Pathways Through Exotic Spheres
Copyright © 2001, David A. Epstein.
All Rights Reserved.


    I never could get the hang of working in a factory. Something about the harsh physical conditions, raucous sounds, pungent odors, and obnoxious people turned me off to that vocational routine. There were several occasions I simply could not enter that place without feeling nauseous. I sometimes questioned why I continued to work there, for it was a repulsive environment. In another vein, I seldom was curious about what the other workers were doing.
    In a nutshell, factory life was dirty, ugly, unsightly, and certainly beneath me; yet I remained steadfastly committed to it. Regardless of the hardships, the life of a factory worker can be rewarding if he is working on something captivating. That was the situation I found myself in.
    It was by sheer accident that I became a metallurgist. I was working on my masters degree in applied mathematics at the university. While studying there, I hooked up with a professor in plasma physics who introduced me to some novel concepts about conversion from solid state materials to ionized gases. Specifically, he taught me about how certain metals can be transformed into different phase states using specialized techniques of current amplification, reverse polarity, and molecular defragmentation. I was very enthusiastic about the possibilities of combining my knowledge of mathematics, particularly topology, with these exciting developments in solid state and plasma physics.
    When I found out they were applying this pioneering research in a metallurgy factory, I was astounded. One would naturally think that such research belongs in the realm of advanced academic study. But the Putman Materials Plant was not your typical place. You see, I was certainly cutting sheet metal, and no doubt that anyone who saw me with my blow torch, or alternatively fusing metals together with a welder, would think that I was your stereotypical blue collar worker. Nevertheless, they could not possibly know that this work was merely the prelude to our core developments.
    What if I told you that we were creating vaporized metallic structures that were oscillating between what we deem to be everyday material reality and abstract mathematical phase spaces? Would you be amazed to discover that such structures were the gateways to higher dimensional worlds? Then perhaps you would find it easier to overlook my immersions into the mundane, tedious labor of factory work.
    The theory behind all of this is quite complex. It involves the creation of what mathematicians call exotic spheres. The process of designing them, however, turns out to be simpler than you might imagine. First, a few "metallic" rings are created, eight to be exact. These rings are interlinked to form a unique sphere. Nothing too exciting at this point; pretty straightforward tasks performed at Putnam. What makes it intriguing is that the interiors of these rings are removed, leaving exterior shells of sorts. Then, these interior "guts" are twisted and then reinserted into the rings. These twists do not change the composition of the rings or spheres; but the mathematical properties of these spheres are radically altered, and that makes all the difference in the world.
    I won't bore you with the details for the time being, but suffice it to say that we have pioneered a unique process of travelling to higher dimensional spaces using these exotic spheres. There are an infinite number of these spheres in 3D. This means we could spend eternity hopping from one 3D sphere to the next; yet who in their right mind would pass up the opportunity to travel to higher dimensions? Not us, that's for sure. We plan to navigate to the fourth dimension for starters. How? Well, each exotic sphere is tangential to the next higher dimensional space; that is, the third naturally leads to the fourth. At a certain point, we will harness the energy boost resulting from this navigational process to slingshot to higher dimensional spaces. Think of these as topological orbitals; higher, mathematical energy states.
    Oh, I guess I haven't formally introduced myself. My name is Charles Jefferson. Some people just call me Chuckie. Glad to have met you. I'm sure we'll have plenty of time to get acquainted later on. But now, I've gotta get back to the factory. There's work to be done; launch plans from "the basement", but I'm not at liberty to discuss it further. So until the next time we meet, just keep smiling, walk straight, and try not to bump into those exotic spheres!



    "Don't worry. We have it all worked out." Professor Stevenson was explaining the logistics for the prototype propagation. The professor, along with an associate engineering specialist, developed the design specifications of the metallic spheres. He proposed a regimen for teleporting them into various mathematical spaces.
    "I'm just concerned about the success rate," I replied.
    "Naturally. But rest assured it will always succeed."
    "How can we be so sure? Surely there are failures we need to be concerned about."
    "We've accounted for all those scenarios."
    "Then you must have evidence to back it up."
    "We do."
    "And the theory behind all of this is sound? It's been tested?"
    "Yes. It's very straightforward." The good professor was more than happy to elaborate. "First, we propel the constructed spheres into their destination spaces. Then, we use diffeomorphism classes to locate, shall we say, the abstract spheres in the different spaces. The physical spheres act as enablers of all the so-called abstract ones."
    "But why do you need a physical sphere to locate an abstract one?"
    "The surgury we perform on the ringed spheres, remember how that works?" he asked.
    "Of course."
    "That's what does it. The physical construction of that sphere, when propelled into the appropriate abstract space, will map to corresponding abstract ones."
    "But how?"
    "Well, read what I say about this in my blog. It has to do with the controlled movement of the twisted interiors of the spheres. When we instigate a series of perturbations of that interior, it points to the other spheres."
    "Is this a mechanical, automated process?"
    "No, it's logistical. You'll see in time how it works. Just continue with your project, my friend. And once you're out there, try to savor the experience of exploring the unchartered domain."
 


