Foundation for a New Consciousness, chapter 6
Consciousness of Paradox

Copyright © 1987 John Caris

Yesterday in the park a butterfly, resting upon a tree branch, fell asleep and dreamt that it was a philosopher dreaming of being a butterfly. And now the butterfly is confused, not knowing who it is.

A prime source for consciousness of paradox is found in Socratic irony. Socrates, told by the Delphic oracle that he is the wisest, cannot comprehend the meaning, for he knows that he is not wise. So he begins a quest to discover who is wise. He questions the experts and finds them wanting. They are opinionated certainly, but their opinions are not grounded in knowledge; they are like thorns growing in a barren soil. When Socrates finally lifts the veil covering the Athenians' eyes, when he forces them to see that the Emperor has no clothes, a majority of the Athenians convict him of treason and award him with a cup of hemlock.

Here, with due thanks to Lewis Carroll, is a story that illustrates paradox. One day a woman and her child are at the beach. The child is playing in the water while the woman is relaxing on the sand. Suddenly, a sea serpent emerges and grabs the child. The woman, jumping up and running to the water, yells, "Let my child go!" Well, the sea serpent is a philosophic type and has been to the best universities in the world. He says to the woman, "If you tell me a true statement, I'll let your child go unharmed. If, however, you tell me a false statement, I'll eat your child for dinner." The woman thinks for a moment and then answers, "You will eat my child for dinner." The sea serpent ponders the woman's statement: "Wow, I'm going to--yum, yum--eat the child for dinner--but wait, if I do then the statement is true and I must release the child unharmed. Wait again! Releasing the child makes the statement false, so I will have the child for dinner!" While the sea serpent tries to resolve the dilemma, the woman runs up, grabs her child, and hurries away.

Notice the rhythm and movement which the paradox has. There is a back and forth oscillation that can imprison the mind. Look carefully at the way the paradox is constructed. It is the sea serpent who, by its action, will make the woman's statement either true or false. And of course the sea serpent is bound by its promise.

A similar paradox is found in Joseph Heller's novel Catch-22. The title itself names the paradox. The story takes place during the last part of World War II and centers on officers of the U. S. air force, who are stationed on an island base off the coast of Italy. Captain Orr, a bomber pilot, has flown enough bombing missions so that he should be sent back to the States. Because of heavy casualties, however, the commanding officer has increased the number of missions. Captain Orr knows that the more missions he flies the greater the chance for his plane to be hit. Orr starts to act crazy, and after each mission his behavior becomes more irrational. According to air force regulations a pilot who is insane can be grounded for medical reasons, but he must ask to be grounded. Orr, as crazy as he is, doesn't want to fly anymore missions because of the danger. But if he asks, Catch-22 zaps him. Catch-22 specifies "that a concern for one's own safety in the face of dangers that were real and immediate was the process of a rational mind." Although Orr is crazy and should not fly any more missions, if he asks to be grounded, he is obviously rational and sane. So Captain Orr is stuck.

Another variant is the truthteller-liar paradox. Assume that you are in a country where half of the inhabitants always tell the truth while the other half always lie. You come to a fork in the road where you meet a native. You do not know whether he is a truthteller or liar, yet you want to choose the road that goes to the seaport. How do you extract correct information from him? Can you phrase a question, answered by yes or no, which will do this? Here is a clue: ask a question which will give you the correct answer whether the native is a truth-teller or liar. This type of question is useful in everyday situations when you do not know the truthfulness of others. Construct your question so that you will receive the correct answer.

Paradox is more than an interesting intellectual puzzle; it is a form of consciousness found frequently in the arts. Many of M.C. Escher's graphic works give us a direct visual experience of paradox. In his lithograph Waterfall we perceive a perpetual motion machine. Here is the world's solution to the energy crisis. The water flows down stream until it reaches the edge and then falls down over the mill wheel, turning it and providing constant energy. How does Escher achieve this visual paradox? Look carefully. Notice the tension between the flat, two dimensional surface and the visual experience of spatial depth. Several columns of each tower are drawn correctly upon a flat surface but cannot exist in a three dimensional space.

In the lithograph Concave and convex Escher has designed a visual flip-flop. What is the unifying principle in this print? Look at the column in the center of the print. Is it concave or convex? Or both? Does it curve outward or inward? Below the center column is a scalloped circle. Is it a depression in the floor next to the sitting man, or is it hanging from the ceiling like the vase? The technique of inversion that Escher uses reflects a type of consciousness which fuses oscillating opposites.

