THE TURING MACHINES OF BABEL29 min read
In most respects, the universe (which some call the Library) is everywhere the same, and we at the summit are like the rest of you below. Like you, we dwell in a string of hexagonal library chambers connected by hallways that run infinitely east and west. Like you, we revere the indecipherable books that fill each chamber wall, ceiling to floor. Like you, we wander the connecting hallways, gathering fruits and lettuces from the north wall, then cast our rinds and waste down the consuming vine holes. Also like you, we sometimes turn our backs to the vines and gaze south through the indestructible glass toward sun and void, considering the nature of the world. Our finite lives, guided by our finite imaginations, repeat infinitely east, west, and down.
But unlike you, we at the summit can watch the rabbits.
The rabbits! Without knowing the rabbits, how could one hope to understand the world?
The rabbit had entered my family’s chamber casually, on a crooked, sniffing path. We stood back, stopping mid-sentence to stare, as it hopped to a bookcase. My brother ran to inform the nearest chambers, then swiftly returned. Word spread, and soon most of the several hundred people who lived within a hundred chambers of us had come to witness the visitation — Master Gardener Ferdinand in his long, green gown, Divine Chanter Guinart with his quirky smile. Why hadn’t our neighbors above warned us that a rabbit was coming? Had they wished to watch the rabbit, and lift it, and stroke its fur, in selfish solitude?
The rabbit grabbed the lowest bookshelf with its pink fingers and pulled itself up one shelf at a time to the fifth or sixth level; then it scooted sideways, sniffing along the chosen shelf, fingers gripping the shelf-rim, hind feet down upon the shelf below. Finding the book it sought, it hooked one finger under the book’s spine and let it fall.
The rabbit jumped lightly down, then nudged the book across the floor with its nose until it reached the reading chair in the middle of the room. It was of course taboo for anyone to touch the reading chair or the small round reading table, except under the guidance of a chanter. Chanter Guinart pressed his palms together and began a quiet song — the same incomprehensible chant he had taught us all as children, a phonetic interpretation of the symbols in our sacred books.
With its fingers the rabbit lifted the book to the seat of the chair, then paused to release some waste gas that smelled of fruit and lettuce. It hopped up onto the chair, lifted the book from chair to reading table, and hopped onto the table. Its off-white fur brightened as it crossed into the eternal sunbeam that angled through the small southern window. Beneath the chant, I heard the barefoot sound of people clustering behind me, their breath and quick whispers.
The rabbit centered the book in the sunbeam. It opened the book and ran its nose sequentially along the pages. When it reached maybe the 80th page, it erased one letter with the pink side of its tongue, and then with the black side of its tongue it wrote a new letter in its place.
Its task evidently completed, the rabbit nosed the book off the table, letting it fall roughly to the floor. The rabbit leaped down to chair then floor, then smoothed and licked and patiently cleaned the book with tongue and fingers and fur. Neighbors continued to gather, clogging room and doorways and both halls. When the book-grooming was complete, the rabbit raised the book one shelf at a time with nose and fingers, returning it to its proper spot. It leaped down again and hopped toward the east door. People stepped aside to give it a clear path. The rabbit exited our chamber and began to eat lettuces in the hall.
With firm voice, my father broke the general hush: “Children, you may gently pet the rabbit. One child at a time.” He looked at me, but I no longer considered myself a child. I waited for the neighbor children to have their fill of touching. We lived about a hundred thousand levels from the summit, but even so impossibly near the top of our infinite world, one might reach old age only ever having seen a couple of dozen visitations. By the time the last child left, the rabbit had long since finished eating.
The rabbit hopped toward where I sat, about twenty paces down the hall, near the spiral glass stairs. I intercepted it, lifting it up and gazing into its eyes. It gazed silently back, revealing no secrets.
Promising to return soon, I followed the rabbit downward. I brought no food and waved no sad goodbyes: I intended only a brief adventure free of my parents. As it happened, chance led to chance and I never returned. Or maybe it wasn’t chance. The rabbit compelled me in a way that gardening and weaving and family did not.
In the glare of the changeless sun, we descended the spiral glass stairs one level at a time. At each level, we crossed the twenty paces west to the nearest library chamber (never the forty paces east to the chamber at the hall’s other end). The rabbit would sniff around the chamber a bit, usually doing nothing of seeming importance, sometimes cleaning or repairing a book with tongue and fingers. Then we would cross back to the stairs and descend to the next level.