    I found the sensation of floating in this peculiar three-dimensional space to be somewhat intimidating. In a strange sort of way, the space was engulfing me. I was not freely moving within it; rather, it was swarming around me. Was I being swallowed by some invisible presence? It felt that way, no doubt about it; though I must confess it was very pleasurable. Still, I became anxious about the uncertainty of what would occur next.
    It did appear that I might be cast in some type of dream state. There was a unique intangibility, a feeling of remoteness from what I was truly experiencing. Of course I vividly remember being launched into this new terrain, so I realized it was reality as such; yet while I retained my usual awareness, more or less, it was sparked with an array of alien sensations. For example, I was barely moving, yet I felt as if I was being mildly stretched in all directions. I could not reconcile these types of dualities in my mind, so I uncritically accepted them.
    At the same time, I did not in anyway feel threatened. I have always relished the prospect of exploring a new abstract world. Here was my finest opportunity right in front of me. I was starting to orbit around this exotic sphere, not knowing what I would encounter, but aware that anything could occur at the slightest turn. Yes, I felt like an astronaut eyeing the great blue ball from beyond the Earth's atmosphere. The main difference is that I saw all types of flashing lights tainted with various tints and hues transcending my wildest imagination.
    The sphere displayed swirling colors interspersed with varying textures. Spots on its surface rapidly expanded and contracted. I could see arcs stretching in several directions tangentially touching its surface. A mathematics professor of mine once explained this forms the basis of the next dimensional space. Whether these arcs were the gateways to this space, I could not decide. I certainly was not brave enough to fling myself against one of those curved figures. "Let's just leave that in the realm of theoretical mathematics," I thought.
    Before I continue on, I just wanted to say a few words about the suits and helmets we were wearing. They were custom designed to provide complete protection from the alien environment while permitting our senses to fully experience it. I found my suit to be very comfortable, primarily because it was made of a thin elastic, non-abrasive material. Special sensors were attached to our equipment which detected external phenomena. They were converted to the sensations which we directly felt.
    Oh, I didn't tell you about my partners in crime, did I? Well, let me introduce you to Theresa and Martin. Theresa was a pioneering topological astronaut for NASA. She made some life-threatening but adventurous trips into all types of abstract spaces like chaotic attractors and Julia sets. An abundance of useful data was collected for the agency; they were interested in alternative simulation environments for long-term, sustainable space exploration. Theresa simply chalked it up as another victory for the professional experimentalist she is. Suffice it to say that she's done it all: skydiving, mountain climbing, hang gliding, isolation tanks, psychedelics, all types of meditation. This trip represented a natural "next step" for her.
    Martin, on the other hand, was conservative in his life style. He played chess, tennis, and his greatest indulgence was crossword puzzles. His training in high energy physics certainly was very beneficial to the group, for he was able to explain what was happening to us during the transitional states. I met him at Putnam when I was just beginning to work there.
    At the edge of this exotic sphere, we were penetrating the boundary of the fourth spatial dimension. This boundary appeared to be a long, semi-permeable, translucent wall that ascended to dizzying heights. We passed into a higher superspace encapsulating the lower world. I became aware of this huge surrounding space, this giant manifold, shaped with strange curvatures and fanning out in several directions. There were flashes of light that perforated my sensitive eyes. This triggered images of laboring at Putnam when sparks would fly by while I was cutting sheet metal. The higher dimension pulsated with the subtle rhythms of a breathing organism. Each apparent rhythm was accompanied by patterns of meshing, dripping colors. It was abstract expressionism of sorts.
    My skin felt stretched like it contained an extra layer of substance. In fact, my entire body was riveted with all types of twists, textures, and crevices. It was vibrating with a new life. My sense of smell was tinged with odors I've never smelled before. The strangest sensation of all was that while my eyes were adjusting to new shapes and colors, my vision incorporated all of the other senses. Can you imagine that? If I were to tell you that I was tasting what I was seeing, you'de think I was at best a creative poet, but more likely a raving lunatic, no?! Well, this was no mere metaphor; it was the reality I was truly experiencing.
    After a flurry of these bizarre sensations, I became acclimated to this new environment. Each of us was exploring a different part of this four dimensional sphere. I continued to orbit around it. While I was drifting at a constant speed, I imagined traveling to the center of the sphere. I stared at its surface. It was intoxicating. There's no way I could adequately describe it. Perhaps if I said it was a fluorescent glow with pulsating bursts of gaseous emissions, that would be a decent start.
    I thought about navigating closer to the surface, but I couldn't figure out how to accomplish this. So I just took a deep breath and visualized what it would be like becoming immersed in its substance. Then, without any warning, I collided with something that completely startled me. I saw this figure in a space suit drifting in space, barely moving. I cautiously approached the figure and looked into the helmet. Inside was a man with an imploded head; his eyes were dangling from its sockets, down near his mouth. I let out a loud scream, but surely nobody heard me. Frantically, I searched for the others. It must have been about one-half hour later when I found Theresa and Martin. Without getting into the details, I described what happen, but they didn't believe a word of it. They wouldn't even give me the benefit of returning to the scene. Instead, we headed back to Putman.

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    We returned to the basement without any great fanfare. The trip back had a few bumps and bruises, some twists and turns, and flashing lights of different colors while travelling through various tunnels; yet it wasn't filled with the high drama I had anticipated. We had experienced a real-time, actual sized adventure in higher dimensional spaces; that's where the real excitement was. Navigating back to ye ole factory just didn't cut it for me. The sole redeeming feature of the return 'flight' was its quickness.
    I was the first to arrive, by the way. This gave me the opportunity to watch the others materialize out of the thin air into the giant bubble chamber, our launching and landing pad. Next came Theresa. She had a rough landing, yet quickly rose to her feet, took off her helmet and exclaimed "awesome". Martin was the last one to arrive. He always seemed to be the last at everything. "Slow, but thorough," is how I would characterize him. His landing was smoother, though he carefully surveyed the local environment before removing his gear.
    "Well, that was a lot of fun," said Theresa.
    "Fun?! Running into a dead topological astronaut isn't my idea of fun." I replied.
    "Oh, come on, you were having 4D hallucinations my friend."
    "Quite contraire, it was even more real than this conversation."
    "OK, I won't belittle you more than need be. But putting that aside, didn't  you get off on those streaking, pulsating lights?"
    "Yeah, they were visually stimulating, weren't they," interjected Martin.
    "OK, it was stimulating." I wasn't about to mince words over something so trivial.
    "Good thing I captured it all on my video recorder." Theresa was certainly one to publicize her activities.
    Theresa walked past the resonant hyperwave generator. This was the device used to propel objects and people into higher dimensional spaces. She opened the plexiglass door of the bubble chamber and walked out into the room. I followed her, and Martin, of course, lagged behind. Each of us removed our containment suits. We hung them up in a large closet where all of our equipment was stored.
    I was too exhausted to engage in further conversation and simply plopped down in a nearby chair. Theresa, certainly the most energetic of the group, did a few stretch routines, light calisthenics if you will. Martin sat down on the sofa and continued reading a book.

