For a long time squaring the circle has amused and puzzled people. Mathematical demonstrations have been attempted without success, yet the symbol continues to live. A square is a rational geometrical shape while a circle is an irrational one. A square's perimeter can be precisely determined; it is four times the length of a side. For a circle the perimeter is the diameter times pi, an irrational number. Mathematically, nature is irrational; only we humans seek neat and precise rational units! Since ancient times the squared circle has symbolized the union of two incommensurable elements. It can be found as a fundamental design in the ground plan of many churches where it symbolizes the mystical marriage of heaven and earth.
The vesica piscis, vessel of the fish, is another ancient symbol for the sacred marriage, and it was used in the construction of churches. To construct the vesica piscis, simply draw a circle and its diameter. Then using the diameter as a measuring unit (it becomes the radius of the new circles), draw two circles whose center is at the point where the diameter and circumference of the first circle touch. A straightedge and compass are all that one needs to try these experiments. The following illustrations can be used as models. And while constructing these figures, meditate on the symbolic meaning.
figure 1
The fish is the curved shape bordering the original circle. Many geometrical forms can be constructed from this design.
figure 2
figure 3
Figures 2 and 3 show how earth and heaven are wedded together. Figure 3 symbolizes the sacred marriage. The cardinal axes (cross of directions) link the limitless cycle of heaven (circle) with the earth (square). Many people believe that the principles of proportion constitute a universal language that can be understood at any time in any galactic location. This space-time language may be the way we will communicate with sentient beings who live in other parts of the universe.
figure 4
Figure 4 shows the construction of a root three rectangle. The proportion is 1:1.732. Where the diagonal and the line perpendicular to it meet is the fish's eye. By touching the rectangle's side, the perpendicular line makes a unit which divides the rectangle into three equal parts.
figure 5
Figure 5 illustrates the way a square, rhombus, and hexagon can grow from the vesica piscis. The two equilateral triangles represent cosmic duality as seen in a flower and its root. During the Renaissance Albrecht
Durer worked out a practical solution to the problem, which he used in his art works. In The Painter's Secret Geometry Charles Bouleau describes how Durer and, other artists used the principles of proportion in designing their art.
figure 6
Figure 6 portrays the union of pentagon and hexagon. Both geometrical shapes have their own symbolic meaning. The number 5 represents the microcosm and human beings. Leonardo da Vinci's famous drawing of a human within a circle is based upon the five-pointed star and the golden section, phi or 1.618. The number 6 represents the macrocosm and is associated with natural forms like snowflakes and cells of a honeycomb. The marriage of five and six signifies the mystical union between humans and the cosmos.
The union of the king and queen can also be signified by one's hands and feet. Looking closely at the front of our hands, we notice that the lines on one hand differ from those on the other. The ancient discipline of palmistry is now gaining some respect from modern medicine. In A Doctor's Guide to Better Health Through Palmistry Eugene Scheimann shows how a reading of the hand will produce medical data. He considers the hand a computer, which prints out data about one's mental and physical health. Each finger is linked to a specific organic system of the body: the thumb to the general state of health and vitality; the index finger to the respiratory system and the stomach; the middle finger to the liver and intestines; the ring finger to the kidney and blood circulation; and the little finger to the feet and sexual glands.
Looking at the drawing of a hand , we see that the traditional seven planets have their own locations. Jupiter is associated with the index finger; Saturn with the middle finger; Sun with the ring finger; Mercury with the little finger; Venus with the ball of the thumb; Moon with the heel of the palm; Mars with positive and negative centers.
The hand is a microcosm connecting the physical, psychic, and spiritual levels. The symbols provide vertical axes for linking these levels. Even the foot is a microcosm. Like the hand, it has areas linked to specific organic activities. The drawing of the foot shows the location of a few bodily organs; actually, all of the bodily organs have their own reflex area on the foot. Gently massaging the foot relaxes and strengthens the connected bodily organ. For example, massaging the throat area beneath the big toe will help rejuvenate the throat. The physical process at work is similar to acupuncture.
The alchemical marriage is represented by the love embrace of the king and queen. When the two power poles are connected, energy flows between them. The product of the two, the result of the proper mixing, is the child of light. It is the philosopher's stone transformed into a higher state. The basic material for the alchemical work is often called the philosopher's stone. This basic material goes through several processes, and when it passes by the final stage, if all has gone well, the material becomes the child of light. The total process, from beginning to end, is called the magnum opus, the great work.
The story of St. Christopher illustrates this idea very well. St. Christopher sets out to find and worship the greatest power. Once he finds this power, he will become its servant. After traveling far and wide, St. Christopher enters the realm of a great and powerful king. He becomes a member of the king's retinue and serves the king faithfully until one day, traveling along el camino real, they come upon the devil's sign. The king halts his company. Frozen and frightened, he will not proceed. Turning his company around, the king rides back to the safety of his castle.
