Flight Demo in Microspace

Copyright © 2001, David A. Epstein.

All Rights Reserved.


“OK, let’s begin our five-step program to get into Microspace. Later, I’ll describe the twelve-step program to get out.” Nobody was laughing at Marvin’s halfhearted attempt at humor. They were too preoccupied with being anxious about their impending excursion into miniaturized worlds.

The group consisted of Patrick Evans, a computer scientist, Emanuel Ramirez, a quantum physicist, Stephanie Frankel, a biochemist, Larry Prescott, a wealthy civilian who volunteered for these flight experiments, and of course Marvin Baker, the chief scientist at StringFlights.com who specialized in topological simulations. To facilitate these experiments, each member of the group, except Larry, had offered their technical expertise. Still, they were primarily enthusiastic participants who could not anticipate what would occur.

 Everyone wore a containment suit and an optical device over the eyes. Marvin explained that this was an experimental government-funded project to test the effects of micro spatial travels upon human behavior and biochemistry.

After conferring with Emanuel for a few minutes, Marvin continued speaking through his headpiece. “A series of progressively, contracting manifolds will be constructed to guide you into the desired Microspace. You’ll be steered through these manifolds and your scale will shrink accordingly.”

He entered some data into a computer and ran a neural network that Patrick helped to set up. It was programmed to collect and analyze physiological data. Some red lasers were projected at various members of the group. They were all sitting on chairs in the transport chamber.

Marvin spoke again. “The first stage is the most beautiful. It’s called Topological Induction. Subtle changes will occur in your occupying space so you’ll be released from it. We alter the occupying space without changing your physiology. You’ll experience no pain and only some disorientation.”

“Disorientation? Who needs that!” exclaimed Patrick.

More red lasers, shining from the ceiling, bathed the pre-Microspace trekkers. Stephanie and Larry shielded their eyes from the rays.

“What the heck is happening to us?” asked Larry.

“Don’t worry. You’re just in an electromagnetic flux,” replied Marvin. “It’ll pass quickly.”

“Won’t these rays harm us?”

“Mr. Prescott, again, don’t worry. They’re merely locating the sensitivity points in your body. That will help release you from your occupying space. Underlying this phenomenon is a process known as transitional-meta pandemonium, or TMP for short. TMP is the force that’ll send you into Microspace.”


“Well, believe it or not, we’re now in stage two,” remarked Marvin. “We’re currently experiencing something called ambient isotopy. Quite exhilarating, huh?” Emanuel was the only person in the group responding somewhat favorably, and that was merely with a faint smile. The facial expressions of the others ranged from pale-white fright to gripping fear. Marvin continued speaking: “It describes the movement of space around you, as opposed to your movement in space. This spatial movement is in fact responsible for releasing you. You’ll feel a bit more disoriented, but it will soon pass.”

As his body emerged from his occupying space, Larry was overcome with fear. He imagined that his body was rising from a pool of jelly. While he floated with some buoyancy, he struggled to maintain his balance. Patrick and Stephanie swaying back and forth as if they were trees in the wind. He asked Marvin whether this was the result of their enthusiasm or a residual effect of the ambient isotopy. Marvin mildly laughed.

 “Keep in mind that your body is connected to its occupying space by a unique network of knots and twisted manifolds. At your sensitivity points, ambient isotopy is untangling and untwisting you away from your occupying space.”

“Hey, this feels great,” commented Stephanie, as she was freely floating in space.

“Of course it does,” replied Marvin. “It should feel very pleasurable. As your occupying space moves away from you, it distorts the space surrounding your body. This distortion is a manifestation of TMP itself.”

“And can we control this distortion?” asked Patrick as he was bobbing up and down in his space suit. His body was two feet off the floor.

“No. It can’t be controlled, merely harnessed. This is pandemonium, my friends. This is going to help us reach our targeted Microspace.”


“Can you believe we’re already in stage three? Where does the time go? Well, we’ll just have to cherish the memories. Anyway, we’re going to see that this spatial distortion we're experiencing will help steer us in the right direction. This distortion is described by what topologists call a homotopy.”

“A homo what?” said Larry.

“Ah, a quick wit,” replied Marvin, sardonically. “OK, Lemme explain. A homotopy is a continuous deformation. In a two-dimensional example, if a circle is deformed into an ellipse, a homotopy joins the circle and ellipse together. We are interested in the ones joining your pre-distorted and distorted surrounding spaces.”

Patrick felt slightly elongated. His body arched mildly. He looked at the others and noticed that they too were elongated. They were bobbing and gently spinning back and forth like rotors in washing machines. He adjusted his optical device to view them more clearly.

At that moment, vapor permeated the room. When it cleared, a group of long, twisted, cable-like structures stretched across the room. Emanuel became mounted onto one of them. An unseen, unbreakable force bound him.

“Seems like Emanuel is getting quite comfortable on one of those vector bundles,” said Marvin.

“Well, it’s not every day I get to lie down on some mathematical construct.” Emanuel started raising his voice, sounding somewhat agitated.