In some chambers my rabbit — for so I had begun to think of it — retrieved a book, always taking it to the central table by the same laborious procedure, and read it, changing one letter, usually in the interior. Sometimes it would change a few letters sequentially. In one chamber, it retrieved six adjacent books, one at a time, and rewrote all the pages from the middle of the first book to near the end of the sixth. How my rabbit knew what to do was not evident to me. It seemed only to be converting one string of random book-nonsense into another.
Most chambers were empty of people. Some contained isolated families or hermits. Sometimes we passed through small centers of population. When we entered an occupied chamber, I acted as the rabbit’s protector and spokesperson, my confidence increasing over time. I prevented children from disrupting the rabbit’s work. I ensured that the curious would touch it only gently, while it rested. I explained that we would probably be leaving soon — or if it looked like the rabbit was ready for sleep, I requested that it be given room and peace. Often, people followed us curiously through several levels before returning home.
The rabbit ate and rested frequently, during which time I also rested and ate. I lived on lettuce and any wild fruit I could find ripe, plus hospitality and handouts, which I loaded into a backpack an old hermit weaver had given me early on.
We discovered one chamber where most of the books had been scattered on the floor in disarray. The rabbit carefully cleaned each book and returned it to the shelves without any apparent sensitivity to order, simply placing each book in the first available spot. With tongue and fingers, it smoothed the books’ wrinkled pages. It spat sharp-scented binding glue on torn pages and lacquer on scuffed covers. When the rabbit was done, the chamber looked as neatly arranged as any other, though one of the topmost shelves had ten empty positions.
Sometimes I met others who knew a little of the rabbits and lingered with us, sharing their memories and ideas. Sometimes the stairwells were so empty I could hear the soft click of fur-cloaked hind nail on the eternal glass steps. I remember a one-armed gardener who offered a disk-shaped blue fruit I never saw again in any of my travels. I remember a round, sedentary book-chanter who spoke so deeply that her voice seemed to rise from a great distance below, as though she had been lowered into ineffable insight by a lifetime of chanting book-nonsense.
I remember a raging cynic. “Why should we revere these books?” he said. Violently, he pulled an arbitrary book from a shelf and opened to an arbitrary page. “h7-M2qd1O85(%naOhY,” he said, reading from the top. Then he thrust the book toward me, still open to that page. “How long is this book?”
“I don’t need to count to know,” I said.
“Of course you don’t! 402 pages! Exactly 49 lines of text on every page. Exactly 63 random characters on every line. Of course!”
“It is always so,” I said. “It is the law of nature.”
“No longer!” He raised the book high over his head toward the shadowy gray chamber ceiling. I could see the lettering on the book’s spine — as always on spines, 28 seemingly random golden characters, limited to the upper-case letters and the blank. His right hand pinched the top of the book’s final page, as if to tear it off. I was too stunned to act.
He began to tear the page. I heard its horrible quiet ripping. But he could not finish, instead collapsing into a sobbing heap. Some neighbors arrived, presumably having heard his shouting. Shaken, I retreated to the hall, where my rabbit was calmly eating cranberries. I sat on the floor beside it, rubbing and scratching its back to settle myself, while a little girl with tangled hair looked on. Neither my rabbit nor I returned to the chamber: not I, because I couldn’t bear to do so, not my rabbit, presumably, because its focus was always only onward and down.
A girl my age — an aspiring painter and storyteller — joined our voyage for a while. What was her name? She brought berry inks and she sketched elongated images of us on the southern glass walls, silhouetted by the sun. She kissed me. When we were tired of the sunny glass stairwell, we let the rabbit hop ahead and she touched my shoulders and legs under my short brown tunic. But some invisible vine tied her to her home. After maybe twenty sleeps she would go no farther.
“If you love me, you will turn around now and return with me to my family,” she said. She looked beautiful in the sun, in her dye-splattered tunic. With one hand, she smoothed my long hair.
“If you love me, you will continue on with me and leave your family behind,” I said.
After she and I parted, my rabbit and I hit a long, unpopulated stretch. I grew thin on crabby fruits and lettuce.
