## 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.

## Gebofal, Day 34

Sunrise: Vibrated the title of leaf 16b. Call to Heptarchical King Baligon. Call/Key 16, (because it’s the 15th spoken call, most practitioners refer to this as call 15). Call to Left foot placed on the seal of King Baligon (over the fire & earth tablets) as a final test of the scheme. Vibrated, in turn, Governor Abriond, Zodiacal King Cadaamp, and King Baligon (seven times each–this is how many times I do so for the preceding calls, sorry for noting this stuff after the fact). After these, the energy from the air tablet was obvious, so I moved the other tablets out of the way and placed the seal atop the air tablet and then both feet upon the seal and tablet. I then vibrated the God-names of MOR, DIAL, and HCTGA, seven times each–update this should be MPH ARSL GAIOL based on the Tabula Recensa. I changed my original approach based on incomplete information from an otherwise reliable source–or I just read them wrong lol).

King Baligon just has me breathe easily. He says he knows it’s been a lot, and kind of confusing, because I’ve been getting these lessons piecemeal, whereas in the Aethyrs it’s more of a stepwise process. Here, it’s been more like, “Here’s this chunk, here’s this other chunk,” etc. These are all roots, he reminds me: roots to the issues of the heart.

He takes me into the clouds, into the air, and he has me observe for just a moment the sphere about the earth, the aerial sphere (i.e., the atmosphere). He notes that something like this same sphere is what I will see when all of these powers are steadied within me. “Just note,” he encourages: “there’s something so beautiful about just having fresh air,” and I reply, “Oh yes! This is something that I took for granted for far too long!”

King Baligon muses, “The nice thing about air is that it conducts sound. People can hear, and they can hear music, and nothing else compares to music. It’s beautiful, it lifts up the soul, and it’s wonderful. The issue with music is that it’s this grand communication, and even when you make these calls,” he says, “you are reading. You are looking, so that’s the fiery part, but you are also speaking, you’re converting that. The energy of conversion is itself fire, but the sound itself, and the way it hits the ears: all of that is conducted through air.

“Let’s ponder what air does,” he suggests. “Air[, like water,] also dissolves, but only to a degree. The main thing that air does is convey, usually not particles so much, but waves. So we have this wave-particle duality, and much of the energy transmitted by fire is of a wave-like nature,” so he notes that I was pondering the discussion of electromagnetism, and how I was concerned about weak force vs. strong force. “Weak force,” he reminds me, “is associated with air, electromagnetism with fire.” Electromagnetism, he says, really is the big one when it comes to this wave-like issue, and air(/weak force) is also like this (note this is unclear to me).

“When you think about a transfer of air, there is a great cycle here on Terra” King Baligon mentions (note: I’m substituting “Terra” for “Earth” throughout this post to avoid confusion with elemental earth), “but it’s very subtle. The plants do their thing, the animals and fungi do their thing, humans and animals do their thing, and so on, but of interest here is the fact that it all comes into one thing. This is not unlike water.”

I interject politely to ask how this relates to points [in geometry]. “Here we have the concept of a–it’s a bit more harmonious, so hence why Venus is here. But it’s more of a harmonious occupation of a space filled with points. So Saturn is happy here because agreement can be reached, like it or not, across the various points.” I interject again: “I’m really hoping for a profound insight, as best I can.”

King Baligon takes my request well, and says, “Let’s get to it.” He goes through a few visual examples, but we settle on first, the picture of wind blowing a wind turbine. He notes that on Terra, most of the winds are caused by the uneven heating of Terra. “And you’ll see that: first of all, air requires an open space to do its magic. However, it can be compressed and studied, and can turn fetid and putrid in the event of air being locked in a closed system, so it prefers openness. So, openness, when you think of a [mathematical] field,” and I’m shown a mathematical grid upon a black background for simplicity, “and you think of openness, you think of this air upon it in an open field.” He takes me to a view of the grid. “What air can do is go anywhere, and how fast it goes depends largely upon the amount of energy [elemental fire], but it wants to go everywhere. It wants to go into water and can dissolve into it. It can go into fire as a flame, feeding it that way. It can go faster or slower, depending upon the amount of energy.

“Most specifically,” he emphasizes, “what air does is it can clear out, but it can also bring in. So, usually, on this planet, it can clear out pollution and smoke from, say, a campfire, and it can also bring in fresh air from trees and such. But both the ancient and medieval thinkers were concerned with fetid air, and the need for fresh air: and all of this was true! The quality of the air matters. And so, that’s why pollution is such a big deal, because air [on this planet] has limits in its ability to carry the bad things away, because it’s not, strictly speaking, completely open [over a short length of time], and it cannot, on its own, completely undo the nature of that which has been entered into it. Same thing for water,” he remarks.

I ask, “What else about air?” King Baligon replies, “Note that the transfer of air tends to happen not with earth, but within water,” hence why Venus is exalted in the water sign of Pisces, because Venus (ruler of Libra) can dissolve into it very well. Nonetheless, Venus also rules Taurus. It’s happy there for a different reason. In Libran air, Venus is happy because of the free flowing of points, the balance of points: the fact that air will naturally undo vacua, and each point will flow to wherever it is already going to flow, absent outside interference. “It’s just going to go where it’s going to go. This is a simple lesson!” he cries, kiddingly.

