Esper sat in a sea of sounds and symbols. All around her, patrons of her new home spoke to each other, the flowing gutteral tongue of this land punctuated by the sharp clinks and clacks of tableware.
She had been sitting with Robin and Alexandria, soaking it in, when Rose had returned to them in poor spirits. She paid attention as her companions spoke about the young girl’s difficulties. Eventually Rose and Robin left together, the former’s voice filled with nerves as it faded out the door. She recognized the pattern, the neurotic hesitance sometimes seen with genius, but it was not her place to interfere.
A fascinating word. That it had come to mind meant Esper was already thinking in the western tongue. She rolled the word around in her mouth, not quite speaking it. Her tongue pressed flat to her palate, a quick undulation, then the tip dipped down to behind her lower teeth. A moment’s pause, then the middle of the tongue touched her top teeth while the tip stayed in placed. Gen, she thought, stopping after the first syllable.
She liked how it felt in her mouth. She could hear the sound in her head, as clearly as if it had been spoken, but sometimes the shape of words told you more about them.
Gen was known to her. It was the gen from generate, generous, geneology. To create, to give, to beget. Genius was a gift you were born with, that was the meaning.
It was not a word from her native tongue. The closest word she had as a child was menscri, but it meant something closer to “scholar” or “he who knows many things”. It was a difference in attitude so vast that Esper thanked the hidden stars she had been born a linguist.
For the word genius perfectly captured an idea which had been stuck in her mind like a splinter. An old idea, a childish mystery, from when she was still too young to understand the shape of things.
It was one thing to be told as a child that your father, who owned many teaching-slaves, and knew many things, was menscri. That made sense. The shape of the word fit the shape of the world. But when your sister, five years your younger, is called menscri before her first blood, it is a more difficult thing to accept. The word groaned under its load, like a flat roof in heavy snow.
Esper had been confused when her sister, Anabi, began to surpass her own accomplishments. She had wondered, her thoughts shaped by her own impoverished vocabulary, whether she had not studied enough. Whether she had frittered away too much of her time on idle pursuits. Whether she had not focused deeply enough, had not truly tried.
But no. If her sister had been studious and diligent, the lie might have stuck. But the girl was a wild child. She preferred the old woods to her classes. She would vanish, returning at night with ripped robes and her hands full of berries. Some clever quip on the tip of her tongue would win their father’s forgiveness in an instant, and that would be that. Unless there was a hidden master in the woods, Anabi had certainly not been more studious than Esper.
When Esper had learned the word genius, as she prepared to travel to the west, everything had become clear. She had learned similar words before, in her studies, but none with such an unabashed presumption that one’s talent was innate. She suspected it was rooted in the long western tradition of hereditary aristocracy.
Anabi was simply born menscri, or at least with the potential for menscri. Saying this hurt. But it was true, and Esper would rather stiffen her heart than her mind.
All Esper had ever wanted was what came to Anabi as easily as breathing. Her sister had a certain insight, a sublime spark, that Esper would never have. Rose shared it, which is what had launched Esper’s thoughts down this track.
The spark seemed rather more common in her new life. Which made sense; the tower trafficked in genius. Dexter had it as well, although his genius put her rather in mind of the genius of the summer isles. They had local legend of a squat imp that sat upon one’s shoulder and whispered secrets.
They called the creature a genius, because of course they did. The language of these parts was a tangle made up entirely of smaller, more densely knotted tangles. The dual meaning of genius survived today only in phraseology. One could be a genius at something, or one could have a genius for something. The latter invoked the genius of the summer isles. She’d always felt the legend aptly captured the experience of insight. Sometimes it felt like the answer just popped into your head.
“Esper?”, Alexandria’s voice spoke in front of her.
Esper roused herself. She was still awash in sounds from her new home, although they had faded while she was in reverie. She turned to point one ear at the girl, the better to sort her noise from the crowd. “Hm?” she said absently.
“I said, I’m going to the shop. Do you need anything?”
“Ah, yes. Could you pick me up another satchel of tea, if you would? The one with the wide leaves from before.”
“The dark green one?”
Esper had no idea if the leaves were green. People tended to forget that she couldn’t see, outside her family. She made a vague rising note with her mouth, which the westerners took for casual assent, and dug around for a few coins to hand Alexandria.
