Pathways Through Exotic Spheres
by David A. Epstein
Created: September 3, 2001
Last Updated: March 4, 2001

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 one of those factories without feeling nauseous. I often questioned why I continued to work in this type of environment. In fact, I seldom was curious about what the other workers were doing at any given time.

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 interesting. 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 in 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 through the use of these exotic spheres. There are an infinite number of these 3D spheres. 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. At a certain point, we will harness the energy boost resulting from this 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!

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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, that's for certain; though I must confess it was more pleasurable than painful. 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 knew it was reality of sorts; 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, but I uncritically accepted them.

At the same time, I did not feel in anyway 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 to expect, 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 there were all types of flashing lights tainted with various tints and hues.

The sphere itself displayed swirling colors interspersed with varying textures. Spots on its surface rapidly expanded and contracted. I could see arcs stretching in several directions which tangentially touched its surface. A mathematician 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, 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 metal sheets. 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, as if 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 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. As I was drifting at a constant speed, I thought about accelerating 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. 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 which 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. There 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 return, by the way. This gave me the opportunity to watch the others materialize out of the thin air into the bubble chamber, our launching and landing pad. Next came Theresa. She had a bit of a rough landing, yet quickly rose to her feet, took off her helmet and exclaimed "awesome". Martin was the last one to return. 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 more real than even 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, in his typical over-analytical style.
"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 multiple dimensional spaces. She opened the plexiglass door of the bubble chamber and walked into the room. I followed her out, and Martin, of course, lagged behind. Each of us removed our containment suits. We hung them up in a large closet where we stored all of our equipment.

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 as I entered the manufacture room. A lab technician was welding the outer layers together so the interior "guts" wouldn't spill out. He then placed it in some cooling liquid which 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 went 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 repulsive scent, so much so that I moved to the back of the room.

Finally, the transformed substance was transported through a wide tube, through a shoot, and 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 manifold 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 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. Guess 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. Just in 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 4D and hang out there for a while." They both gave me this incredulous look.
"Yeah, we'll go to 4D, but quickly launch from there to seven dimensional space. Got that?" exclaimed Theresa.
"But there's still so much to explore in 4D," 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. "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, more like pre-excursion anxiety. I put my arm around his shoulder to comfort him.

At a certain point, Theresa was surrounded by this luminous glow. Her body was transformed into a gelatin like substance. I watched her twitch a bit. Most people would undoubtedly grimace with pain under such circumstances. She, on the other hand, seemed to thoroughly enjoy it. Instantaneously, she flashed away out of our view.

Then I turned my attention to Martin. He still was quite nervous. I anticipated that 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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Deacceleration took its toll on both my mind and body. No amount of pleasure could convince me otherwise. 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 viewing attractions, however, were these phantom like presences emanating from her. Each was vibrating in different rhythms and colors.

Was this a symptom 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 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 couldn't help but think that I was resisting the force of a real presence imposed upon me.

If the mind played tricks on us, then it was certainly a master magician out here. There were times when 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 smelled. 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 which 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 has yet to loosen you up."

We sporatically engaged in this type of fluff 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 something like 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. "Must have gotten wiped out from the slingshot propulsion from the fourth dimension."
"Sure. I could, yes, undoubtedly ... 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 make it into the 7th dimension. Even Martin was coming to his senses once again. 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 that 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. How's that for funny?"
"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 proceeded to approach the surface as cautionsly as possible. The problem was that it bent in various directions, with so much undetermined curvature and invisible extensions that it appeared the surface was miles away. Unfortunately, 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 make out. 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 give it several boosts of energy. "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."
"But what's really happening here?" 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."
"It's not even that weird. You see, the shadows are in fact orientable. Essentially, they must be smoothly continuous and differentiable to each other."
"And what does that have to do with anything?" asked Martin, again.
"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 be projected to the flatland shadows."

I watched Theresa beam down to the left chart. She landed on her buttocks near the edge, but rose to her feet and strolled around the surface. Then, I pointed 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 in all its glory. 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, 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 surpassed my wildest 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 no hint of anything that would have indicated 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. 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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