Phoresis

1

Freya walked slowly across the ice, using her rake to scrape aside the thin cover of dirt and crystalline powder, peering down into the translucent slab below for any sign of a slender rootlet struggling to force its way out into the air.

Something dark and linear caught her eye, about a hand’s breadth deep. She stopped walking and squatted down for a closer look, then she took her pick and swung it into the ice. Once the surface shattered it was impossible to see anything beneath it, but after a dozen blows she stopped and cleared the debris out of the hole she’d made. She’d exposed the inclusion, but it wasn’t a root: it was just a streak of trapped gravel.

The sun was behind a bank of reddish clouds that covered most of the western sky and left the ice field in a state of ambiguous gloom, so she glanced up at Tvíburi, hoping to find that the time had sped by while she worked. But the twin world was still just a crescent: the afternoon shift was barely half over.

Freya was tired and hungry. She took a deep breath and held it in to make the most of it; by the time she exhaled she felt a little steadier. The air was thin from the sun’s recent tantrums, but thousands of villages besides her own would be performing the same time-tested remedy. The Yggdrasils thrived on the temperature difference between the buried ocean and the cool of the surface, but sometimes their roots didn’t make it all the way through the ice. Chipping away the final barrier let them complete their journey—and once they were exposed to the open air, they were free to dispense all the volatile treasures they’d pumped up from below.

Off to her right, her nearest neighbor was intent on her own patch, and too far away to converse with unless they shouted. Freya stopped procrastinating and recommitted herself to the task. The sooner they’d reached their quota, the sooner they could all go home.

The communal tent was noisy, and the long table was more crowded with diners than food, but Freya was glad to be out of the cold, walking barefoot on the tent’s tattered rugs. She eyed the remaining provisions and estimated a fair share, then she gathered the food up quickly before someone assumed she’d lost her appetite.

It was only as she sat down to eat that she realized she’d arrived in the middle of an argument. “And what about the soil?” Gro demanded. “This is just a stopgap! It might help us breathe, but it’s not going to give us so much as a handful of new soil.”

“You want to dig a whole new geyser while we’re out here?” Hanna teased her. “Cleave through a few thousand strides of ice and…” She gestured with her hands, miming an eruption. “What could be simpler?”

“So if we don’t know how to fix the problem, no one should talk about it?” Gro retorted. “In my mother’s day, the yields were at least a third more than they are now!”

“So tighten your stomach,” Bridget advised.

“And keep your brothers in check,” Hanna joked.

Gro’s demeanor was becoming increasingly sour. “Will you laugh when your children are born too small and sickly to survive?”

“You didn’t tell us you were pregnant,” Erna interjected solemnly, tentatively offering Gro some of her own food.

“I’m not!” Gro gripped the table in frustration. “So does anyone else believe that there’s a problem? Or am I just imagining it?”

Freya said, “The yields are going down, everyone’s seeing it.”

“At last! Thank you!” Gro stood up, as if to walk over and embrace her in gratitude, but then she changed her mind and sat down again.

“But I don’t know what we can do, except hope for a fresh geyser,” Freya added. She had never heard of any kind of intervention that could achieve such a goal.

Gro said, “How about acknowledging that this isn’t going to fix itself, and turning our minds to finding a solution?”

There was a moment of silence from the other members of the group, and then Hanna conceded, “There must have been a time before anyone thought about exposing the roots. When they all just sat around, too tired to move, waiting for the air to replenish itself.”

“Exactly,” Gro replied. “And if they’d kept on that way, we might not even be here now.”

“But a geyser?” Bridget protested.

“If it were easy,” Gro said, “it would have happened long ago. Keep it in your minds, that’s all I’m asking. Search your thoughts while you search the ground. It might even help you pass the time.”

The next morning, Freya took Gro’s advice, staring into the ice as diligently as ever as she trudged across the unbroken plain, but letting the impossible problem sit like a nagging onlooker in the back of her skull.

Geysers came and went, with no apparent pattern to their arrival: bursting out of the ice and then flowing twice a day, lasting anything from a year to a century. As fickle as the sun’s own eruptions, they provided an erratic counterbalance to those air-ablating blasts. But while Freya had no idea what caused the solar flares, every child was taught the origin of the geysers.

As Tvíbura and Tvíburi turned together, their mutual orbit swung them around in a single day, compared to the fifteen days it took them to circle the sun. So Tvíbura’s choice to fix her gaze upon her twin precluded the same relationship with her light-giving mother—and just as well, on every count Freya could think of. People joked about the lonely cousins in the realms where Tvíburi was hidden from sight, but while the gifts of nocturnal light and an immovable beacon to navigate by were great boons, if the world had instead been divided into the eternally sunlit and the eternally dark, neither half would have been grateful.

But the other benefits of Tvíbura’s rotational allegiance were just as crucial. Only a single point at the center of the world could fall freely, surrendering completely to its mother’s and sister’s pull; the rest of the rock, ice and ocean that was dragged along with it was forced to compromise, struggling to hold together despite gravity’s predilection for tugging harder on whatever happened to be nearest. And unlike the force wielded by Tvíburi, to which the world could accommodate once and for all, the sun’s stretching and squeezing cycled relentlessly as it rose and set. The rock at the core grew hot from this endless kneading—which kept the ocean around it from freezing solid all the way down. The ocean, trapped between rock and ice, was forced to push hard against its confines, and the same gravitational edicts acting on the ice itself left it groaning and splintering. When the flaws in the ice lined up, the pressure of the water was enough to drive the ocean’s riches all the way to the surface and beyond—restoring the air, and raining fresh, fertile soil down upon the land.

Freya paused to examine a dark smudge in the ice. But it was too diffuse to be a rootlet; it was just dirt, trapped beneath the now-compacted crystalline snow from some long-extinct geyser.

It took the strength of the sun itself and the rush of two worlds through the void to crack the ice and squeeze the ocean into the sky. The pause they were suffering was not from any lack of the usual forces; it could only be that the fractures required for a geyser were currently misaligned, present here and there at different depths but failing to meet up. If water had been finding a path to the surface lately, word of the event might not have reached the village—but the thicker, sweeter air it brought would have made itself known long ago.

Freya held the image of frustrated fissures in the back of her mind as she worked. Even if she’d identified the true nature of the problem, it was hard to imagine any way that a few thousand surface dwellers could influence the behavior of cracks in the ice so far beneath their feet.

A part of her counseled: Time will fix it. The geysers had flowed freely in the past, and if chance alone had stymied them, by chance alone they should return.

But how quickly? How certain could she be that any children she had wouldn’t starve before the resurgence?

She looked up at Tvíburi. A slender white streak was clearly visible, rising up from the sunlit edge, bright enough to stand out against the sky. Their twin wasn’t suffering from the same hiatus, but Freya didn’t know if she should read this as a promise that the two worlds’ fortunes would converge, or if Tvíburi was simply mocking her: flaunting the very thing her people needed, while knowing it was utterly beyond their reach.

“There must be life there, surely?” Freya asked her friends around the table. “If Tvíburi’s made of the same ingredients as our world, experiencing the same conditions…?”

“I looked at it through a telescope once,” Erna said. “At a traveling fair. You can see the geysers clearly, and the soil they’ve spread over the ice. That much seems to be the same.”

“No farms?” Hanna joked.

“Farms might be a bit small to see, but I couldn’t spot any grasslands either.”

“I bet there are methanogens in the ocean,” Gro declared. “Whether or not there are creatures on the surface.”

“If the surface is barren,” Bridget replied, “why wouldn’t the ocean be barren too?”

Gro said, “Think how close these worlds are, and how long they’ve been together. How many chances would there have been, over the eons, for a geyser to blow spores all the way to Tvíburi?”

Freya laughed; she was not dismissing the idea, but it made her giddy. She said, “If that’s true, why don’t we follow them?”

This suggestion was enough to plunge the group into silence. Even Gro looked at her as if she’d lost her mind.

“What?” Freya protested. “If there is good air, and fertile soil…” She trailed off, unsure just what inspiring conclusion she’d thought she was reaching for. Quite apart from the absurdity of hoping that a band of explorers could cross the void like a spore on a water spout, if there had been geysers to ride there’d be no reason to ride them.

Erna said, “If we want a new geyser, maybe we should poison some roots. If they shrivel up faster than the ice reclaims the channel, it could leave a gap.”

Freya was horrified, but Hanna had more practical concerns. “A gap all the way down to the ocean?” she asked.

Erna hesitated. “It would have to be.”

“So you think we could more or less kill a whole Yggdrasil?” Hanna was incredulous. “You might as well talk about snuffing out the sun!”

“The upper roots are all too narrow anyway,” Bridget added. “Even if they died and turned to dust, any water trying to take the same path would freeze before it reached the surface.”

Erna didn’t reply immediately, but nor did she seem willing to concede the argument.