She held them out over the table, palm down. She had to guess from sound and the subtle movements of the air, to know when Alexandria’s hand was beneath hers. She waited an extra moment to be sure and then released them.
That was another strange thing she’d found after leaving her home. Her family all had the milky eyes. As a result, there was rather more touching. Handing things over, indicating a direction, many things relied on touch. The western polities were oddly anxious about such gestures. It was fine, though. She’d learned to make do.
“I’ll be back soon,” Alexandria said. “Watch my things?”
Esper had long ago decided to consider the obliviousness of the sighted comical. “I’m afraid I can’t,” she said. “Perhaps you could ask our gracious host?”
“Er, right.” Alexandria replied awkwardly. Esper heard her walking away.
She leaned her head back, turning her attention back to the conversations all around her.
There was so much to learn from casual conversation. The content was trivial, the ordinary back-and-forth of people everywhere. Even at the foot of the tower interesting topics were rare. But the patterns were fascinating. People’s speech in this inn seemed to be drawn to three poles.
There was the speech of low nobility, formal and over-enunciated. It spent its words freely on social matters, flattering or giving face, and distained slang or slurred phrases. “Well, I say! While I would never wish to sully the name of such-and-such, I must remark that blah blah blah.”
There was the casual and rapid patter of academics everywhere. A strange mix of common language and specific terms, distinguished mostly by the number of syllables involved. “So the flormlglorbl hits the glorblflorml and goes fwoosh. The rule of inter-florml-glorbl-ormorbling means that you can’t really predict blah blah blah.”
And finally, there was the urban patois peculiar to this town at the foot of the tower. Every large settlement had one. Shortened names for places, phrases that had grown more common than they had any right to, things of that nature. “This weather is wearing on me; I could use a few of the good ones. Jenny, could you jog down to the Olbury and blah blah blah.”
These three variants of the western tongue bled together in the people here. The degree to which low-noble speech seemed to be freely intermixing with the other two was striking. Traditionally the upper crust used their unusual way of speaking to distinguish themselves, but here they were too common for it to truly distinguish them. More, the tower loomed over everyone, and so its verbal tics and markers loomed in their speech. With a little more time, she could probably date the arrival of the upper-class students by the degree to which academic speech had colonized their mother dialect.
Esper listened. Time passed. She began to fade, growing distant from herself, as the thoughts and words of others washed against her mind. At one point she might have taken a nap, the dreamlike state of quiet observation blending seamlessly with true dreams.
When dinner time came – and she could tell it was coming by the swell in the crowd, the hungry anticipation in their words – the door to her new home flew open, familiar voices flowing in, snatching her attention from the sea of sounds.
Robin’s voice: “It worked, didn’t it?”
Rose’s: “She hates me!”
“She wasn’t exactly your biggest fan before.”
“That’s the problem!”
“No, your problem was that she wouldn’t let you read the book. Now she will.”
Rose made a strangled, inarticulate sound.
“Geez, last time I try to help someone. You’re fine. Just go to her place tomorrow morning like whats-his-name said.”
The two voices drifted past her, heading toward the stairs. Esper smiled to herself. She wasn’t quite sure why.
Rose overslept. Normally she woke with the first rays of sun, but today it was cold and foggy again. She might have woken early anyway, but she’d had trouble falling asleep.
Her cloak had gotten wrapped around her in the night, her weight holding it shut. She wriggled until she could roll out of bed. What time was it?
Her eyes darted to Dexter’s bed. No sign of him, no sign he’d been here. That was two nights he’d been missing, now. Maybe they should tell someone?
Rose chewed her lip. She’d ask Alexandria. The blonde girl always seemed to know what to do.
Rose stretched, bouncing on her feet to try and get her blood flowing. She had things to do today. She made her way out of the room, sparing only a single additional glance at Dexter’s empty bed before putting it from her mind.
There was another class with Merzhin this afternoon. Then Alexandria had scheduled something for her, and Boromir wanted to show her a class at the refinery. There had been something she was supposed to do in the morning, though…
She remembered, and her eyes widened, her feet hurrying to carry her down the stairs. Lo’loth! The girl had agreed, through gritted teeth, to let Rose share her book this morning. Rose’s shoulders cringed inward as she remembered the awkward confrontation. Robin had found Lo’loth at Merzhin’s class, cornered her just as it was ending, and pressed her on the book in front of Merzhin and everyone.