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    I had inquired about the status of the exotic sphere we were preparing to jettison into hyperspace. The finishing touches to the sphere were being applied when I entered the manufacture room. A lab technician was welding the outer layers together to prevent the interior "guts" from spilling out. He then placed it in some cooling liquid that compactified its contents and smoothed its surface.
    The next step was the most fascinating to witness. The sphere was inserted into the vaporizer. While the electromagnetic pulsations were being applied, it was amazing to watch it dematerialize into some hazy, colorful, misty substance. It passed through several transitional phases, each with its own color, texture, and sound effects. Difficult as it was to describe, I could smell the strong odors of the metallic vapor. It had a definitive repulsive scent, so much so that I moved to the back of the room.
    Finally, the transformed substance was transported through a wide tube, then through a long shoot, and finally down into the basement. It was injected into the bubble chamber where it was placed on the launch platform. At that point, the resonant hyperwave generator was just warming up. I rushed downstairs to witness the launch festivities. What can I say? It's not every day that you get to see something propelled into higher dimensional spaces.

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    I wanted desperately to return to the fourth dimension. Yes, you guessed it. First, to re-experience the joy of floating in that most pleasurable realm. Second, I just had to find out what happened to that dead, floating man. It was driving me crazy. I attempted to convince the others to return to that sphere, maybe send out a search team to recover the body; however, the others wanted no part of it. They thought I had flipped out. All they wanted was to delve into the seventh dimension.  
    Why the seventh dimension you ask? Well, starting in 3D, exotic spheres skip four dimensions. They exist in 7D, 11D, 15D, and so forth. So naturally, my partners wished to explore the next higher realm. There were 28 exotic spheres in the 7th dimension. Plenty to explore no doubt, before passing into the tangential 8th dimension.
    Theresa entered the chamber. She was already prepared to go, suit and all. Martin came about five minutes later. He wasn't in his usual jovial mood; more nonchalant than anything. Perhaps he wasn't too thrilled about taking the trip after all, not now anyway. I, on the other hand, wanted to get right back out there; but only into the fourth dimension.
    "Let's goooooooooooooooo, comrades." Theresa was first to step under the hyperwave generator.
    "Can't we wait a while? I'm not feeling too well right now," replied Martin.
    "Oh, you'll feel just peechie once we get out there. Just a bunch of nerves."
    "Maybe we should take it slow at first, let him get acclimated to the environment. Start out in 3D, then go to the fourth dimension and hang out there for a while." They both gave me a most incredulous look.
    "Yeah, we've gotta go to the fourth, but then we'll quickly launch from there to seven dimensional space. Got that?" exclaimed Theresa.
    But there's still so much to explore in the fourth dimension," I replied.
    "Forget about that guy, Chuckie. He won't be waiting for you anyway," said Theresa, wryly.
    I just couldn't reply to that. Martin mildly chuckled while shaking his head at Theresa. "Sometimes, I just don't know what to expect from you."
    "You shouldn't have any expectations to begin with, Marty ole boy. Just get out there and try not to puke."
    The generator was turned on. It revved up to full capacity within a few seconds. High frequency waves were created before settling into a stable oscillatory pattern. As we were bombarded by these waves, Martin put his hand on his chest. He didn't appear to be in any pain, but more like pre-excursion anxiety. I put my arm around his shoulder to comfort him.
    At a certain point, Theresa was surrounded by a luminous glow. Her body was transformed into a gelatin-like substance. I watched her twitch a bit. Most people would undoubtedly grimace while experiencing such pain. She, on the other hand, seemed to thoroughly enjoy it. Perhaps there was a trace of the Marquis De Sade in her. Instantaneously, she flashed out of view.
    Then I turned my attention to Martin. He still was quite nervous. I anticipated he would be the next one propelled into the higher manifold worlds. Instead, I felt these chilling sensations running through my own body. I was wobbling back and forth. My flesh vibrated with increasing intensity as my mind diagrammed all types of doomsday scenarios. In a nutshell, I thought I was going to explode; however, as I took a look at Martin, who himself was undergoing some transformation, I noticed that I was rocketing through some streamlined medium of streaking lights. 