I had taught myself to arrange vines into a comfortable nest for the rabbit, and I would reach down the highest fruits and lettuces for it, if they seemed the best. I pressed my nose into its soft fur, smelling sweet hints of the foods it preferred. We began to sleep closer together. Eventually, the rabbit dreamed in my arms — of letters, I suppose, or of God’s voice, or whatever it is that rabbits dream — cradled by a soft nest, ringed by my devotional fruit, always in the shadows of the south wall of a vacant chamber. We traveled continually down, never up, until we were many thousands of levels below the place of my birth.
We hopped into a chamber where four burly men were waiting. Vines wrapped the men’s chests in a style I didn’t recognize, and the men’s hair had somehow been colored to match the golden starfruits. “We’re taking that rabbit,” one of the men said, the tallest. “Stand aside.”
I told them what I had by then come to believe: that the rabbits’ reading and writing was the blood and purpose of the cosmos, that their actions constituted the divine mind. We humans must not interfere.
“God’s mind needs changing,” the tall man said.
Three men held me while the tall one snatched the rabbit from the floor. I screamed and struggled and bit, but the men bound me tightly in vines. The rabbit remained seemingly unperturbed, too sure and perfect, perhaps, to be troubled by human affairs. The men left, carrying it.
After the men were well clear, a woman and child entered the chamber. They were dressed in the same foreign style. The woman began carefully unknotting the vines that bound me. She offered me gooseberries and cantaloupe, which I ignored.
“We have found a sentence with meaning,” she said. “Amid the uninterpretable tangle of letters in all the books in all these chambers, we have found a sentence. It can’t be chance.”
“What? What sentence?” I was watching the woman’s child, a boy, old enough to walk but not much older. He had pulled a book from the bottom shelf and was running his nose across it. In my neighborhood, it would have been unthinkable to let so young a child so casually touch a book.
“An ominous sentence,” the woman said. With her fingertip on the bare desk, she traced the letters:
AnD t7he sUN D-escEnd.
“Chance!” I said. “Look enough and there will be a chance phrase, somewhere. Especially one like that, with errors. “
“Seventy-three possible characters plus the blank,” the woman said. “Almost every page of these books contains a few three- or four-letter words, but those words swim in nonsense. They aren’t marked off like this, with spaces in a grammatical sentence. We think it is a prophecy.”
“Then you should fight the sun. Let your men reach through the glass and hold up the sun with their fingers!”
The boy had begun to lick the book that lay open on the floor before him. By this time, I was free of the vines. I ran over and grabbed the book, reshelving it.
“The men have scrambled the books in these chambers as a temporary act of resistance,” the woman said. “And we have begun to write our own books.”
The woman held up a sad collection of crude pages. Most human cultures have aimed to imitate the structure of our universe by breaking fruits into ink and then tracing rough letters on the floor, or sometimes on pale mats of dried vine fiber, casting our spoken language, approximately phonetically, into these abstract figures from which so much of the world is built. The “book” in the woman’s hands consisted of several dozen crooked mats, with faint plum-colored letters, woven together with thin fibers at one edge. It was certainly not 402 pages. The writing was too large and awkward to arrange into 49 rows of 63 legible characters. “We will perfect the art,” she said. “We will shelve each room with our own prophecies and thus command the rabbits.”
“You people are insane,” I said. “No rabbit will fall for your tricks! The sentence you found is no prophecy.”
I fled the room where the madmen had kidnapped my rabbit. I wandered lost for several sleeps and wakings, east, west, up, down, chasing rumors. Finally, an old man dressed in a more familiar style led me to a chamber with a mangled, stinking rabbit corpse. Pages were strewn about the room, partly soaked in blood. Among the pages of nonsense I found one sentence, so conspicuous in the middle of the page that it was like a bright red apple in a tangle of green, a sentence with blank space on each side. It was of course the sentence the woman had drawn with her finger, exactly as she had drawn it. Its letters were smudged, as though someone had tried to erase them, perhaps with the rabbit’s tongue, which had been torn out and discarded in one corner of the room.
I dropped the page with the awful seeming-prophecy, then bent over to lift it again, my mind buzzing.
“I have heard that far above us is the ceiling where the gods converse, ” said the old man.
I had heard something similar, among all the inconsistent lore. I resolved to try for the summit.