A dozen people must have been watching. Just remembering it made Rose want to sink into a puddle and seep through the floorboards. She felt for her stone, to put her mind back on track.
The stone’s surface was cold and smooth. The embarassment didn’t matter. What was done was done. Lo’loth probably hated her, everyone she’d never met before in that class probably thought she was pushy and difficult, Merzhin must…
She rubbed her thumb over the stone as she exited into the inn’s common room. It didn’t matter. She just needed to figure out what time it was.
“‘Morning!” called the girl behind the counter. She was cleaning glasses with a white rag. “Morning,” Rose said back hesitantly. Let’s see, if she was cleaning up that meant it was after breakfast, but not yet lunch…
Wait. She was being stupid. “Er, excuse me,” Rose said. The girl – Rose should really learn her name – looked up, surprised the interaction wasn’t over. “What time is it?”
“Two hours to noon, a little less.” The girl shrugged.
Rose blinked. She couldn’t remember the last time she’d slept until ten. “Thanks,” she said absently, turning to look around the room for Alexandria. The other girl was nowhere to be found, though. The entire place was almost empty.
Rose made a beeline for the door. If it was already ten, she’d barely be able to get a few hours in with the book. A part of her was still worried about Dexter, but he wouldn’t get any more disappeared if she waited a few hours.
“Er, do you want some…food…” the girl called, trailing off as Rose strode through the door without slowing to listen. She remembered the way to the essence shop pretty well. Should she run? She should probably run.
Rose slowed to a stop before the door of the essence shop, her face flushed and her breathing heavy. It felt good to run. Her muscles were warm and well-used, just beginning to complain, and her blood was pumping fast and hot. It pushed away some of the early-morning chill.
It seemed like a lifetime since she’d entered the catacombs, but in reality it had only been about two weeks. Her legs still remembered running through fields and climbing up trees, snatching up bird eggs to bring home to her dad…
She frowned. She hadn’t thought about her dad much. There was some kind of feeling she couldn’t identify, when she thought of him, something far away and a little sad.
It was silly, right? She’d see him again. She needed to be careful not to say that out loud, but she would. If her mom had made it off the mountain, she could too, after she’d learned every secret there was to learn.
Still, the feeling persisted. She turned it over in her mind like a strange pebble as she waited for her breathing to slow. Something to think about. She brushed a hand over her glass, for a moment, remembering to come back to the thought, and then she was moving forward.
The door opened with the sound of a tinkling bell. The owner was standing on a stool this time, carefully arranging the strange bottles on the shelves. There didn’t seem to be any customers this morning.
Rose gave him a polite nod and brushed by, heading toward the back. She made her way down to the basement until she was standing once more before the imposing hardwood door. It seemed ominous, somehow, and her heart which had just begun to slow from her run began to beat quickly again.
Lo’loth probably hated her. She was going to knock, and it was going to be a whole thing. She’d offended the greengrocer in town, once, when she was young. She hadn’t realized how stores worked, and had eaten an apple right off the shelves. He’d yelled at her, and she’d begged her dad to do the shopping without her for a whole year.
Then again, what had actually happened? He’d yelled at her and that had been that. Maybe Robin was right. A little unpleasantness was a small price to pay if she got what she needed.
She reached her left hand into her cloak, fingers wrapping around her iron, and with her right hand she banged firmly on the door.
Nothing. No response. She debated knocking again, but she really didn’t want to aggravate Lo’loth any more.
Eventually, she heard footsteps, and the door swung open. Lo’loth looked slightly less imposing today. She was rubbing her eyes, and her clothing was rumpled, as if she’d just thrown it on.
“Of course it’s you,” she said, her voice’s natural sharpness dulled by a yawn. “Tell me, why is it that surface crawlers wake up with the sun?”
Rose wasn’t sure how to answer that. “The sun rose several hours ago,” she said finally.
Lo’loth rolled her eyes. “Yes, of course, how silly of me.”
The dark-skinned girl turned around, heading back into the room. Rose craned her head around, absorbing the decor. She gripped her iron tight. “Can I come in?” she asked.
“Yes, that was the implication. Hurry up. You can sit in the corner and read.”
She seemed…not terribly mad? That was promising, if perplexing. Rose tiptoed through the door.
