Mathematical education is all about quantity, for numeracy is as important as literacy in our Western world of clocks, commerce and computers. Yet mathematics and geometry are usually devoid of any reference to their inherent qualities. The deeper spiritual aspect—studying the repeating shapes, forms, symbols and patterns in nature—is all but lost in our work-a-day world. We need to bring the traditions of “sacred number” and “sacred geometry” back into view, and what better way to begin than with vision itself.
Number One
The ancient Greek mathematical philosophers viewed the number one as unity, a wholeness that provides a divine order to the cosmos. The circle, which is constructed from a central point, is the sacred geometric representation of this wholeness, the One that forms the Many.
Circular shapes abound in nature. Of particular significance is the circular shape of the human eyeball. Ralph Waldo Emmerson wrote, “The eye is the first circle, the horizon which it forms is the second.” Other circles in the eye are the iris, the colored portion, and the pupil, the black area which dilates and contracts in response to changing light stimuli.
Deep within the eye, unbeknownst to an observer, the point and the circle play an important role in how we visually perceive the world. The inside back portion of the eye (the “retina”) contains numerous light receptors called “cones” packed tightly in a very small center area called the “fovea centralis.” The cones gradually diminish in density as the distance increases from the fovea centralis. The cones are virtually non-existent at the outer circumference.
The cone distribution means that we see the clearest in the central point of our sight. Objects in the periphery are less clear, so the focus is different than that captured by a camera. Because the cone distribution in the retina follows a geometric pattern similar to the energy distribution in a concentric wave, I call it “concentric focus.” A principle of healthy vision is awareness of this concentric focus. Attempting to see everything clearly at once is a strain that lowers the vision.
Also within the retina are receptors called “rods.” It is believed that the rods sense movement in our peripheral field. The rods are distributed opposite to the cones, since the rods are non-existent in the center and gradually increase in density towards the periphery. That’s why something moving in your peripheral field of vision can abruptly grab your attention.
Another sacred principle of the circle is the continuous rotary motion of cycles and rhythms. With eyesight, oscillating rhythms manifest in several ways. One of the most obvious is the continuous blink reflex. Our eyes also respond in cycles by closing at night and opening in the day. During sleep, the eyes have an alternating motion called rapid eye movement (REM), and when awake, they have numerous subconscious micro-movements—some vibrating at the frequency of a strummed guitar string—to key in on objects and maintain focus. The motion is contrary to that of a still camera, for without the continuous rhythmic activity, objects would quickly fade into blur.
Number Two
The root word for “nature” means “to be born,” and the number two emerges through a birth-like process. This process begins symbolically as the circle divides and replicates itself—just as a living cell does. The geometric representation is two circles of the same diameter each having their center points touching the circumference of the other. The One projects forth as a reflection of itself and a “true” mathematical line is created from point to point.
The sacred principle of number two is polarity, whereby the line forms a tensile link between opposite poles. Paradoxically, there is both a separation and an attraction that binds the two, yearning once again for wholeness. It’s the yin/yang principle of Taoist thought. The human body has a left side and a right side, a feminine side and a masculine side, an intuitive side and intellectual side, and so on. Not only does each eye see things from a slightly different angle, the modern left brain/right brain theory suggests they are extensions of the brain’s two hemispheres.
The concept of “two” in eyesight has further spiritual significance beyond the apparent. In Plato’s Timaeus, eyesight is described as a two-way process; the eye mediates between the inner realm and the external world of objects. The fire of the soul was said to emit a gentle light from within, flow through the eye and meet the outer daylight. Like falls upon like, coalesces and forms the perception of sight. In this philosophical view, the eye acts as a portal, the proverbial “window of the soul.”
The portal is actually a symbol that arises geometrically from one circle beginning to replicate into two. The fish-shaped vesica piscis is the area of overlap between the linked circles. It has been venerated throughout history by various cultures and nations and dates back to pagan and mystical religions. The early Christians considered it the link between heaven and earth, a bridge between spirit and form. Consequently, much medieval art symbolically depicts Christ within the fish-shaped area. In ancient architecture, particularly in cathedrals and holy temples, the vesica piscis was used extensively in the design of doorways. They were portals which permitted entry from the mundane world of reality into spiritual space.
Applying the metaphor of a portal to the eyes, one is immediately drawn to the distinct vesica piscis shape which the upper and lower eyelids produce. Within the eye itself, the same pointed oval shape is found when studying the anatomy of the lens from a side view. The lens is the part of the eye where light rays emitted from an external object refract in such a way to form an image on the retina.
The inner and outer aspects of eyesight are linked, as the mind and emotions have a great impact on how well we see. For relaxed vision, perhaps a good mental image is to imagine the gentle light of your soul meeting the external light in the vesica piscis of your eyes.
Number Three
Our two eyes work together in harmony to fuse a single image. An outcome of this reunion is the emergence of the number three. Three dimensional (3D) vision provides depth to our world view, a level of understanding that goes beyond a two dimensional (2D) flat surface.
The triangle, which is formed within the vesica piscis, is the sacred geometric shape for number three. An object in our sight is the third point midway between the eyes, the vertex that balances the opposing views of each eye’s unique perspective. The ancient philosophers valued the triad, assigning it qualities such as piety, friendship, harmony, peace, justice, temperance and virtue. It is the symbol of wisdom, for living prudently in the present requires learning from the past and planning for the future.
The triad principle is also evident in a metaphysical sense. Mystics describe our human constitution as a three-fold constitution—body, soul and spirit. A “third eye” between the brows is said to be the seat of the spirit. Seers have supposedly awakened the eye of the spirit, resulting in clairvoyant vision. The third eye, which remains dormant for the majority of people, may also be responsible for triggering hallucinations and out-of-body experiences. The pinecone shaped pineal gland, located between the brain’s two hemispheres, is claimed to be the location of the mysterious third eye.
Awakening the third eye may be highly elusive, but re-awakening a diminished sense of 3D vision is more easily attainable. Prescription glasses provide immediate artificial clarity, but they don’t restore eyesight to a normal state. The lenses, although curved to help light rays converge properly inside the eye for better acuity, act as a barrier. Colors are less intense through the glass and objects are distorted in size. For people wearing glasses for distant viewing, the lenses diminish 3D perception. The condition is reversible, for people who improve their eyesight naturally invariably notice a marked improvement in their ability to see 3D again.
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Mathematics and geometry are applied with efficient precision in our technological era. A prime example is the science of optics, where good vision is reduced to purely a numerical term, 20/20. Ironically, as the vision industry has grown and prospered, we’re collectively seeing worse, not better. The incidence of vision difficulties in North America signifies the imbalance. Fewer than three percent of children are born with visual defects yet, as they reach adulthood, nearly two thirds will become dependent on prescription eyewear. Non-industrialized nations are virtually free of such widespread vision problems. To help restore a quality outcome, perhaps it’s time we return to the spiritual teachings of sacred number and sacred geometry to understand what really “counts.”
Doug Marsh is the author of Restoring Your Eyesight: A Taoist Approach, a natural vision improvement book published by Inner Traditions/Bear & Company. His website is www.taosight.com.