by Sonia Balcer © April, 1990
In honor of Kathryn Jewell, whose childhood musings about mirror images
formed the inspiration for this story
"These are the mountain ranges beyond," said Kelly, pointing to a large photograph as she described the terrain of Earth to QueFoure, the youngster who had come with them from a universe with four spatial dimensions. "I wish you could stay longer so that we could take you there, "she said as she ran her fingers over the raised texture on the mug that was sitting between her and the Professor. She had always enjoyed the pattern on that mug. It bore the insignia of the Oakworth University, where her father worked, along with a simple but striking rendering of oak trees along a stream that blended into a bluish-green backdrop of North-American forests as viewed from space. With its strong, peaceful appearance, it reminded her of her favorite place in the mountains where the family at times retreated for vacation. She handed the mug to Mrs. Bundle, who was making one last sweep through the living room for dishes. Professor Bundle pushed his glasses up on his nose and rose from his chair. "Yes, we should be going. I'll take you home now. Kelly, Jeff, and Greg, you should stay here since the trip will take several hours and tomorrow is a school day." After the children had exchanged their goodbyes, the Professor and QueFoure went out to the yard where the Spacebender had landed earlier that afternoon. "I've packed up some victuals for your trip," said Mrs. Bundle affectionately as she handed her husband a little box with two mugs of hot chocolate and some snacks. The Professor smiled tenderly at her and touched her elbow in an implied embrace. "I'll see you soon," he said as they got into the Starship and closed the door.
"I'll set the manifold-curvature coordinates such that we will move through the Sigma sector-that's a particularly active and beautiful region at the interface between our universes-one of my favorites," the Professor said as he engaged the Spacebender sequence. Instantly they were treated to a dazzling array of colorful, pulsating effects-"Gravitational Optics", as he had named them. Because he had worked out the Theory of Folding Manifolds and applied it to the invention of his Manifold-Curving Starship, he had been the first to see these effects, and he never tired of sharing them with those who went with him on these "inter-universe jaunts", as his wife, an Artist and Chemist in her own right, had fondly and admiringly called them.
As they enjoyed the stellar sights, the Professor used the opportunity to quiz QueFoure on Manifold Geometry, an advanced form of mathematics that described the underlying fabric of space-time itself, and which the inhabitants of the boy's world could more easily understand since they had four spatial dimensions to experience and visualize things in. "Alright, here's a good question: how many independent angles for rotation are there in five dimensions?" The boy paused for a few seconds. "Uh, it's so hard to visualize, for I have only a four-dimensional body," he said, looking up into the kind face of the Professor. "Just start with the lower dimensions and work your way up," the Professor suggested. The child's brow became knit in concentration. "Okay, let's see. In two dimensions there's only one angle, because that's the minimal Space in which you can even have a rotation. In three dimensions there's three: one in a given plane and two independent ones relative to a line intersecting that plane. In four dimensions there's one and two and three, which is a total of six. In five dimensions there must be one and two and three and four, which is ten." "Yes; very good!" the Professor said encouragingly. "Then, it must mean," said QueFoure, who was quite adept with algebraic summation series and saw an exciting application for them in this geometry question, "that in 'n' dimensions there are (n-1)+(n-2)+ . . . all the way to (n-[n-1]) or 1, which has (n-1)/2 terms of n, so that would be n(n-1)/2 directions! Is that how it works?"
Prof Bundle never had the opportunity to answer QueFoure's question. Their attention was suddenly diverted by a gut-wrenching lurch and the sound of objects falling off the conference table. The motion tipped them up on end and sent them tumbling across the room, where they landed hard against the great stellar map that covered the starboard wall. The ship's gravity field simulating frame was not only rocking vigorously, but the floor itself was undulating in rippling waves. With violent torques and starts, the automatic "space-smoothing" system of the Spacebender struggled against an unseen force that was threatening to pull them apart.