“Anyone else know how to cure the world’s problems?” Freya interjected. Some of their neighbors were casting worried glances at the group; the sooner they stopped talking about poisoning roots, the better.

“It’s only been a day,” Gro replied. “After a day, if you came to me covered in fresh soil and led me by the hand to the geyser it came from, I still wouldn’t take you seriously.”

Freya woke and disentangled herself from her blankets, then lay on the floor of the tent for a moment. Twelve days into their collective endeavor, all of her friends had liberated at least one root from the ice, some of them two or three. Either she’d been unlucky, or she’d allowed her attention to wander. If she really had been negligent, today was the day to make up for it.

As she stumbled across the tent in the half light, she bumped into Bridget, but they exchanged nothing more than the grunts of acknowledgment that minimal civility required. No one was talkative in the mornings. Freya ate quickly, but when she started dressing for the ice she noticed that two of her brothers were stirring. “Go back to sleep, you idiots,” she whispered, almost wishing they could understand her words, however disturbing that would have been. They kept reading the proximity of so many women as some kind of opportunity, when in truth it was the last thing on anyone’s mind. Of all the customary prerequisites for conception, a guaranteed air supply was among the most prudent.

Freya left the tent and set out for the patch of ice she’d been allocated for the day. The advance party had pegged out rectangular sections before most of the searchers had arrived, so all she had to do was find the right marker for the corner of her latest piece of the grid. Above her, Tvíburi was little more than one-quarter lit—and when she took in the rising sun in the same view, her sense of longitude became an almost palpable thing, as if she’d physically paced her way west from the prime meridian where the twin would be perfectly bisected at dawn, watching the perspective shift along the way as it did for a nearer object if she merely leaned to the left or right. No doubt the lonely cousins were happy with their lives, but she would have felt bereft if she’d been forced to live beneath their flat, distant sky.

When she reached spike number seventy-three and looked out across the territory it marked, Freya’s spirits sank. There was a plateau of blue ice rising up from the plain, occupying at least half of the patch. If the roots couldn’t break the surface where she stood, what chance would they have to climb higher? So much for catching up with her friends’ tallies.

It was hard not to feel cheated, but that was no excuse to shirk. Freya decided to ascend immediately and search the whole elevated region first. The approach was quite steep, and slippery with a lingering ethane dew; she had to use her pick a few times to give herself purchase.

When she reached the top of the plateau, she found that although the ice leveled off, it wasn’t flat like the plain around it; the surface was dimpled and lumpy, rising and falling with every few strides. Freya had never encountered anything quite like it.

The dips in the ground held much more dirt than she was used to, but she worked assiduously to rake it aside. In compensation, the mounds were much cleaner, though none of the ice itself was particularly clear: it was full of tiny defects that diffused the light, leaving it bluer, and much harder to inspect. She presumed it was newer than the ice of the plain; there hadn’t been a geyser around here in living memory, but there might have been one recently enough that its accumulated snowfall had yet to be entirely leveled by erosion.

When she reached the drop at the far end of the plateau, she reversed, pacing out a parallel strip. The uneven terrain made every step different from the last; Freya could only hope that the novelty would help her keep her mind on the task, for whatever that was worth up here. She wasn’t sure how long it would be from the time an active geyser refroze to the time a Yggdrasil would get around to sending roots through the new ice, but if there had once been a torrent of water shooting into the sky here, ripping up whatever had come before it, that could only lower her chances of success.

She arrived back at the edge where she’d started, and reversed again. She was beginning to view her lack of success with a degree of equanimity; she might be teased a little, but everyone knew her as a hard worker on the farm, and they all agreed that the tallies were mostly down to luck.

Freya stopped to rake the dirt out of a furrow. It was stickier than usual, and darker—not quite like soil, but not as loose and powdery as the fine gray dust that blew across the plain.

The rake met an obstruction. Freya kneeled down and started scooping the dirt aside with her hands. She could smell a buried fragrance rising from the furrow—several odors, in fact, some sweet, some pungent.

As the dirt parted from the thing it had concealed, she saw it plainly: a fully formed root flower, with six cooling petals arrayed around the central stalk. Freya laughed with delight; a shallow burial in such porous material probably hadn’t been doing much to limit the flower’s outgassing, so this didn’t really count as a victory for the atmosphere, but it was still more than she’d expected to find. Why hadn’t this root given up while the whole plateau was still above it, when so many others had barely made it within sight of the surface, down on the plain?

She spent a while savoring the discovery, brushing off as much of the clinging, aromatic dirt from the flower as she could, as if she were cleaning an old agricultural implement she’d chanced upon buried in a field. Then reluctantly, she rose to her feet and continued.

A few furrows later, she found a second flower, similarly buried in the dirt. Then a third, and a fourth. She was beginning to wonder if anyone would believe her when she reported the finds, even if she declined to claim them for her tally.

When the string of successes petered out, Freya wasn’t surprised; the cluster must have come from rootlets branching off from a single, tenacious progenitor—one chance event out of sight to explain all four on the surface. Nonetheless, as she paced back and forth across the plateau three more times without another sighting, she found it harder to resign herself to the outcome than before, when she’d expected nothing.

And after one especially deep and dirt-filled furrow proved flowerless, her disappointment took hold of her. She swung her pick into the ice: six blows, a dozen, eighteen. She stopped, feeling foolish; she didn’t have the time or energy to waste on pointless acts of frustration. And she very nearly walked on without even clearing away the shattered ice, but then that seemed doubly wasteful, so she squatted down and started pulling the shards out of the pit she’d made.

There was a root. She’d damaged the top of it with the pick, and it was seeping sweet-smelling alkanes onto the ice, but if she exposed some more of it, more carefully, there was no reason why the unbroken part wouldn’t shed the injured section and flower.

When she was done, she went back to the previous barren furrow and attacked it. There was nothing to be found, at any depth she could reach. She went to the furrow before it, and tried again, stopping to remove the fragments of ice after each blow. There was a root not far below the surface—out of sight when she’d first looked, but the ice here could obscure anything.

By the time Freya had backtracked all the way to the fourth of the dirt-buried flowers, she’d exposed nine roots. She stopped to catch her breath, happy but bewildered. If the pattern continued, she’d have no hope of exposing every accessible root on the plateau before nightfall—which was glorious, but utterly perplexing. How could this much extra ice be anything but an obstacle? What was it that she didn’t understand?

“It’s not about how far the roots have grown,” Bridget argued. “It’s about how hot or cold they are. If you pile up a lot of extra ice above the plain, that’s going to trap the heat: if you dug down a couple of hand’s breadths from the top of your plateau, you’d find it was every bit as warm as if you did the same anywhere on the plain. So the root tip isn’t going to stop growing, just because it’s come a long way from the ocean. It will only stop when it’s cool enough.”

“That makes sense,” Freya conceded. “But it doesn’t explain everything. The top layer of ice on that plateau has more roots in it than anyone’s found on the plain. I can see why it might be the same, but… why more?” She looked around the table, trying to judge her friends’ moods; she didn’t want to annoy anyone by seeming to gloat about her find. But it was still too strange and wonderful to be treated as purely a matter of chance, requiring no further discussion.

Erna said, “You mentioned a lot of dirt in the furrows?”

“Yes.”

“That would trap the heat even more, wouldn’t it? And it would reflect less sunlight than bare ice.”

“Right.” Freya felt a little foolish now; everyone knew that dark objects grew warmer than lighter ones. “So maybe the real puzzle is why the furrows are so deep.” Given their shape, it wasn’t surprising that they filled up with dirt, but even if it would take eons for the whole plateau to be eroded away, it seemed odd that the wind hadn’t yet sandblasted the top of it flat.

“I wonder what happens when a root flower is buried in a little valley like that,” Gro mused. “I mean, it’s still giving off methane and water vapor, but how freely does it all escape?”

Hanna said, “The methane would pass right through the dirt, but I think most of the water vapor would freeze on the grains of sand.”

Freya looked at Gro, wondering if they were thinking the same thing. But if they were, Gro offered her the chance to speak first.

“The whole shape could be a kind of growth pattern,” Freya said. “The dirt in the furrows traps water vapor from the root flowers as it turns to ice. That ice piles up, the furrows grow into mounds, and all the dirt that blows in on the wind spills off them onto the old mounds—which are now valleys and furrows themselves. And so it all starts again.”

Hanna laughed. “So the roots keep re-burying themselves in ice made from the very water they’re trying to get rid of! Which means they’re raising the plateau higher and making their own job harder—but as long as there’s enough dirt around to keep them warmer than they want to be, they’ll keep trying to push their way up into the cold.”

Gro said, “If that’s really what’s happening, I don’t know if we should be surprised that it’s the first time we’ve seen anything like it—or surprised that the phenomenon isn’t so rare that no one’s ever witnessed it at all.”

