Standing Waves

The sun was just breaking through the fog as I stood in front of the small pool of water amongst the yawning trees of the courtyard.  The air had a freshness about it that invigorated my surroundings and revived the memory of all I had seen.  My gaze was transparently fixed beyond the movement of fish in the pond as I remained motionless, my hands calmly geminated behind my back.  I was contemplating just how far I had come and the virtually invisible horizon of secrecy this place held. I must have been standing there for an hour when a man's voice broke the silence, startling me and hushing every bird within the vicinity.  "Water.  Oh, how its surface echoes the majesty of movement, making way for whatever path that graceful goldfish chooses." In a moment, as if time were slowing to an eternal halt, a drop of dew slipped from the leaf of an overhanging tree, plunging to the pool beneath and disappearing into the vast mirror of water.  The consequential ripples on the surface were all that kept me from identifying the man's reflection that quickly faded away behind mine.  I turned, the stretch of courtyard tapered into the distant, looming buildings that surrounded me; no one was there at all.  The sound of that lonely drop echoed with a piercing magnitude... I shot up in my bed, drenched in a cold sweat -- it was more of a memory than a dream.  Restless, I threw off the covers, hustled to the den to power up my laptop, and began writing. "In a small pool on the plaza, partly surrounded by the copper plate, water will be turbulent and provocative, constantly agitated into standing waves," Sanborn described the symbolic dissemination of information with an unknown destination. What is a standing wave, exactly?  The answer can be complicated, but the process by which the superposition of this special wave occurs is easy to grasp.  A standing wave (or stationary wave) is a sign wave, sound wave, electromagnetic wave, light wave, or liquid wave in which the ratio of its instantaneous amplitude at one point to that at any other point does not vary with time.  In other words, if a standing wave is graphed or seen as ripples in water for example, it's effect does not appear to travel horizontally but seems to oscillate up and down in a stationary location. Standing waves are the result of two sinusoidal waves of the same frequency in a common medium traveling in opposite directions.  The displacement of each wave has a combined affect that produces the superposition of a stationary wave. It may be easier to visualize three separate waves.  The first wave (above) appears to be traveling in a horizontal direction while the second wave is traveling in the opposite direction.  The two waves do not collide; rather the amplitude of each at any given moment is combined into the effect of a single amplitude resulting in the standing wave.  If the troughs and crests of the traveling waves range in maximum displacement of -1 to +1 unit, the troughs and crests of the standing wave will have a maximum displacement of -2 to +2 units. The figure to the right depicts water ripples traveling outward from two origins.  Surprisingly, the ripples are not really traveling horizontally.  The reason standing waves occur is entirely the result of vertical movement of the water, albeit the location of this vertical movement continuously proceeds horizontally away from the disturbance.  If this principle were not so, waves and ripples would collide instead of aggregating.  In this example, the highlighted area where the ripples intersect have a displacement equivalent to the displacement of the two traveling ripples.   The standing waves of the pool in front of the copperplate of Kryptos are demonstrating invisible forces of nature.  Although we do not readily see the traveling waves, by studying their behavior, we know they exist in their most simple form underneath the stationary waves. Like the crypto-crystalline structure of the quartz used in the sculpture, perhaps Sanborn intended only to demonstrate another hidden force of nature.  I am somewhat biased to this view, because I firmly believe a correlation exists between this phenomenon and anomalies that occur in other parts of the sculpture. The copperplate is arranged with two halves of a cylinder displaced to form a sine wave when viewed overhead.  The tableau half has backward text, but this would not be inconsistent if the two halves were put back together.  From the outside of the cylinder, all text would be legible and the only viewpoint rendering backward text would be from the center of the cylinder, and you would have to be in a pool of standing waves.  I wonder what would happen if a light source was placed in the center!  Maybe the sun ray's angle would allow light into the cylinder through one half, reflecting off the surface of the water, and filtered through the other half, projecting an image onto one of the nearby buildings.  The sine wave of the copperplate could represent two traveling waves.  Light could represent the medium by which those two waves are superpositioned into a standing wave.  Alternately, light projected through the two halves as they are could yield some very interesting results. Not only does superposition occur in the pool of water; it occurs in K3 of the copperplate (the third passage which is located in the bottom half of the cipher text side).  The position of three of the characters are superscript or super-positioned.  In fact, those characters are Y, A, and R consecutively.  Perhaps the YA and R spell RAY backward, representing a light ray traveling in the opposite direction of another.  Remember: the principle of waves applies to electromagnetism and light as well as other natural occurrences.  Directly under the superscript is the word REY. Sanborn commented, "I will say that I have left instructions in the earlier text that refer to later text.  That's as far as I'll go." Somehow, I think I am already on to it, Mr. Sanborn.   Superposition of Waves http://www.kettering.edu/~drussell/Demos/superposition/superposition.html