“Okay!” I cry back. Is there anything else he has to show me? “No, this will be a much shorter series of visions.” I thank him and thus ends the vision.

Noon: Similar procedure.

I feel energy come up off the tablet, now the seal, and now off of the leaf of Amzes Naghezes Hardeh (Liber Loagaeth), and to some degree the table. The angels are bidding me to chill out. Now King Baligon bids me take his hand, extended from a cloud, and we’re in the air again.

“Let’s take each of these [air astrological signs] in turn,” he cuts right to it. “So what does Gemini do? Gemini, the twins: it is communication, it is the circulation of air and sound. This is how it is best thought of.” He makes an aside, “We may even go in reverse [zodiacal] order.”

King Baligon continues: “But it is the circulation air: it goes from one source and goes to another, and then returns back, and then back, and forth. This could be a bigger cycle, from A to B to C and ultimately to Z, and then back to A again: or A to Z and then reversing that pattern. This is the returning of the air, the spreading out of the air: the point which, again, is in an open field, but here we have the tendency of air, it can go anywhere! and so it may return to the same spot. This is air: this is how these points manifest.

“Looking at Aquarius,” King Baligon transitions, “the easiest way to think about this, obviously, is what we have right now: fixed air (i.e., air fixed by mask and PPE use), fixed ideas, and, oftentimes the reality or actualization of that idea, that which needs to be communicated, does not match the ideal, and so it is very depressing to the individual. Hence, they often just want to walk away from people,” he chuckles. I’ll note that I saw a meme of this earlier this year on AstroTwitter, which essentially was someone saying to an Aquarius, “Hey, you’re my best friend.” The friend approaches the Aquarius, who reciprocates the expression of friendship. Then, inexplicably, the Aquarius walks away. It’s like, “What?” So the closeness is one of ideas, and the air of Aquarius tends to want to just stay in one spot. So it’s not necessarily fetid air, but it could be like that, but the sign is ruled by Saturn, so you could have these stuck ideas which do not want to change. On the lighter side, it could be like a sealed capsule (like a space capsule or a submarine) of fixed air which goes into outer space or into the depths of the ocean. The air is sealed within, and the submariner or astronaut has enough time to live in that capsule–similar to the “castles in the sky” idea put forward, again, by Austin Coppock–for some time, and then come back down and report whatever there is to communicate. Such a person would do that because the goal of that (in the case of scientific submarines! and space missions) was science, which was to see what could be communicated via such means.

Finally, we have Libra. Libra is a difficult one for me, King Baligon tells me: it’s my third house, hence the house of Goddess, but Venus, the ruler of the 3rd house, is in the 9th house, the house of God. What I’m told is that at its ideal, it balances, and you see that even with someone like Stephanie Miller, whom I have listened to. She is a Libra sun in a day chart; she did have more of a team-like energy about her, circulating communication about her team, a Venusian balance of harmony (yet she maintains pointed political critiques). Generally speaking, the tone of her show is pleasant, and even if it can’t be pleasant, well, at least let’s make some jokes about it, and the angels remind me that cynical Saturn tends to have a cold and dry wit in response to the things going wrong, and is exalted in Libra.

I try to concentrate into this, and King Baligon says, “Let’s take a deeper look at Libra, which means ‘scales.’ We see this in relationships, right? This is the creative use of air: wind blowing one way here, and another way here in order for harmony. Harmony is a key signification of Libra, and what do you think of when you think of with music. It is the harmony–the collection of sounds, in such a way that the air moves. It communicates sounds that way, via sound waves. So we have communication (Gemini), the fixity of what is communicated (hence, “castles in the sky”), and, finally, we have the creative impulse of Libra, to either create harmony of the thoughts and communications of people (groups of friends, for example), or we have music itself.”

The angels ask me to concentrate on this, and actually the sense I’m getting–King Baligon, who I now see in classic medieval angelic form (with wings), he’s saying that the thing I’m seeing now is that I have completed this first round about the elements, so it will be completely finished tonight. However, because I’m more than halfway done with this round so he wants to let me know: “Yes, so the issue with getting at the square root of the circle:” (see yesterday’s post) “the problem is similar to getting at the square of the circle” (squaring the circle).

King Baligon illuminates me: “The square root of the number of degrees of the circumference [plus one for the center]”–361–“is 19; in order to square the circle, however, you need to take the square root of π (the side length of the square). You see how you need to get at the root of the circle (or the irrational transformative constant of the circle), in order to square the circle. But in order to get at the square root of that circle, you need to get at the squaring of the square (a square of side length 1 has a perimeter of 4, and squaring that length leads to a perimeter (and area) of 16, the number of elemental watchtower calls). Add this to the “mystery of the trinity” spoken of by the angel Galvah: this can be derived by multiplying a diameter of 19 times π = 59.7 ≈ 60 by rounding, the number of degrees of an equilateral triangle. Furthermore, going on to inscribe an equilateral triangle within this circle gives the triangle a side length of 9.5 * √3 = 16.45 ≈ 16 by rounding, to each of three sides (16,3,361: “the last shall be first; and the first, last“); again the same number of watchtower calls, with three remaining.