“Indeed. But don’t get all worked up Manny. Get ready to enjoy the ride of your life.”

The rest of the group was auto-strapped onto other bundles. Marvin pointed to a video screen that was over the transporter device. He then explained what was happening. “These homotopies map to a set of vector bundles spanning from a unit surface to a projected surface. We’re going to direct these bundles to point to our desired destination in Microspace. Think of them as topological road maps to Microspace.”


Marvin and the group were blazing across space. They were now encapsulated in a clear dome. Larry was terrified as flashing lights, chiefly blues, whites, and reds, streaked passed them. His heart palpitated like a machine gun. While he saw a man’s shirt fly by his head, he was compressed against the back of the dome. There was a continual buzzing sound inside the dome.

As he was bracing for a fatal crash, he heard a voice whisper in his earpiece. “You seem to be somewhat distressed,” mentioned Marvin. 

Larry anxiously spoke into his mouthpiece. “We’re moving way too fast. We’re going to lose control.”

“No. We’re not moving that fast at all. It’s an optical effect.”

“What’s that?” replied Larry.

“The manifolds we’re traveling along are being created very rapidly. This creates a blurred sensation which makes it appear like we’re moving faster than we actually are.”

“Manifolds? What are you talking about?”

“We’re in stage four, my friends.”

“Whoa. Why are we slowing down? ... Whew, that’s better.”

“It’s an auto-stabilization procedure. We’re halting the construction of the manifolds so we can observe what we’re experiencing. Kind of like a tour bus that stops at certain sites. You’ll get to see how the manifolds are actually created. I call it topological breeding.”

“So what about these manifolds you’re so crazy about?” asked Stephanie.

“Think of them as ‘spaces with connections’. They’re Riemannian spaces containing a collection of mappings which facilitate movement from one place to another.” Marvin pointed to hilly, multi-colored overlapping spaces in front of them. “While you’re traveling along a manifold, another is being created in front of you. You’re persistently attracted to the next one by a TMP field derived from a map called a diffeomorphism. Think of a diffeomorphism as a pathway between the manifolds. The actual movement along an individual manifold is guided by a process called parallel translation.”

“Is that like parallel parking?” asked Patrick, smiling.

“Very funny Patrick. Anyway, take a look over there,” said Marvin, as he pointed to a manifold being created in front of them. “Do you notice the lines being formed?”

“Yes, I see them,” said Stephanie. “They’re straight for awhile, then they appear to curve downward.”

“Precisely,” replied Marvin. “The parallel translation is a set of operations to approximate the curve of the surface by using broken lines consisting of geodesic arcs. Sum up these arcs and we get what is known as the Gaussian curvature. This curvature permits smooth movement along the surface.”

The dome proceeded to move forward. In front of them, a manifold revealed a tapestry of varying textures and colors.

“It’s stunning,” remarked Stephanie.

“Absolutely a visual delight. And do you notice how comfortable the ride is?” asked Marvin.

“Yes,” she replied. “Looks like you’ve taken some of the measures we discussed to insure that the rapid changes in Microspace don’t radically alter human physiological functions.”

“Indeed. We’ve imposed certain mathematical properties to insure that pressure is normalized, the temperature is tolerable, and other environmental conditions are favorable.”

“Why are we getting smaller?” asked Patrick, as the group was shrinking.

“Our researchers have termed it iterative manifold contraction. Each manifold is a contraction of the previous one. We are smaller once we reach the next one.”

The group was hovering above a vibrating surface riddled with holes. They were bubbling with a light blue, vapor-like substance along their rims. Arch-shaped handles protruded from the surface; the dome cruised right under one of these arches. Emanuel was momentarily in silence as he observed the presentation of an abstract reality that he had only read about in textbooks.

 “It’s amazing, isn’t it?” said Marvin, as he put his arm around Manuel’s shoulders.

“I can’t describe how I feel. All I can say is that reading about topology and related topics is interesting; but to experience it directly, cruising the surface of a manifold like this, well, it’s simply …” He took a deep breath and started shaking his head.

“Quite impressive, indeed,” said Marvin. “We’re taking plenty of video shots along the way.”

“Now, how are these holes and arches created?” asked Patrick.

“The TMP I discussed earlier provides the initial seeds of this process by generating values which create the number of holes and handles in the manifolds. We can’t predict these initial values, but once generated, they remain constant throughout the process. The formal study of these holes is called homology.”

Marvin navigated the dome into the center of one of these holes. It had a smooth, light-blue surface. It was about five times the height of the dome, and approximately the scaled size of a football field. Just before landing, a four-legged platform emerged from the bottom of the dome. Once it made a soft landing, Larry wanted to leave the dome; but Marvin told him that it was not possible, citing the risks of leaving their space ship. There were three other holes in the manifold, but they were out of view.