Lo’loth lived in a single enormous basement sized for the shop above. The floor was hard stone, with overlapping rugs tiling it, except for an area at the back. A small rectangle of was left bare, with a heavy wooden table standing on it, and a row of shelves against the wall.
The table was strewn with tools. The shelves were cluttered with boxes and bottles. Above the table was an enormous metal chute. The bottom of the shute widened like the lip of a drinking glass, ending only a few feet above the table, while the top disappeared into the ceiling.
It was a workshop of some kind, she was sure of that. Lo’loth cleared her throat, and Rose flinched, turning to look. Lo’loth had a skeptical eyebrow raised.
The other girl was standing by a richly-appointed bed. The mattress was at least two feet thick, and the top was covered in silks and furs. Next to the bed was an odd device, with a small flame in the back and a glass pitcher. As Rose watched, dark black liquid seeped out of the top of the device into the pitcher. The smell reached her quickly. Coffee?
“It’s rude to gawk,” Lo’loth said. She yawned again, raising a delicate hand to her mouth. Gold bracelets jangled on her wrist.
“Sorry,” Rose said quickly. “Thank you for, um…”
“Mm.” Lo’loth interrupted her. She pointed at the corner of the room closest to the door. There was a dark hardwood chair, as uncomfortable-looking as a chair could be without looking shabby. The sort with a decorative back that you just knew would dig into your spine. Resting on the arm of the chair was a thin book.
Rose strode over, cloak flapping behind her. The strange table and the bubbling coffee and everything else in the room were forgotten. Just before she picked up the book, she hesitated. Her social skills were yelling at her, in a tiny far-away voice, that she was supposed to say something.
“Er,” she said, not quite able to take her eyes from the book as she reached for it. “Thank you. For, um, not being mad.”
“Oh, don’t thank me,” Lo’loth said. There was a pause, marked by a dainty slurping sound as she drank some coffee. “I’m absolutely furious with you. I just haven’t woken up yet.”
Rose nodded absently, book in hand. She swept her cloak around herself, letting it pad the stiff wood of the chair, and sat down cross-legged to read.
There was an old story that Rose’s mother had told her, more of a joke really, about a wizard who invented time travel. He’d gathered his colleagues together to show them his machine. It was a little metal room with a chair inside of it.
“Sit in the chair,” he told them, “and pull the lever. You’ll travel into the future at a rate of one minute every sixty seconds.” It was something like that, but the pacing was better. More dialogue back and forth.
Rose had been working on a better version of the joke. The wizard’s colleagues would complain that the machine was stupid. He would tell them: “You want to travel faster? Here!” and hand them a good book.
She was still working on it, because when she told it to people nobody laughed. But she knew there was a good joke in there somewhere, because like all good jokes, the punchline was true.
The small pamphlet had a red cover with bold black lettering: Binary Arithmetic And More: A Primer. She cracked it open, read through a boring introduction and a few definitions, then reached the first problem. She carefully nestled into the chair to work it out. She arranged the book, her blank notes, a piece of charcoal in one hand and her glass in the other. Then she started thinking, and teleported into the future.
Suddenly she was at the end of the book. She’d scrawled a dozen pages of notes and twice that again in scratchwork. Her right hand was cramped from writing. Her eyes were dry from staring. Her glass was safely back in her cloak, after she’d squeezed it so hard she almost cut herself, and her driftwood now kept her company in its stead.
Her thoughts were alive and humming, flashes of numbers still popping in and out of her mind’s eye unbidden.
The little pamphlet was fascinating. She’d known numbers since before she could talk, and she’d learned to write them not long after. But all this time, all these years, she’d been writing them the same way, and it turned out there were other ways.
She’d learned to write numbers using ten symbols, 0 through 9. You would count up – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 – and then when you got to the end of the symbols, you’d add another one and start over. 10, 11, etc.
She’d never thought of it before – and in retrospect, it was shocking, a lack of imagination that boggled the mind – but the number of symbols was totally arbitrary. You could do the same thing with just two, and everything worked out exactly the same.
0 0 1 1 2 10 3 11 4 100 5 101 6 110 7 111 8 1000 9 1001 10 1010 11 1011 ...