The Mobius strip offers another example. Take a narrow paper band of sufficient length, give it a half twist, and connect the two ends. The two surfaces have become one. The Klein bottle, a three dimensional analogue of the Mobius strip, also has only one surface. There is no inside distinct from an outside; the inside and the outside are one and the same. Perhaps, as in Escher's Concave and convex, we experience the surface first as one and then the other. Yet can't we learn to experience the surface as both simultaneously?

The Klein bottle symbolizes the transformation "of the inner and the outer." This is how the magnum opus is performed. A correspondence exists between mental activity and physical activity, between our external environment and our inner mindscape. Changes occurring in one are reflected by changes in the other.

Charles Harness poses the paradox of conflicting theories of the universe in The Ring of Ritornel. Two major religions--Alea and Ritornel--compete for religious dominance. Alea is the deity of chance while Ritornel is that of predestined design. The government of the empire, not wishing to offend either religion, gives them equal status. And with this comes the inevitable conflict of two opposing interests. Both believe that a cycle of birth, evolution, and death exists. The Aleans believe that the cycle exists by Alea's pleasure and that it will be broken by her pleasure. The followers of Ritornel, on the other hand, believe the cycle will eternally recur. As new galaxies evolve, old ones die; as the universal laws of nature are constant, the process will repeat itself endlessly. The protagonist, James Andrek, tries to reconcile the differences during an argument between an Alean and a Ritornellian. He proposes that both sides might be correct. No doubt, he is thinking of modern probability theory. For he argues that "when chance operates on a very large scale, the result is no longer chance, but a statistical inevitability.''

Later in the story Andrek challenges a long time opponent, Vang, who happens to be an Alean, to a test of strength. Who is stronger, Alea or Ritornel? Andrek proposes a simple experiment. They will take turns rolling a die. Each number that comes up will be marked on a piece of paper. A line is drawn on the paper, and its center point is used for the first move. The number will be placed in a position relative to a clock's face. For example, if "6" is thrown a line the length of the die's edge is drawn from the starting point down to the position of "6" on a clock's face. An "X" is marked at that spot. On the next throw pretend that "9" comes up and so a line is drawn from "X" to the position of "9" which becomes a new point of departure. The die will be rolled twelve times, and a new terminal point will be marked for each throw. They agree that Ritornel dominates if the line eventually returns to the starting point, but if the line zig-zags randomly without returning to the starting point, then Alea is supreme.

Andrek, who is trying to lose the experiment, figures that according to the drunkard's walk theorem the line will randomly wander around the final point but never reach it. The experiment begins. The first number thrown is "1"; the next is "2" and the series continues in order 3, 4, 5, 6, 7, 8, 9, 10, 11. At this point both Andrek and Vang are astonished. Since Andrek wants to lose, he calls the game before the last number is rolled. Vang is very happy to win in this way. Both Andrek and Vang feel deeply that the next throw if a "12" will show the true power of Ritornel. Yet, what is the probability of this sequence? The reader is left with the original dilemma. Perhaps, it is Alea's pleasure to order this sequence.

During meditation we can actually insert programs into our unconscious. Such programs should be clear and precise. It is like wishing. So often we make a wish, phrased in general terms, that when it comes true, we are unhappy with the results. W. W. Jacobs' story "The Monkey's Paw" is a well-known example. We should be aware of how the wish, should it be actualized, will affect the fabric of reality. The same attitude applies when we insert new programs into the unconscious, so the first stage during meditation is to observe the workings of the mind. As our understanding grows, we can observe the environment for signs or other reflections of change. This is important feedback; the environment agrees or disagrees.

In Rosencrantz and Guildenstern Are Dead Tom Stoppard makes a Klein bottle transformation in William Shakespeare's Hamlet. Stoppard turns the play-within-a-play device inside out. It continues its function of disclosing in the present what had happened in the past. The play "Murder of Gonzago" reflects the past deeds of Claudius when he murdered Hamlet's father. Stoppard adds another dimension when he extends the "Murder of Gonzago" into the future. The traveling actors perform the sequence of events that culminate in the execution of Rosencrantz and Guildenstern, who are not as sharp as Claudius, for they fail to identify themselves in the play. Claudius, of course, realizes that Hamlet is aware of the crime, so he decides to send Hamlet to London for a rest, a permanent one. Rosencrantz and Guildenstern notice something familiar in the actors' performance, but, like Vladimir and Estragon, they cannot accept the truth even though it will free them.