No matter how he tried, the Professor could not make it to his feet. Only by crawling and sliding along the floor while holding onto stationary things was he able to make his way back to the front of the ship. The Curvometer's needle was fluctuating wildly, and with each fluctuation the room seemed to stretch and contract. As he strapped himself into his seat, he glanced over the array of instruments to see if he could find some clue about the topology of the space-time fabric they were in, but the displays did not seem to make much sense. Some of the instruments were "negative", which seemed to fit the pattern of a Fold-Wave, but others were off-scale, as if the space they were in was being strangely shaped and twisted. The relentless undulations of the Fabric were beginning to hurt, and he sensed their time was running out. The Spacebender was showing signs of structural stress-the indicators were so far in the red that he cringed when he saw them. Frantically he adjusted knobs and levers to evade the center of this "storm", but they seemed to be getting pulled closer and closer to it. He thought of those at home, of Mrs. Bundle making hot chocolate at home, of Kelly with her geometry homework, of Jeff playing with Bunsen Burner; images of the University with his colleagues and students, his friend and Kelly's father, Trevor. The images became frenzied and horrid, QueFoure's parents in grief, mourning the loss of their only son, his kind wife alone and weighed down with sorrow.
"I have to get us out of this thing, whatever it is!", he told himself as he tried tweaking a few more levers. Just then he looked at the massometer, which tells how much mass is nearby to bend the space-time fabric. Even a little bit of matter in the vicinity would be enough to require some adjustment by the ship's space smoothing system so that they would not become "desynchronized" by not following the contour of the fabric exactly. This is what the ship was designed to do, and it performed quite well even in the presence of uncharted planets, moons, and asteroids. But what he saw he almost couldn't believe: the meter was totally off-scale. Only one conclusion was possible, and it was the one scenario which he had hoped would never happen. They were being pulled into a worm-hole, an incredibly heavy star which had emerged totally unannounced by "tunneling" from a "black hole" in another universe.
What if they were beyond the point of no return? This was the worst of predicaments that a space-bending starship (and its occupants) could find itself in, for the gravitational field around such an object is so strong that, once inside, even light cannot escape. The probability of such an object tunneling into their universe during one of their trips was incredibly low, but the professor had always been aware of the possibility and had prepared for it by designing everything, mechanical and electrical, as robustly as possible. But unless they did something very quickly, they would soon be totally crushed, since the Spacebender's ability to bend space for travel would be no match for the oppressively tight curvature near one of these objects. Had they been in an ordinary ship, they would have been torn to shreds much earlier. In the Spacebender, the "Smoother" was valiantly protecting them against those destructive forces, but it couldn't hold out for much longer.
"Professor!" QueFoure called suddenly, "how about using the pop-out maneuver from last time?" Though his head throbbed painfully, the professor's face noticeably brightened at the idea. Indeed, the last time he had gotten into trouble, stumbled into a stormy region between two universes and gotten horribly space-sick, QueFoure's parents had mapped out a safer route for traversing the interstitial space between the universes. Although in some respects this was a much different situation, there were similarities which might allow him to use certain geometrical aspects of the pop-out trajectory to safely maneuver them out of this region of the universe.
Without hesitation, he made an adjustment for their present position and trajectory, and started the sequence that would "pop" them right off of the fabric of their universe and into the interstitial, inter-universe subspace, hopefully a different one from where the wormhole was originating. The ship moaned one final time. He marveled that the structure, a composite alloy that he and his wife had shaped with their own hands, didn't disintegrate into a billion imploding pieces of mangled hull. He caught a glimpse of QueFoure, hanging onto the conference table, surveying what was going on around him. From the way their trajectory felt and how the dials moved, it was clear that the Spacebender was taking them through some manifold shapes they had never been in before. He had just decided that maybe the pop-out maneuver was going to work out smoothly, when suddenly there was one last wrenching motion that felt like a whiplash, no doubt the result of being "popped off" of a region of such radically curved Space-Time fabric. His eyes began to see a haze of red, and the room began to get blurry. Quickly he swiveled his chair around to a clear "workbench" portion of the console where he could lay his head down to keep from hitting the controls as he lost consciousness.
