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.