Approach to a Loagaeth Solution, Part 3

Just another note on the general structure of the tables of Liber Loagaeth which are to be completed by the magician; there are 1201 cells visible to the magician on most of the tables to be completed on most of them. It turns out that, like the 113 letters of Table 49, 1201 is a centered-square number. What are the other two integers that (by definition) go with it? 1,200 & 49. Interestingly, 1201 + 1200 = 2401, which is 49^2. “Multiplied and dignified” numbers indeed!

Additionally, 1201 is a “super-prime.” To explain this, consider the first few prime numbers: 2, 3, 5, 7, & 11 would be the 1st, 2nd, 3rd, 4th, & 5th primes. Of these, 3 (prime number 2, which itself a prime number), 5 (prime number 3, also prime), & 11 (prime number 5, also prime) would be called “super-primes.” Interestingly, 1201 is the 197th prime number, yet while 197 is the 45th prime, 1201 is the 45th super-prime; additional dignity! 1201 is also the 25th (5^2) centered-square number, and the 15th centered decagonal number. 25 +15 = 40, and to make sure we multiply and dignify further, 4 (for squares) times 10 (for decagons) is also 40, and of course 40 is highly significant biblically & in Gematria as the number of water, and is also the number of cells in the ring around the SDA. Water is indeed mentioned by Galvah when asked about the letters of Leaf 49: “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.”

Now that this seems to be exhausted (but you never know if Terence Tao will happen upon your blog!), let’s look at some of the exceptions to this. Leaf 43a, the first (technically, the first half) of the last 7 leaves of the 49 total (“So the last shall be first, the first last”) shows the a 7×7 square in the upper-left corner (but in Enochian/angelic letters, these would be in the upper-right). It also has the entire first row (rather than missing half its letters). In all, this makes 1246, which is a centered tetradecagonal (4+10=14) number, the 28th (14*2).

441, which is “Truth” in Gematria and additionally the sum (heh) of the outer ring of the SDA (as we saw in the previous post), is also a centered tetradecagonal number, the 17th, and for other reasons 441 is a very cute number: the sum of the first 6 cubes (“the mystery of the divinity” as promised by Galvah). 441=21^2 (21 letters in each of the 5 triangles in Leaf 49), which means there’s a further mystery of the trinity expressed through this leaf.

It’s not exactly clear, but either Dee or the angels or both seem to have also given us help on the other half of this leaf (Leaf 43b) but this time just with the first row, which means we have 1225 letters in all, or 35^2, or 5*5*7*7. We see yet again the expression of threes and fives in addition to the ubiquitous seven.

I noticed something else at Leaves 29a & 29b; Leaf 29 is the first of the fifth seven, and because five is the number of humanity, it makes sense that this is these are the first tables to have missing information (for we begin in a state of ignorance relative to the angels). Unlike the other leaves, which only leave out every other letter, Leaf 29a also has two complete 7×7 squares and two 8×7 rectangles at the left and right & top and bottom, respectively, each with capital letters where there would otherwise be blanks in every other cell. The use of 7 and 8 in this case is suggestive of the 113, or 7*7 + 8*8, letters in leaf 49. There are also four standalone letters at the corners, for a total of 110 (product of the 1st, 3rd, & 5th prime numbers). Altogether there are 1311 letters, which is 3*19*23. Leaf 29b looks nearly identical to 29a, except it has four 7×7 squares for an additional 100 letters and 2 letters in each corner for 108 (2^2*3^3) in all, or 1309 letters. 1309 is 7*11*17, and is the first sphenic number (numbers that are products of three primes) to be followed by two more sphenic primes (1310 and 1311, the latter of which we’ve seen before, which of course is the same first/last reversal we’ve seen repeatedly, since 1309, the earlier of these, comes last, while 1311 came first).

I’ll keep plugging away at this, but I thought I’d share the thoughts as they came to me!

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….