Analog SFF, January-February 2008

by Dell Magazine Authors

  In a tenth gee, falling down was no big deal. Lee twisted around and tried again, and with practice found he could stand almost without conscious effort.

  As if being able to stand up would do him any good.

  Or would it? Wait, if he could stand, couldn't he jump? In a tenth gee, he ought to be able to jump pretty high. Wouldn't there be some way he could just jump that tiny distance from the top of his trajectory to the rim?

  With a little practice, he discovered that indeed, he could push himself off the ice hard enough to get momentarily airborne. It took concentration and a lot of coordination to actually jump, instead of just having his limbs flail out in all directions across the ice. (Not ice, he thought. Mirror. It's not really ice.)

  But as quickly as his elation rose in him at the sudden hope, it drained away. Being able to jump didn't do him any good, because he could only jump straight up. No, not even straight up—he had no traction at all, so he could only jump in a direction exactly perpendicular to the surface of the mirror. He called up the picture of his trajectory across the mirror in the heads-up display and stared at it, trying to see a flaw in his reasoning. Suppose he jumped right at the moment he reached his highest point. But the slope of the mirror was the wrong direction; he'd actually be jumping away from the rim. No help. If he jumped a little early? No, still no good; he'd always be jumping the wrong direction.

  He drew himself a little diagram in the heads-up display and put an icon of a man in a spacesuit on it. Any way he studied it, though, he couldn't see a way that jumping was going to help him. In fact, it even hurt him—if he could add just a little bit to his velocity toward the rim, he could make it, but his jumping added velocity away from it.

  Or, wait, was that right? His jumping would actually be perpendicular to the way he was moving. So it wouldn't change his velocity along the mirror. Or would it? He wished he understood the physics a little more. The mirror was curved. It sure looked like there ought to be a way to make this work. His jump was a vector, and there had to be some way to make that vector work in his favor. But he couldn't see it. It was too complicated for him

  Appraise resources available and apply them to solving your problem. His resources were himself, the child on the world's biggest swing set ... and a databot tutorial about physics.

  He flicked back to the tutorial, searching through screen after screen explaining simple harmonic motion. That was his situation, he saw; sliding in a parabolic potential well. But nothing in the tutorial discussed pushing off in the third dimension. It explained that his motion followed a perfect sinusoidal curve—he knew that already—and that the period of oscillation was constant, a fact that didn't help him any. Then the tutorial went on to cover the case of driven oscillators, when there was an external force pushing in time with the oscillation. Even a very small force, if he could apply it in phase with his motion, would quickly increase the amplitude of his motion. Even a small force—he wanted to scream at it. That was the problem! He didn't have a small force, and the tutorial wasn't giving him any clues. Instead, it wanted to tell him about kinetic and potential energy.

  When in doubt RTFM, he thought. Read the fancy manual. A hundred times he'd gotten that advice, although sometimes the adjective used was something other than “fancy.” And the tutorial on simple harmonic motion was the only manual he had. If the answer was anywhere, it had to be there.

  He started in on the chapter on harmonic motion, reading from the beginning, working the problems, single minded in his approach. Once he looked up, checked the heads-up display, and realized with a shock that over an hour had gone by, three full oscillations, while he hadn't been paying attention. With his attention fully engaged, the material was interesting, he thought, worth studying just for its own sake. He could suddenly see why physicists were so passionate about their work. The solution had to be there, it had to be hiding somewhere in the mystery of kinetic and potential energy.

  And it was.

  He almost laughed when he finally saw it. It was the swings.

  He needed to get serious. He checked his display and realized that he had been studying the physics text for over three hours. The Sun had set. While he hadn't been paying attention, he had made eight trips across the mirror and back. He checked his power level; about nine hours of battery life left. But he had the sequence worked out in his head.

