Review of Freemasonry

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The Freemasons’ Magic Square
by Bro. William Steve Burkle KT, 32°
Scioto Lodge No. 6, Chillicothe, Ohio.

Author's Note: This is not a scholarly article of the type which one normally sees published here at PS Review of Freemasonry, but is rather an account of the exploration of our Masonic tradition, and the resulting discovery of what is either a startling coincidence, or true information hidden within one of our most cherished Masonic symbols. Regardless of which in finality you believe it to be, it certainly makes for interesting reading. I hope you will join me in my exploration of what may be a rediscovered meaning of the Masonic Square and Compasses. I also beg your tolerance if what I propose here seems entirely impossible.

Although the Square and Compasses have been the preeminent symbol of Masonry for many centuries, it is not entirely certain when the Square and Compasses were first adopted as a symbol for Freemasonry. Further, to my knowledge, the adoption of this symbol by Freemasonry is not recorded, although there are many copyrights of the symbol which seem to be of recent date (circa 1984).

During our initiation rituals the metaphoric meaning of the Square and Compasses is clearly and unambiguously communicated; however during a period of research on the topic of Magic Squares, in particular that Magic Square known as the Freemasons’ Magic Square, a possibility arose which I found most interesting. I would like to relay a purely conjectural notion that the symbol of the Square and Compasses communicates a cipher.

A short narrative journey as to how I arrived at this conclusion will follow. During the journey we will touch upon several key areas which will include magic squares, the kabalistic art and science of Gematria, the system of Pythagorean charts, a Rosicrucian (and Alchemical) practice involving Sigils, and lastly I will explain how I believe the Square and Compasses may fit into this complex scheme.

Magic Squares

A Magic Square (Kamea in Hebrew) is an array of an equal number of rows and columns containing numbers which are arranged so that the sum of any row is also equal to the sum of any column in that square. Additionally, the sum of either of the two diagonals of the square also equals the sum of either a row or column in the square. Magic squares have been esteemed for their magical and mathematical properties for thousands of years in China, India, and the Middle East.

The figure illustrates the concept:


This is a 3 X 3 magic square, a magic square made up of three rows and three columns. Try adding the numbers in each of the three individual rows. They all add up to the number 15. If you add the numbers in each separate column, each column adds to 15. If you add the numbers across the diagonals of the array, they too will equal 15.

More specifically, the above 3 X 3 magic square is that which is called a Freemasons Magic Square. I hope to reveal the reason why it is called that in the text which follows. It should be noted that this same magic square also appears in the I Ching, in Hebrew Kabalistic texts (where it is associated with the Tetragrammaton), and it is sometimes called the Saturn Square, because of it’s Kabalistic associations with the third Sephirah or sphere in the tree of life (called Binah).

Note that in a nine number (3 X 3) magic square, the numbers from one to nine are used. Similarly in a sixteen number (4 X 4) magic square the numbers from one to sixteen are used, etc.

Also note that if you add all of the numbers together in the 3 X 3 magic square (as shown above) you get:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

This number (45) also has special significance to students of the Kabala. By-the-way, if you divide the sum of the numbers of a magic square by the number of rows or the number of columns you get the sum of the numbers in an individual row or column. In the 3 X 3 square above, the sum of the numbers from 1 to 9 is 45. If you divide 45 by 3 (the number of rows or columns) you get 15 (which is the sum of the numbers in each row or column.

Further note that the numerical sequence 3, 5, and 7 forms the center row of the Masonic Magic Square. It is this numeric sequence which first led me to investigate magic squares. I happened to serve as the Inspection Candidate for our Lodge’s Fellowcraft Degree, and during the initiation ritual I became curious about the 3, 5, and 7 steps leading to the Middle Chamber of King Solomon’s Temple. While the metaphoric explanation given at the time was quite clear to me, I simply couldn’t help but feel that these numbers must have a deeper and far less obvious allusion.