St. Christopher, realizing that there is a power greater than the king's, leaves his service and goes in search of the devil. After many adventures he finds the devil and enlists in his service. One day while journeying through the countryside, they come upon the sign of the cross. The devil responds in much the same manner as the king. He cannot proceed; he must go back.
St. Christopher then goes in search for the greatest power. Finally, he accepts employment as a ferryman, helping people across a river. One night the bell rings, announcing that someone needs assistance crossing the river. St. Christopher finds a small child standing by the bell. Placing
the child upon his shoulders, he starts to carry him across the river. As they proceed, the river current becomes swift and strong. St. Christopher feels a heavy burden upon his shoulders and slowly sinks lower and lower into the water. Struggling against the raging torrent and increasingly heavy burden, St. Christopher finally reaches the other shore and places the child safely upon the ground. From this moment on St. Christopher, as his name means, serves the greatest power in the cosmos. And in passing we can note that, unlike Hermann Hesse's story about Siddhartha, St. Christopher lets the child go--he does not try to retain him. As William Wordsworth once framed it: "The child is the father of the man." This is what Juliet in Federico Fellini's great film Juliet of the Spirits learns finally.
This story holds an honored place in alchemical lore. For on one level of interpretation, we notice parallels to the ideas about the life force. St. Christopher is, of course, a Christian symbol, yet one that other traditions can understand. For it speaks about the journey of life and provides
clues for a successful trip.
In the poem Odyssey Homer recounts the wondrous adventures that Odysseus and his men have on their way back to Ithaca. Hidden below the surface of these marvels are dangers and deadly traps; in fact, Odysseus is the sole survivor, arriving home ten years later. As a symbol the journey, like the quest, expresses multi-levels of meaning. Early in their journey Odysseus and his men encounter the land of the lotus eaters, who feed on a strange plant that causes forgetfulness. Later on, they sail by the island of sirens, who with their melodious voices beckon unwary travelers to land on their reef-protected shores. If we see Odysseus' journey as an allegory, we can enter the mystical dimension and understand the purpose and goal of our life.
In the first century A.D. an important religion was born at the same time as Christianity. This was the Gnostic religion, which in two hundred years gained enough popular support to give Christianity a serious challenge. Although there were many different Gnostic denominations, some of which were Christian, they all shared a set of common beliefs and symbols. The name "Gnostic," which is the key concept of the theology, means knowing or knowledge.
Several Gnostic symbols are still relevant today. One important symbol is the alien, who, as a stranger on spaceship earth, suffers from loneliness and has great difficulty comprehending the conventional lifestyle of human society. Aliens can ease their suffering by becoming "children of the house," but by doing so they become estranged from their origin. They can become loyal members of the garbage dump but only on penalty of losing their soul! Tied to the alien symbol is another one that describes a different world or the beyond. The aliens come from another reality and are only sojourning on spaceship earth. At this point we can raise the question of their origin: where is their home? Is it located in our galaxy or in another dimension?
The inherent duality assumes the idea of many worlds, for if two separate realities exist, perhaps a multiplicity of them forms the cosmos. Such a multiplicity would form a labyrinth of interconnecting realities which are all contained in a larger universe. If such a universe exists, the aliens would need Ariadne's thread to find their path back home. Wandering about the maze of realities, these strangers encounter many traps from which escape is difficult but not impossible. The multiplicity of worlds is both spatial and temporal, so they will wander through different spatial settings and for ages or aeons before they reach the journey's end.
An ancient symbol pictures the universe as an onion; the universe too has many layers. All onion farmers know that nematodes can destroy their crop. What if we add nematodes to our image of the universe? These cosmic creatures will gnaw holes through the onion layers. Astronomy has found something analogous in the universe, but only the holes have been discovered; the hungry creatures have not been sighted. Two kinds of holes, black and white, have been identified. Black holes pull energy out of the universe while white holes emit energy. If we imagine the universe as one onion layer, we can visualize many universes making up the onion. Perhaps, black and white holes are energy exchanges between universes, and they might form corridors through the many layers.
Let us add time to the picture. The layers may not have the same time zone or even the same number of temporal dimensions. In some languages like English time is conceived as a 1D line which has three parts--past, present, and future. Modern science uses this concept of time. Imagine yourself in Flatland as a 2D figure. Would your time sense differ from that of a 1D or 3D person? Is there a connection between spatial and temporal dimensions? If the number of spatial dimensions is increased, perhaps time would also add dimensions. See if you can imagine 2D or 3D time!