Professor Bundle felt strange and woozy. He desperately wanted to sit up and check on their course, but his mind seemed to be wrapped in thick cotton. For a moment it seemed that he could step outside of himself and get above the cotton, but even the self that thought this was within a haze. He half dreamed, half realized that his ship had gotten into some twisted subspace wherein the Bender could only compactify the manifold into "strings" of space, so that it was forming a bundle of fibers. These were like a forest through which the Ship was slowly making its way. But the thing kept turning, slowly turning, leaving the Spacebender without a point of reference-hopelessly disoriented in a subspace they might never be able to find their way out of
A clearer level of reality became superimposed on the dream. He was turning, yet stationary. It left a sickening feeling in his stomach. He was on the floor, and his torso burned where the seat strap had been. His head was throbbing, and there was a sound in his ears like a waterfall. "Bad sign. I've cracked my skull open," a part of him conjectured with clinical detachment. Someone was speaking, trying to be heard above the roar. He concentrated, trying to make out what the voice was saying.
"Ess her Un-dull . . . PROFESSOR BUNDLE." Slowly his face drifted up and out of the cotton. His eyes opened. A concerned, four-dimensional face was peering at him from beside the console. "I thought you'd never come to." It took a moment for the meaning to catch up with the sound. "Son, are you alright?" his voice cracked as he lifted his head slightly. "A bit shaken up, but I'm okay." He carefully turned his head, unable to raise it yet on account of the throbbing pain. "Ah, good. No doubt your four-dimensional body is better suited for little excursions like this-there are more ways for it to adapt geometrically to the changing manifold shape than mine has," he mused in a mumble that the boy could barely make out. "Professor, stay awake," QueFoure urged, fully aware from the last time of the dangers of cardiovascular swelling in the head. "What kind of condition am I in?" "Your eyes are very red and there's some blood coming out of one of your ears, but it's nothing that my parents couldn't fix."
The Professor smiled inwardly. He knew that four-dimensional medicine could work wonders on three-dimensional bodies-there wasn't the limitation of either working only from the outside or having to do surgery on the person. They could go right to the damaged tissue and treat it directly, accessing everything and damaging nothing. "But you shouldn't sit up yet, not until you take one of those Whatsit pills from the trauma kit," the boy quickly added. "Yes. Aspirset." "The one that keeps swelling and inflammation down but seals off the bleeding?", QueFoure said as he retrieved the box and took out a medicine wafer for the Professor to put under his tongue. "Uh hungh," the Professor nodded as he took the tablet gratefully, immediately feeling an easing of the pain which by then had risen to an alarming level.
After a few minutes he sat up slowly. "Let's see where we are," he said as he gingerly made his way to the Starboard map. "Actually it looks like we are not far from my home," said QueFoure pointing to the place where Corridor World was located on the map, "except that something isn't quite right. There's our neighboring planet. But at this point in its travel around our star, it should be on the other side." "You're right," said the Professor. "In fact, everything seems to be switched around somewhat. It's as if we are looking at a mirror image-left and right are completely reversed! If that is so, then maybe we have found a parallel universe: same planets, same people . . ." His voice drifted off as he thought about this. For as interesting as it was, he knew that since the way they had gotten into this universe was a way they would never want to go through again, it might be terribly difficult to find another way back into their own universes-QueFoure's and his.
With a sinking feeling, he began to worry very much about getting QueFoure back to his parents, not to mention himself back to his own home. Would he ever see his wife and the children again? He put these thoughts out of his mind and tried to figure a way out of this dilemma. QueFoure must have been thinking about the same things, for he said, "I wonder what will happen if we go down to what looks like Corridor World. I mean, will I meet the mirror image of myself? And what if we can't get back to my own parents?" The Professor put his arm around the boy's shoulder reassuringly. "Let's not worry about that right now. The first thing we should do is go down to that world and try to meet your, er, mirror image parents. Since they are Geometers and Medical scientists, perhaps they could help us find a way back to your own universe."