As the dome jettisoned from the surface, Marvin pressed a few buttons on the control panel. An additional hole was instantly created on the surface. The dome jerked upward, then partially spun clockwise. “You see, if there are extra holes, this unfavorably alters our movements. Now, watch what happens if we add a handle to the surface.” After a couple of buttons were pressed, an additional handle was created. The dome violently swung to the left. “Now you understand why we keep the number of holes and handles constant.”

After Marvin normalized the flight path, Stephanie pointed to a bridge-like structure connecting two manifolds. It was slightly concave, dark green, and surrounded by a viscous substance. It was gently swaying horizontally.

“That’s an immersion,” said Marvin, as he maneuvered the dome to hover above its surface. “Based upon a diffeomorphism, it’s a continuous, smooth differentiable map that permits us to move freely between these manifolds. As I said before, TMP draw us to the next manifold, across the immersion; but while primarily a smooth ride, it does cause some quirky motion. Any unintended movements are corrected using fuzzy controllers.”

Marvin pushed a couple of levers on the panel. The manifold construction process returned to its normal speed. Patrick felt a jolt through his body. He moved backwards in reaction to the sudden motion. The group was moving quickly, but they also were rapidly changing direction.

“Through the wonders of TMP, we have stumbled upon a method to induce space-time to open its hidden corridors and allow us to freely pass through them. These corridors are topological pathways that branch into many different worlds. We learn to navigate these pathways by using innovative techniques like transversal steering.”

“Feels like we’re auto-racing or something,” said Larry.

“A good analogy. There’s a shift of angular force upon a map’s tangential space, allowing us to control what branch we take and continue steering us to our targeted Microspace. We're moving in the opposite direction to this shifting force. You should feel something similar to G-force.”


When the manifold hopping came to an end, the dome collapsed. Patrick was rapidly sliding down some type of tunnel filled with a misty, fog-like substance. He let out a loud scream. For the most part, he was moving downward through twists and turns; but at the tunnel’s end, it became horizontally level. He slowed down to a smooth halt. Marvin, with arms folded, was awaiting his arrival.

Larry, feeling nauseous, climbed out of the semi-transparent tunnel. “Why did the dome fold up like that? Why did we have to free fall?”

“I wanted you to directly experience it,” replied Marvin. “Besides, you did enjoy it, didn’t you? It’s as easy as going down a water slide.”

“Yeah, thanks Marvin. I’m not too amused,” said Patrick.

“Come now,” laughed Marvin. “You handled it quite well.”

Once the rest of the group came out of the tunnel, Marvin continued with his explanation.

“We are now in the fifth and final stage of the process. This involves the transport from the last manifold to the targeted Microspace. In turn, this depends upon the nature of the targeted state. For example, if our intended destination is the molecular world, we need to transport the traveler to a designated nanoport. If it’s the quantum world, then we send him into a Hilbert Space. Finally, if it’s the world of superstrings, we propel him into a ten-dimensional world with an E8 by E8 supersymmetry.”

“And just how do we get to these different destinations?” asked Stephanie.

“This is very difficult to describe. To reach the final destination, it is necessary to implement the appropriate gauge field transformations and to achieve resonance with the wave patterns of the targeted Microspace. These oscillations will vary with different Micro spatial domains. The smaller the target, the more difficult the transformation.”

“What about these strange, enclosed objects that we just passed through,” asked Stephanie.

“They’re called tubes. It has to do with tubular neighborhoods of a closed manifold. Remember those vector bundles we traveled on? They were our road maps. And those bridge-like structures connecting manifolds, the immersions? Well, it turns out that for certain submanifolds, these tubular neighborhoods are a pairing of those vector bundles and particular immersions called embeddings. Since the boundary of each neighborhood is a differential form constructed from the Riemann curvature tensor, tubes naturally arise from the Riemannian space.”

“Now what does that mean in English?” asked Patrick, sarcastically.

“Yes, probably a bit too technical,” interrupted Emanuel. “Here’s how I would describe it. Consider these tubes to be a collection of underground passageways. Think about moving through a labyrinth of passages connecting many different places.

“Now, the road maps which we used to travel across manifolds also helped get us out of the labyrinth. The so-called embeddings are nothing more that the passageways in the maze. Each roadway in the map connects to a specific passageway.”

“Thanks, Manny. Now I can retire,” said Marvin. He pressed a few more buttons. The group headed out of the tube. They were led into a terrain that featured rolling hills, valleys and all types of bright colors.

The group landed in their targeted Microspace. They were now in a world filled with all types of molecules. Quirky atoms were bound together by pulsating chemical bonds. They landed on a nanoport platform. It hovered above a dark, viscous molecular substance.

“Riemann manifold hopping, once all of the kinks are worked out, might become a leisurely activity for adventurists,” said Marvin. “Think about tourists flocking to resorts built along quantum shores or in the secluded subatomic terrain of scenic topological mountains and valleys. Tropical paradise getaways could be set up on chaotic islands of stability or in quark symmetries. There are no limits to the possibilities.”

“This concludes the flight demo. In a few minutes, we’ll head back home.”