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    It was fascinating traveling along various manifolds to our destination. I enjoyed viewing the mapped connections between the various spaces; however, the end of the trip was quite rough. Deacceleration took its toll on both my mind and body. No amount of pleasure could negate that reality. As I came to a halt, I looked around for Martin; but he was nowhere in sight. Theresa was adventuring ahead. She was performing all types of flips, gyrations, and dervish-like movements with her body. The main visual attractions, however, were these phantom like presences emanating from her. Each was vibrating in different rhythms and colors.
    Was this a characteristic of the seventh dimension? Maybe so, though I certainly entertained the notion that I was tired and merely seeing things. This included siting variations of myself emerging in space, with flickering visuals and robust intonations. In other words, I saw myself instantaneously pop up in multiple locations. Each new being was connected to the others with a blurred light; it was like a time-released continuum of clones of myself. Perhaps this was the result of my senses adjusting to the new environment; yet I could not help but think I was resisting the force of a real imposed presence.
    If the mind played tricks on us, then it was certainly a master magician out there. At times I wasn't sure if I could think in any conventional manner. It appeared as if any thought became a visual drama that could be felt, heard, and smelt. Thoughts would instantiate a series of phenomena detectable by all the senses. As I was contemplating this process, I literally bumped into Theresa. Well, actually it was one of my nearby clones that first collided with her. Seems like she was already making headway in exploring the spatial terrain.
    "Oh, so glad to meet your acquaintance once again."
    "I guess Martin hasn't made it yet," I replied.
    "Maybe he missed his flight."
    "Very funny."
    "Yeah, I see multidimensional travel hasn't loosen you up yet."
    We sporatically engaged in this type of fluffy conversation until Martin arrived. He looked decrepid. I was stunned to see how bent out of shape he appeared.
    "Martin, what happened?" I asked. He didn't initially respond. He reached for his helmet, clearly ready to remove it. I immediately rushed over to him to prevent this suicidal act. "You can't do that. We're not at liberty to breathe freely out here."
    "As ... As of right now. I'm ... I just can't think of, of what to do," he replied, obliquely.
    "You look completely whacked out," said Theresa. "You must have wiped out during the slingshot propulsion from the fourth dimension."
    "Sure. I could, yes, undoubtedly ... I see why you'de think that."
    "Tell us, what happened?" When he didn't respond, I asked him a second time.
    "Yeah, tell us already. You look like you saw a dead person," said Theresa, as she gave me a sharp elbow.
    "Well, ... no." He started trembling steadily. "Actually, I saw two."
    Theresa quickly administered some first aid. She was the most experienced in the group in this area. She gave him a couple of anti-anxiety pills and some water for starters. Then she firmly embraced him to stop the shaking. It took about half-hour, or so it appeared, to get him under control.

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    There are an infinite number of exotic spheres in 3D, but the number of definitive survival pathways to the fourth dimension is limited. Most pathways along the boundary "wall" lead to an unknown fate. Some of our pioneering astronauts made it into the fourth dimension, but never returned back to our ground state reality. Martyrs or unsung heroes perhaps, but never to be seen again.
    Well, we somehow managed to delve into the 7th dimension. Even Martin was returning to his senses. All of these quirky sensations I've been mentioning were amazing to experience. When you realize that there are 28 exotic spheres to explore, each one touching the 8th dimension, it just blows you away. There are 28 ways to get to the 8th dimension. The question is what is the right one?! We've discovered that 27 of them will lead to uncertain destinations. Some return to lower dimensions, but some don't return at all. It's topological Russian Roulette, folks.
    I was certainly cautious about what moves I would make. Martin, unsurprisingly, didn't wish to venture out to an unknown space. He remained stationary in his comfort zone, behind me. Theresa, on the other hand, was in a gambling mood. She jettisoned to the nearby sphere with rapid propulsion and exuberance. With some timidity, I followed behind. I needed to convince Martin to come along.
    As I approached the sphere's surface, I couldn't directly distinguish the unique directions of its curved space. Translation: either I was disoriented, or that was one helluva space to mentally grasp. Stubborn as I could be to disavow any psychological breakdown, I chose to believe it was the sphere, and not myself, that was messed up.
    "You look a little confused, Chuckie boy," exclaimed Theresa. "Don't you know where you are?"
    "Yeah, very funny. Doing your stand up bit even out here in this manifold world, huh?"
    "OK, I can see that even curved space can't give you a sense of humor."
    "Well, I can see it has warped you."
    "People, people. I can only take so much of this meaningless banter," interjected Martin.
    "Nuff said," I replied. "Let's just move in and take a closer look. Just be careful."
    We approached the surface as cautiously as possible. The problem was it was bent in various directions, with so much undetermined curvature and invisible extensions, that it appeared the surface was miles away. Unfortunately, that was an optical illusion, for without any warning, we slammed right into it. Martin was the first to scream.
    "I said be careful."
    "But I didn't see what was in front of me," said Martin.
    "Yes, it was difficult to detect. We were disoriented because it itself is disoriented."
    "What the heck are ya smoking," commented Theresa.
    "Simply put, the exotic sphere is a curved space lacking orientation."
    "Meaning what?" asked Martin.
    "Meaning we can't directly describe its directions or movement in that space."
    "OK boss, whattaya suggest?" replied Theresa, glibly.
    I withdrew my laser gun from my coat pocket. I pulled the excitation lever to boost its energy level. "I'm gonna use this laser to create an atlas and some flat surfaces called charts. That'll make things easier for navigation. Just stay back while I fire away." When I pressed the activation button, parallel beams of blue and red light were emitted from the laser gun. It created this reference object, the atlas, which contained all types of elastic "cords" connecting the curved space to 'shadows' on the charts.
    "Awesome. Simply awesome. So cool of you, Chuckie, to put on a show like that."
    "Yes, it's quite an amazing thing to view. But what's really happening?" asked Martin.
    "Simple topology. The atlas projects overlapping regions of the curved exotic space onto two shadows such that the shadows themselves have a special equivalence relationship with each other."
    "Sounds kinky," replied Theresa. "Like some type of weird therapy."
    "You see, the shadows are orientable. Essentially, they must be smoothly continuous and differentiable to each other."
    "And how does that relate to what we're experiencing?" asked Martin.
    "Well, it indirectly gives the curved space, the exotic sphere, some orientation. By monitoring our movements on these charts, we can experience what's happening on the sphere."
    At that point, I adjusted the mode selector on the laser gun for human application. I pointed the gun at Theresa, admittedly with some degree of glee. The blue and red beams merged together.
    "Hey, watch where you point that thing. It'll mess up my face."
    "Not to worry, nobody will notice. We're merely going to project ourselves to the flatland shadows."
    I watched Theresa beam down to the left chart. She landed on her buttocks near the edge, but quickly rose to her feet and strolled around the surface. Next, I aimed the gun at Martin. It took a few seconds to project him to the right chart. Finally, I pointed it at myself. I ended up suspended between the two charts! Within this realm, our projections were subjected to the motions and actions coherent to us in our ordinary wordly existence. The charts gave us a sense of direction and movement. This permitted us to experience the corresponding curved space with all its variation. Yes, we were exploring the realm of the exotic sphere; but only the shadow knows. Sure enough, we were exposed to the multivariate sensations of this flatlander environment. And I could distinctly recognize that metallic odor I first smelled at Putnam.