First, though, I would place my beloved rabbit among the consuming vines, that it might in time become fruit and lettuce. As I lifted its corpse, I noticed a strange structure in its back. Carefully peeling away the skin, I discovered a complex array of tiny tendons hooked to tiny bone knobs. A bit of study established that each knob had 74 notches and that the knobs were arranged in rows of 63 and columns of 49, stacked into 402 panels, just like the pages of a book.
Somewhere there is a book that consists of nothing but AAAAA from beginning to end. There must be infinitely many such books — indeed infinitely many columns of a hundred thousand chambers, all of whose books contain nothing but As. The people who live there will understandably, but falsely, believe it could not be chance. They will regard their column as the privileged center of the universe, with constant, simple laws, and the “W8bKFebBq’9:pc(” etc. columns on either side will seem to them a garbled vacuum.
Somewhere, everywhere, infinitely in all directions, there are pages that contain, by chance, the same lettering as the page you now see. Somewhere, everywhere, infinitely in all directions, there are books that tell the true story of your life and death, differing from each other not at all, or only in a comma, or only in the final word. The distance you would have to travel to obtain one of these books, however, must far exceed human imagining; and along the way, if you could live so long, you would find vastly many more books that tell the true story of your life only up to the point of your reading, containing gibberish thereafter, or that tell only the most horrible lies and predict how you will angrily shred them. Somewhere, everywhere, infinitely in all directions, is the one true theory of the cosmos. Somewhere, everywhere, in every possible language — in one possible language if only you could decipher it, right here in your hands — is the vindication of your life. Somewhere, everywhere, are the preserved and perfected words of every storyteller, in every translation. Somewhere, everywhere, are the words you would have spoken to your dead beloved if you had been a better person.
In the time it took me to ascend, my beard filled in, my legs strengthened, and my soles hardened. My knowledge of the rabbits also grew, as the lore I heard gained detail and began to lose its mythical quality. I learned of a scholarly community spread thinly across the summit, studying and protecting the rabbits. About three thousand levels from the top, I heard rumors of a rabbit nearby, also ascending. I rushed to join it, my thick, bare thighs powering me up and up.
A small crowd was gathered at the door of the chamber, looking in. I caught my breath on the stairs, watching as the people grew bored and in turns wandered away. The rabbit emerged — subtly different in coloration and body shape than the one I had loved — and began to eat. Children lifted it and petted it and fed it from their hands, parents hovering. A gray-haired woman also stood by, leaning slightly against the north wall. I broke some vines and began to weave a nest. When the children tired of the rabbit, it hopped calmly toward the stairs where I sat.
“You don’t think the rabbit will sleep on that clumsy tangle that’s falling through your fingers,” the woman said, meeting my gaze for the first time. “Do you?” She looked down at my calloused feet and large, sweaty calves, appraising me.
The woman’s dress was woven more finely than I had ever seen, with fibers so thin my eyes couldn’t discern their texture until she was two strides away. I stepped aside, then followed her and the rabbit upstairs.
“I think for you three thousand levels will seem to be only a little farther,” she said.
On the top floor, I became Dulcinea’s — the woman’s — apprentice, and then her favorite and lover. Apart from our small group, the summit was empty for dozens of hall-lengths in both directions. The fruit did not grow quite as well there, and the scholarly community was anyway sparse. Dulcinea and I and three other apprentices lay almost naked in the sunlight, practicing chant and lore. We ran afield for fruit, which we ate raw and simple. We closely observed the rabbits as they nosed through their books, sometimes taking notes on pale woven mats. Visitors came: other scholars, or dignitaries from east, west, or below, sometimes bearing clothes or food or craftwork, and we would exchange lore. With one exception, none of the twelve rabbits we tracked was ever gone for more than eight sleeps or descended more than a couple hundred floors. The one exception was a brown-tinged rabbit with one flopped ear, whom Dulcinea sent Sampson after. We never saw rabbit or apprentice again. I imagine them still traveling, Sampson now an old man. Or maybe their adventure was cut short, to a bad end? After about a hundred sleeps, a new apprentice arrived who took Sampson’s place.
Dulcinea and I sat side by side, resting our backs gently against the shady bookcase of a south chamber wall, our shoulders touching. She had sent the others away to gather fruit. She leaned over to kiss my cheek, her soft, loose gray hair brushing my face.