Freya wasn’t sure that they’d solved the mystery, but she doubted they’d come up with a better explanation if they sat around talking all night. Every scrap of food had vanished from the table long ago, and they’d all have to rise at the usual time in the morning.

She said, “To be honest, I haven’t worked as hard as I did today since my first harvest. Whatever made the plateau the way it is, I’m going to need to get to sleep soon or I won’t be able to face it again tomorrow.”

Bridget said, “You do know that we’re all coming with you, to help?”

Freya glanced at the others, but they seemed to be in agreement. “What about your own patches?” she asked.

“We’ll return to them when the plateau’s done,” Hanna replied. “If that’s where the roots are, that’s where our time’s best spent. No one expects you to break your back trying to get through all the work up there, alone.”

As the five friends set off across the ice together, Freya wondered if her companions were sufficiently awake yet to hear the wild thoughts that had kept her from sleep. She wasn’t even sure that she was in any state herself to decide what was worth repeating. As she’d lain on the blankets with her limbs aching, picturing the roots that stretched down to the buried ocean beneath her, the ideas that flowed through her head had seemed urgent and compelling—for all the uncertainties, and all the questions they raised. By daylight, the case was not so clear.

But when the blue ice of the plateau came into sight ahead of them, she realized that she had no hope of remaining silent all day, and it would be better to speak and be ridiculed now than to interrupt her friends when they were trying to work.

“If we placed mounds of black sand over the ice in the right pattern,” she asked, “do you think we could grow a plateau like this somewhere else?”

“I don’t see why not,” Bridget replied, managing to sound both intrigued and annoyed—as if she resented being forced to think about anything when the sun had barely cleared the horizon, but found the idea too enticing to ignore. “If you covered a big enough area, there’d probably be some roots positioned in the right place to get things started. It might take a while, but maybe it would be worth it, just to be ready for the next solar flares.”

“I’m thinking about more than the flares,” Freya confessed. “With the natural version, in the end most of the dirt will get stuck in the ice or blown away… but if people were actively tending the surface, who knows how high we could make the plateau?”

Gro said, “I think I know where you’re heading with this.”

“You do?” Freya waited, hoping to be spared the humiliation of having to spell it out herself if Gro had already decided that the idea was preposterous.

“Raise a tall enough mountain,” Gro guessed, “and the sheer weight of it will start to create new fractures. What better way to encourage more geysers?”

Freya wasn’t sure how to reply. If it was true that the ice would crack all the way to the ocean under the kind of load she was imagining, that would be the perfect outcome. But it would be dishonest of her to take credit for it. It wasn’t what she’d had in mind at all.

“That might happen,” she said. “But can we be sure that it would?”

Hanna said, “That depends on how long you can keep adding more ice.”

“Suppose we can coax the roots into doing the job for as long as we like,” Freya replied. “Keep the tips warm, so they can’t tell that they’re already high above the surface, and keep capturing all the water vapor they put out.”

Hanna grunted irritably. “If there’s no limit to how high you go, then of course the mountain’s going to break the ice eventually. You might as well pick a number, tell me to start counting, then ask if I’ll ever reach a number greater than yours.”

Erna said, “That’s not true.”

“It’s basic arithmetic!” Hanna retorted.

“It’s basic arithmetic that counting takes you past any given number,” Erna agreed, “but the comparison is false. Just because the height of a mountain increases without bounds, that doesn’t mean its weight will do the same.”

Hanna was silent for a while, then she conceded, “You’re right.”

Bridget said, “What?”

“Gravity is stronger close-up,” Hanna replied. “The farther you go above the world, the weaker its pull will be.”

“Yes,” Bridget agreed, “but it never goes away completely.”

Hanna said, “It does, when Tvíburi’s gravity cancels it out and starts pulling in the other direction.”

“Who said anything about putting the mountain right below Tvíburi?” Bridget protested.

“Nobody.” Erna was amused. “That’s not the argument I had in mind! Though if you want to put the mountain there, that will only help make it lighter.”

Freya kept quiet; her friends were doing all the work for her, and any contribution she could make would be superfluous.

But now Hanna was confused. “How does the mountain not grow heavier, if you don’t use Tvíburi?”

Erna said, “What’s one, plus a quarter, plus a ninth, plus a sixteenth… and so on, forever?”

“I have no idea,” Hanna replied.

“Nor do I,” Erna admitted, “but if I had to guess, I’d say it’s less than two, and I’m sure it doesn’t grow without bounds. The weight of a mountain would be like that—at least until it grew so tall that its own gravity started to affect the result as much as the gravity of the world itself.”

“I think we can rule that out,” Bridget said dryly. “However eager the roots are to oblige us, they’re not going to drain the whole ocean.”

“No.” Erna turned to Freya. “But it’s your mountain, after all. Where do you want to put it?”

“Right under Tvíburi,” Freya confessed.

Gro said, “That makes no sense! Why reduce the weight?”

The group had almost reached the plateau. Freya was having second thoughts; perhaps she should accept the alibi Gro was offering her, and be done with her own madness.

But she couldn’t stop herself.

“If we can break the ice and make new geysers, the job would be done,” she said. “But if that doesn’t work, if the ice bears the weight… then maybe we can build a mountain that takes us halfway to Tvíburi.”

Her companions became quiet. Freya listened to their footsteps crunching through the powdered ice, grateful that at least no one had fallen to the ground laughing.

“Why only halfway?” Hanna asked.

Freya wasn’t sure if the question was meant sarcastically, but she took it in good faith. “Tvíburi isn’t perfectly still in the sky,” she replied. “It moves slightly nearer and farther away, and even turns its face a little. If we tried to make a solid bridge of ice all the way between the worlds, it would just snap.”

“All right. But why stop at the halfway point? Why not get closer? Three quarters? Nine tenths?”

Freya said, “I suspect that ice is like most things: better at holding together when you squeeze it than when you pull on it. We know it can take a lot of weight pushing down on it—but imagine a column of ice, as tall as the two worlds are distant, just hanging from the sky above Tvíburi. I think it would break long before it reached that size. And even if I’m mistaken, I doubt that the root tips would keep growing in the same direction once gravity was telling them they were headed down, not up.”

“I can’t argue with any of that,” Hanna declared. “But it makes the next question more painful.”

Freya said, “Do your worst.”

“What possible use would it be, to go only halfway? If we could travel to Tvíburi itself, it might have the best soil and the thickest air we could hope for. But halfway through the void, there won’t even be air. We’d struggle to survive for a day! What would be the point of getting there?”

Freya had lain awake contemplating exactly that problem. “I can’t be sure,” she said. “But we’d be closer to Tvíburi, and we wouldn’t just be staring up at it, hoping for some impossible magic to raise us into the sky. Instead, we’d be staring down at it, hoping for something less magical: a way to descend. There are lizards that glide down from the tallest cliffs—and a few crazy people have mimicked them, riding contraptions that use the same principles.”

Bridget said, “But even from a cliff, it’s dangerous, and you can’t take much more with you than your own body. If you want to relocate whole villages to Tvíburi…”

“I know,” Freya replied. “But if we could send a dozen people across, with enough supplies to get started, that would be something. They could found a new village on their own. Then at least life would go on, however bad things became on Tvíbura.”

From the silence that followed, it was clear that no one took much comfort from that prospect.

Freya said, “Or, Tvíburi might have Yggdrasils too, and then the people who crossed over could start raising their own mountain. If we could grow two separate mountains, both reaching into the void, we might be able to join them with a bridge of ropes, long and flexible enough to survive the changing positions of its endpoints. Then we’d have a path all the way from the surface of Tvíbura to the surface of her twin. And if the fortunes of one world fell while the other’s rose, we could take our pick between them.”

2

Freya stood outside the meeting hall, hugging herself in a vain attempt to ward off the chill of the night air, gazing in through the windows at the crowd gathered in the lamplit room.

Britt emerged. “I was wondering where you’d gotten to. We’re ready for you.”

“All right.”

“Don’t look so worried! We always treat our guests with respect,” Britt assured her.

Freya followed her into the hall. There were about eighty people present—mostly standing, with a few seats for the elderly and infirm. At least that was likely to discourage most of her audience from dozing off, while forcing her to put her case as succinctly as possible. If she kept people on their feet too long, their patience would run out very quickly.

She took the speaker’s position at the front of the hall. “Thank you for welcoming me into your village,” she began. “And thank you for coming here tonight, to hear the reasons for my visit.”

Freya had been intending to open with a reminder about the diminishing yields that everyone was facing, but as she took in some of the gaunter figures in front of her, it suddenly felt both superfluous, and too bleak a beginning. She wanted her potential allies thinking about their own strengths, as much as their problems—and something her host had told her over breakfast had remained with her all day.

