Introduction to Masonic Geometry
Posted on | August 4, 2005 | No Comments
Introduction to Masonic Geometry
© 2005 Kevin E. Houchin
Draft 1.0
It’s no secret that Geometry is important to Masons. Everyone can see the square and compass in our symbol, and only the most non-thinking human would miss the connection between our most visible symbol and geometry. Of course non-masons are not expected to UNDERSTAND the connection. Unfortunately, many masons don’t take the time to engage and understand the connection either. In this brief essay I hope to give you an overview of why geometry works so well with Masonry, and hopefully engage your interest enough to engage in your own study, or at least recognize the connections as you attend to the work of your lodge.
The first step toward understanding the connection between geometry and Masonry is to recognize that geometry was the first science of reasoned, abstract, thinking. To understand geometry humans had to make the mental jump from working through a physical project (like marking boundaries of property) to working through an abstract IDEA that could be applied to a physical project. With this in mind, defining “geometry” as the study of spatial order through the measure and relationships of forms becomes understandable . Remember the words “study,” “order,” “measure,” and “relationships” as we proceed. Geometry, as Masonry, requires one to think, to engage one’s brain, to always question and seek more light. This is a helpful distinction between Masonry and many religions as sometimes religions ask followers to turn off their brains, stop questioning, and fall in line.
From it’s earliest days, geometry shed light on the order of the world. Some would say it sheds light on how God “built” the world. In this sense, geometry leads to a better understanding of our physical environment. However, it didn’t take ancient geometricians long to find situations where geometry put man in his place relative to God. Many geometric relationships are easy to understand and work very well into whole numbers and nice, reasonable functions. However, a few geometric relationships quickly show man the limits of his knowledge, and give us a glimpse of God.
These relationship include:
1. The square cut by its diagonal: Square Root of 2
2. The Vesica Piscis: The Square Root of 3
3. The Square root of 5
4. The “Golden Section:” Phi
5. The Circular relationship: Pi
Writing and interpretation of these numbers literally fills volumes – written from the dawn of man to present day. It’s not my goal in this brief introduction to show how these ideas have manifested in architecture and religion through the ages – that’s part of the fun of discovery. But I will share the kernel: all these numbers are non-repeating, never-ending decimals. They are “irrational” numbers. We humans can’t nail them down, yet these relationships form the very heart of nature; the nautilus-shell spiral, the harmonics of musical scales and octaves, and arguably the most important: the proportions of the human body which the Bible tells us is “made in God’s image.” When we study these numbers, we touch both the finite and the infinite at the same time. These numbers never die – they are the earthly manifestation of eternity.
When understood in this way, geometry is the balance and combination of science and spirituality. It’s a metaphor of universal order. As Miranda Lundy states: “Sacred Geometry charts the unfolding of number in space. The basic journey from a single point, into the line, out to the plane, through to the third dimension and beyond, eventually returning to the point again, watching what happens on the way.”
Our Masonic work is a similar journey from the point that is each of us, to the lines that are the relationships between ourselves and our brothers, families, and neighbors. We move into the third dimension as we effect our community, and into a forth dimension as we make a difference over time. In geometry and Masonry we find a visual vocabulary for understanding and building a sense of personal balance. In geometry and Masonry we find a way to visualize how we fit into the world, one working block at a time.
In 1813 John Playfair, Professor of Mathematics in the University of Edinburogh wrote the following in his preface to a wonderful reprinting of Euclid’s Elements of Geometry:
“To all this it may be added, that the mind, especially when beginning to study the art of reasoning, cannot be employed to greater advantage than in analyzing those judgments, which, though they appear simple, are in reality complex, and capable of being distinguished into parts. No progress in ascending higher can be expected, till a regular habit of demonstration is thus acquired; it is much to be feared, that he who has declined the trouble of tracing the connection between the proposition already quoted and those that are more simple, will not be very expert in tracing its connection with those that are more complex; and that, as he has not be careful in laying the foundation, he will never be successful in raising the superstructure.”
One would be hard-pressed to find a better summation of the Masonic work of becoming better men.
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About Kevin
Kevin E. Houchin is an attorney, artist, teacher, author, and principal of
Houchin Consulting, PLLC, a copyright, trademark, arts & entertainment,
business development, and branding firm located in Scottsdale, Arizona.
To schedule Kevin for keynote speeches, workshops, or seminars, call 970.231.2426
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kevin@kevinhouchin.com.