“Hamete,” she said. “My love. Feel this.” She took my right hand in hers and rested it upon her right breast. Her breast felt wrong, too firm, too large, hot through the thin weave. She winced back from my gentle pressure. It had felt large and hot a few sleeps before also, when we had last made love, though I had said nothing. It was now worse.
“Find those hard, green lychees on the second level,” Dulcinea said, “the ones a little wider than your thumb. Soon you will need to fill my throat with them.”
“Oh Dulcinea!” I said. “No! This is nothing. A passing infection!”
“I think we must each be our own Library, Hamete,” she said. “And our thoughts only the actions of rabbits.”
“What? What? The metaphysics of — of Trifaldi the Afflicted? But –“
“Shh.” Dulcinea turned to kneel in front of me, her hands on my arms. “I am a child again, scared of the sun. I am not your teacher. Here’s what I’d like to think: I am only a prefiguration of the true Dulcinea. I’d like to think that in this infinitely repeating cosmos, I will arise again and do it right, completing our work.”
“What work? What didn’t we do? We’ll do it! It’s only a flu you have.”
Dulcinea didn’t answer, instead looking me in the face. I couldn’t withstand her gaze, so I closed my eyes, listening to her breathing, feeling her touch, imagining her terrifyingly hot breast. I heard the soft sound of a rabbit sniffing along a shelf toward a new book.
Twelve sleeps later, Dulcinea woke coughing blood, choking, feverish, hardly breathing. I sent the other apprentices away in search of a cure, which I should have done sooner. I went to the second level and brought back the thumb-sized lychees. Dulcinea took one in her mouth, but I couldn’t bear to force it down her windpipe. She died with it still on her tongue, round and hard and bumpy.
After Dulcinea’s death, I fled west along the summit, as if to escape the memory of my failure. I rediscovered the power of movement. Movement became a habit, then a way of life. Why should I stop? I aged and learned, traveling hundreds of thousands of chambers west, across large, deserted regions without human or rabbit, through thriving cultures that had learned to weave and pulp vines in incomprehensibly subtle ways, through other cultures that appeared to be thriving but which had destroyed their rabbits and books for what they regarded as material or religious glory, and through many more primitive lands like my own, different in detail.
As I traveled, the spoken language began to diverge, though the books remained always the same, until eventually people were pointing out “words” that I would not have judged to be words, giving phonetic value to characters I saw as mere punctuation, interpreting as punctuation characters I saw as having phonetic value. Some of these languages I learned the basics of as I walked. I met geometers, philosophers, calculating prodigies, musicians who tapped the glass with hollow gourds, inventors who made delicate leverworks of dried vine. In a public debate, I defeated the great Galilei, famous for his conjecture that the Library moves insensibly around the sun.
My renown as a loremaster grew, and youths began to accompany me. Boys ran to send word in advance of my arrival, and the local leaders showed me their precious texts:
or similar strings in different languages. It is human nature to find meaning in chance.
On the top level, rabbits do one thing they do nowhere else: They share books.
The meeting places are the midpoints of the summit corridors. A rabbit will go to a corridor midpoint, either thirty paces east or thirty paces west from its home chamber, and wait. Sometimes the rabbit will wait for only a few breaths. Sometimes the rabbit will wait for a few or many sleeping periods or — I have been told — several human lifetimes. A rabbit that ceases waiting will return to its chamber and resume rereading and rewriting its books. Eventually it will try again. Sometimes, a rabbit will travel more than one column east or west before returning — the only condition under which they will ever travel sideways.
In one case I was privileged to see a rabbit that had been waiting for six human generations finally make contact with the rabbit for which it had been waiting, which had been below for even longer than that, having gone who knows how many millions of levels down. The newly returned rabbit, not at all tired that I could see, had rewritten a few pages in its summit chamber, and then had nosed a book out along the hallway floor. When it reached the midpoint, the waiting rabbit, in a manner neither fast nor slow, neither seemingly surprised nor relieved, ran its nose through the first 22 pages of the book, then returned to its own chamber, rewrote a single character in a single book, and descended. Sixteen men changed religion at that moment, claiming the experience so profound as to make them hallucinate.