All the same rules worked. Addition, subtraction, multiplication, even long division. There was nothing special about 0 through 9. The order was arbitrary, the symbols were arbitrary, the number of symbols was arbitrary. Arbitrary arbitrary arbitrary. All the math she’d ever done had been in a tiny cage of her education’s own making.
She was in an uncomfortable chair in a dim basement, nothing in her line of sight but paper and charcoal and the floor, and yet she felt a sense almost of vertigo. It was like when she’d sat in the catacombs, looking out at the moonlit landscape from higher above it than she’d ever been. She tucked away her wood and found her feather, stroking the soft edge as she let her mind glide over the new landscape.
Her stomach growled. How long had it been since she’d eaten?
She put her things away and stood, stretching the kinks out of her legs. That chair really was abominably uncomfortable.
“Finally,” a canorous voice said to her left.
Rose jumped, startled, and turned to see Lo’loth looking at her. The dark-skinned girl was leaning on a stool at the workbench, her weight half off her feet. A single elegant eyebrow quirked upward. “You read the whole thing?”
Rose nodded, unsure what to say. The girl made a hmphing noise, turning back to the table, where she had arrayed a handful of colorful liquids directly underneath the odd metal tube that went to the ceiling. “Liar.”
Rose’s mouth fell open. “What?”
“You’re a liar. It’s been half a day.”
Now it was Rose’s turn to make a hmphing noise. It wasn’t intentional, it just slipped out, higher-pitched and more indignant than the other girl’s.
“I am not a liar.”
“Isn’t that what a liar would say?”
“I am not.” Rose stamped her food, the hard stone underneath hurting her knee a little even through the rug. It didn’t make nearly as loud a noise as she was hoping for. “You are a very rude person.”
“What did you get for 10.C, then?” Lo’loth asked. She sounded annoyed.
Rose’s eyes darted to the upper left, trying to recall. 10.C, 10.C…10 was the chapter on parity, and 10.C had been the second one with the prisoners.
There was a room with 32 pedestals arranged in a line. Face down on the leftmost pedestal was a deck of twenty red playing cards taken from the same deck. 40 prisoners were led in one by one in an unknown order. The first 39 were allowed to look at the top card of the deck, put it on the bottom, then move it to any pedestal they wanted.
The 40th prisoner to be led in was instead asked to name the card on top. If he was right, they all went free, otherwise they were executed. If they can plan together, what should they do?
It hadn’t been a very hard problem. They’d given it right after the chapter introducting xor.
The xor operation was a curious one. It was sort of like addition: it
took in two numbers and spat out a third. For every digit of the
numbers, it compared them, substituting a 0 if one number was longer.
If the two digits matched, the output digit was 0, otherwise it was 1.
11010 xor 10011 was
1001, but by the end of the
pamphlet Rose has in the habit of leaving the 0s on the front while
doing arithmetic). There had been some sort of complicated
explanation for why it made sense to do that operation, but Rose
hadn’t really cared.
More interesting were the properties. Any number xor itself was 0,
obviously, because all the digits matched. And any number xor 0 was
itself. Xor was also associative and commutative.
(a xor b) xor c
was the same as
a xor (b xor c) or
c xor (a xor b). You could
move the parentheses and order around all you wanted and get the same
Combine those three facts, and the answer was easy to see.
“You assign each pedestal a number from 0 through 31, starting from 0 on the left, and assign each possible red playing card a number from 0 through 25. Each prisoner takes the number of the pedestal the deck is on and the number of the card they flip, xors them, and moves the deck to the pedestal that corresponds to the new number. When the last prisoner comes in, all the cards except for the one he’s about to flip have been xored in twice, yielding 0, and the card he’s about to flip has been xored in once. So he just says the name of the card whose number matches the number of the pedestal the deck is on. Right?”
Lo’loth didn’t answer. She turned back to her table and moved a few pieces of glasswork, with an air of distraction rather than purpose. “What about 10.D?” she asked, after a moment.
10.D was the same problem, but with 60 prisoners instead of 40. It looked similar on the surface, but with 60 prisoners, most of the cards were seen three times, except for a single card that was seen twice. If the initial pile had contained all the red cards from a deck, it would have been trivial, but with only twenty it was a small trick to it.
Rose shrugged, not that the other girl could see her with eyes glued to the table. “It’s, um, basically the same answer,” she said. “Right?”