Magic comes in many forms, including ones you wouldn’t expect, such as the Magic Square. From the famed Chinese mathematician Yang Hui, to Corneluis Agrippa, whose work is so well known that he’s mentioned in the Harry Potter book series, to the musings of Benjamin Franklin, Magical Squares of varying kinds have been found in many cultures throughout the years. Many of them appear to be riddles of varying kinds, and may implement the use of numbers as a form of math game, letters for word puzzles, and some even use colors! The square you see here was recorded by a Jewish German, Abraham Von Worms, after learning a magical system from an Egyptian. His work has two separate English translations, and now little ol’ American me has, in the course of my lycanthropic studies, done a bit of artwork based upon it. If that isn’t a neat mix of culture, I don’t know what is.

Regardless, pictured here is the Diseebeh Square, which is said to allow a properly prepared magician to transform a person into the visage of a wolf. To do so, the person must be shown the paper upon which the square has been drawn, and that square must then be brought into sudden contact with the person’s body, causing instant transformation. To reverse this, the square is to be placed on the head, and then struck with a wand.

The word Diseebeh is possibly derived from the Arabic word Zabh, which, depending on what you read, can be equated with the wolf. This, it appears, may not be entirely accurate. It seems that it is actually a word indicating the slaughter an animal in the name of God, by slicing the throat, either for food or necessity. Interestingly enough, when watching wolves hunt, once the prey is hindered by pack members slowing the animal down, wolves will often go for the throat. (However, wolves generally don’t just straight-up slice or rip the throat out; they clamp down on the trachea and suffocate their meal. But the similarity remains.)

You may be wondering why I am depicting the Diseebeh Square tilted to the left, thus making it into a diamond. The reason for this is simple: Patterns of varying kinds seem to be rather important in the construction of magical squares, and should you rotate this square widdershins (counterclockwise) 45 degrees, the square has bilateral symmetry. This is the same kind of symmetry that you find in many fauna, including the human and wolf.

In addition, walking widdershins is to walk opposite the direction of the path of the sun (In the northern hemisphere), and thus, is effectively walking in the direction of the oncoming night, a time for which the wolf is far better suited than we are. The Merriam-Webster dictionary defines widdershins not only as counterclockwise, but as “in a left-handed, wrong, or contrary direction” that is, the opposite direction, a reversal. This has some symbolic significance, because historically speaking, the human and wolf were sometimes seen as adversaries, perhaps even opposites, even though we are more similar than some of our ancestors would have liked to admit. Europeans of that time often thought themselves to be kind and civilized, while wolves were thought of as cruel and bestial.

Since the Diseebeh Square doesn’t appear to be acrostic, I started to wonder if it was actually mathematical. Many numbered magical squares are mathematical in nature. One example of this is the Kamea, which is a square in which all of the lines, horizontal, vertical, or diagonal, add up to the same number. My favorite of these, naturally, is the Kamea of Luna, the moon, which reads thus:

37 78 29 70 21 62 13 54 05

06 38 79 30 71 22 63 14 46

47 07 39 80 31 72 23 55 15

16 48 08 40 81 32 64 24 56

57 17 49 09 41 73 33 65 25

26 58 18 50 01 42 74 34 66

67 27 59 10 51 02 43 75 35

36 68 19 60 11 52 03 44 76

77 28 69 20 61 12 53 04 45

(It is interesting to note that the diagonal line starting at the upper left-hand corner to the lower right-hand corner displays 37-45 in numerical order, with 37 being a prime number.)

Regardless, after a lot of failed attempts and messing around, I decided on a conversion method for all of the letters of the Diseebeh Square into numbers. Pythagoras felt that there were nine basic numbers and that all else was repetition (Zero is a more modern concept). So, I used a simple 1-9 repeating cypher:

1=AJS 2=BKT 3=CLU 4=DMV 5=ENW 6=FOX 7=GPY 8=HQZ 9=IR

However, to my disappointment, it quickly became apparent that the lines would not all add up to the same amount. Regardless, I added all of the lines just the same, and arrived at the summations for the vertical, horizontal, and both diagonal lines. Most of these fall between 30 and 45, but there is one outlier. The diagonal line that vertically bisects the square as it is shown above adds up to 62. While mathematically unsound, in numerology, when presented with a number with multiple digits, they are sometimes added together to create a single digit. This is called reducing, and is something we will briefly come back to later. So, here, if you add the digits together, they equal 8, which relates back to the composition of the square because it happens to be the number of squares in each line. In the soul plane in numerology, 8 is a number of duality, something that resonates with lycanthropic studies, due to the duality of a creature that is both human and wolf. Physically, 8 denotes independence, while spiritually, it indicates wisdom, seeming to mimic the strong points of each creature: the physical prowess of the wolf that allows it to work individually as well as in a pack, as well as the spiritual wisdom of the human, who has the luxury of contemplating such things.

I then found that if I took all of those previously calculated sums, and added them together, the total was 738. I then took that number and began dividing it by prime numbers, since, according to Pythagoras, prime numbers are to be given preference.

738/1=738

When I was in school, 1 was considered a prime, though it isn’t truly, since a prime number is generally considered to be a number that cannot be divided by any number besides 1 and itself, but is also greater than 1. Regardless, I felt it was worth doing for the sake of thoroughness.

738/2=369

An interesting result. Not only is this clearly divisible by 3, the next prime on the list, but the numbers themselves are a progression of the addition of three. 3+3=6, 6+3=9.