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    They say that when you're one of many, you feel diluted in the greater scheme of things. Well, in this case, I was even more negligible than that. You see, it's not every day that you have the joy of experiencing one of these fabulous spheres, a passageway to a higher superspace encapsulating this world. The wonder of exploring its phenomenal terrain penetrated to the inner core of my being.



    We had finished exploring our eighth sphere in the seventh dimension. Each one had a unique landscape and texturized surface. Some rotated about a tilted horizontal axis, others pulsated or throbbed like an excited amoeba. One even glowed with a striking luminescence that is still quite visible in my mind. The variation of complexity even surpassed my highest expectations.
    There can be no question, however, that the last one we visited left the deepest impression on us. For what appeared to be a couple of hours after we departed from its hyperbolic surface, the strangest thing happened. One second, I looked back to view its mystical, misty exterior. About a minute later, it simply disappeared. Where did it go? Why did this occur right after we visited it? I could not imagine. There was not the slightest indication it was going to completely vanish like that. It's as if it willed itself out of existence.
    I wondered what caused this seemingly magical act to occur. Indeed, I was mesmorized by this unexplainable phenomenon, what appeared to be a paranormal event. It left me breathless and speechless. A few minutes later, I came to my senses. At that point, I began to entertain more "rational" thoughts about what happened. For example, in terms of mathematics, I thought it could have been the result of some type of topological instability. Perhaps it was a dissipative system. Or maybe we entered a strange time loop and viewed its pre-emergence. The various possibilities certainly piqued my curiousity.
    For a while, we were travelling in empty space. I could not see anything in any given direction.With nothing to use as an external reference, it was nearly impossible to determine where we were headed or how fast we were heading there! Fortunately for us, our navigational systems were functioning correctly. They assisted us to head in the right direction.
    As we headed to the next sphere, our last one to explore before bolting to the eighth dimension, we entered a pinkish-blueish haze. I could hardly see Theresa and Martin. They spoke into their mouthpieces, so I heard them in my earpiece; but their voices got progressively fuzzier. Finally, I lost communication with them. I had no idea where they went, and undoubtedly, they did not know where I was located.

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    Eight dimensional space. I had made it this far and I was going to enjoy my stay in this higher realm. I started taking pictures with my video recorder. My friends back home would not believe me otherwise.
    No sooner than beginning to adjust to this new environment did I feel an intense jolt through my body. The video recorder slipped out of my hands. I reached back to grasp it, but I was suddenly propelled into space by some invisible catapult. That's the image that came to my fuzzy mind anyway. As I was accelerating through space, rapid impulses of multicolored light bombarded my senses from all directions. Space warped into some sort of strange giant tunnel riddled with various holes and oblique shapes. I wondered why I did not slip through those holes.
    Based upon what we discussed at various research seminars, I surmised I was traveling inside some type of manifold, in effect being 'mapped' from one spatial domain to another. But where was I headed? What had triggered this sudden departure from the eighth dimension?
    There was no time for any further questions to come to mind. I had seen the light at the end of the tunnel. Literally, there was a light at tunnel's end! It was a bright white glare, and I was heading right into it. I had apocalyptic visions of an impending end. Interweaving with these gloomy thoughts were more romantic notions of merging with the divine light. Crash. Merge. Kaboom. Melding. Bang-bang. Bathing in it. These oscillating images of death and birth, the end and beggining, destruction and creation, departing and becoming, all flashed through my being at an ever increasing rate. Finally, when I reached the end of the tunnel, the dualities fizzled into one defining singularity: I had passed harmlessly through the light.
    And what had awaited me at the other side? It was simultaneously awesome and obscene. There were many bizarre objects, neon signs, space cars whizzing by. I saw this sign which advertised excursions to superstring worlds. My initial thought was that I stumbled upon some hyperspace colony. It was baffling to me. Was this some "extra terrestrial" civilization? Or a secret government-funded project?
    Hovering above was this giant razor with "Occam" written on it. It swooped down towards me, but I simply managed to outmanoever it. Fortunately, it was a one time occurance; yet I couldn't help but think that things were getting a bit too complicated for my liking. "Ah, he's finally arrived," cried out a voice from an unknown direction, with a deep resonating echo. "Welcome to the eleventh dimension."
    I looked upwards to see who was speaking. There was nobody in sight. I replied, "who's there?". There was no response. So I auto-jetted to the spot where I believed the voice originated; but again there was nothing. I felt anxious about all of this, but what could I do?
    "Better adjust your hyperspace goggles." The voice had spoken again. I was tempted to search the area again, but I didn't get the chance. You see, at that very instance, everything went dark. All of those signs, racing cars, buildings, etc., I could no longer see any of it. The lights had gone out, and I felt completely immobilized.
    "Come closer, son. Come to the dark side." The voice was getting eerier. I charged towards it, though the voice emanated from yet another direction. "You're losing your touch, my son. Feel the force. Feeeeel it, for God's sake." I was getting frightened at this point. I replied, "Stop it. Don't hurt me. Please, please leave me alone." Then without any warning, I saw a small light flickering to my left. It became brighter and brighter. I auto-jetted in that direction.
    All of a sudden, I could view some people who started laughing hysterically. "Baaah haaaa ha ha ha ...". The first person I could make out was Theresa. Then I saw Martin. Finally a couple other people I didn't recognize.
    "That was some cool trick we pulled, Marty old boy," said Theresa.
    "Yeah, pretty neat holographic projections of a complete city," replied Martin.
    Theresa laughed even louder. "I can't believe you fell for it. You should have seen the look on your face. Heck, you should even see it now."
    "Ah yes, very funny. Right, very funny indeed," I said. "Guess the whole thing is a great trick."
    "Oh, no," replied Theresa. "We are really in the eleventh dimension alright."