“I believe that many young people in this village, before settling into adult life, follow the tradition of the Great Walk: taking thirty days to trek the whole way around Tvíbura. I must confess that I’ve never made that journey myself, though I expect to cover a similar distance soon, as I travel back and forth seeking help with the endeavor that I’m here to talk about tonight. But since so many of you have the experience of setting out from your home one day, heading west, vowing never to turn around until you find yourself back where you started… that seems like the perfect measure of just how great a feat any one of us can accomplish. One and a half million strides! When I speak those words, it sounds impossible. But you know that it isn’t. All of you here have done it, or know someone who has.”

She paused to gauge the effect of her words. The reception so far appeared friendly, but some people were already fidgeting; they had better things to do than listen to her flattery.

“One and a half million strides,” she said, “is twice the distance from this village to the nearest point on the surface of Tvíburi! And I’m here to ask for your support to make a new kind of Great Walk possible, perhaps for the great-grandchildren of the youngest people here in this room. I want to start growing a mountain of ice that will reach up toward Tvíburi, as the first step toward making it possible for our descendants to travel there, live there, and farm there, almost as easily as they would walk to new farmland on our own world.”

Some people were gawping incredulously now, but others were smiling at the audacity of the scheme, and no one was fidgeting anymore.

Freya described the plateau she’d found out on the ice field, then sketched her plans for a faster-growing, artificially sculpted version. “We would need to make this mountain hollow, both to keep it light and to provide a route for travelers once the air out on the slope became too thin. But we would also need to partition it, building floors along the way to catch the air that the roots release, lest it all fall to the bottom and leave the upper reaches of the mountain no different from the uninhabitable void.” She was honest about the uncertainties, both in the construction process, and the ultimate usefulness of the result. “Will there be a safe way to fall from such a height, on to Tvíburi? We can’t know that, until we’ve tried to fall on to Tvíbura from a similar height. Will there be Yggdrasils on Tvíburi with roots rising up through the ice, allowing us to grow a twin for this mountain and bridge the gap in comfort? We can’t know that, until the bravest of our descendants have set foot on that world to learn the answer for themselves.”

She stopped and asked for questions. For a moment everyone in the audience seemed dazed, and as they broke their polite silence and began to talk among themselves, Freya prepared herself for the usual objections. Surely the roots would stop growing? Surely the mountain would topple to the ground?

“You say the mountain might crack the ice beneath it, bringing new geysers?” an elderly woman asked.

“Yes. That’s always possible.”

“But you’d be taking steps to spread the load, and to make the mountain as light as you can?” The woman’s tone was puzzled, verging on reproachful.

“Yes,” Freya admitted. “Some of my friends have chosen the opposite tactic: they aim to build a mountain that works like a pick, with its weight concentrated on the smallest foundations possible. They hope to raise it at the western setting point, where Tvíburi does nothing to lessen the mountain’s weight.”

“Tell them to come here,” the woman replied. “What we need are fresh geysers, not some nonsense about a ladder to the sky. I’d happily vote for my farm to help feed them.”

“I understand,” Freya said. “But they’ve chosen a place where the gravity will give them an advantage.” In fact, they would have gained even more weight at the poles, but the selection of the site was further complicated by the way the sun tugged on the ocean; at the poles, it was never pulling water toward the surface. “They’re not going to make their job harder by trying the same thing here.”

“Then perhaps we’ll do it ourselves,” the woman retorted. “We’re not afraid of work, and the world can’t have too many geysers.”

“That’s true,” Freya agreed cautiously. “But the trouble is, we don’t know if it’s possible to create them that way. If it turns out not to be, all the work will have been for nothing, and it might be too late to try anything else.”

A younger woman, further back in the crowd, joined the discussion. “Then raise a mountain here that does its best to break the ice, and if it fails, it will still be in the right place to reach toward Tvíburi.”

“It’s not that simple,” Freya replied. “The two aims are so different that they shape the designs in different ways, even from the start. A mountain built to exert the greatest possible pressure at its base will not make a safe bridge, even if it fails to crack the ice to the depth needed to bring forth new geysers. Who in good conscience would send travelers across the largest bridge ever built, if its shape was a compromise—a way of making do, a way of patching over the failure of an entirely different structure, with entirely different needs?”

The older of her two interlocutors was undeterred. “Then do what you like, wherever you like, but don’t expect us to feed you! Unless you’re offering a chance to bring back the geysers, you’re not worth taking food out of the mouths of my grandchildren!”

Freya lowered her gaze, chastened. The woman’s position was understandable—and there was no point repeating one more time that the best-designed mountain for the purpose she sought might fail to crack the ice, when it was equally true that Freya’s own version might fail to be of any use at all.

When the meeting was over, Freya stayed in the hall and shared a meal with Britt and half a dozen of the other villagers. They were all polite, and almost apologetic that she’d come so far only to be rebuffed, but none of them were willing to vote for their own farms to contribute food or supplies to her project.

“Things are tight,” Aslaug explained, contemplating the less-than-lavish feast that they’d prepared for their visitor.

“Which is why I’m doing this,” Freya replied, trying not to let her exasperation spill over into discourtesy.

“But no one believes they’ll stay that way,” Britt added. “We’ve always come through the quiet times in the past.”

“There were less of us in the past. And what if the quiet times are growing longer?” Freya was beginning to wish she’d taken this more somber line with the whole gathering.

But it showed no sign of working on her present audience. “Everything’s cyclic,” Hetty declared confidently. “Can you name one thing in nature that goes just one way?”

Freya said, “If one example would be enough to kill us, why would I expect to be able to do that?”

Everyone around the table smiled, trying without success to conceal their amusement. Her words were empty sophistry. Her intentions might be noble, her purpose sincere, but nothing she’d said had been the least bit persuasive.

Freya lay awake between the blankets on the floor of Britt’s guest room. She was close enough to the window that she could see the bright edge of Tvíburi, protruding past the gutter that ran along the side of the roof above her. It was hard to sleep with her brothers fighting, wrestling with each other, mewling and hissing.

When Freya had been a child, she’d been sure that she knew all three as individuals—not by tracking their locations from moment to moment, but by recognizing their idiosyncratic temperaments. But now she was far less confident that this told her anything. If one of the erstwhile subjugated pair succeeded in upending the hierarchy, would she be able to tell the difference, or would the result be indistinguishable to her? She wasn’t even sure that the brothers themselves had any sense of their identity that ran deeper than their awareness of their own current status. If a jealous pretender finally usurped the previous proud-but-wary ruler, would he know or feel anything that his predecessor hadn’t known or felt?

Britt said, “Are you awake?”

Freya rolled over and peered toward the doorway, where her host appeared in silhouette against the gray of the hall behind her. “Yes. What is it?”

“We’re too inbred in this place,” Britt replied.

For a moment Freya thought she was apologizing for her fellow villagers’ lack of foresight, but then a low howl and a palpable thump against the inside of her abdomen reminded her that the fighting had probably not gone unnoticed outside the confines of her body.

“Are you sure that’s what you want?” she asked.

“We can’t all stop having children until the geysers return.”

Freya laughed wearily. “No, we can’t.”

“We don’t have a lot of visitors from as far away as you’ve come,” Britt explained. “I tried to get pregnant when I did my Great Walk, but I must have had bad luck.” She shifted tentatively in the doorway.

Freya said, “If you’re resolved to try again now, you’re welcome.” Anything to quieten these idiots down.

Britt approached and knelt down on the edge of the blankets. “I haven’t done this for a while,” Freya confessed.

“Were there any children from the other times?”

“No. But I was young, and I think my brothers were so evenly matched then that they got in each other’s way.”

The two of them worked in silence for a while, trying to get into position, while whoever had won the fight in Freya’s belly moaned impatiently. Britt’s own brothers were quiet, recognizing the nature of the situation, but Freya remained wary; she’d heard stories about women surprised by an unexpected reversal.

Freya closed her eyes and felt the dominant brother begin protruding. She forced herself to relax and let him emerge unhindered. It was uncomfortable at first, from sheer lack of practice, but she’d be unwise to flinch now if she ever wanted to face childbirth.

When something close to half of the brother’s body was inside her, Britt began to sigh. Freya held the woman’s shoulders, bemused as ever by this intimacy in which she was almost, but not quite, a participant. At least there were no embarrassing mutinous tussles to complicate the exchange; whatever their long-term aspirations, the losing pair from the night’s ruckus seemed to have accepted their place, for now.

When it was over, Britt rested her face on Freya’s shoulder while Freya’s brother withdrew, then the two women parted and lay side by side on the blanket.

“Do you know if your own brothers have had children?” Freya asked.

Britt said, “I think so, but I’m not sure. That’s part of what went wrong on my Great Walk—they had to have it their way.”

“That must have been annoying.”

Britt took her hand and squeezed it. “I’m sorry you didn’t get what you wanted here.”

Freya said, “Well, at least I’ve made one of my brothers happy. If only there were some favor he could do in return.”

Britt snickered. “Plow a field? Help with the harvest?”

“I’m sure there’s a children’s story where someone was in trouble—injured out on the ice… or maybe captured by their enemies?—and they sent their brother crawling off for help.”