I have come to believe that every column of chambers is a rule-following device of infinite capacity — somewhat like a math prodigy operating on knotted cords and mats of dried vine, but incomprehensibly larger and more complex — and each rabbit implements the device’s rules for reading, writing, and symbol transfer. Because the number of devices is infinite and the calculational rules governing each device entirely random, every possible finite set of rules is implemented somewhere, executing every possible finite process infinitely often.
An infinite number of rabbits have shown their eastern neighbors a book that contains only the sentence “How is the lettuce growing in your column?” followed by 401 pages of blank space. Since their neighbors are randomly constituted, the chance is minuscule that any one of those eastern rabbits will reply in a sensible way, but an infinite number will in fact give a sensible reply. For instance, the eastern neighbor might, after who knows how long, pass back a book that says, “The lettuces are good several levels down and the humans kind enough to massage me when I am weary.” The chance that the western rabbit will sensibly continue the conversation is again minuscule but finite. And thus, multiplying the minuscule upon the minuscule upon the minuscule again, there will be an infinite number of conversations that endure for generations and that people would interpret as expressing the most magnificent heights of literature and philosophy, in whatever happens to be the local language. No human witness of such an exchange would doubt an intelligence behind it.
The rabbits themselves do not appear to understand these conversations. You cannot speak to them. They do not speak to each other independently of their role in the devices, unless with an invisible profundity so deep that it circles back around to mild lettuce-eating. Nor does there seem to be any mechanism by which the rabbits could report the actual state of their lettuces: The machines’ only input is the writing in their neighbors’ books.
Most of the machines will not understand each other any more than the rabbits do, even among the tiny fraction of machines regarded as intelligent by their human neighbors. Nevertheless, a tiny fraction of the machines, by chance, must instantiate rule-patterns that operate so deftly that it is no longer right to call their responses chance. There must be infinitely many columns that will calculate primes. One column might count the dots in the book its neighbor shows it, returning a dot and a Z if and only if the number of dots is prime. It might be so well structured that it not only determines the primeness or not of all input actually received, but also it would have correctly answered any prime or nonprime input it might hypothetically have received. With this move from actual to counterfactual robustness, chance undoes itself.
A fine picture of the cosmos I had at this time. Almost true, I dare to think! But I knew my understanding was still somehow flawed, since there was one giant fact that jarringly failed to fit.
My hair grayed and then whitened. My powerful legs, of which I had been so proud, could no longer outpace aspiring apprentices. So I found a second-level chamber in a thinly populated area, in the midst of seven consecutive columns of active rabbits. I observed the rabbits carefully, taking notes on mats made by a few apprentices who had gathered around me. But I made no progress on fundamental issues.
After maybe two hundred sleeps’ worth of this new life, an adolescent girl strode into my chamber unannounced. My mats were strewn and stacked on the floor, leaving the table clear for the rabbits’ use. I was kneeling among them, probably squinting, probably choosing a mat to lift up toward the sunbeam.
She didn’t introduce herself. She didn’t bow. One of my apprentices arrived behind her, panting slightly, and looked at me with a query in his eyes.
Her first words were exactly the question that baffled me. “Why,” she said, “are the desks and chairs and shelves and stairways human size?”
“So convenient for us,” I said. “So inconvenient for the rabbits. It is as though the universe were designed for humans, not rabbits, to work the books.”
She looked at me silently. Her clothes were strange, from far below, maybe, or far to the west where I had never been — a hood for head and shoulders, a band across breasts and belly, a long skirt, all brown and dyed with streaks of a yellow I had never seen. She and I both knew that my answer was no answer.
“I was told,” she said, “that no one knows more about the cosmos than you.”
“There must be infinitely many scholars who know more than I.”
My false humility seemed to bounce right off her shelf-hard face.
“Perhaps we used to work the books but we declined,” I ventured.
“If we had been around long enough to have declined in the unremembered past,” she said, “rogue men would have killed off many more of the rabbits by now.”
“The rabbits might replenish at intervals too long for us to see. Maybe they breed far below. Or maybe the universe completely refreshes every twenty generations.” My other two apprentices had now arrived to witness the exchange. “Alternatively, some lore masters say that we are made to first understand and then replace the rabbits, to learn to do the reading and writing ourselves.”