Through the magic of the internet, and with a little help from, I was able to explore this notion. During the course of my internet search I was surprised to see numerous references to magic squares, and when I found there are numerous associations of magic squares and freemasonry I was more than a little bit curious. What I discovered was that there was a magic square, specifically called the Freemason’s Magic Square, and that it contained the 3,5,7 sequence. I also discovered that no less a Masonic Luminary than Benjamin Franklin himself was acquainted with magic squares, and that a Freemason’s Magic Square was discovered among his papers after his death.

Although intriguing, I remained perplexed as to how the magic square was related to Freemasonry, and totally still in the dark concerning the meaning of the 3,5,7 sequence. It was only when another piece of the puzzle, called Gematria, fell into place that I would feel as if I had made progress.

In summary, a Magic Square consists of a table composed of an equal number of rows and columns. A minimum of three rows and columns (called a 3 X 3 magic square) for a total of nine (9) numbers, is required, however there is no maximum number of rows and columns which may be used. I will here end my discussion of magic squares per se, although there is a huge volume of literature dealing with them. The remainder of this article will deal only with the Square of Saturn, a.k.a. the Freemason’s Magic Square, and only with those properties of the Freemason’s Magic Square (there are many more) which pertain to the topic of this article.


My continued fascination with magic squares and my conviction that they could contain a cipher, led me to undertake an additional exhaustive internet search. This particular search was based upon another curiosity which I discovered, which concerned the Rosicrucian Seal, and the use of that seal as a sort of an encryption device.

The Rosicrucian Seal depicts a single red rose crucified on a cross, circumscribed by two outer circles of Hebrew Characters. Several examples of the Seal may be found on the internet.

The concept is that one could encode and decode information into Hebrew characters using this seal and through the use of Gematria, decode the meaning of this information. Gematria is an ancient art and science which involves substituting numbers for alphabetic letters (generally Hebrew or Greek Characters). Gematria is a highly complex subject, and is well beyond the scope of this small work of mine;

For our purposes, simply consider that the principle of Gematria is that words may be assigned numerical values based upon the characters or letters they contain; and that words having the same numerical value may be substituted for one another. In Gematria, words themselves, especially in Holy Scripture may carry magical allusion, and many deeper meanings can be concealed within such written text, many of which may only be revealed through numerical analysis. In ancient days, letters often were used as numbers (i.e. Roman Numerals). The result was that some numbers would spell significant words, and some words had significant numerical values. I have included below, a table showing the Hebrew characters substituted for the numerical values in a Magic Square. Note that the number Five (5) is represented by the Hebrew character “heh”. Heh is commonly used by Kabalists to represent the name of God. This seemed an interesting concept to me, and I learned that the Rosicrucian cipher was communicated by connecting the Hebrew letters in the concentric circles arranged around the Rosy Cross with straight lines. In this scheme each letter of a word was connected to another letter of that word by a line, in a sort of ancient puzzle. The line pattern which was formed during this process was called a Sigil. Consequently, a person who was in possession of this Sigil, had only to overlay it on the Rosicrucian Seal, note which Hebrew letters were involved, assign each letter a numeric value using Gematria, and convert the number into the words and phrases which were the message.

Fascinating though this was, it certainly didn’t shine any more light upon the problem at hand (finding the meaning of 3,5,7), although it had familiarized me with two very important new terms, namely Gematria and Sigils.

Pythagorean Charts

With the words “magic square”, “Gematria”, and “Sigil” entered into my Google search engine, I set off yet again on my quest. I was, by this time, convinced that the numbers in some way were associated with the Freemason’s Magic Square; after all it couldn’t be mere coincidence that the 3,5,7 sequence formed a major part of the Magic Square.

I actually struck gold with this search as it took me to a page on occult symbolism (non-Masonic), in which an ancient technique for creating sigils using magic squares and Pythagorean Charts was discussed.

The concept presented was that by using a Gematria composed of the Modern English alphabet (called a Pythagorean Chart), together with a magic square, a Sigil could be created. I will use the Freemason’s magic square as my example. However first I will recreate the aforementioned Pythagorean Chart.