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    Needless to say, exploring the eleventh dimension proved to be more eventful than the lower dimensional spaces. Every action had visual activity and reverberations extending in multiple directions out to the horizon. Moreover, there was a unique phenomenon we had not yet encountered: dual dimensions intertwined as one. One could actually view a spatial direction wrapped around another one. In an ordinary plane, an object can move along one axis, then along the perpendicular axis. This was not possible with these two dimensions. Movement along the straight dimension would be followed by a spiral motion around it. Think about a cooked piece of spaghetti wrapped around a stiff uncooked piece.
    I watched the others explore these special two dimensions. Theresa whirled around the "stiff" dimension like she was riding a high-speed roller coaster. That fit her character to a tee. Marvin was more cautious as usual. I just viewed it from a distance, though I was interested in giving it a try.
    After a period of a few hours exploring this new spatial domain, we congregated together to discuss our next move. Theresa wanted to go to the twelth dimension to explore its exotic spheres. But we did not even see any of these spheres from the eleventh. I argued against doing anything of the sort unless we could reliably calculate where they were located.
    Marvin and I talked about what we could find in the eleventh dimension. He mentioned that superstrings are found in it's microcosmic regions.
    "But I thought they were supposed to exist in ten dimensions," I replied.
    "They do, but in normalized eleven dimensional space. Remember that here, the two wrapped dimensions act as one," he explained.
    "OK, so you're saying they discovered this from superstring theory."
    "Absolutely. Superstring theory helped us discover the intertwined dimensions."
    "And how are the dimensions related?"
    "There's a natural bridge between the tenth and eleventh, unlike anything else in the universe. They are, in effect, the same space.
    "I wonder if there are possible pathways from 11D exotic spheres to superstrings."
    "In theory, it's possible," he replied.
    "Right, I'm just thinking it's remarkable that the two exist in the same space. And if we move backwards one tangential dimension to the tenth, in concordance with exotic sphere theory except moving in the reverse direction, we're back to the superstring manifold space. And if we go backwards four more dimensions, we're in the sixth, the home of the Calabi-Yao manifold, the contracted counterpart to our expanding 4D universe. If we continue on four more, we get to the base 2D space. Remember, that each superstring itself has two dimensions. You see where I'm going with this?"
    "Yes, and it's a bit too creative."
    "Well perhaps. But let's continue on. How about going in the other direction now, skipping four at a time as again prescribed by the exotic sphere theory. Here's the series: 2, 6, 10, 14, 18, 22, 26. OK, stop! That's  10 and 26 as in the number of dimensions where clockwise and counterclockwise spinning superstrings exist respectively. And the number of four-step hops from 10 to 26 is, OK now hold your breath, is four. 10 to 14, 14 to 18, 18 to 22, and 22 to 26." I admittedly was getting very excited about this.
    "Hmm. You're mystical, too."
    "That's it. The mystical numerical connection between exotic spheres and superstrings."
    I would have done anything to explore string worlds, but we knew fully well that the technology to jettison into miniaturized space was flawed. We had the means to get there, but the risk was we might not return. Marvin pointed out that the technology was improved, but admitted that it was still a risky venture. Theresa, of course, wanted to go anyway!
    In a very strange moment, I saw something incredible happen. I watched Theresa once again spiral around the stiff dimension. This time, however, it snapped back and recoiled, flinging her high across the space in a flat arc. Without any significant gravity to dampen her motion, she continued flying out of sight. It was fortunate for her that she used her auto jets to maneuver into safety pattern. A few minutes later, she rejoined the group. I was most curious about what caused that wrapped dimension to react the way it did. It was like a living being unleashing his wrath with complete fury.