She was joking, but Britt didn’t reply. Freya pulled her hand free and turned to face the window. Maybe it was time for some new stories, where Tvíburi wasn’t Tvíbura’s twin, but the mother of her brother’s child.

She closed her eyes. There had to be words that would work, that would make it happen—or at least make it possible. But she hadn’t found them yet.

3

When Freya saw that the fair was in town, she almost turned around and walked back onto the ice. No one would be interested in hearing her talk about the death of their crops when there were far more cheerful diversions to be had.

But the wind was relentless, and she hadn’t eaten for days. Even with the fair competing for the villagers’ time and generosity, they would never refuse food and shelter to a traveler.

The wind whipped gray sand around her feet, stinging her through the cloth of her trousers, and as she reached the first paved street she realized that the dusty barrage was coming from the village itself, not blowing in across the ice. She’d seen this kind of thing a few times before, when the soil that had supported a whole swathe of farmland suddenly lost its ability to cohere. The ring of roads and buildings that encircled the farms was usually enough to act as both a barrier against the wind and a trap for drifting soil, to the point where at least the bulk of it could be contained and brought back to the fields. But there seemed to be some threshold where the over-cropped soil became so loose and light that nothing could be done to hold on to it.

The fair had set up its tents at the western edge of the village, and as Freya trudged around the ring road, the sound of people talking and laughing rose and fell with the wind. Normally, a villager would have stopped to greet her by now and ask where she’d come from, but there was no one in sight. Everyone was at the fair.

She approached the cluster of tents reluctantly. She was tired, and even if she’d been in the mood to spend time gazing at the exhibits she had nothing to offer in payment. All she could do was try to find a corner out of the wind and hope that an observant local would realize that she had no connection to the fair. Freya had never been too proud to accept the kind of hospitality that she’d offer any traveler who came to her own village, but it would be humiliating if she had to explain herself in order to make her situation clear.

She weaved between the tents, squeezing past queues of people waiting to enter, and found herself on a patch of ground that was open to the sky but sheltered from all sides. In the middle of this square, a woman stood by a telescope, touting for customers. “See the mountains and ravines of Tvíburi! See the geysers of molten ice, close enough to touch!”

Freya found a place to stand where she wasn’t blocking anyone’s way, and put her dusty pack on the ground. The telescope woman turned toward her and smiled. Freya nodded a greeting, but kept her distance; it would be rude to approach, as if she were a potential customer, only to plead poverty at the last moment.

As the afternoon wore on, the other touts seemed to be drawing ever larger crowds, but the telescope remained unvisited. Freya glanced up at the waxing crescent, wondering why no one seemed interested.

The telescope woman approached her. “I’m Inga.”

“Freya.”

“You’re not from this village, are you?”

“No.”

“Do you want to take a look?” Inga offered cheerfully.

“I…” Freya lowered her gaze, ashamed.

“No charge for a fellow traveler,” Inga assured her.

Freya followed her over to the instrument, and lay down on the bench beneath the eyepiece. She wasn’t sure why she had never done this before; maybe as a child, other attractions had grabbed her attention first, and by the time a closer look at Tvíburi had begun to seem alluring she’d spent what her mother had to spare.

She squirmed across the bench and squinted into the eyepiece, trying to turn the confusing puddle of light she was seeing into something sharper. “I can’t…” she complained. But then she craned her neck and suddenly, she could.

The view showed an expanse of pale blue ice, covered in fine fractures like the lines on an old woman’s skin.

“Use the wheels,” Inga urged her. She guided Freya’s hand to a pair of disks with corrugated edges, connected to shafts on the telescope’s mount. “Turn the top one to move the view from side to side, the other to move it up and down, as you’re seeing it.”

Freya swung the telescope to the left too fast, transforming the landscape into a blur, but when it became still again she was staring down at a canyon. “Have you ever seen anything like that on Tvíbura?” she asked, before realizing that Inga would have no idea what she was looking at. “A furrow in the ice so deep?”

“No,” Inga replied. “We’re flatter, for sure.”

Freya nudged the wheels, searching the ice for a deposit of soil. Finally, she was rewarded: a deep brown splotch, piled up in the middle, tall enough to cast a shadow. As far as she could tell, it was barren, with no trace of wild grasses. But did that mean the soil itself was incapable of supporting life, or simply that the right kind of plants had never arrived, or arisen, on Tvíburi? It was certainly sticky enough to have held together despite the lack of vegetation; that alone made it seem more promising than the gray dust here that was blowing away on the wind.

She slid off the bench, afraid of becoming engrossed in the view and outstaying her welcome. “Thank you,” she said. “I’m glad I saw that.”

“It’s easy to take Tvíburi for granted.” Inga glanced around the square at the oblivious fair-goers. “Half the world has spent their lives looking up at it, but some people think that means there’s nothing more to see.”

“Believe me, that’s not how I feel.” Freya hesitated, reluctant to burden this woman with the details of her increasingly unlikely ambitions. But even if Inga had no crops of her own to offer to a team of mountain-builders, she was entitled to know what could be done in the face of dwindling yields and desiccated soil. If nothing changed, her grandchildren would starve even sooner than those of any farmer.

Freya said, “I think we need to build a bridge.”

Inga listened attentively, and if she seemed to be struggling to keep herself from interrupting, she had the demeanor, not of an exasperated skeptic eager to declare the whole idea preposterous, but of someone who kept anticipating both problems and solutions, who was waiting to hear whether the speaker would eventually catch up with her.

By the time Freya finally stopped talking, she must have addressed most of those concerns, because Inga just smiled and said, “That has to be the most intrepid plan I’ve ever heard.”

“I’ll take that as a compliment,” Freya replied. “Though I’m not sure it’s the kind of endorsement that would recommend the idea to many farmers.”

“So you’re traveling from village to village, trying to get support?”

“Yes.”

“Any luck?”

“About as much as you’re having with your telescope.”

Inga frowned. “Why? Do people not believe that any of this is possible… or do they not believe that it could help?”

Freya explained about Gro’s competing project. “Everyone wants that to work instead. A better result, and a faster one—if it happens at all. But it makes my own plans sound like a waste of time.”

Inga pondered this. “You need props,” she said.

“I need what?”

“Objects that help you demonstrate your point. You need to make it easier for people to see why even the tallest mountain might not create a geyser.”

Freya said, “How can I make people see something that I’m not even certain of myself?”

“You’re not certain—but do you think your doubts about your friend’s scheme are well-founded, or do you think you’re just too stubborn to give up on your own idea?”

Freya was bemused. “Can anyone answer a question like that?”

Inga said, “If your doubts are well-founded, there must be something you can do to get them across to other people.” She glanced away; someone was finally approaching her telescope. “Meet me here when the fair closes, and I’ll see what I can do to help.”

Freya passed the time walking around the fairgrounds, trying to keep warm, too embarrassed to start approaching people and beg them for food and shelter. If anything, she tried to remain inconspicuous; if a villager did offer her hospitality now, how would she keep her appointment with Inga?

Halfway between sunset and midnight, as the laneways between the tents started emptying, she made her way back to the telescope. Inga still had one young customer, but when the girl left—beaming at what she’d seen—Inga gestured to Freya to approach.

“We’re here for two more days, so I won’t be packing this up,” she explained. “I just have to cover it to protect it from the dust.” She took some sheets of heavy fabric out of a box, unfolded them, and pegged them in place over the telescope.

She led Freya through the fairgrounds to a small, drab tent, and lit a lamp just inside the entrance. Most of the space within was taken up by two carts, piled high with wooden crates.

“How do you people lug all this across the ice?” Freya wondered.

“It’s not that hard, if you know what you’re doing; once you’ve got the wheels rolling, the carts only need an occasional push. The most dangerous part is when we have to stop in a hurry—that’s when I wish things had more weight and less momentum.” Inga was rummaging through one of the carts as she spoke, but then she stopped and announced happily, “Here it is!”

She carried the box she’d found away from the cart and placed it on the floor of the tent, then opened it and began removing some of its contents. “The first thing you want to impress on people is that, no matter how much ice you pile up, there’s a limit to how much it will weigh.”

Freya accepted that, but Erna’s mumbling about “one plus a quarter plus a ninth” didn’t really translate into anything she could sell with conviction to a room full of farmers. “Impress is a strong word.”

Inga was fiddling with some contraption from her crate. “Every child learns the inverse-square law, though?”

“Yes,” Freya agreed. “But the law itself is one thing; all its consequences are another.”

“So you need to make this consequence visible,” Inga replied. She took the gadget and offered it to Freya. It was a long tank with a square cross-section, and a flexible partition inside. The partition was connected to a series of pegs that protruded through holes in the side of the tank and emerged along an attached board, on which a grid had been drawn, its intervals marked with numbers.

“Set the pegs to the inverse-square law,” Inga instructed.

