Squaring the circle

Carl Jung is credited with introducing the mandala to the West

…The sky is round, and … the earth is round like a ball,

and so are all the stars.

Black Elk Speaks

In the West, both the circle and the square shape have been, and are, used to cast a horoscope. Before we discuss why one is chosen over the other, I thought it would be interesting to detour into an explication of archetypes. Both the square and the circle are more than geometrical shapes; they also contain powerful symbolic significance.

In her book Signs of Life: The Five Universal Shapes and How to Use Them (Arcus Publishing: 1992) cultural anthropologist and counselor Angeles Arrien provides a comprehensive overview of what five different shapes (circle, square, triangle, equidistant cross and spiral) symbolise for those of us in the West who have imbued these mathematical planes with mythological and metaphorical meaning.

Arrien states that because these shapes are found in every country, their meanings are based on multicultural themes and patterns that influence us all. In every culture, the circle represents “wholeness and the experience of unity.”

From Native American medicine wheels to Hawaiian Menehune rings, the circle remains humankind’s primary symbol for unity and stands for the mythic theme of individuation. Mythologist Joseph Campbell reminds us in his book The Hero With a Thousand Faces, that the myths most associated with the process of individuation are the stories every culture tells about its heroes and heroines… [t]he journey of the hero or heroine is a universal myth found in the lore of all cultures… [a]ll heroic myths describe the process of individuation and the reclamation of the self (pp. 31-33).

Avebury from the air. Older than Stonehenge.

The square, augmenting the message about the idea of the self found in the circle, symbolises stability, solidity, and security. The act of drawing a square mirrors perfectly the process of constructing a foundation, says Arrien.

Wherever the square appears in art, and whenever examples of foundation metaphors are expressed in myths, the process of stability is being reinforced. In many cultures, it is believed that the four points of the square symbolise the foundation of life itself. Examples of foundation metaphors found in myths include the four seasons, the four elements, the four directions, the four Gospels, and the four noble truths of Buddhism.

Most acts of creativity generate stability and security, according to Arrien. “When solid foundations exist, creativity, responsibility, and authenticity are usually present” (65).

Four Evangelists, Book of Kells

The geometrics of the astrological chart create various patterns. These patterns begin with either the concept of the circle or the square and what it symbolises to you, your response to each shape.

Although the shape we use to draw the chart in might seem a simple matter of inheriting the Hellenistic ideal of the heavenly bowl over our heads, once you begin to add meaning found in the shape itself, you begin to see that the ideas lying behind the horoscope are actually much more complex, since the horoscope is thought to be unique to each person and therefore focuses on what the “self” means. In some sense, then, the horoscope is the earliest evidence we have that humankind has always been fascinated by who and what we are, what we’re capable of, what we aspire to, and what will happen to us.

Interestingly, the circle, with its emphasis on wholeness and connection to Platonic ideals of  the transcendental, can be seen to represent the soul. At the same time, the square shape would represent the body, in its connection to material reality. We see this dichotomy in the relationship between Platonic and Aristotelian thought, when Plato argues the supremacy of the immortal soul, existing a priori, not dependent upon the material form of the body; in contrast, Aristotle contends that the soul can only exist in a material body, and that the one is not possible without the other.

Two of the four heavenly kings

The shapes we choose, then, can be seen as potentially revealing of a deeper purpose, one based on ancient myths, beliefs, and representations about the self. The circular astrological chart does not only represent the idea of a circular heaven above us, constantly moving, with the earth in the center; it also implies wholeness.

The square astrological chart does not only represent early attempts to capture mathematical planes, reflecting the four cardinal points, the ultimate definition of ‘where you are now.’ It is also a reflection of the idea the four points represent, the mathematical division of one’s life into defined space and time.

Ascendent, medium coeli, imum coeli, descendent: these were the four markers of one’s life, and these four points gave the astrologer the foundational structure—the square’s strength—to point to moments in time, reflected in the movement of the heavens.

But before we can create the astrological chart, we have to have the fundamental concepts that underlie the chart’s reality. The horoscope is a convergence of time, space, and movement of the heavenly bodies. What connects time and space and tells us precisely where we are is the gnomon, the upright stick or spear stuck into the ground, providing a shadow, a direction, showing us true North, what our latitude is; in other words, locating us at a specific place and time.

Without the gnomon, we cannot square the circle,” marrying astronomical cycles of time, marked by the moving shadow of the sun, with the square of space, the four cardinal directions and solstice-equinox “corners” of Earth. It is with the gnomon, and the shadow it casts, the circle it draws on the ground, and the architecture that it inspires, that we can begin to think in terms of radius, and then finite divisions of a circle, leading to the ability to draw a round horoscope. 

A crude circle resembling a clock face divided into quarters, with 12 sets of Greek letters around the outside