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    As I propelled from higher to lower dimensional space, I noticed that I was progressively contracting. Of course this mirrored the expansion from lower to higher space, but it was more intense descending to the lower dimensions. Throughout the return journey, I experienced all of the sensations that I had mentally recorded during our excursions into so many different spatial domains. Nothing, however, compared to my reentry into the fourth dimension.
    The exaltation of returning was short-lived. I did not feel any great prolonged joy. Martin, who was still haunted by his previous journey, anxiously moved about in the "new" space. I kept close tabs on him. The others, for various reasons, remained behind in the "factory". The deciding factor why I was his sole traveling companion, however, is that I was the only one who believed him.
    "I ... have no doubt we will find other bodies if we look long enough," said Martin.
    "Try not to thing about it," I replied.
    "It's out of my hands."
    "Well, we'll explore a little longer, until it appears to be futile to search anymore."
    For a while, our efforts appeared to be pointless. At times, we weren't certain what we were looking for. Dead bodies? Debris? Whatever. There wasn't a definitive purpose; but a few more minutes down the line, the tide turned. We came across a most unusual site. As we approached the rear of the exotic sphere, I noticed a loose patch along the perimeter. Why was a patch fastened to an exotic sphere, like it was some type of retread tire?! It's not like they are constructed by mere whim, designer choices, or consumer tastes. They're formula driven, based upon sound mathematical principles. I constructed several back at Putnam and I know how they're made. Something was definitely amiss.
    As that sphere was coming undone, it rapidly became deformed. Clearly a defective product, it appeared to be ripping at the seams. "The seams?!", I thought. "Like this was a work of stitchery." Anyway, I didn't have the luxury of dwelling for any lengthy period of time upon any such trivialities, for before too long, it was scattering in all directions. We struggled to avoid, shall we say, its' deleterious effects. We were in danger.

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    "Chuckie, what are we going to do?". Martin was at the brink of complete panic. Chunks were flying towards us. We desperately dived out of the way of one renegade piece, and Martin was nearly hit. I managed to steer us to a place of refuge: behind a larger, more stable remnant of exotic sphere. While it was hit by several pieces, like a moon being bombarded with meteors, we didn't feel the immediate impact of the collisions, merely the vibrations. Fortunately for us, within a few minutes, the topological meteor shower subsided, and we were out of danger for the time being.
    "OK, it appears to have stopped," I noted.
    "Well, they're certainly not that exotic anymore," quipped Martin.
    "Perhaps quixotic is more like it."
    "Yeah, right. Try plain ole toxic. Toxic spheres, that's what we're confronting."
    "Something very strange is going on here. Nothing like this was supposed to happen. It's not like they're some type of balloons that can pop.
    "That's exactly what they turned out to be. Defective balloons. Wait till I tell Ralph Nader about this."
    "But nobody will believe us. We're out here in this alien abstract space that no one knows about, save for a few of us hapless souls. They'll think they were filaments of our crazy minds."
    "For lack of a better phrase, right?!"
    Martin and I continued to find shelter behind the large chunk of the sphere, until it was unsafe to do remain there. Several pieces of flying debris perpetually bombarded our protective shield to such an extent that it began to crack. We were clearly in a perilous situation. I gave Martin the signal to initiate the return flight back to the Putnam basement.. While he was doing this, the chunk of sphere split in half; we were exposed to the line of fire from whatever direction was more in vogue at that given moment. Fortunately, before we were hit, we managed to fly away.
    It was a rocky return trip to our ground-state world. Nearly every turn greeted us with a few unpleasant jolts of motion. At times, it appeared we were significantly deviating from our charted pathway. I've been on wild roller coaster rides that were smoother than this. I kept thinking to myself, "something is definitely wrong". It just didn't add up for me; but as I was making some progress developing that thought, I was met with more bumpy moments, unexpected twists, a few flip-overs, and the worst of the lot, sudden bursts of acceleration and increased exerted force.
    Somehow, we made it back to the Putnam basement. We emerged in our proverbial bubble chamber. The landing, fittingly enough, was as bumpy as the ride back.

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    "How could you send us out in such a dangerous place? Didn't it occur to you we might be killed?" I was extremely angry at the professor. Not only did I completely place my trust in his theories, and the soundness of his calculations as well, but equally as important, his judgement. It was the breech of the latter, which I had so much faith in, that elicited this latest outburst.
    "Now, Charles, you've been forewarned how many millions of times about the inherent risks of topological travel?" said Stevenson.
    "Yes, millions. As accurate a count as your predictions."
    "I told you that for every pleasurable moment, you would encounter many more tense ones. We trained you to react to every conceivable hazard you might encounter."
    "That's not what we're indignant about," interjected Martin. "And you know it."
    "Know what? I can't even fathom why you're reacting this way. I've told you ..."
    "We don't care what you told us," I replied. "It's what you didn't mention that almost cost of our lives."
    "You can't blame me for problems encountered during your travels or excursions."
    Martin took a few steps towards the professor. "What about the defective patchwork on the spheres?" He too was livid with anger. It's just that he didn't yell at him. He just gazed at him with a hard stare.
    "That's right. Those spheres were models of perfection. Why would they need to be repaired?" I asked.
    The professor started to laugh. He sat down on a nearby chair. More laughter.
    Martin and I looked at each other for a few seconds. Then, Martin grabbed the professor by the collar of his shirt. "What's so funny Stevenson? Didn't it register with you, that YOU ALMOST KILLED US."
    Stevenson still continued to laugh.
    I approached him. I wanted to punch him in the face. Perhaps I would have done so if ...
    Theresa walked into the room. She pointed a gun at us.
    "What the ...," I uttered with a combination of shock and disgust.
    "You guys are just too much. Chuckie and Marty. You've been meaningful guinea pigs, but useless idiots. Doesn't the irony of that just drive you nuts?"
    Martin let go of the professor. Stevenson finally stopped laughing. He looked at us, paused for a few seconds, peered at me for some time, then stared at Martin, and finally burst into laughter again. Then he turned away from us. He placed his hand on what appeared to be his chin, and pulled it off. He turned around, and once again looked at us ... It was no longer the professor. He wasn't even a human. I don't know what he was or what happened. He just stared at us for some time. The shock of such overwhelming unfamiliarity could have killed us, if we weren't in fact dead already. I couldn't look him squarely in the face. Was it a phantom before us? Where we still in Putnam? Reality was performing a flip-flop on us, relentlessly calculating our fate while we were flickering between various blind states. Then, the lights went out. I felt something tug at me.