“I don’t understand,” Freya confessed.

“The first peg is the number one, for a distance of one. The inverse square of one is one, so make the height of the part that sticks out equal to one.”

“All right.” Freya did as she’d been told. “But the next peg isn’t ‘two’; there are six pegs before the next number.”

Inga said, “So the next peg is seven-sixths, and the inverse square of that is thirty-six forty-ninths. If you raise the peg almost halfway between four sixths and five sixths that will be close enough.”

“You expect my would-be investors to juggle fractions like this?” Freya joked.

“They won’t have to fret about the details,” Inga promised. “You just have to get things right yourself, and then show them a nice smooth curve along the tops of the pegs that passes through all the easy points that they can check themselves if they want to.”

Freya kept at it, until all the pegs were set—with the last one barely protruding at all.

“And this tells us…?” she wondered.

Inga handed her a flask full of ethane. “Fill it up,” she said.

Freya tipped ethane into the tank, into the space between one wall and the partition now shaped by her carefully positioned pegs.

“Now pour it all from there into here,” Inga suggested, passing Freya a much smaller, unadorned and unmodified tank, cubical in shape.

“Will it fit?” Freya wondered.

“Go ahead and see.”

Freya raised the larger tank and drained it carefully into the smaller one. There was no overflow; if anything, a narrow gap remained at the top of the second tank.

The two tanks had the same square cross-section, but though the first tank was eleven times longer in total, the volume that remained below the inverse-square curve of the partition was no more than that of the single cube.

Inga said, “So the weight of a mountain whose peak is twelve times farther from the center of the world than the ground is would actually weigh very slightly less than a mountain that only stretched from the ground to a height twice as far from the center of the world… if in the latter case, gravity didn’t vary with distance at all.”

Freya was confused for a moment, but then she understood. “People have no experience of gravity growing weaker. Our intuition comes from such a small range of heights that we can only imagine the weight of objects that obey the rules we actually see—where piling up a stack of rocks doesn’t mean the top few rocks weigh less than the bottom ones.”

“Exactly.” Inga took the small tank from her and placed it on the ground. “But now you still have to persuade them that a mountain of ice as tall as the center of the world is deep—with every portion weighing what it would at ground-level—might not be heavy enough to break the crust of ice beneath it.”

“How am I supposed to do that?”

Inga said, “Show them exactly how strong ice is, and how little it weighs. You can’t show them the mountain they need to imagine, but you can show them something smaller, supported by a smaller crust.”

“So… I just use two slabs of ice in the same proportion to each other? Like a map drawn to scale?”

Inga thought it over. “Not quite. If you shrink everything by the same amount, the weight of the load gets smaller faster than the area of the ice resisting that weight: the area of the vertical plane separating the adjacent regions in the crust that the load is trying to shear apart. So you actually need to exaggerate the size of the mountain compared to the depth of the crust, in order to make a fair demonstration of the necessary strength.”

Freya said, “Some people won’t understand that. It will look like I’m cheating.”

Inga was amused. “But not in favor of your own argument! If anything, it will look as if you’re being unfair on yourself, and trying too hard to break the crust.”

So she should try, not excessively hard, but fairly. Freya wanted to know the truth; if she’d been wasting her time that would be a painful thing to learn—but better to find out now than keep wandering from village to village when she ought to be helping her friends achieve their own saner and more modest goals.

“I don’t really know exactly how I should scale things,” she admitted.

“Let me think,” Inga replied. “I promise you, we get a good enough education in the science of forces and motion to keep our acrobats safe, but you’re calling on ideas I don’t use every day.” She closed her eyes, grimacing. “The height of the ground-level equivalent for an infinite mountain would be two hundred and fifty thousand strides—the same as the distance to the center of the world. Most people agree that the crust is at least one tenth as deep. If we want something smaller that gives a fair test of the strength of ice, we need to keep a constant ratio between the volume of ice in the load, and the area resisting the shear. So, whatever scales we apply to the height and width of the mountain, we need to apply both of them to the depth of the crust.”

“All right.” Freya was hanging on to the argument, just barely. “So for a start, we need to know the width of the mountain?”

“Yes.”

“The one my friends are considering would be a thousand strides across,” Freya recalled.

“So what’s a manageable mountain for an exhibit?” Inga mused. “It need not be as tall and skinny as the imaginary one. Maybe two strides tall, and one stride wide?”

“All right.” Freya didn’t want to think about the logistics of rolling such a cylinder from village to village, but if she pleaded to make the toy mountain any smaller, she feared the toy crust would end up thinner than a knife blade.

“So all in all, we need to scale the crust by one hundred and twenty-five million.” Inga laughed. “That brings it down to one five-thousandth of a stride.”

“That’s not going to work,” Freya concluded glumly.

“No, it’s impractical,” Inga agreed. “No lenses I’ve ever made are that thin. We need to multiply by five, at least: make the crust one thousandth of a stride deep, and the mountain ten strides tall.”

“Ten!” Freya didn’t think she’d ever seen an artificial structure ten strides tall; even the largest of the fair’s tents probably fell short of that by a stride or two. “It was kind of you to give this so much thought, but what you’re describing is completely beyond me.”

Inga said, “You want to build a bridge between worlds, but not a tower ten strides tall?”

“I don’t have the tools,” Freya replied. “I don’t even have a cart.”

Inga stood silently in the lamplight for a while, weighing up the problem. “This is important, isn’t it?” she said finally. “One way or the other. I’ve seen what some of the farms are like. We need new geysers, or we need to reach Tvíburi.”

“That’s what I believe.”

“Then you’d better come and meet the others,” Inga decided. “And see if we can talk them into it.”

Freya said, “Talk them into what?”

Inga smiled. “Letting you join the fair, along with a new exhibit: either a tower of ice that weighs so much it might as well be infinite, supported by a sheet of ice a fraction of its height… or a tower of ice that shatters that support, and shows us the way to make geysers. But whichever it is, it will be in aid of something marvelous: a bridge to Tvíburi, or the pick to end all picks, rising up from the ice field into the sky.”

Freya watched from the ground as Inga and Naja fitted the final level to the scaffolding. She hated standing by when other people were working, but her new friends had spent half their lives performing similar tasks, and she’d already slowed down the construction too much by getting in the way and trying to learn everything at once.

“Done!” Naja called down, before jumping off the edge of the platform. Inga took the ladder, and she had advised Freya to do the same. “Falling eight or ten strides is painless—and mildly entertaining the first few times—but your older self will thank you for protecting your knees from unnecessary jolts.”

Inga and Freya rolled the last piece of the column over the ice field to the edge of the structure, and maneuvered it into the sling. Freya’s hands were still tender from the dozens of small cuts she’d acquired while learning to carve a roughly hewn slab into a cylinder like this. But the version in front of them now had been rolled back and forth over five different grades of abrasive sand, to the point where it was almost smooth. Inga had promised that if they went ahead and took the exhibition to the public, she’d show Freya how to give the cylinders a near-optical polish, so they gleamed in the sunlight.

While the two of them hauled on the pulley rope together, Naja climbed the ladder beside the ascending cylinder, steadying it and making sure it didn’t slip or start swinging. They were lucky: there was almost no wind today.

When the cylinder reached the top platform, Naja adjusted the ropes connected to the sling so that Freya and Inga’s next few pulls would make the thing vertical. Then they clamped the rope and rested for a moment, before taking the ladder to join Naja.

“This is it!” Inga marveled. “Once we add this piece, the tower will be as good as infinite.”

Freya remained silent; she didn’t know what she was hoping for any more. The work had proved so exhausting that by the time they were raising the third piece, she’d been desperately willing the surrogate crust to shatter, just to spare her any more labor. And if it had happened then, or with the addition of the fourth, the result might have been convincing enough to persuade her that Gro’s project was the only one to back.

But if it happened now? Nobody knew exactly how thick the real crust was, or what other errors their imperfect model might contain. If their mock-infinite tower broke its supporting base, that would be enough to put an end to any hope of proceeding with the bridge, but Freya would be dead long before it was certain that geysers could be summoned this way.

The three of them worked together, unhooking the cylinder from the vertical rope that had raised it and attaching it to the horizontal loop that would carry it for the last stage of its journey. Freya imagined a crowd of spectators below, some of them still hoping to win prizes for guessing the correct breaking point, or wagering on the crust’s invincibility.

“Won’t word of the result spread between the villages?” she’d asked Inga.

“It will, but no one will believe what they haven’t seen with their own eyes. People will bet on their own instincts about the forces at play here, not someone else’s claims that contradict those feelings.”

Freya tugged on the rope, while Inga and Naja walked beside the cylinder toward the hole in the center of the platform, from which a stubby portion of the existing tower could be seen protruding. When the new piece was hanging right over its four predecessors—each one a little narrower than the last—Freya joined them. If something went wrong in this final stage, the more hands there were to steady the tower, the better their chances would be to keep it from toppling.