  He was lying on his back, sliding downward, so the first thing was to roll over onto his belly. He called up the graph of his position and velocity, watching his progress in the display, and as he approached the bottom, he got ready by pushing himself onto his hands and knees. When his velocity reached maximum, at his lowest point on the pendulum swing, he got up onto his feet.

  That was it. That was his plan.

  It was a trick to stay upright on the slippery surface for the twelve minutes it took him to slide toward the rim. When he was vertical, he'd raised his center of gravity by perhaps seventy or eighty centimeters. Not a lot.

  The rim approached. Standing, he could now see over the rim onto the snow-covered plains, even though he was tilted significantly away from the edge. The snowcat was nowhere to be seen.

  Still, though he could see outside the bowl, the surface beyond was still out of his reach. No matter. As he coasted to his momentary hover just short of the rim, he implemented the next phase of his plan.

  He sat—or, rather, allowed himself to fall down—and then pressed himself down against the surface of the mirror, trying to squeeze himself as flat against the surface of the mirror as he could manage.

  That was it. A small change in center of gravity, but—he hoped—if repeated enough, a significant one. Every time he passed the bottom of the bowl, he raised himself up—at each rim approach, he lowered himself down. It was like pumping a swing; each time he was pushing just a little bit of energy into his motion. Whenever he crossed the bottom, by raising himself up he moved his center of gravity just slightly toward the invisible pivot point of the swing, and his speed increased infinitesimally. When he lowered himself at the rim, he was hardly moving, and so he lost nothing. Each cycle, he would gain just a little energy.

  Another cycle: stand at the bottom, drop at the rim. Again. Again. Was the rim closer? Hard to tell. Again. Again. He allowed his mind to go blank, concentrating on nothing other than his moves. He was back on Vesta, back on the swings with his brother, trying to pump the swings enough to race his brother to take the swing up over the bar. Again. Again.

  Now the rim definitely was closer—as he dropped down, he stretched his arm out as far as he could, and his fingertips touched snow. Not enough to get a grip, but still, progress. He tried to pull himself up by one fingertip, but no success.

  Down. Up.

  Again, a little closer; this time he got two fingertips over the rim, and he pulled as hard as he could. Again. Again. Now he could get his entire palm over the rim, and he pushed down with all his strength, pulling himself up and almost succeeding in getting his elbow over the rim before he slid away.

  On the next slide, he had both his hands over the rim, he pulled himself up to his elbows, pushed up, then flung his knee up over the edge, teetering for a moment and then flopping awkwardly out onto the rim, onto the surface.

  He was out.

  He was on the surface, spread-eagled in the snow, and wasn't even breathing hard. It had been easy! “Physics,” he said. “It's all in the physics.” He crawled away, not trusting himself to stand, putting a few meters between himself and the treacherous edge. He checked his power. Almost an hour of battery left, but that was plenty. As soon as he got to the snowcat, he could plug into the cat's power supply. And the cat was—

  The bottom dropped out of this stomach. The cat was nowhere near.

  He checked the inertial navigation system in his display, disbelieving the figure it was telling him. The cat was twenty kilometers away!

  The display showed his position relative to the snow cat clearly. He'd come out on the wrong rim. />
  He sat down on the snow and checked the display again, and then once again, trying to make it come out right by concentrating. How could he have made such an elementary mistake?

  The cat was on the opposite rim, but not precisely across from him. During the hours that he had been sliding across the mirror, the planet had rotated under him. He'd come out on the same side he entered from, but the planet itself had moved. The snowcat was about a 150 degrees around the circumference. That was better than having it be exactly on the other side—it would be only twenty-nine kilometers for him to walk around clockwise, a little less than the full thirty-five kilometers around the rim.

  But twenty-nine kilometers might as well have been a thousand, or a million; there was no way he could walk that far in the remaining—he checked his display—fifty-two minutes.

  He lay back, suddenly exhausted. How long had he been awake, anyway? He could just go to sleep—

  That wouldn't get him anywhere. He sat up again, the emergency protocols played in his mind like a mantra. First, take whatever immediate actions are needed to prevent the situation from deteriorating....