This comforted them both, and the Professor set the coordinates, carefully compensating for the mirror image-reversal, and landed them in Entrance Tower, the equivalent of the structure from which they had left many hours earlier. To their surprise, they were immediately greeted by QueFoure's parents, who looked at their son with a mixture of joy and concern. "We were worried about you, dear," said his mother as they helped the woozy Professor to the nearby resting station for medical evaluation. "This was a particularly severe Fold-Wave, and I'm so glad you're safe." The boy considered her in puzzlement as they reached the Station. Apparently there was no mirror image of him-this was his mother, and she had been waiting for him. But before he had a chance to form his question, she voiced what they had all been noticing. "Something looks different about you." "Yes, both you and Neubert look somehow changed," said QueFoure's father, "are you alright?" "Yes, although everything seems to be mirror-reversed since we had an encounter with a wormhole," the Professor mumbled half-coherently from the comfortable Homeostatillie as he began to doubt what universe they were in. The Doctor looked carefully in her son's face, touched his left cheek, then took his right hand in her own. "Honey, you learned to write with your left hand. How is it the callouses are now on your right?" "But this is my left hand," said QueFoure with even more puzzlement and amazement. As they talked and compared notes, the situation soon became clear. They were in no mirror universe; they were in QueFoure's own world. It was they who had become reversed.
After QueFoure's mother, the medical scientist, had attended to the Professor's injuries (carefully compensating for his mirror-reversed brain anatomy), and provided for a brief but needed rest, they gathered together and discussed the situation. Devcor, QueFoure's father, conjectured that when they performed the pop-out maneuver, the extreme curvature of the manifold caused by the presence of the wormhole had thrown them into a six-dimensional "super-space", an occurrence which he had predicted many years before in his own Manifold Geometry work. In this space, they had been free to rotate about a "super-axis" which could possibly flip their "left" to "right" and visa-versa. And it just so happened that they had reentered QueFoure's universe in this reversed state. "I certainly wouldn't want to stay this way for the rest of my life, but it's much better than not being able to get home," the Professor said with a mixture of relief and pensiveness as he thought of the implications of having to relearn the layout of virtually every building, every machine, every landscape he had ever known-not to mention the fact that reading was going to be a bit awkward with the left and right reversed.
"There may be a gentler way to reverse it than the way you came," said Devcor thoughtfully. "According to some work which I did a few years ago, it should be possible to use a pulsating star to get into the superspace, although it has never been tried because the manifold-bending mechanisms of our spacecraft are not yet capable of safely creating such tight curvatures-but your novel Spacebender "Manifold-Smoother" design can perhaps achieve this." The Professor nodded, "And just to think there are those who don't know that science is both useful and fun I'm looking forward to trying it!" he said with a twinkle in his eye. "After we check out the Ship's physical health;" QueFoure's mother Taldiara said fondly, "we want to get you both back in good condition, which I'm sure Meara would appreciate too." The thought of his beloved SpaceBender's structure painstakingly being checked out by four-dimensional imaging technology under the watchful eye of his medically astute friend added to his joy in a quiet sort of way, and he looked forward to sharing all these things with his wife.
After more discussions between the Professor, QueFoure's family, and Devcor's colleague Heptov, their plan was carried out. Guided by the calculations of Devcor and selecting just the right pulsating star, the Professor took himself and QueFoure back into the six-dimensional superspace, performed a controlled half-rotation, and was treated to some indescribable optical effects which they had missed during their first traumatic episode. When they reemerged into QueFoure's universe, they were back to normal, to the relief of everyone. With this unexpected confirmation of his Superspace Window theory, Devcor's work made a significant contribution to the field of Manifold Geometry (not to mention four-dimensional StarShip design), to the enrichment of all on Corridor World. And because the Professor, during the maneuver, had left behind the mugs from the snackbox, he had a most fitting souvenir of the experience to take home to his favorite little girl.
The End (for now)
Sonia Balcer © April, 1990
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[notes about tesserects]