The history of art provides a rich storehouse of human visual expression stretching back into the early days of humankind. Architecture, sculpture, and painting resonate with the energy of human creativity. Within this visual record there is no shortage of examples that are capable of engaging our imagination by offering insights into the life-affirming beliefs of the people who produced them. Among the insights and beliefs that have been incorporated into humankind’s visual record, none is more intriguing than the tradition surrounding the transcendent capacities of a unique proportional relationship. This proportional relationship is most commonly called the Golden Mean.
When and where the notion began that a specific geometric relationship could shed light on cosmic mysteries is somewhat unclear. Although the study of geometry is generally considered to have been developed in Alexandria by Euclid in the 4th century BC.
The Golden Mean can be mechanically created by combining a circle and a square. The only tools necessary are a straight edge and a compass. Absolute precision with the forms is unnecessary as it is unattainable. We need only a close visual approximation to trigger an intuitive understanding of this unique internal relationship. The Golden Mean is a unique proportional relationship in that it generates an infinite progression of identically proportioned line segments or rectangles. Because of this self generating capacity it has often been referred to metaphorically as a “visible echo of the infinite” or a door to infinity.
The Golden Mean is represented by the Greek letter (Phi) in homage to the Athenian sculptor Phidias (ca480 – 430 BC) who achieved fame as the designer of monumental statues of the Greek gods. The numerical approximation of the Golden Mean is generally expressed as the smaller unit being 0.6180 of the larger unit of 1, or the larger being 1.6180 of the smaller unit of 1.
Pythagoras, a Greek mathematician and mystic from the 6th century BC was the first to openly declare that the essence of all things was accessible through simple mathematics.
When looking at the great pyramid of Giza, half of it’s base is 0.6180 of it’s sloping side. This proportion establishes the visual character of the elevation of the pyramid and can be interpreted as a proportional technique for bringing the eternal (infinite) into the realm of space and time.
There are other ancient monuments that also seem to anticipate the Greek fascination with Phi (The Golden Mean) as a vehicle for exploring the riddle of the cosmos. Curiously there are numerous earthen, wooden, and stone monuments in Britain whose internal alignments suggest that they were designed to function as astronomical observatories, with major emphasis on the movement of the sun. The best known of these monuments, Stonehenge, was built in England between 3100 and 1900 BC. The first and third stages of the monument’s design are laid out in accordance with the proportion of the Golden Mean.
As with the Great Pyramid, this combination of astronomical precision and mystical geometry coexist in what has proven to be one of the most powerful and intriguing visual messages from the distant past.
Solomon’s Temple was constructed in Jerusalem. Here again we come across circumstantial evidence of a belief in geometry as a tool for revealing a transcendent reality. The main hall is of particular interest because a rectangle formed by two adjacent squares contains a subtle but precise expression of the Golden Mean.
Pythagoras taught that number was the essence of all things and that one can arrive at an understanding of the dynamic force of the universe by using small numbers. He taught that the divine (infinite) is not to be discerned in the multiplicity of forms that are around us, but in a unifying principle running through these forms. He believed that the divine is manifest in both shape and number. Pythagoras believed that a temple or a sculpture could be proportioned in accordance with the cosmic dynamics and resonate with the presence of the divine.
The Parthenon was constructed between 447 and 432 BC. This temple, designed by Ictinus and Callicrates, was dedicated to the city’s patron goddess, Athena. Unlike the Great Pyramid, Stonehenge, and Solomon’s Temple, the design of the Parthenon grew out of the historically verifiable tradition of Pythagorean ideas that had, by this time, thoroughly infiltrated Greek thought. The Parthenon was described by its designers to be an embodiment of the sacred principles of the Golden Mean.
Plato, born in Athens to the generation that constructed the Parthenon, is considered to be one of the most important thinkers of Western culture. Central to his philosophy was the Theory of Forms, also known as the Doctrine of Ideas. It is based on the rational notion that abstract concepts have more reality than do physical things. Plato was influenced by Pythagorean thought and not surprisingly made the study of mathematics central to his educational system. In Plato’s Timaeus, his Pythagorean roots are clearly revealed as he describes his search for counterparts of the infinite in the realm of space and time. With his search for divine truth so clearly stated, there can be little doubt about the mystical implications when he calls Phi the most binding force in the universe.
Roman monuments and temples frequently conform to the proportion of infinite generation. Roman belief in the mystical implications of geometric relationships is documented in Ten Books on Architecture by the 1st century BC Roman architect Vitruvius.
There are colourful tales of a secret brotherhood of architects and stonemasons preserving mysterious ancient wisdom. Secret brotherhoods are difficult to verify, but it can be argued that the present-day Order of Freemasonry was at one time just this sort of secret organization. Even though Freemasonry is not directly affiliated with either Christianity or Judaism, its oral tradition claims it to have descended directly from a Phoenician architect named Hiram, who is thought by Freemasons to have designed the Temple of Solomon. Regardless of the role of the Secret Brotherhood of Masons during the Middle Ages, it is clear that the Golden Mean appears countless times throughout medieval church architecture. Haga Sophia in Istanbul (sixth century) and St Mark’s Cathedral in Venice (twelfth century) are but two examples of widespread use of the Golden Mean.
The Golden Mean was well understood in the Renaissance and the frequency with which Phi appears in the art of the period clearly suggests that it was embraced as an expression of a mystical truth.
Following the period of the Renaissance, much less is written about the spiritual tradition associated with the Golden Mean. The use of the proportion itself, however, continues uninterrupted as an effective formula for arranging elements in an artwork.
The Pentagram contains multiple Golden Mean relationships in its linear segments. The pentagon at the center of the pentagram can be used to generate an infinite number of smaller pentagrams. A pentagon can be inscribed around the outside of the large pentagram and that in turn can generate a larger pentagram, an infinite number of smaller and larger pentagrams and pentagons, the “window on infinity”, was a sign of good omen.
Other examples include the reverse side of the dollar bill which is comprised of two Golden Mean rectangles that overlap in the center. Michaelangelo’s, Creation of Adam from the Sistine Chapel, Vatican. Michaelangelo uses The Golden Mean for composition and balance by placing the spark of human enlightenment, the height of the dramatic action precisely at the point of infinite (divine) progression.
A logarithmic, equiangular spiral moves outward at a constantly expanding rate that duplicates the geometric progression of the Golden Mean. As with Fibonacci numbers, this progression generates an infinite series of identically proportioned segments or modules. The proportion of infinite generation can be found in the swirling arms of hurricanes, in every self-similar progression of the randomly generated images of a Mandlebrot set (chaos theory), and in the structure of our Milky Way galaxy.
– Drawing from Observation, by Brian Curtis (second edition)