“The rabbits’ task is too dull,” the girl said. “We can’t follow simple rules all our lives. And we don’t live long enough to conduct their deeper tasks. Repetition can’t be our purpose.”
“You have a better answer?”
“The tables and desks and shelves,” she said, “are God’s rebuke to us. With them, he shames and challenges us. They are visual proof that we are not meant to idly tend the rabbits. They are the mystery that will force us to rise.”
To this, I had no answer. I asked her name.
“Dulcinea,” she said.
I pictured a woman repeating, repeating, like countless books.
I had seen people interfere with the rabbits, but never with Dulcinea’s systematicity. I had thought the only alternative to the lore masters’ passive observation was destructive, chaotic intrusion. Dulcinea lifted the rabbits away from the books after they had erased a character but before they could write a new one. Then she reshelved and rearranged the books, noting patterns in the results.
Dulcinea managed to turn the fifth of my seven rabbits into an eraser. She did this by putting the book to be erased in a certain shelf position at the top of Column 5 and then exposing Rabbit 5 to a book we thought of as the eraser-program book. After nosing across the spine and first twelve interior characters of the eraser-program book, Rabbit 5 would retrieve whatever book was in the target shelf location, bring it to the reading table, and erase the first five non-blank interior characters it encountered. By repeating this process multiple times, Dulcinea could erase whole pages in any book she chose.
Dulcinea began to learn the quirks of the other rabbits too, shuffling books around, offering books with blank first pages or books primed with particular letters on the spine. She posted the other apprentices to capture any rabbits that might start a descent, presenting the rabbits with a new book that caused their return. She swapped the books that the rabbits would nudge across to each other in the middle of the summit hall, all the while taking notes on mats that we arranged in growing piles on the third level. And thus she — or rather we — began to master the rabbits. Each rabbit worked differently, perhaps because of different settings in the knobby bone structures beneath their skin.
“We will send a picture from one rabbit to another,” Dulcinea announced one time as the other apprentices and I were lunching on durian and mango. She had by then lived with us for maybe four hundred sleeps.
My apprentice Cardenio declared this impossible. I was also skeptical, but I didn’t voice my dissent. “Show us,” I said.
Dulcinea had devised an arrangement of book swaps by which she could command Rabbit 1 to place an “O” in any arbitrary position on the first page of a blank-beginninged book. She drew a 40-by-40 grid on the floor, then sketched a passable image of a human hand on the grid, using only Os and blanks. She noted every grid position that had an O, and then, one O at a time, she programmed Rabbit 1 to produce Os in those same positions on the page. When Rabbit 1 was done, it nudged the book over to Rabbit 2, who began to copy the pattern of Os, using a book-swap-intensive copy-input procedure that we had begun to devise.
“That’s no picture!” said Cardenio, when Dulcinea had finished. “We see a hand, but that’s just human interpretation. The machines see only a meaningless string of blanks and Os. A picture has to represent something.”
I half-agreed with Cardenio. It was a picture, but not the profoundest kind — a picture to our eyes, but not to the machines. The machines couldn’t process pictorial input as pictorial. They could only represent abstractions. They couldn’t represent shapes laid out in space. They were disembodied angels, unable to see a physical world.
“This is the story of Don Quixote,” said Maritornes, my newly arrived apprentice from far down-east. “Don Quixote, the man confused by books — as we too are confused by books.”
“You underestimate us,” said Cardenio, but I quieted him with a glance.
Maritornes sang the long story, beautifully, across three waking periods, with breaks only for meals and sleeps. It told of man who imagined impossibilities: great, spherical Libraries without shelf or book or hall, stiff vines growing unsupported straight up and spreading across a miscolored sky, hard-footed rabbits large enough for men to ride, suns that rise and descend, and wilder things too — a lovely story, skirting the boundaries of human imagination.
“You are no apprentice, Maritornes,” I said when she was done. She no longer looked as young to me as when she had begun. “You are a master, but of something else.”
“I believe that if we can teach the rabbits to move in the right way,” she said, “this world can become that one. We can bring Quixote’s open-sky, spherical Library into real, tangible existence.”
“Now you have truly gone beyond imagining!” said Cardenio.