Everything I said yesterday, he’s giving me a huge clap, because I was saying everything, but now it’s clear the way that everything is lining up. He says, “You need to get that exaltation in Libra [symbolized by the squaring of the circle] in order to do so, so that all of the ideas can come together in harmony.”

I’m very pleased with all of this. I thank the angels and the Divine. The angels add: “Tonight, it’s going to be a little different, but you’re going to get the sense of the air about an individual and their aura, but you’ll also start to see into and get a preview into the actual thoughts and communications that are going on, and several things will become clear to you at once. The correspondence of the classical elements to each of the universal forces: that will be one. The correspondence of the classical elements to the usual suspects (astrology, etc.), and finally this will happen not only with an individual whom you’re encountering but also within a group dynamic. It will be a massive change.”

King Baligon is just giving me a lot of love and warm feeling right now, just so that my heart will be ready for this, so I’m expressing gratitude, but I notice a little bit of a lamprey like monster, and King Baligon says, “This is it: you’re getting into the thorns. They are not about you as opposed to you holding the thorns.” I say, “OK,” and express further gratitude.

“This is the beginning of digestion, so do not worry: you’re just being digested now for the rest of this process. The end is imminent.”

Thus ends the vision.

Sunset: Similar procedure.

I feel a whole-body buzz at the arrival of King Baligon. He notes the breath of fresh air. He says to consider “someone who has music in their soul or their heart.” Describing someone this way is to say that they have found their harmony with themselves and with the universe that they did not have before. “And so, with this: consider what it means to receive air from another, and what it means to take air from another. When we say that ‘air has been taken out of the lungs’: a freedom has been lost, an openness has been lost.” (Note: or even that one has lost one’s spirit!). “Being ‘free to fly the friendly skies’ means there is no limit to where one can go.

“Very simple expressions,” King Baligon remarks, “but they serve a point here. So, ideally, because of this competition for the same air,” (i.e., freedom within a given, otherwise-open area), “agreements must be reached. One person wants the freedom to take money from another person, but that other person says, ‘Well, I will, if…’. It has to go beyond mere ‘Let’s talk about this,’ because you begin talking about the idea of it, with Gemini, and you develop a sense of harmony that could be reached if you work together,” (as with Venus in Libra), “and then that harmony must be enforced by agreements such as with Saturn” (in Libra), “but also, these agreements are informed by what an ideal actualization of an idea may be,” (Aquarius), “and then it’s never going to live up to that, with a very strong Saturn. Or, one learns to accept [something] close enough to one’s ideal.

“So that’s what it means. So when one is providing air, one is perhaps giving the idea, or the ability, the freedom of communication to speak about things that perhaps they did not dare speak, and in speaking about something, one is allowing for the elaboration of these points. In other words, when air is compressed, or not allowed the freedom to move about,” and here King Baligon cautions that this is slightly different from Aquarian fixed air, but we will return to this idea. “This is an uncirculated air that just sits and doesn’t circulate. Consider this in relation to the heart: if the air is sitting, if this tendency of the heart to want to move about openly, in ways that speak to it, but is not able to: then suddenly it becomes constricted, and it seeks smaller and smaller avenues with which to move. It seeks to find the openness, and finding little or none, its dreams tend to die out. Its view of what is possible tends to die out. The geometry collapses, or even if it doesn’t collapse, it becomes rather dull,” (like a balloon which only expands on a fourth of its surface, unable to measure correctly to the center from the circumference).

“It doesn’t make connections among other points,” King Baligon adds, sadly, “because, though it moves, the limitation of a point that cannot reach out and make a connection with another point is problematic. So, the problem is that the relationships or connections between other points (such as those with another person or from one idea to another) are lost, or are not made [to begin with]. That’s ultimately the issue there. Similarly, with restricted air when it comes to Libra, connections are lost: this time not between ideas, necessarily but points and systems between people, or as someone’s ideas about whether they are allowed to relate and their own behavior.

“And finally,” King Baligon wraps up the air trio, “when it comes to Aquarius, when air is restricted or limited or lacking, then a person’s ability to create an idea about how things ought to be, how rules ought to be, become restricted. Those become thoughtcrime,” King Baligon concludes.

I ask whether there be anything else, and he says no, because the introduction of air is merely the reverse of all of these. Someone who has too much of this maybe gets a little too focused on the ideas of freedom, or where one can go or what one can do, and it just becomes a lot of ideas: a lot of ideas about doing something, and then never doing it, and that’s a problem, and this is where the introduction of [elemental] earth could be helpful.

King Baligon says that’s it. “Good job! No hints as far as tomorrow” (when King Bnapsen of Saturn does not line up well with the sign of Water, which means either he will have poorer dignity or the associated tablets of the next four days will follow a different pattern), but to indeed call King Bnapsen.

Once again, I’m so grateful to the angels for this, and thus ends the vision.