  He stared out at the black mirror. He visualized where the snowcat must be, on the far rim of the bowl, invisible in the darkness.

  ...Item five: Appraise resources. Apply the resources available in the most efficient way to effect rescue.

  The resource he had was one frictionless bowl, perfectly black, perfectly smooth, perfectly frictionless.

  It was the last thing he ever wanted to do, but waiting and thinking wouldn't help; all it could do was to delay him, and maybe he would lose his courage. It had to be done now.

  He stood up and walked away from the rim, then turned and fixed his eyes on the edge. There it was.

  It was the laws of physics again. He had been trapped in the mirror because he had entered it with insufficient energy to get out again. All he had to do now was go straight across, a little bit to the right, but of course he would have to aim further to the right, compensating for how the bowl would shape his motion into a curve. As long as he had enough energy, as long as he entered with enough speed, the mirror would be no trap. If he ran into the mirror, instead of allowing himself to fall, he would come out again.

  It was physics.

  His hindbrain was screaming to him that it was suicide, but there really wasn't a choice. There never had been. He got a running start and dove into the mirror.

  His dive took him on a long flat curve, and in the low gravity he seemed to hang in space, the blackness below him mirroring the infinite depths of space above him, weightless in his arc for a moment that seemed like forever.

  And then he hit the surface of the mirror, sliding, sliding. In his helmet, the display showed his trajectory, projecting his motion across the mirror.

  But he wasn't paying attention. He knew his trajectory was right. He could feel it.

  At last, when it counted, he had made it over the top.

  —for Ross Rocklynn

  Copyright (c) 2007 Geoffrey A. Landis

  "Maybe teachers ought to approach astronomy from a hammock on a deserted beach as well as from the lenses of giant telescopes. The earlier in life we know we are part of something magical and mysterious, the better off we are."—Jimmy Buffett

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  * * *

  Novelette: THE NATURAL WORLD

  by DON D'AMMASSA

  Discoveries aren't always made by those in the best position to do something with them....

  “I really think you should consider getting an aquarium, Miss Wilson. Then you would be able to enjoy the beauty of God's creation without having to submit to these tedious and unsanitary excursions. These are the 1870s, after all. One doesn't need to be discomforted while viewing the natural world.”

  Emma sighed and wished once again that she'd been able to find the right words to dissuade Jared Rackham from accompanying them this morning. She and her younger sister, Virginia, were quite capable of looking after themselves and in fact they were both more at ease covering the rough terrain along this part of the shoreline than their ungainly companion. Ever since their arrival from London, he had been appearing with distressing regularity at the cottage. It would not have been such a trial if he'd been content to abide by the customs of decent society and depart promptly after paying his respects and remaining away for a decent interval between visits, but he was clearly enamored with her, although he had not said as much, and returned with distressing regularity. Her polite but firm refusal to respond favorably to his veiled advances had so far made no inroads on his enthusiasm.

  “Perhaps you are right, Mr. Rackham, but one can only stare at the same pressed leaves and flowers for so long, after all, and the fresh air and exercise is good for the health.”

  They had been picking their way across a fairly steep, rocky slope and Rackham had managed to stumble over every third irregularity, giving his progress an erratic, uncertain quality. “There is no end to the wonders imbued in even the simplest of His creations,” he answered somewhat breathlessly. Rackham had recently been promised a living as curate of Merrivale when the incumbent retired, and had discovered within himself a previously hidden piety. “As to the value of fresh air, I must say that I fear it is most overrated. I find settled air much more conducive to my own health and have not suffered the ague or similar ills since mending my habits.”

  Emma turned away to conceal her annoyance, and raised a hand to shade her eyes. Virginia had run ahead of them, her long legs covering ground quickly and effortlessly. She would be a stunning young woman once her body had regularized its proportions, but at the moment she seemed even younger than her thirteen years. “Ginny! Please wait for us to catch you up!”