Another important and universal symbol is the serpent. In the Garden of Eden story it acts as tempter, but it is not actual evil. For Christians the serpent is associated with Satan only in the Book of Revelations. In fact, Jesus tells his followers to be as wise as a serpent. (Matthew 10:16) In other cultures the serpent is beneficent. In India today many rural people still venerate the cobra, and in China the dragon can be seen as an oversized serpent. The ancient Babylonian epic Gilgamesh treats the serpent as a symbol for everlasting life, for it is the serpent which steals the tree of life from Gilgamesh. By shedding its skin, the serpent symbolizes rejuvenation and the healing powers of nature.
Hermes' caduceus, the emblem of the American Medical Association, has two serpents intertwined along a rod. Here the serpents represent the active power. The image of Ouroboros, the serpent biting its tail or sometimes two serpents biting each other's tail, signifies the dormant state of power--potency. If we can make the connection between serpent power and human life, we can understand why Hermes is the patron of alchemy and why Eastern sages speak about Kundalini. When modern science cracks open its shell and steps into the world of nature, it will then experience the wonder and awe which human tradition speaks of. When modern science finally taps the hidden recesses of life, its tree of knowledge will commence blooming. In the waste land nothing blooms and will not until the king is healed. Healing means that the opposites are harmonized and that the dual process of coagula and solve have been accomplished. Once modern medicine views the body as a living entity rather than as a corpse that is dissected in class, then it will be prepared for the awakening.
Hermes' caduceus symbolizes nature's renewal power. The two serpents are opposing parts of the serpent power, which is called Kundalini in India. The staff symbolizes the cosmic vertical axis, the tree of life, and our spinal column. The wings suggest the brain with its two hemispheres,
symbolize the thousand petalled lotus, and denote the quality of volatility. When we peek behind the veil, we see that Hermes' caduceus is a Western image akin to Kundalini. Both of these involve a process of transformation and have a shared cosmology. The Indian system of chakras illustrates the common bond. A chakra, which literally means wheel, is a rotating energy field. Every human being has seven major chakras and several minor ones. Two important minor chakras are located at the wrists and ankles; this is where the binding begins. Look at the drawing of the young woman and notice the six chakras that are plainly illustrated.
The first is at the base of the spine. Visually, it appears to have four spokes radiating from a center. The energy flows easily to the genitals, but the spiritual challenge is to direct
it up the spinal column. This is where the Kundalini energy begins its journey upward.
The second chakra, which has six spokes, is located at the genitals. Modern Western thought, instead of using the genital chakra, places the spleen chakra under that image. The function of the spleen chakra is to absorb vital energy from the environment. Tradition has it that trees like the pine and eucalyptus release a lot of excess prana, which they cannot use, and the energy can be picked up by human consciousness. Memory of astral travel is increased when the spleen chakra is developed. According to the Tibetan tradition, though, the energy of the genital chakra, dangerous as it may be, can be used to push and sustain Kundalini on its upward path.
The third chakra is found slightly below the navel; it can be drawn with either eight or ten spokes. When it blossoms, the consciousness of astral influences awakens, like those associated with particular locations.
The heart is the fourth chakra and it has twelve spokes, which glow with a golden color. Development of this chakra increases one's instinctive and intuitive understanding. Let us notice here that the heart symbolizes not only sympathy and feeling but also understanding.
Located at the throat, the fifth chakra has sixteen spokes, which shine with a bluish silver tone. The awakening of the throat chakra gives power for acute hearing on the astral levels; this hearing is associated with sounds of an unusual quality. Here we discover a clue about the language of the birds.
Continuing upward, we find the sixth chakra, which has 96 spokes, appearing in the middle of the eyebrows. Commonly called the third eye, this chakra seems to be divided into two halves, one a rose-red and the other a purplish blue. The colors refer to the two ends of the visible spectrum and to the royal marriage. The sixth chakra gives one the power to see astral objects and to magnify vision.
The final chakra, the mystical seventh, is positioned on the top of the head. It is illustrated in the drawing by the oval formed by the head and neck of the two serpents. Although this chakra is called the thousand petalled lotus, it actually has only 960 spokes. The complete awakening of the seventh chakra signifies the perfection of all faculties. Once the lotus chakra is fully opened, one is able to leave the physical body and re-enter in full consciousness. The wise say that the roots, embedded in heaven, shall give forth the tree which does blossom in the world.
The sleeping serpent at the spinal base is awakened, and energy slowly moves up the spinal column. When all the chakras are vitalized by this energy--and their sequence of vitalization differs according to the individual--the thousand petalled lotus unfolds and the child of light is born. All traditions speak of the many dangers that can destroy the unprepared if the process is not properly performed.