First, since the Freemason’s Square has nine (3 X 3) squares, I write the numbers from 1 to 9 in a row like so:

1 2 3 4 5 6 7 8 9

Now, below each number I begin to write the English Alphabet, beginning with “A”, and ending with “Z” by wrapping the letters to a new line each time I reach the number 9. This is how it would look:

1 2 3 4 5 6 7 8 9

Note that in the above Pythagorean Chart, the letter “A” is associated with the number 1, as is the letter “J”, as is the letter “S”. Generally, when decoding, you simply choose one letter, evaluate it in terms of the overall word ,and then try it again using the another letter of the same value. That value which makes the most sense is then considered correct.

To convert a word into a number I would simply write the corresponding numerical value of the letter until the word was completely spelled. Let’s say I wanted to encode the word “MAGIC”, as in Magic Square.

4 1 7 9 3

“MAGIC” would be 41793

Using the Magic Square I would now produce a Sigil (I have shifted some of the numbers in the square slightly to enhance clarity):


If I have this Sigil, and a Magic Square, and my Pythagorean Chart, I could decode the series of straight lines into the word “Magic”.

Naturally, it would be quite a simple thing to do this, and if I wanted to add the word “Square” I would simply draw a second Sigil over top of the first one. If I wanted to make the cipher more complex, I would simply shift the alphabet; for example I would shift the column of letters under the 7, to the left, so that the letters G, P, and Y are instead under the number 5. I could even give a clue that I had done this by writing the letter G on the magic square in place of the number five (5).

The Square and Compasses

I assume that by now you are way ahead of me. If I superimpose a line drawing of the Square and Compasses (complete with a “G” in the center), over the Freemasons Magic Square it would look like this:


Now, by noting the numbers which are connected by each line, I would get: 8, 9 ,6 and 3, 1, 7 or alternately 6, 9 ,8 and 7, 3, 1 (since we don’t know if we should start from the left or right end of the Sigil).

Then, by shifting the Gematria left until the letter G is in column number 5, I have a means of converting the Sigil to letters (see below).


For 8, 9, 6 this would give:

J K H (First Word or Phrase)
E C I (Second Word or Phrase)

Since there is no letter in the third row which is associated with the number 9, we can disregard that row in our solution. (Note some would argue that point). We could also use a letter value for our numbers from either of the two rows, which are in the same column). i.e.

S T Q (First Word or Phrase)
N L R (Second Word or Phrase)

As you can see there are numerous possibilities for arranging the combinations of the various letters to form words. I am of the belief that it is intended for the compasses to represent the first word and the square the second word. This is based upon the fact that our initiation ritual attaches special importance to the position of the points of the compasses elevated above the square.

I am also struck by the fact that the “G” coincides with the number 5 in our Gematria. As you may be aware, the 5 pointed blazing star, or pentagram at one time occupied the place of honor in the symbol of our Fraternity, which is now occupied by the letter G. I believe that the fact that the number 5 represents the Hebrew character “heh” which means “God”, lends more credibility to the use of the shifted Pythagorean Chart (so that the 5 represents “G”), especially since our tradition and ritual tell us that the Masonic “G” represents God.

What hidden cipher does our Square and Compasses reveal? Because of the numerous possible answers to this question, and depending upon the word or words one chooses to associate with each of the letters, this is not something to which I am yet willing to commit. My current plan is to determine each possible combination of letters which may be produced by the numbers 8, 9, 6 and 3, 1, 7 (I intend to use a tree chart for this purpose), and to then examine each combination of letters for possible meaning. I will also take each combination of the three letters and convert them to Hebrew Characters. There are several available internet sources dealing with the Kabala, which contain charts of Hebrew character triads, which have special or sacred meaning. I am also further examining the direct relationship between the Freemason’s Magic Square and the Tetragrammaton. Interestingly enough the Freemason’s square can actually be rendered in the form of the Tetragrammaton, with the numbers/letters representing the names of God remaining intact.

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