The Second Degree of Freemasonry charges newly-Passed Fellowcraft Masons to broaden their knowledge. It does this by encouraging the study of the seven liberal arts and sciences. These are separated into two groups: the Trivium and the Quadrivium. The Trivium — composed of Grammar, Logic, and Rhetoric — teach Mankind how to organize their thoughts and communicate with one another. Through the study of the Quadrivium — Arithmetic, Geometry, Music, and Astronomy — we begin to learn how to understand our place within Nature.
Within the whole of Freemasonry, Geometry is held in very high regard. Its generalities are given to us, and we are instructed as to several real-world applications for its uses — the so-called “Advantages of Geometry”. These are all easy concepts to grasp — how geometry aids in architectural design; troop arrangements on the battlefield; cartography; and more.
But what does any of that have to do with morality?
This concept was explored in-depth by the ancient Greek philosophers more than two-thousand years ago. In Plato’s Parmenides dialogues, the idea of shapes not truly existing in our world appears.
Dr. Piers Bursill-Hall, in his fantastic essay Why do we study geometry?, has the following to say on the matter:
One of the ways Plato argued for the existence of this dual kind of reality was with the use of geometry: we all know that when we draw a triangle in the sand it isn’t really a triangle because its edges are not really lines, the lines are not really straight and thin, and they certainly don’t intersect at points. But the individual triangle we draw in the sand is taken to be representative – or a way of talking about, or thinking about – what triangles are really like. But … what is that? Of what is the triangle in the sand a rough individual copy?
Plato suggests that the archetypical Form is something like the ‘real’ triangle or other mathematical entities: something we can think about and conceive of, if we work at it, and even reason about and gain knowledge of … but which is non-material and clearly not something that we can find ‘existing’ in the material world. It exists in a different, other kind of reality, and we use pure (logical, geometric) reasoning to gain sure and certain knowledge of it. So when we talk about triangles, and prove theorems about triangles, we’re really talking about something like the Form of triangle.
Geometrical shapes — and Geometry as a whole — are symbols. They are examples of the perfection that we should strive toward, and that we will always fall short of.
In our Lodges, we don’t do a good job of imparting this lesson to our Fellowcrafts. We know that Geometry is important to Freemasons, but most of us take it at face-value for the meaning that sits so obviously on the surface. It is very fitting that the letter “G” sits inside of the Square and Compasses; Geometry sits at the center of the Craft. Once you have a grasp of how vital Geometry truly is to the Freemason, it pulls everything into proper alignment — all of the Working Tools, the Apron, our Degree work, symbols, allegories — everything.
The construction of a Spiritual Temple is the same as building yourself into the ideal Man — the ideal you. We can visualize what ideal looks like, but we can never achieve it. It’s our responsibility, however, to come as close to that perfection as we can.