“Ready?” Inga asked, kneeling down at one side of the cylinder while Naja kneeled at the opposite point.

“Yes,” Freya replied.

Inga spoke a brief, guttural word in the fair’s dialect that had no precise translation, though its present usage was transparent: as she finished uttering it, she and Naja simultaneously sliced through two cords at the bottom of the sling, which were holding its two halves together. The tensed, elastic structure snapped apart and the cylinder began to descend.

The final piece of the column had barely a thumb’s breadth to fall. It landed squarely in place with a thud, and with the sling clear of the impact. Freya waited, arms spread, ready to respond as Inga and Naja climbed to their feet. But nothing had skewed the release, and as far as she could tell the cylinder wasn’t shaking or swaying at all. Let alone falling.

They’d placed the thin sheet of ice that was supporting the whole structure on top of two square blocks half a stride high, and two strides apart. If that crust cracked and the base of the tower dropped to the ground, the effect would not be subtle. But so far, it was holding.

The three of them stood motionless for a while, their eyes fixed on the top of the tower. Then Inga said, “Let’s go down and see what’s happening.”

As they walked across the platform, Freya kept looking back, expecting the cylinder to plummet at any moment. She was last onto the ladder, and she gripped the side rails tightly, prepared for the scaffolding to lurch wildly if the tower collapsed, with the five pieces tumbling as they fell, crashing into the beams around them.

Back on the ground, as they approached the sheet of ice, Freya would have sworn she could discern a subtle change in its shape. But when it came to her turn to squat down and inspect the graduated rods beside it, there was no sign that it had sagged, buckled or bent. No cracks or flaws had appeared. The strain of holding up the completed tower was not enough to deform it to any measurable degree, let alone tear it apart.

Freya remained as she was, too unsteady to rise, but Inga reached down and clasped her shoulder. She said, “It’s starting to look as if my great-grandchildren might just get a chance to visit Tvíburi.”

4

Gro finished her inspection of the double doors at the top of the stairs. “One down, twenty-six to go,” she said.

Freya glanced over her shoulder at the next platform they’d be visiting. The slanted legs of the would-be tripod had come a long way toward their meeting point, but though the straight-line distance between the tops of the columns was barely fifty strides now, the trip down to the ground then up again would take at least half a day. “I won’t be happy until the ice has grown around the frames, and we can check that the gap can be made airtight,” she replied. All they’d shown so far was that the doors themselves, and the box between them, wouldn’t leak.

Gro gathered up her tools into her pack, and motioned for Freya to go before her. There was something dreamlike about stepping through a door whose frame was surrounded by thin air, into a dark wooden box, and emerging through a second unwalled doorway to confront a flight of stairs so long that its lower reaches were impossible to perceive, shrunken by perspective into a crack in the side of the tripod’s leg.

Freya hooked her safety ropes onto the stair rail and waited for Gro to join her. There was plenty of room for two people to descend side-by-side, and Freya hated having someone behind her, an invisible presence constantly threatening to stumble and send her sprawling.

“Do you want something to eat?” Gro asked, attaching her own ropes to the right-hand rail.

“No.” Freya never brought food of her own on these trips; the idea of eating on the platforms, let alone the stairs, made her uneasy. Anything that needlessly distracted her, lowered her guard or occupied her hands, could be dangerous. And whether or not that fear was justified, it was more than enough to guarantee poor digestion.

Gro reached back and managed to pull a small loaf out of her pack without unstrapping it, then started chewing as they began their descent. “Here’s a hypothetical to ponder,” she said, her words muffled by the contents of her mouth. “If a dozen new geysers appeared tomorrow, what would you do? Walk away from all this, or keep going?”

Freya wasn’t sure that her own choice would really matter, now. “Wouldn’t it make more sense to ask one of the youngsters?”

Gro didn’t dispute that, but she’d already decided to have her say. “If it were up to me, I’d keep going.”

“Really?”

“The geysers will always come and go; we could never be sure we wouldn’t face the same problem again. And having come this far, we’d be foolish to waste it—to throw away all that expertise, in the hope that we could start again from nothing if we had to.”

“Hmm.” Freya was inclined to agree, though she doubted that the farmers would be willing to keep feeding them. “You haven’t heard rumors, have you?” If there’d been an eruption nearby, half the farmers in the area would already have departed to stake their claims over the fresh soil. But if a geyser had appeared on the other side of the world, with no hope of any of the locals benefiting, word of it would come far more slowly, and take much longer to be confirmed.

“No, I’m just thinking out loud.”

In the silence that followed, Freya’s thoughts drifted, only to settle on her unnatural surroundings. The stairs were set deeply enough in the slanted column that she suffered no fear of toppling sideways, even if that offered the most direct route to death: if she somehow ended up on the cylindrical surface, she would rapidly slide around it, plummet through the air, and crash into the plain below. But it was the unobstructed descent ahead of her that always seemed most perilous, beckoning her forward, inviting her to trip and fall. And however confident she was, intellectually, that any such fall would drag her no farther than the next supporting post for the safety rail, some part of her mind refused to accept that: the slender ropes from her wrist to the rail felt like ineffectual talismans, utterly useless against the power of the stairway’s vertiginous gradient.

Everything about the construction so far was a triumph of fact over intuition. She still couldn’t stare at the slanted tripod legs without expecting them to topple over. The counterweights that rose vertically from each foot, lessening the risk that the torque would tear the base from the ground, just looked like a joke, a gesture, as manifestly inadequate as the ropes. She wouldn’t be happy until the columns actually met up, visibly supporting each other. But then the whole construction would need to be repeated for the next level, even more precariously, with the legs of the new, wider tripods rising up from the tops of the old ones.

“Do you think we’ll live to see the second level complete?” she asked Gro.

“We might. If the Yggdrasil keeps pumping the same amount of water in total, those columns should rise three times faster.”

As noon approached, they were still only halfway down the stairs. They stopped to rest, waiting out the darkness as the sun disappeared behind Tvíburi. Against the backdrop of stars, the black disk of their twin softened to a bluish gray, lit by the half of their own world that was not yet in shadow, glowing in the Tvíburian midnight sky.

When they reached the ground, Erna was waiting for them.

“There’s been a fall,” she said.

Freya nodded grimly, sickened but unsurprised. She’d heard that some of the younger workers had stopped using safety ropes on the stairs, and apparently all her warnings had come to nothing; some people were just too impatient to care. “Who is it? Is she in the medical tent?” Freya started walking toward the tent, trying to control her anger. Reprimands could wait; the poor woman would be suffering enough from her bruises.

“It’s Sonja,” Erna replied, hurrying after her. “They’ve taken her to the tent, but…”

“But what?”

“She’s dead, Freya.”

Freya stopped. “How can she be dead?” No one had mentioned any accidents before she ascended that morning for the inspection. “How long were they treating her?”

“She died when she hit the ground. She fell straight down, from the very top.”

“Not down the stairs? She fell from a platform?”

Gro had caught up with them. “How?”

Erna said, “I don’t know. You’ll need to talk to the people who were up there with her. But we’re still waiting for them to arrive.”

The body lay on a stretcher on the floor of the medical tent, covered by a tarpaulin. Freya lifted one corner, then replaced it.

“Do you know if her mother’s still alive?” she asked Gro.

“She is.”

“I’ll need to go to the village and tell her.”

“Of course,” Gro replied. “But I think you should wait until we have some idea what happened.”

Freya covered her eyes with her forearm. Maybe it had just been a matter of time, but they’d come a long way without a single death. She’d always imagined that if it did happen, it would be part of a calamity that ended the whole project—some miscalculation that saw a whole column of ice snap at the base and crash to the ground. And though she could see why some people resented the encumbrance of the safety ropes on the stairs—where a tumble would be brutal but might well be survivable—surely everyone’s natural instincts compelled them to take infinitely more care around the edges of the platforms.

She turned to Erna. “Which tripod was it?”

“The northernmost.”

“When should the witnesses be down?”

“Soon.”

“I’m going to go wait for them.”

The three of them trudged over the ice, huddled against the biting wind. Maybe the whole thing had been the purest kind of accident, with a gust of wind knocking Sonja off the platform as she switched her second safety rope to a new anchor, and by chance the first one frayed, or its point of attachment came loose. The air was thinner up there, but the wind was faster; it could take you by surprise.

“Which leg?” Freya asked, as they approached the northern tripod.

“I’m not sure,” Erna admitted.

Freya’s anger returned; every ascent was supposed to be logged in detail. “Do we even know who was up there with her?”

“Lofn, Juliet, and… your niece.”

Gersemi. Freya felt a pang of shame, as if this compounded her own culpability. But she had never been softer on Gersemi than she had on anyone else. And apparently it made no difference anyway; they all ignored her pleas to take the protocols seriously.