All of the symbols that we have discussed so far speak about strange and magical powers, which human tradition has conveyed for thousands of years. These powers have been given the name ESP (Extra Sensory Perception) by modern scientists, yet the name may be inaccurate. A better label might be USP (Unused Sensory Perception). It is well-known that humans use only a small portion of their brain capacity, something like ten percent. What is the purpose of the remaining ninety percent? Why did the human brain evolve to its present design? These are questions only for those imprisoned in their closet with their word processor. Many people today are inspecting their mind and discovering its potential. One knows the fruit by eating it. "And the man shall know the woman and the woman shall know the man." What other way is there?
In Aboriginal Men of High Degree Adolphus Elkin describes the strange and magical powers of the Australian shaman. One of these mental powers is thought transference, which occurs by intense concentration and visualizing. The shaman can pick up the mental content of others who are either in the immediate vicinity or at some distance. The mental content includes both present images and past memories. This telepathic power, when extended and amplified, is called the "strong eye"; it allows the shaman to see the spirit or soul of those either living or dead. Elkin mentions that the "strong eye" power is useful for solving a crime because the actual event, including the criminal, can be "seen." Another strange power is the "magic cord," which is used to travel through space, often in an upward direction. This power emanates from the navel chakra and allows the shaman to perform standard magic tricks like creating illusions and making things, including himself, disappear and reappear.
In Foundation's Edge, the fourth book of the series, Isaac Asimov dramatizes powerful mental abilities at work in the cosmos. Political power in the universe is divided between two opposing groups, the First and Second Foundations. Both groups share a common goal, which is to follow a plan given to them thousands of years earlier by their sacred prophet Seldon. The First Foundation, whose knowledge of the physical sciences gives them political dominance, operates openly to ensue the success of Seldon's plan. Secret and hidden, the Second Foundation uses its knowledge of mind science to move the universe toward its destiny.
The two main characters, Golan Trevize and Stor Gendibal, are youthful rebels who are desirous of ridding their own ruling class of its aging chief administrator. Each sees a fallacy in the official interpretation of the plan's continuing success. Trevize challenges Harla Branno, the leader of First Foundation, by arguing that the prophetic plan does not exist because it matches too closely the present situation! Gendibal confronts Quindor Shandess, the first speaker of Second Foundation, with the irony that Seldon's plan is fatal because it lacks a flaw! Both Trevize and Gendibal notice the same phenomenon but come to different conclusions, yet they will be led toward each other so that they can form a unity.
The technological strength behind Trevize includes a new spaceship with super capabilities; it can jump through hyperspace very quickly and accurately. Highly developed mind power supports Gendibal even though he sails in an ancient spaceship. Eventually, the two collide near a strange planet called Gaia, which captures them by mental control. The Gaians tell them the secret of their immense mind power. The power is built up through the synergy of all life on Gaia; each living organism adds its mind to Gaia's consciousness. Asimov uses this third element to bind together the original duality, but a hidden fourth also exists. Trevize's traveling companion is Janov Pelorat, a historian whose sole goal is to discover Earth, the ancient source of all the humans now inhabiting the universe. Pelorat's dramatic purpose is to ask the question "where is our home"!
The Second Foundation has so developed the science of mind power that its advanced members can perform rather amazing feats that are very similar to the shaman tradition. The focal point of mental power is telepathy. The mind of a Second Foundation speaker, an advanced member, is able to discern minute changes in the mental pattern of another human. Because of this ability, each speaker can set up a mask that will hide a part of the mind. All speakers are aware of a mask and so understand what is happening--that so-and-so wants to hide something. Gendibal can visualize another person and through this stargate can add his mind power to the other's. Here it becomes a matter of strength; will there be a dominance or a sharing?
Tradition has often spoken about magical powers, which always involve the mind. A galactic leap is not required to see the connection. As Dante Alighieri dramatically expresses in his poem La Commedia, human institutions and fossilized customs frequently interfere with natural growth. Legends, myths, and the official knowledge of today may all contain some truth mixed with many inaccuracies. The artistic tradition, however, in its quest for beauty and truth focuses on the duality and thrusts it into the conventional program of human thinking. The arts have kept the faith; have science and technology?
A branch of holistic medicine developed by Randolph Stone, called Polarity Therapy, uses negative and positive forces for healing. The perineum, seat of Kundalini, is a focal point in this method. Gently massaging the perineum awakens the serpent which, when it ascends the spine, divides into two energies, the red and the white. These two spiral upward, each moving in a direction opposite to the other. This is the image of Hermes' caduceus. The ascent takes time, effort, and patience. The alchemists speak of many repetitions and seven basic cycles. Perhaps, they mean the seven chakras and the long time spent meditating. An interesting meditative image is the caduceus. Visualize first the vertical axis and then the two serpents slowly ascending. Make sure that they spiral upward in opposite directions.
chapter 4