369/3=123

By some fluke, the result also represents the numerical progression I’ve been using to divide by! Unfortunately, the next prime I’d use is 5… but 123 is clearly not devisable by 5, nor is it divisible by 7, and 4 isn’t a prime, so, I’ll go with 3 again.

123/3=41

Here, the result is a prime number, and it cannot be divided again. However, curiously enough, when you reduce the number like we did earlier, you get 5, the next prime in the progression I was heading for.

Also, curiously enough, there is an odd sort of pattern in the numbers used to divide by. 1,2,3,3. If you look at the pattern as a combination of symbols rather than just their numerical values, (two away from Same, one away from Same, Same, Same)The pattern of these numbers is, in a way, a reversal of the start of the Fibonacci sequence, 1,1,2,3 (Same, Same, One away from Same, two away from Same). This is a stretch of course, but it also happens to mimic the physical turning of the square done initially: a reverse rotation of the square, a reversal of the pattern of numbers.

The Fibonacci sequence is important, because it is interconnected with the golden mean, a visually appealing proportion that is not only common in art but also in nature, including the proportions of man and wolf. For instance, this can be seen in the proportions of your hands and arms, and the bones of the wolf’s foreleg happen to be similarly proportioned.

One of the most common depictions of this sequence is the spiral (A symbol I personally love), the same sort of spiral you’d see in a snail shell. To draw a rough version of this spiral, you’d start off with, interestingly enough, a square like this one (followed by one of an identical size, then one twice as large, etc). Draw an X through the center, and mark approximately the 1/4 point on one of the diagonals. Then draw an arc from one corner of the unmarked diagonal, through the one quarter point marked previously, connect it to the other corner, and continue with the rest of the squares.

Curiously enough, the intersections, including this one-quarter point, seem to be marked on the Diseebeh Square. I started with the diagonal beginning with D: DSROORSD. This line is symmetrical with letters and thus it is symmetrical when converted to numbers. Then, I went to the other diagonal, with H’s at each end. That diagonal reads HRRNNIIH. While this is not symmetrical when using letters, when converted to numbers, it creates a palindrome that reads 89955998. Coincidentally, diagonals intersect in between both 5’s and the arc for drawing the spiral would cross between either set of 9’s you wished to use.

When looked at in this way, the Diseebeh square not only mimics the bilateral symmetry seen in many animals, but also begins to show the viewer the start of the spiral representation of the golden mean, so that it relates to basic structures found in both art, the natural world, to which we are all, in some small way, related. It’s curious that this square is used to change the appearance of a man into that of a wolf. The wolf, a creature that we have feared, hated, but also loved and cherished, so much so that we became their companions and throughout the years, side-by-side, have evolved both into modern man, and the ever-loyal dog. Yet, we have done so without forgetting their wild natures and the dark of night, which resonate in our legends and folktales, like those of the werewolf.

Sources:

The Book of Abramelin: A New Translation By Abraham Von Worms, Georg Dehn (The original translation was by Abraham ben Simeon, S. L. Mathers-MacGregor)

Sacred Geometry: Philosophy and Practice By Robert Lawlor

The Magician’s Tables: A Complete Book of Correspondences by Alan Richardson

Geometric Magic Squares by Lee C.F. Sallows

Numerology By Daniel Heydon

The Complete Book of Numerology By David Phillips

Numerology for All By Pt.Ashutosh Ojha

The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition) By George Gheverghese Joseph

Benjamin Franklin’s Numbers: An Unsung Mathematical Odyssey By Paul C. Pasles

Binding Words: Textual Amulets in the Middle Ages by Don C. Skemer

The Magical Arts by Richard Cavendish

Werewolves By Jon Izzard

Canine Behavior: A Photo Illustrated Handbook By Barbara Handelman

Book of Secrets, The: Esoteric Societies and Holy Orders, Luminaries and Seers, Symbols and Rituals, and the Key Concepts of Occult Sciences Through the Ages and Around the World By Daniel Pineda

A Dictionary of Islam: Being a Cyclopædia of the Doctrines, Rites, Ceremonies, and Customs, Together with the Technical and Theological Terms, of the Muhammadan Religion by Thomas Patrick Hughes.

Disclaimer:

Not only is there a wealth of other relevant information that I couldn’t discuss here, the sad fact is that this is pretty much all coincidence. The truth is, while I find connections and patterns in this… people are rather hardwired to look for patterns, even if it means skewing logic until we have all the pieces to complete said pattern. This sort of fallacy can be dangerous when discussing things that are more important than mere mathematical musings on ancient talismans, and sadly, is implemented commonly if it supports the viewpoint a person personally has or wants to see. This, in a way, is also representative of the werewolf… The true man, on one side, would use logic and be willing to change his or her actions or opinions based upon new information and the impact on others, while a man of primitive intellect would continue on with its own desires in mind, in spite of all evidence to the contrary, or the wellbeing of others.

On my end, I would like for there to be more to the Diseebeh Square than it appears, and, in looking for that, I have incorporated systems of thought that can be difficult to validate, and stretched logic rather thin. However, I doubt this could being any harm to others, and my goal for this study of this square was simply to try looking at it in a different way, and, I think I make some interesting observations and musings. I think I was successful at the end of the day, especially since it was done for the sake of curiosity and amusement. Regardless, while my musings here are a long shot, I do hope that they were entertaining to you at the very least, and, perhaps, at best, may have rekindled some interest in math for some of you. After all, you never know what you may need when studying werewolves; if you had told me that I’d be using math to try to study lycanthropy ten years ago, I would have laughed in your face, and yet here it is.