When they reached the nearest leg of the tripod, Freya peered up along the staircase, but she couldn’t see anyone descending. She wasn’t going to run back and forth between the three legs, waiting for someone to come into view; she sat down on the staircase and motioned to the others to join her. At least here they were sheltered a little from the wind.

Gro said, “They must have been fitting the last sets of double doors.”

That made sense, but Freya still wondered about the timing. “Then they were well ahead of schedule.” She and Gro had only just started their inspections; it would be days before they reached this tripod. And in any case, she never put pressure on anyone to rush their work. It was the ice that set the pace in the end; they wouldn’t get to Tvíburi a day sooner by hurrying some bit of carpentry.

Freya heard footsteps from above. She turned and looked up, then rose to her feet and walked away to get a better view, but she could still only see one person descending—bounding down the stairs with the kind of urgency that made Freya wonder bitterly if this woman thought there was still a chance that she could help her friend.

“I think that’s Lofn,” Erna said.

“So where are the others?” Gro asked.

Freya almost replied, Taking their time and using the ropes, because they’ve finally learned their lesson. But she had to get her anger under control; it was no more helpful now than Lofn’s haste.

Lofn slowed as she approached the ground, but Freya waited for her to step onto the ice before speaking.

“You must be in shock,” she said. “You understand that Sonja’s dead?”

“Yes.” Lofn couldn’t look her in the eye.

“Is anyone else hurt?” Freya asked, as gently as she could.

“I don’t think so. They’re coming down the other way.” Lofn gestured to the north, toward another of the tripod’s legs.

Freya was surprised. “You weren’t all together up there?”

“Two of us were, at the start,” Lofn replied, staring at the ground. “Then we started crossing over.”

“Crossing over?” Freya’s puzzlement didn’t last long: there was really only one thing the words could mean. “And that’s how Sonja fell? Crossing over?”

“Yes.”

Freya stepped forward and embraced Lofn, as much to control herself as to try to comfort the woman. Screaming questions at her while she was standing in the wind, shivering with grief, would be unspeakably cruel.

Juliet and Gersemi approached. Gro walked over and met them, speaking with them quietly. Juliet started sobbing.

Freya was tired. “Let’s get out of the wind,” she said.

In the evening, the whole crew assembled in the dining tent to remember Sonja. Freya hadn’t known her well, but she clutched at every anecdote and every kind word, trying to prepare herself to meet the woman’s mother. She helped her friend Carla through her illness. She found a way to make the worst of the vegetables the farmers sent us almost palatable. Freya wasn’t going to traipse into the woman’s village, pushing the corpse ahead of her on a cart, only to blather on about Sonja’s noble sacrifice that had brought them all closer to Tvíburi.

She waited until the morning to take Sonja’s three colleagues aside. She sat them down in the planning tent, with a pile of work logs by her side.

“How long has this been happening?” she asked.

“About thirty days,” Gersemi replied.

“So talk me through it. You throw ropes…?”

“Yes,” Gersemi confirmed. “One person goes to the top of each leg of the tripod, and we throw ropes between the platforms to join them all up. Once they’re secured, we can cross over.”

“Along the ropes. Hand over hand?”

“Yes.”

Freya said, “How could you imagine for a moment that that would be safe?”

Lofn said, “You want us to spend our whole lives reaching for Tvíburi—and at the same time, you want us to be so timid that we can’t even cross fifty strides on a rope?”

Freya understood what she was saying, but the answer still didn’t satisfy her. “There are risks that we won’t be able to avoid. But this wasn’t one of them. You should save your courage for the times when it’s needed.”

“And you should do the same with your rules,” Gersemi replied.

Freya was stung. “Are you saying this is my fault? For asking you to protect yourselves on the stairs?”

“No.” Gersemi was abashed, but she added, “No one’s happy wasting their time on the stairs—and the safety ropes made that seem even more foolish. But I’m not making excuses for what happened to Sonja. If we wanted this, we should have done it openly. We rushed things, we cut corners, to keep the supervisors from finding out. That was our fault, and no one else’s.”

Freya sent them away and went to prepare the body. She bandaged the broken limbs as best she could, trying to bind them into some semblance of the natural shape that the woman’s shattered bones were no longer able to impose.

As she wound the fabric around Sonja’s leg, her forearm brushed against the dead woman’s abdomen, and she felt it twitch. She dropped the bandage and stepped away, wondering if she should run and fetch the medic. But that was insane; Hanna would never have stopped treating Sonja if there’d been any chance that she was still alive.

Freya approached the body and spread her hand over the place she’d inadvertently touched. The flesh was cold and yielding; even a person who’d lost consciousness and gone days without breathing would not be like this. But after a moment, she felt the movement again. The muscles of the abdomen itself weren’t contracting; rather, something was pushing against them. Sonja had not survived, but one of her brothers was clinging to life.

“Hanna!” Freya shouted. She wasn’t sure where her friend was, but she was usually close to the tent. “Hanna!”

Hanna came running, then stopped, confused. “What is it?”

Freya explained. “That’s impossible,” Hanna declared. “I palpated and listened, five or six times.” But she walked up to the body, and Freya stepped aside.

Hanna dug her fingers into Sonja’s belly, and Freya saw her start in surprise. “I don’t know how I missed it. Do you know anyone who could…?”

“I’ll do it,” Freya replied. One of her brothers had died a while ago, and the remaining pair had grown docile with age. They were sure to resent the newcomer, but they wouldn’t have the strength to kill him.

“Are you sure?”

The only thing Freya was sure of was that she owed this to the family. She said, “We don’t have time to look for someone else.”

Hanna fetched a scalpel. Freya couldn’t watch; she sat on one of the beds, facing away, trying not to interpret the sounds she was hearing.

After a while, Hanna said, “I’m sorry. He was too badly injured.”

Freya was numb. “I can’t take her back to the village like that.”

“I know. I’ll stitch her up.”

Freya cradled her head in her hands and listened to Hanna moving around the tent, fetching what she’d need.

Hanna said, “Did you know she was using a pessary?”

“No.”

“That’s why I missed the signs: there weren’t any.”

“Well, no one wants to have children out here.” The herbs were meant to render a woman’s brothers quieter, but Freya had never felt the need to take such intrusive measures herself. She was about to ask why the pessary had suddenly stopped working and let the surviving brother wake, but then decided that she really didn’t want to hear a detailed account of post mortem changes in the womb.

“She didn’t get it from me,” Hanna said. “And it looks stronger than anything I would have supplied. A dose that high risks losing your chance to have nieces.”

“Why would anyone do that?” Freya turned to face her; thankfully, Hanna’s task was almost finished.

“When your brothers fall into the deepest sleep,” Hanna explained, “it’s easier to do certain things. Working at heights, for example.”

Freya was confused. “Why? You mean some women lose their balance if there’s a brawl?”

Hanna laughed curtly. “Not that I’ve heard. It’s subtler than that. You know they share our blood supply? Just as an unborn child does.”

“Yes.”

“Well, they don’t just take from it, they put back as well. And what they feed us can make us more cautious… or at least, that’s the case when they’re fully alert.”

Freya had heard something like that when she was a child, but she’d thought it was just a folk superstition.

“Are you serious?”

“I’ve seen the difference it makes,” Hanna insisted.

“But why would it work like that?”

“If your survival depended entirely on your sister’s, wouldn’t you want to do everything you could to discourage her from killing you both?”

Freya said, “Yes—but I expect she’d already be quite keen on staying alive herself.”

“Of course.” Hanna looped the needle through one last time, made a knot, then cut the thread. “But she’d also be capable of taking into account considerations to which her brothers were entirely oblivious. Do any of our brothers know what’s happened with the geysers? Why we’re building the tower? What’s at stake here?”

“So you think some of the women have started silencing their brothers’ qualms? They know that what we’re doing is worth the risk—and they want that to be enough to keep them going.”

“I think they want a fairer fight,” Hanna replied. “They want to conquer their own fears, one against one—instead of four against one, with three adversaries who can’t be reasoned with at all.”

Freya went to find Gro, to tell her that she was leaving for the village.

“Have you decided on a punishment?” Gro asked.

“I’m not going to punish them,” Freya replied. “They know what they did wrong. Now we need to find a way to make it safe.”

Gro was bemused. “The tripods will meet up soon, and the temptation will be gone. Why not banish anyone who tries the same stunt again, and leave it at that?”

Freya said, “The first level of tripods will meet up soon, but what about the next one? And the next? Do you think people will climb up and down all those stairs, just because we asked them to, long after we’re dead?”

“Maybe not,” Gro conceded.

“This thing isn’t ours anymore.” Freya laughed. “If it ever was. All we can leave behind is what we’ve learned: about the strength of ice, about the way the roots grow, about gravity, torques and forces. The rest is in other people’s hands, and the ones who’ll matter most haven’t even been born yet.”

She returned to the medical tent with a cart, then set off across the ice.