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    We were in another place. While I entertained a few notions in my head, about my whereabouts, in reality I had no idea how I arrived here. All I knew is that I was floating around with wild abandon in this empty space. There were no others except for one other person whom I did not recognize. He was a few feet away from me, wearing a yellowish space suit. When I saw this, I was curious why he needed one, and I, in fact, did not.
    The man approached me and started making a gesture with his right hand. He held it up over his head, but I could not fathom what he was attempting to convey. It made no sense to me.
    In turn, I approached him and started to speak. I don't recall exactly the first words I spoke, but it was something along the lines of "Who the h*ll are you and what the f*ck are we doing here." I've never been so blunt in my life and it would be so easy to dismiss this as the effects of the psychological nightmare I imagined myself to have recently encountered.
    Even so, he was a perfect gentleman to me. He simply replied that he wasn't exactly sure, but he surmised it was some type of topological prison.
    "A prison? Out here in outer space?"
    "Who knows where we are. It's just that we can't escape. No matter where we go, and I've been trying for several years now, we eventually end up in the same place."
    "It appears that there are infinite paths fanning out in every conceivable direction, twisting, turning, and sprawling through every corridor of space. I would be amazed if they all returned here."
    "Oh, but they do. I have corroborated that time and time again. We are at a singularity point."
    "What," I exclaimed. "We're not, no, ... are you saying, we're in a black hole?"
    The stranger started to laugh. He was trying to say something, but then reverted back to his continuous laughter. I stood in bewilderment about what he found so utterly amusing.
    "My god. We are inside of one. And yet ..."
    "And yet what?" He started crying out in the midst of his laugher.
    "We're not being destroyed."
    He laughed some more. Then, he paused for a brief interlude and uttered "How can you be sure of that?"
    "Because we're here. We're here and we're not facing overwhelming forces of annihilation."
    "Well, maybe not now," he chortled. "But who knows what will be happening a few seconds from now."
    "What? How would you know what's going to happen?"
    At that point, he ceased laughing. He removed his helmet or whatever contraption it was. "That's how," he succinctly replied. I was staring at Professor Stevenson.

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    The good professor began laughing again. Why was he so cruel? To say the least, I was disconcerted, confused, fearful, angry, and certainly anxious. I was wondering how I could escape from my captivity. I thought that if I could manage to turn the tables on him, then it was possible I could throw him off balance and make a run for it. So, rather than start yelling at him, or asking him questions that only results in giving him the upper hand, I decided to join him in laughter.
    "Yeah, that's a good one," I said. "Ha -- hahahaha."
    "Oh sure, son," replied the professor. "You think that was funny ...". He started laughing again, stopped for a second to catch his breath, then continued, "Wait till you see your friends. Hahahahaha."
    "My friends? Haha.What friends? I don't have any," I continued laughing.
    "Of course, that's easy for you to say."
    "I'm sure it is, but undoubtedly I don't know why," I gave my rejoinder. "So tell me, why?"
    "Because it's true."
    We were both busting up. Laughter, laughter, more laughter. Then, I shoved him hard. I tried flying away, but he managed to thwart me, chortling away as he did so. He embraced my waist and held me in place. "Son, ya gotta hang around for the big show."
    "The show? What show?"
    At that moment, I heard a few voices approach me from behind. Literally, that's what it appeared to be: just voices. I turned around and did not see anyone. Then I pivoted to break free of the professor's grip. Amazingly, I could not slip away.
    The voices turned to outright laughter. I look around again, and saw ...
    "Hiya Chuckie. Fancy seeing you here." It was Theresa. She approached me and put her hand around my shoulder.
    "Yes, Charles. What could possibly bring you here." It was Martin. They both started giggling. I did break free of the professor's hold, but I certainly wasn't going to dash away at this juncture.
    "Martin. What are you doing here?" I asked. "I thought they captured you."
    "The only thing that captured me was your gullibility. It was absolutely terrific how you fell for it." Again, they laughed.
    "And Chuckie, pal. Try not to frown," interjected Theresa.
    "You see," added the professor, "we truly did travel to many exotic spheres and it was a resounding success. But interspersed with these adventures were some full-emersion simulations conducted by the factory's R&D team."
    "Simulations? You gotta be kidding."
    "Right. Consider these simulations to be placebos. We put you in double bind experiments, not revealing to you that some of the explorations were in fact illusions, and not only that, you believed you were actually exploring these exotic spheres at that point," said Theresa. "Well, you were travelling alright. Journeying in your imagination with the help of a holographic light, within artificially reconstructed spatial domains, my friend."
    "But why? Why did you do it?"
    "To monitor your psychological reactions." The professor chuckled.
    "And those spheres, they weren't real. Hmmmm," I uttered. "I was wondering about the patches."
    They all started laughing again. "That should have been the surest giveaway. Why would we patch an exotic sphere? That doesn't make sense. We were giving you a great hint there, but you continued to be absorbed in your zombie state," said Martin.
    "And the dead men I saw? What about them?"
    Theresa cleared her throat. She waited a few seconds, then motioned to my right. The two dead astronauts emerged from the empty space. They approached me, flew towards my head, and I quickly ducked; but they, they seemed to pass right through me. I didn't feel anything, except a state of anxiety morphing into perplexity. Then they disappeared off to my left.
    "Just holograms, zombie man. Nobody died, except us dying laughing," said the professor.
    "And we didn't hoodwink you just once, but twice. You do remember the fake city, don't you?", asked Theresa.
    I was speechless for a few seconds. Then I just couldn't help myself. "Well, I guess it's true what they say. Fool me once, shame on you. Fool me twice, ..." We all laughed.

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Created: September 3, 2001
Last Updated: January 10, 2005