Dulcinea had a plan for a new sort of picture. She had found a way to program Rabbit 3 to pass “requests” to Rabbit 2, calling for books from particular shelf positions. Upon receiving such a request, Rabbit 2 would pull down whatever book was in the requested position and nose it over to Rabbit 3. If the first character on the book’s spine was “L”, Rabbit 3 would write a “7” on the first page of its “picture” book, in the corresponding position — the top line corresponding to the top shelf, the second line corresponding to the second shelf, etc. Otherwise, Rabbit 3 would leave the position blank. Dulcinea scrambled the books various ways and still it worked. Rabbit 3 could produce a page of 7s matching the layout of Ls in a portion of its neighbor’s top chamber.
Was this page now Machine 3’s picture of Machine 2’s interior? Or to be a true pictorial representation, did the machine need to put the information to some use? Did it need to have something at stake — goals, possibilities of success or failure, reasons to engage with the world around it?
People had begun to travel from afar to see Dulcinea’s and my laboratory. I sent a call for more apprentices. I also called to break a taboo that I would earlier have thought inviolably sacred: We wanted to remove some rabbits from their home columns and install them in a string of columns adjacent to ours, columns continuous with our seven but whose rabbits were either dead or so far down as to be beyond our reach. I wanted to see if a rule-program could become contagious, transferring without human aid from one column to the next, replicating like a disease.
I sat in my desk and chair on the second level, reading a book that was, as I knew it would be, far from nonsense. I had been born in the time before clocks, but now we kept time using a rabbit that ascended and descended the stairs, writing one character per ascent into an otherwise blank book. It was, by Dulcinea’s estimate, my 10th pagewaking, 10 times 63 times 49 sleeps. The book before me was her gift to me.
The book told the story of Don Quixote, as related to Dulcinea by Maritornes. Dulcinea had printed the book with great effort from programmed rabbits. Now that it was complete, duplicates could easily be made with our streamlined copy-input programs. In a world where, until recently, “AnD t7he sUN D-escEnd.” was a stunning streak of meaningfulness, a 402-page book that made sense from beginning to end would seem a nearly impossible miracle to those who saw it. We were ready to share our invention. We knew that news and copies would travel in all directions, east, west, and down, as fast as human boys could run.
Our clock program had already traveled like the flu, borne by human carriers who valued it. We had also released a few short messages and pictures, amazing the people who saw them, who sent us a crowd of students and emissaries, some bringing their rabbits and some bringing goods to trade for our programmed rabbits.
We had also managed to program some rabbits to travel horizontally for great distances before returning, delivering messages contagious to a small subset of rabbits whose existing programming had certain vulnerabilities. The vulnerable rabbits, sometimes after many sleeps’ delay, would then in their turn go horizontal with the same message. Some of these contagious horizontal rabbits also had features attractive to human carriers, such as the ability to produce a page of blanks or a page with a picture or inspiring sentence. I wondered if we were building the world or destroying it.
Dulcinea, radiant, laid her hand on my frail right knee.
“If the universe is infinite,” I said, “we can’t be the only ones who have done this.”
“The others must be far away indeed,” said Dulcinea. “We would have heard tales of them or caught their horizontal rabbits.”
“If mentality is only calculation,” I said, “if all our perceptions and thoughts are only complex computational processes — as Trifaldi the Afflicted once believed — then somewhere there is a column which is executing the same program as my own mind is now executing, coupled with another column that is executing the same program your mind is executing, but all in much slower motion, instantiated by rabbits and books.”
“Hemete, my friend,” said Dulcinea, smiling but with a disappointed brow. “Do you still think that the rabbits and the books are real? Haven’t you yet unpuzzled the true secret of the chairs and desks? All this is only your own spherical Library.”
The universe is hallucination. By random chance, machines instantiate every finite program, executing every finite process. By random chance, every mental state is instantiated infinitely often. Infinitely often, something instantiates the experience of my seeming to write and the experience of your seeming to read, the experience of my imagining a universe of hexagons and halls and stairs, of books and humans and rabbits and vines. I must forget this dead and reborn Dulcinea; I must forget my imagined travels and my engineering and this philosophy itself, for I am only the eastern rabbit passing my book to you the western rabbit in a world that really has no east or west or rabbits or books, and we must all vanish in a moment — for in the infinitely random mind of God, the nth instruction is almost always followed by meaningless noise in the n+1th.
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