The other dimension is significant. Most human societies assume two realities, the everyday world and the other reality; often, they are labeled the profane and the sacred. For many tribal people everyday reality is only a shadow world that is projected from a spiritual realm, and so visions can open the door into a higher dimension. Mircea Eliade has investigated this field and has uncovered sufficient evidence to show that a basic duality exists between humans and the physical world. In The Forge and the Crucible Eliade proves that all human crafts, whether viewed scientifically or artistically, have a similar set of cosmological assumptions; they all assert certain basic truths about the universe.

One important idea inherent in the craft tradition involves imitation of nature. In the Poetics the philosopher Aristotle uses imitation of nature as a concept that underlies his treatment of tragedy in particular and art in general. Looking deeply into reality, the artist soon becomes aware that the cosmos is formed out of chaos. A spiritual vision can give us a more vivid and accurate understanding, but all we really need is careful inspection of nature. In the Big Bang cosmology a byte of matter explodes and grows into the known universe; even so, an opposing seed sprouts forth, blooming into entropy. The two twins, action and reaction, now exist, but where did they come from? Johann Goethe explores the idea in his poetic drama Faust. Only after Faust makes the wager with Mephisto does he become aware of Mephisto's true nature, which Goethe expresses as the principle of entropy. Mephisto wants to stop all life, which is his enemy, and push all things back into chaos. Because of his nature, Mephisto is trapped by the wager he makes with Faust. The wager centers on whether Faust will ever want the passing moment to stop? If he holds onto a lingering pleasure or if he is ever completely contented with himself, then he loses the bet and Mephisto wins his soul. Goethe has focused on an important truth that is reflected in reality's many dimensions.

Another concept found in the craft tradition involves space and time. Simply stated, spatial directions and celestial cycles, including solar and lunar ones, are part of the cosmic web. The four major directions are used in sacred architecture and in religious ceremonies. Many temples and churches have been built on an orientation of the four directions. Numerous Christian churches are constructed with the nave lying on an east-west line so that the morning sun shines through the apse onto the altar. The seasons can be measured as sunlight moves from one side of the altar to the other. Many American Indians set their ceremonial lodges on the spatial cross so that the spiritual energy flows between the rising sun and the setting sun.

Celestial cycles add the temporal dimension and so make us aware of the four dimensional continuum that we live in. Nature is irrational and does not use the rounded-off numbers that our everyday thinking requires. Pi and phi are two important numbers found throughout nature, yet we have difficulty with their indefinite quality. So too are the solar and lunar cycles irrational. We must add a day every four years to the calendar so that it will stay close to cosmic time. The Mayan culture constructed a very accurate calendar that connected the two cycles. Cosmic symbols found in ancient art designate the sky as a circle and the earth as a square. When the ancients talked about squaring the circle, they meant on one level the cross of the cardinal axes, which mediates between the earth and sky. Among some American Indians the ceremonial pipe is raised to the four directions and then to grandmother earth and grandfather sky.

The portal of Chartres Cathedral has three doors and above each is a sculpted relief, the tympanum. The left hand bay (north) portrays Christ ascending to Heaven while the right bay (south) shows the Virgin and the nativity scene. In the center Christ is seated in His Glory. Within the solar symbolism each door is a special gateway. The north is winter solstice, the south is summer solstice, and the center opens onto Heaven.

By using the analogy of inversion, we notice that a psychic center is located in each human being, yet there is only one center. We can visualize this concept by seeing humans placed on the surface of the earth. The center in each person is a radius to the center of the earth, and so of the universe.

A cosmic puzzle that has challenged many philosophers is whether the universe is finite or infinite. Two leading thinkers of modern science, Isaac Newton and Gottfried Leibniz, hold opposing views. Newton argues that the universe is finite and bounded while Leibniz believes that it is infinite and unbounded. Their basic disagreement centers on the concept of plenitude.

Let us visualize the universe as a group of galaxies. Each galaxy is a ball that is connected to others by a stick (the distance); this model is similar to the conventional one of a molecule. Now a finite universe has a boundary, so some galaxies lack neighbors on all sides. It is the emptiness that Leibniz cannot accept, and so he argues that all galaxies have neighbors on all sides; in other words, the universe is unbounded and infinite.

Later in the 18th century Immanuel Kant discovers the antinomy of space. He rejects both Newton and Leibniz's views by combining essential features selected from each. Kant argues that the universe is both finite and unbounded; he calls the ensuing paradox the antinomy of space. All three philosophers share the 18th century belief that Euclidean geometry applies to galactic space. This belief is the third ingredient in Kant's paradox. We should be able to construct an exact scale model of the universe, but Kant argues that such a model, finite and unbounded, cannot be constructed.

