Masonic G = 2n-1

Masonic G = 2n-1

Please accept this definition and history on Gnomon as it is much better than I can hope to achieve:


[A gnomon ([ˈnoʊmɒn], from Greek γνώμων, gnōmōn, literally: "one that knows or examines"^[1][2]) is the part of a sundial that casts a shadow.

The term has come to be used for a variety of purposes in mathematics and other fields.

Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Greeks.^[3]Oenopides used the phrase drawn gnomon-wise to describe a line drawn perpendicular to another.^[4]Later, the term was used for an L-shaped instrument like a steel square used to draw right angles. This shape may explain its use to describe a shape formed by cutting a smaller square from a larger one. Euclidextended the term to the plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successive figurate numbers, including square and triangular numbers.

Hero of Alexandria defined a gnomon as that which, when added to an entity (number or shape), makes a new entity similar to the starting entity. In this sense Theon of Smyrna used it to describe a number which added to a polygonal number produces the next one of the same type. The most common use in this sense is an odd integer especially when seen as a figurate number between square numbers. - https://en.wikipedia.org/wiki/Gnomon ]

The above comes directly from the Wikipedia page on gnomon.  It is a succinct summary of what a gnomon is and the history of a gnomon.  My job in this article then is to connect your synapsis of dots esoterically and Masonically. 

First as a sundial, a gnomon is a three-dimensional instrument, embodying two dimensions (a plane is length and width), that uses light to determine the fourth dimensional concept of time.  Immediately, it should be self-aware that a gnomon is extraordinary.

Using light to cast shadow, a gnomon gives us insight to how the duality of this world, symbolized by the two pillars upon the porch, can not only be understood but also manipulated. No more shall be said here, except that the division of earth into degrees of day and night is a dual process of two right angle (gnomonic) forces known as Centrifugal force (earth rotating on its own axis) and Centripetal force (earth rotating around the Sun).

The very shape of a gnomon makes the Greek letter Gamma which is our equivalent of the English letter "G".  The same letter in the center of the compasses and the square of our beloved symbol. G is the seventh letter in the English alphabet. But Gamma (gnomon) is the third letter of the Greek alphabet and Gimel is also the third letter of the Hebrew alphabet.  Three, of course, is the magic number. (Forgive me School House Rock!)

So as Masons we “square” our actions and it should be obvious that the Square is a gnomon.  Morally we should make sure that our actions are “right”.  But esoterically, this can mean that we should make sure that our actions are “seeded for growth”.  

You see, when you add a gnomon to a square (geometrically AND mathematically) you create another square.  See the picture below to understand geometrically of how when you add a right-angle gnomon to a four-sided square you get another four sided square.  

Note that gnomons are odd numbers.  Odd numbers are masculine.  Masculine is seed. (Even numbers are feminine. Feminine is fertile.)  

Mathematically, therefore, adding odd numbers together gives you squares.  (Side note:  Notice how the numbers of the squares below oscillate from feminine to masculine.)

1 is a square 1 x 1= 1       Add odd number 3    to get   4 which is the next square

4 is a square 2 x 2= 4       Add odd number 5    to get   9 which is the next square

9 is a square 3 x 3= 9       Add odd number 7    to get   16 which is the next square

16 is a square 4 x 4= 16  Add odd number 9    to get   25 which is the next square

25 is a square 5 x 5= 25  Add odd number 11    to get   36 which is the next square

Ad infintum……

 So then the equation for a gnomon is (2n-1) where "n" is the size of the side of the square (pictured below).  

Or to put differently, "n" is how big you want it to be grown.  Knowing how big you want something to grow will tell you the size of the gnomon (right force) that needs to be applied to it.  

The point is that masculine activity (making it happen), as opposed to feminine activity (letting it happen) is the gnomon that grows a square.  The gnomon and its applications can readily be seen in the Mosiac pavement that adorns our floors and lives. 

Hopefully this is enough, to allow you Fellows of the Craft to be able to apply your Square to Self in an esoterically different way for the benefit of us all.

PM John B Love, III 33°
Right Illustrious Grand Lecturer

Most Illustrious Prince Hall Grand Council of Texas Royal and Select Masters