The Golden Ratio is inextricably linked to a numerical series known as the Fibonacci numbers [sequence]. Named after the 13th century mathematician credited with introducing the Arabic numbering system to Europe, the series of numbers is formed by adding the previous two numbers to produce the next. This results in the following eternal string: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...ad infinitum! Amazingly, if we divide each number in the series by the number before it, we discover that the result gets closer and closer to the Golden Ratio the further we progress into the series. Thus, the Fibonacci series expresses the Golden Ratio. While by no means a constant of nature, Fibonacci numbers appear regularly in the forms of Sunflower seed heads, pine cones, and other plants, as well as in the aforementioned nautilus shell. They can be observed in the growth patterns of leaves, in the family tree of honeybees [sacred in ancient Egyptian culture], and even in the syllabic patterns of ancient Sanskrit poetry. Interestingly, Fibonacci is not thought to have discovered the series himself, but to have learned it from the same Indian scholars who taught him about Arabic numerals.
The Human Connection
Our two hands (with three bones to each of their five digits) express "Phi" in the ratios between the length of each of the bones in a single finger. The belly-button also divides the height of the human body into the Golden Ratio. Even more startling, a single DNA molecule measures 21 x 34 angstroms. 21 and 34 are neighbors in the Fibonacci series, thus the ratio between them is 1.61904..., very close to "Phi." In the Vitruvian Man, Leonardo da Vinci famously illustrated the pentagonal shape of the human body when arms and legs are outstretched. Whether it is because the Golden Ratio and the Fibonacci series are so omnipresent in our experience, or because our physical forms are built according to these mathematical patterns [ask your dentist why he/she uses a Fibonacci gauge when forming replacement teeth - yes, it's because the Golden Ratio is in the structure of our mouth as well], we have a visceral reaction when we encounter images that express these forms. Our brain innately recognizes these forms at the subconscious level. For this reason, Sacred Geometry can be considered a kind of Universal language, perhaps the most universal the world had even known. It contains symbolism much more powerful than any written language.
As we have seen, Geometry is deeply rooted in our body, cell memory, and consciousness. Therefore, concentrating on Sacred Geometric shapes can bring a lot to the surface to be healed. Sacred Geometry can be used to help you find insights into your patterns and what emotions influence them. You will find answers to questions like: Who are you? Where are you now? Where are you going?
Here is why I believe Geometry is a central teaching in our Masonic tradition: by meditating on Geometric shapes and seeking knowledge of and from Sacred Geometry you can activate and awaken the inherent [ancient] Wisdom encoded within you! You can awaken that spark ("Light") of divinity that resides in you. This is what we "desire most" because it directs us to where our spirits originated; The Great Architect of the Universe!
The complex Sacred Geometric forms resonate with our subconscious. Since humans are built according to a certain geometric model, including our DNA, this geometry has a healing effect on our body and mind. The unlocked internal codes support us in realizing our positive personal goals and processes of necessary change. They are here to stimulate and awaken us [think Bach's "Sleepers Awake."] .
Music itself has a profound relationship to Sacred Geometry. There is much to be discovered about the relationships between sound, light, and geometry, which if you recall, are all used in Masonic ritual. But that is for another article! Until then, go online (Google, YouTube, etc.) and search the term "Sacred Geometry." You will begin a journey that will awake and enlighten you more than you ever dreamed and inspire you to take our shared Masonic commitment ever more seriously.