematria. Thus 15 reconciles Yesod (2+2+5=9) with Binah (15 as the the sum of any row in a Saturn Square–you could also say it is 45 (the sum of the entire Saturn square) as seen through humanity (5). 15 itself relates to Hod, leading us back to the 8 and thus 8^2 +49 = 113. 15 itself comes to 6 in Gematria–suggestive of Tiphareth.

112 is not only the first product of 7 with its first 2-digit Kabbalistic form, 16 (16*7=112), it also expands into 12544, which comes to 16 & then to 7. I see this more as a reconciliation of the 7 planets with the product of quadriplicity, the elements interacting with themselves. Alternatively, Jupiter/Chesed is its own product (4^2) and Mercury/Hod meets itself (8*2)–Mercury being a pretty dualistic planet in its own right). On its own, Gematria for 112 includes “To thrust” which suggests Chokmah (it reduces to 4 which is Chesed again, which links directly with Chokmah on the Pillar of Mildness on the Tree of Life), which has been linked to KAOS/disorder in the Aethyrs, and indeed Galvah says of this table, “[I]t signifieth a disorder of the World, and is the speech of the Disorder or Prophesie.”

113^2 is 12769, which comes to 25 & 7 via gematria. 113 itself reduces to 5, suggesting Geburah. The largest number in this Pythagorean triple expands Creation to a balance between Mars (5^2) & Venus at Tiphareth. Creation is balanced within itself. Note that 15=6, 112=4, and 113=5 suggests the central world of Creation.

So I’ve offered two pairs of approaches to solving it, laying out some ideas of what a solution to Loagaeth may look like. The math here is incredible and I respect Dee’s ability as a mathematician, the words within Loagaeth itself do not seem to be glossolalia, and I look forward to finishing copying the book and seeing whether I can combine these insights with 46a (hey, how many chromosomes do humans usually have again?).

One additional thing I would like to do is see what happens when you draw, from the center of the Holy Table of Practice, lines from the center to each of the 7 ensigns and see which letters on the outer square you pick up….