  But if Virginia had heard her sister, she chose to pretend otherwise and a moment later disappeared from sight, having reached the crest of this particular rise and descended beyond it. This was the farthest they'd come along the coastline since moving to Seamouth, and the difficulty of the walk had taxed their resolve, but not even this hardship had dissuaded Rackham from accompanying them.

  Emma picked up the pace although the backs of her legs were aching and she was breathing heavily. She used a handkerchief to wipe beads of sweat from her forehead before Rackham could see them and launch into another panegyric about the ill effects of overexertion. Given the man's indolence, she was amazed that he had reached the age of thirty without spoiling his figure. He was still quite a handsome man, she admitted, although the effect was quite spoiled whenever he chose to speak.

  They reached the crest almost simultaneously, and Emma suppressed a smile when she saw that her companion was mopping his own brow now, apparently too breathless to speak. That suited her own mood precisely, because the vista that opened before them deserved at least a brief moment of silent, appreciative contemplation. The land fell away spectacularly, revealing a narrow defile that seemed to cut down directly into the Earth. From the opposite side, a narrow brook rushed to the brink and toppled over, sending light spray sheeting down over a riot of wildflowers, bracken, various ferns, and twisted vines that seemed to gather all the rest together. Emma experienced a sudden but brief alarm because it looked as though there was no place Virginia could have gone except a deadly plummet into the depths, but then she heard her sister's voice from quite close at hand, calling to her.

  “Emma! Come down! You must see this!”

  At first, she had no idea how to comply. She appeared to be faced with an impenetrable wall of thorn-bearing shrubbery. A brief investigation revealed this to be an illusion, however. There were overlapping ramparts of branches and stems, but it was a simple matter to move among them once the trick of perspective was revealed.

  “I say, Miss Wilson, is that wise?” Rackham made as though to take her arm, thought better of it and hesitated with one hand half raised. “The footing here appears quite treacherous.”

  “Please don't fret, Mr. Rackham. I shall take care.
Please make yourself at ease here until we return.” She thought she might escape him at last, if only briefly, but before she'd taken a dozen steps, he stirred himself to follow.

  Twice more she had to pause and search for a way to proceed, and on several occasions she'd been able to keep her footing only by grasping sturdier branches or gnarled saplings growing out of the cliff wall. It was, indeed, a cliff face they were descending, crumbling and treacherous, and she would have turned back if Virginia had not continued to call from below, even if that had meant admitting defeat to the odious Mr. Rackham.

  But at last she reached bottom and saw her sister, crouched at the edge of a pool of water only a few steps away. The hem of her skirt was heavily stained and Emma felt momentary irritation before glancing down and noticing that her own clothing, snagged by thorns and brushed by damp soil, appeared nearly as disreputable.

  “Come over here, Emma. Look at this!”

  Waves crashed against rocks only a few meters away, but the sound was muted by the convolutions of this sheltered cove. There were several brackish pools near at hand, and occasional droplets of sea spray speckled their surface. The foliage above them had formed into a canopy, and it was almost as though they'd stepped forward through time into dusk.

  “Oh, there you are!” Rackham came up behind her so precipitously that he brushed against her arm, perhaps inadvertently, and she instinctively drew away. But for once she wasn't irritated by his advent, because she was so overwhelmed by the new environment in which she found herself. It was like a great, natural cathedral, the riotously colored plants mimicking stained glass, the filtered light from above, the muffled sounds of the outside world. “I don't look forward to ascending again,” said Rackham, apparently unaffected. “The footing is quite treacherous. I should think the local council would have erected some sort of barrier, or at least a warning sign.”

  Emma refused to let his tedious chatter spoil her mood. She moved toward her sister, picking her steps carefully. There was water everywhere, and any solid ground was covered with delicate plants, which she did not want to crush under her feet. Fortunately, a scattering of smoothly worn rocks was profuse enough that she could pick her way from one to the next.