In the 20th century Albert Einstein offers a radical solution by accepting the universe as both finite and unbounded, yet rejecting the application of Euclidean geometry. Visualize, for example, five galaxies all equidistant from each other. We can easily visualize four galaxies, for this is a tetrahedron.

tetrahedron

Now, where shall we place the fifth galaxy so that it is equidistant from all the others? We can construct a double tetrahedron.

double tetrahedron

Line AB is not the same length as the other lines, and so we cannot construct an exact scale model based upon Euclidean geometry. It is here that Einstein forsakes Euclid and embraces the geometry of Georg Riemann, a 19th century mathematician. Einstein argues that line AB is actually the same length as the other lines; only the human model is distorted! Yet the distortion of distance illustrated by the model is really a property of space; it is called curvature. Gravity forces space to curve into a finite but unbounded sphere.

Visualize the earth; place a finite number of humans on the surface. We now have a two dimensional manifold that is finite and unbounded, for everyone has neighbors on all sides. Because the universe is a three dimensional manifold, we must be concerned with volume instead of surface. If the volume is curved, each galaxy has neighbors on all sides. Now projecting the curved space onto a flat surface causes distance distortions. Compare the conventional map of the earth with a globe. Notice that the land areas around the poles appear larger on the map than they do on the globe. Einstein uses the distance distortion on the map to determine the curvature of galactic space. Distortion and curvature are different aspects of the same thing. Perhaps, we can learn from Escher and perform a mental flip-flop. This is an anamorphic movement from one dimension to another.

Visual artists have always been concerned with surfaces. From cave paintings to 20th century art works the surface is the basic given. When Renaissance painters began to project the illusion of three dimensions onto the canvas surface, they made distance distortions, and after many experiments they learned the technique of foreshortening. The breaking of the painting surface in the 20th century gave birth to collage, a technique using many surfaces linked together. An analogy can be made with Einstein's attempt to map galactic space. Let us use the idea of an atlas that contains many maps or charts. Each map covers a small area. If we link the maps together, we will have a composite map of a large area. The more maps our atlas has, the greater the area we can interpret.

Each map describes a local situation. For Einstein, this is where Euclidean geometry will apply; but it will not apply to the global scene, that is, the atlas. Escher's Waterfall illustrates this concept. Any small area seems normal, but the total effect is impossible! 20th century abstract painting--whether by Wassily Kandinsky, Helen Frankenthaler, or Victor Vasarely--also calls our attention to the local-global relationship. The collage technique opens our awareness to an experience of surface and depth radically different from the Renaissance's.

A literary use of the collage technique can be found in the works of T. S. Eliot, James Joyce, and Doris Lessing. In his poem The Waste Land Eliot combines phrases and idioms from different social classes of European society with fragments from classical literature. In his novel Ulysses Joyce constructs a series of episodes, each of which are different surfaces or scenes that occur during one day. Each local event has its own texture and voice; each signifies a special meaning for that particular space-time coordinate. Lessing weaves a cosmic allegory. In Canopus in Argos: Archives, a set of five novels, she stages dramatic happenings on planet earth as well as on other galactic locations. Using an interplay of forceful ideas, she tells a poignant and at times humorous story of life and death. How do we feel about the end of human habitation on planet earth? Many 20th century artists are raising this question.

The artistic act of making a finite set of surfaces forks into several paths. Some of the directions are dada, Marcel Duchamp's Large Glass on which he attempts to project a greenhouse of his ideas, constructions and action painting, and, culminating in the 1950's, the artistic concept of the "package." The dada gesture attempts to break up conventional images, which often have a paralyzing effect on the mind. Because stereotyped thinking leads away from life, the imagination is liberated, and the artist savors new and unusual perceptions of nature. The dada mirror reflects the world's multi-dimensional essence. When we look into it, we become aware of our reality-making and our personal choices. The Large Glass (or as Duchamp originally titled it The Bride Stripped Bare by Her Bachelors, Even) is a painting on glass that was never completed. The painting portrays a symbolic reality that has its own physical laws and units of measurement. The viewer sees painted images that reside between the everyday world behind the glass and reflections on its surface.

As part of the pop art movement in the 1950's, the popular image of a commercial package is fused with the craft tradition of the fine arts. A package is a finite set of things, surfaces, or events. Compare a constructed package by Joseph Cornell with a painterly image of a Campbell soup can by Andy Warhol with a soft sculpture by Claes Oldenburg. A package of objects constructed by Cornell suggests the idea of chance or random arrangement, yet if it is an art work, we should be able to discern the principle of unity. Warhol's image of a container, the Campbell soup can, suggests the surface as it hopefully mirrors the contents. Oldenburg's sculpture of a giant hamburger reflects the reality of our "packaged" lifestyle.

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