Adventures along a Contour

Copyright © 2001, David A. Epstein.

All Rights Reserved.

 

      An old man and his grandson were walking along the edge of some sparsely populated region of space. Seldom were people found to venture into such dynamic areas. They were off limits to speculators, developers, entrepeneurs, pioneers, and a host of other folks who hoped to settle in the area. The complex plane police were busy arresting trespassers throughout the day; yet that did not prevent the occasional drifter from entering the premises.

      The mysteries of the enclosed mathematical region were legendary to those who straddled the perimeter. Few willfully dared entering the interior, for it was precarious enough to reside on the perimeter without experiencing the additional hazards of what lied within. Stories had made its way into the oral tradition describing those brave souls who had the gumption to explore the inner territory. They were the adventurous types who were never heard from again.

      The man and boy were privy to such stories. The interior “black hole”, as it was called, was an allure for lunatics, crackpots, degenerates, and crazy folks who craved leaping off the edge. An occasional thrill seeker would skydive into the region, yet because they never lived to describe their experiences, nobody could corroborate what they encountered when they plunged into that pit of death. Still, there are legends about survivors who withstood the trauma of nighmarish scenarios.

      It was about that time of the day for the routine, counterclockwise zero-sum integral sweep around the smooth, closed contour. Grandpa and grandson timed it perfectly, leaping synchronously over the rippling tide passing them by. The integral motion subsumed all of the impurities which accumulated along the periphery during the day. Every point along that continuous pathway, analytical and clearly defined, was impeccably cleaned. This made the work of the complex plane police much easier. They could more easily find derelicts and transients along the perimeter; in fact, the sweeps sometimes just eradicated them altogether.

      The two cohorts continued to walk along the exterior in the direction of the wave motion. There was some vegetation along the outside of the contour. How such plants and trees came to inhabit an abstract space was a mystery to those who dared think about this nontriviality. Could it have grown from spores that somehow seeped into that landscape? Or spontaneously emerged to fill a vacuum? Perhaps some explorers brought it from their hometowns as visible markers for future visits. All of this was mere speculation.

      When the grandfather stopped to view the scenery, the grandson exhorted him to keep moving forward. The boy started running ahead, occasionally looking back to see if the old man was following him. He was not. After a final sprint forward, the youngster finally stopped and waited for him to catch up; but the old man was fixated by the beautiful scenery, and because of that, he was intractable. All the boy could do at that point was breathe a heavy sigh, for he was not the type of kid who would get easily agitated.

      At that point, the boy moved towards his grandfather. As he approached him, he noticed that the elderly man was gasping for air. The boy’s eyes bulged and his face turned white with fright. He quickly put his arm around him. The old man waived him off. “I’ll be alright.” He breathed heavily for a few seconds. Then, he continued walking along the contour.

      For a few minutes, they walked steadily without interruption; no distractions, diversions, or tense moments. There was no sound to hear, no pleasing site to view, no scents to smell, essentially nothing on that part of the contour. They continued strolling in these conditions for what actually was a few hundred yards by scalar conversion.

      Grandfather continued walking ahead, somewhat oblivious to his surroundings. The boy was a different story. Along the pathway, he saw a rock resting on the ground in front of him. He wondered why a rock lied on the path. After all, the integral tide should have swept everything up. Out of curiousity, he picked up the rock and rotated it in several directions to view its shape, smooth parts, indentations, and jagged edges. After this cursory analysis, he threw it into the interior of the contour.

      The boy looked into the interior. Along it’s edges, there were some steep cliff-like drops, valley descents in other parts, and leveled mesas located in the middle. Rising spiked pinnacles and a few hilly regions also populated the region. Somehow, the rock fell between the pinnacles and mesas. After a few seconds, it hit some giant projectile. The boy heard a faint thud.

      As the two relatives walked further, they noticed a young woman emerge from the interior. They were surprised to see another human. She looked emaciated and unkempt, and was out of breath. “Do not go anywhere near that place,” she said.

      “Where did you come from? ” asked the boy.

      “We went to a place not well defined. I managed to get away, but my friends, well, they … ”

      “Get away from what? What were you doing there anyway?” asked grandfather.

      “It’s hard to explain. All I can say is they were captured and turned into residue.”

      “Sounds like a group of bandits, gangsters, or terrorists,” said the grandfather.

      “There was nobody in sight. It was some unexplainable force that drew us in.”

      “Like a whirlpool?” exclaimed the boy.

      “Something like that. Anyway, it was a long climb out of that hole. I fell a couple of times as I scaled the valley walls. It was very scary at times. Even as I was leaving the region, this rock flew right by me.” The youngster looked away, feeling a bit ashamed.

      “Well, try not to think about it. Why don’t you walk back with us. It’s been a long day anyway, and returning before it gets dark would be a good idea,” said the old man.

      “OK, I’ll go with you. It'll be good to return home.”

      The old man watched her walk with his grandson. He stopped and looked up at the sky and thought about what she had endured. What was that mysterious force that consumed her friends? Was it the same one that captured all of the people described in popular myths? Was she really the first person to escape? He did not think about this for two long, for he did not wish to fall behind his grandson. Within seconds, he caught up with them.

      The group walked towards the entrance of the contour. As the region became darker, one could see the colors change dramatically in the interior. The contrasts between the everchanging landscapes were quite pronounced.