Creating Sigils using the 3x3 Magic Square having a sum of 15 What are sigils? I am not going to relay a great deal of information on the definition or history of sigils. Instead I refer the interested reader to the topic at any number of locations on the Internet; www.wikipedia.org and www.thelemapedia.org contain nice articles that will send you on to other o ther references. It’s enough for our purposes to say that a magical sigil is a reduction of a phrase p hrase or word into an abstract linear figure. Some of the most famous are the sigils relaying the names of angels and demons within the pages of the Goetica . More recently, practitioners or chaos magic have started developing sigils using a variety of methods. While I h ave no recollection of where I learned the following method, I now relay a way of o f sigilizing any phrase or word through the use of a magic square. What is a magic square? In a strange twist of human interest, it was a friend’s interest in the current Sudoku puzzle craze that triggered my memory of magic squares and their use in creating sigils. Sudoku is like a crossword puzzle using only the digits 1 through 9 and a simple set of rules to determine how the digits may be arranged in a 9 x 9 grid. Watching my friend complete the puzzle made me think of magic squares. Simply, a magic square is a n x n grid which has been filled with numbers in such a way that each row, each column and each diagonal sums to a single number. As a computer programming student, I recall being g iven the assignment to computer the number of unique magical squares of size n x n which might be formed with a given set of numbers. The problem for a general size n and a general set of numbers is an interesting one but we shall avoid discussion of such topics here. If you are interested in reading more on the topic of magic squares, there are literally hundreds of sites available on the Internet. Instead of considering the many varieties of magic squares, we shall limit our approach to the use of a single type of magic square: the 3 x 3 square whose rows, columns and diagonals sum to 15. 1 5. The nice thing abou t this particular choice is that there is only 1 solution. Well actually there are several solutions but they all represent symmetric transformations of the same square. The 4 x 4 grid on the other hand has something on the order of 880 8 80 solutions! Now, when I say the 3 x 3 grid has only one solution, I mean the numbers have to appear in a certain way. w ay. As I said, you can move things around a bit but you will find the same combinations in the rows and columns each time. I will give you a few examples of what I mean. These are 3 examples of the 8 possible ways to fill out the grid, all of which can be transformed into one another through a translation about a vertical, horizontal or diagonal axis.
8 1 6 3 5 7 4 9 2
2 9 4 7 5 3 6 1 8
4 9 2 3 5 7 8 1 6
So how does this relate to making a sigil? Well, as you may recall, the goal of sigilization is the creation of an abstract linear form. Now, while several artists are great at creating abstract forms I find it easier to have some sort of ruleset that helps me. If I do this right, I will start with a word or phrase and finish with an image that I can draw easily, suitable for carving into candles, wood o r even marking with chalk around my sacred space. The image should have nothing to it that immediately draws my mind back to its original form as a word or phrase. I want the result to be completely abstract. To do this, I reduce the letters of my word to numbers using a scheme that is familiar to anyone that has played around a bit in numerology. I first map each letter of the alphabet to one of the digits 1 through 9.Feel free to do this however you wish but for the simplicity of this example I will use a very simple method.
1 2 3 4 5 A B C D E J K L M N S T U V W
6 7 8 9 F G H I O P Q R X Y Z
Using this chart we pick out the digits corresponding to the letters of our target word or phrase. To begin with a simple example let’s use the word HOSPITALITY: H = 8, O = 6, S = 1, P = 7, I = 9, T = 2, A = 1, L = 3, I = 9, T = 2 and Y = 7. That sequence of numbers forms the “map” by which we create our sigil. I also throw in the “hot spot” for the sigil by going through a standard numerological reduction of the map to find a single digit to represent the entire word. I do this by summing the digits from the map (e.g. 8 + 6 + 1 + 7 + 9 + 2 + 1 + 2 + 9 + 1 + 7 = 53) and then repeatedly summing the digits of each result until I find a single digit result. HOSPITALITY => 8 + 6 + 1 + 7 + 9 + 2 + 1 + 2 + 9 + 1 + 7 = 53 => 5 + 3 = 8 Thus the “map” for my hospitality sigil is the sequence 8, 6, 1, 7, 9, 2, 1, 3, 9, 2, 7 and my “hot spot” is 8. Drawing the sigil Finally, we get to the fun part: making up the symbols that will form your sigil and actually drawing out the map. First, let’s pick one of the 3 x 3 magic square solutions to use. I arbitrarily chose the following one. Remember that all you do in changing which 3 x 3 solution you choose is picking a particular reflection of the same sigil.
8 1 6 3 5 7 4 9 2
To draw out the map, simply draw lines connecting the centers of the boxes containing the numbers in the map. Connect the boxes sequentially and we’ll add some interesting symbols to keep everything from appearing like a stick figure. I’ll expand the size of my magic square and trace out the map here for you.
8 1 6 3 5 7 4 9 2 There’s the first step, 8 to 6. The second step goes back to 1 and traces over the line segment we drew from 8 to 6. I like to denote this action on my sigil by adding a special symbol for such “reflections” in the direction of my drawing. You may or may not choose to use any symbol at all but I generally use a nice small solid-colored circle.
8 1 6 3 5 7 4 9 2 I add an open circle to mark the “hot spot” number for the idea being sigilized. In the case of our hospitality, the “hot spot” was found to reside in the 8 square.
Now, removing our numbers, we begin to see the form of our sigil for hospitality. We have achieved a rather simplistic and somewhat pleasing figure. To add a bit more symbology, I generally like to add an indication of the starting and ending points; triangles indicating the direction of the line within the map.
The variations are endless. You will find special circumstances that you may wish to mark with new symbols. I generally mark repeated nu mbers with two small lines perpendicular to the path of the map. For spaces between the words of a phrase I draw a small square centered on the path. For ease, I keep the symbols very simplistic. Circles, lines, triangles and squares are easy on the eye and require limited skill in transferring the sigil to clay, paper, wax, etc.
HOSPITALITY
