Ambiguity Machines: An Examination Read online

  So the two women went to the tree-shaded lane where the courtyard lay undisturbed. The tiles were bordered, as before, by grass and wildflowers, and a heaviness hung upon the place, as though of sleep. The church was silent; the only sounds were birdsong and distant traffic noises from the main road. The mathematician began to climb the railing.

  Don’t, her lover said, but she recognized that nothing could stop the mathematician, so she shrugged and followed suit. They stood on the perimeter, the Italian woman remembering, the Turkish one thinking furiously.

  Thus began the mathematician’s explorations of the mystery of the courtyard. Her lover would stand on the perimeter with a notebook while the mathematician moved from tile to tile, flickering in and out of focus, like a trout in a fast-moving stream when the sun is high. The trajectory of each path and the result of the experiment would be carefully noted, including discrepancies in time as experienced by the two of them. Which paths resulted in time-shifts, and by how much? Once a certain path led to the disappearance of the mathematician entirely, causing her lover to cry out, but she appeared about three minutes later on another tile. The largest time-shift so far! exulted the mathematician. Her lover shuddered and begged the mathematician to stop the experiment, or at least to consult with someone, perhaps from the nearest university. But, being an artist, she knew obsession when she saw it. Once she had discovered a windblown orchard with peaches fallen on the grass like hailstones, and had painted night and day for weeks, seeking to capture on the stillness of canvas the ever-changing vista. She sighed in resignation at the memory and went back to making notes.

  The realization was dawning upon her slowly that the trajectories leading to the most interesting results had shapes similar to the very patterns on the tiles. Her artist’s hands sketched those patterns—doing so, she felt as though she was on flowing water, or among sailing clouds. The patterns spoke of motion but through a country she did not recognize. Looking up at the mathematician’s face, seeing the distracted look in the dark eyes, she thought: There will be a day when she steps just so, and she won’t come back.

  And that day did come. The mathematician was testing a trajectory possessed of a pleasing symmetry, with some complex elements added to it. Her lover, standing on the perimeter with the notebook, was thinking how the moves not only resembled the pattern located on tile (3, 5), but also might be mistaken for a complicated version of hopscotch, and that any passerby would smile at the thought of two women reliving their girlhood—when it happened. She looked up, and the mathematician disappeared.

  She must have stood there for hours, waiting, but finally she had to go home. She waited all day and all night, unable to sleep, tears and spilled wine mingling on the bedsheets. She waited for days and weeks and months. She went to confession for the first time in years, but the substitute priest, a stern and solemn young man, had nothing to offer, except to tell her that God was displeased with her for consorting with a woman. At last she gave up, embracing the solitude that her Turkish lover had shrugged off for her when they had first met. She painted furiously for months on end, making the canvas say what she couldn’t articulate in words—wild-eyed women with black hair rose from tiled floors, while mathematical symbols and intricate designs hovered in the warm air above.

  Two years later, when she was famous; she took another lover, and she and the new love eventually swore marriage oaths to each other in a ceremony among friends. The marriage was fraught from the start, fueled by stormy arguments and passionate declarations, slammed doors and teary reconciliations. The artist could only remember her Turkish lover’s face when she looked at the paintings that had brought her such acclaim.

  Then, one day, an old woman came to her door. Leaning on a stick, her face as wrinkled as crushed tissue paper, her mass of white ringlets half-falling across her face, the woman looked at her with tears in her black eyes. Do you remember me? she whispered.

  Just then the artist’s wife called from inside the house, inquiring as to who had come. It’s just my great-aunt, come to visit, the artist said brightly, pulling the old woman in. Her wife was given to jealousy. The old woman played along, and was established in the spare room, where the artist looked after her with tender care. She knew that the mathematician had come here to die.

  The story the mathematician told her was extraordinary. When she disappeared she had been transported to a vegetable market in what she later realized was China. Unable to speak the language, she had tried to mime telephones and airports, only to discover that nobody knew what she was talking about. Desperately she began to walk around, hoping to find someone who spoke one of the four languages she knew, noticing with horror the complete absence of the signs and symbols of the modern age—no cars, neon signs, plastic bags. At last her wanderings took her to an Arab merchant, who understood her Arabic, although his accent was strange to her. She was in Quinsai, (present-day Hangzhou, as she later discovered), and the Song dynasty was in power. Through the kindness of the merchant’s family, who took her in, she gradually pieced together the fact that she had jumped more than 800 years back in time. She made her life there, marrying and raising a family, traveling the sea routes back and forth to the Mediterranean. Her old life seemed like a dream, a mirage, but underneath her immersion in the new, there burned the desire to know the secret of the tiled courtyard.

  It shouldn’t exist, she told the artist. I have yearned to find out how it could be. I have developed over lifetimes a mathematics that barely begins to describe it, let alone explain it.

  How did you get back here? the artist asked her former lover.

  I realized that if there was one such device, there may be others, she said. In my old life I was a traveler, a trade negotiator with Arabs. My journeys took me to many places that had strange reputations of unexplained disappearances. One of them was a shrine inside an enormous tree on the island of Borneo. Around the tree the roots created a pattern on the forest floor that reminded me of the patterns on the tiles. Several people had been known to disappear in the vicinity. So I waited until my children were grown, and my husband and lovers taken by war. Then I returned to the shrine. It took several tries and several lifetimes until I got the right sequence. And here I am.

  The only things that the Turkish mathematician had brought with her were her notebooks containing the mathematics of a new theory of space-time. As the artist turned the pages, she saw that the mathematical symbols gradually got more complex, the diagrams stranger and denser, until the thick ropes of equations in dark ink and the empty spaces on the pages began to resemble, more and more, the surfaces of the tiles in the courtyard. That is my greatest work, the mathematician whispered. But what I’ve left out says as much as what I’ve written. Keep my notebooks until you find someone who will understand.

  Over the next few months the artist wrote down the old woman’s stories from her various lifetimes in different places. In the few days since the mathematician arrived her wife had left her for someone else, but the artist’s heart didn’t break. She took tender care of the old woman, assisting her with her daily ablutions, making for her the most delicate of soups and broths. Sometimes, when they laughed together, it was as though not a minute had passed since that golden afternoon when they had lain in bed discussing, for the first time, the tiled courtyard.

  Two weeks after the mathematician’s return, there was a sudden dust storm, a sirocco that blew into the city with high winds. During the storm the old woman passed away peacefully in her sleep. The artist found her the next morning, cold and still, covered with a layer of fine sand as though kissed by the wind. The storm had passed, leaving clear skies and a profound emptiness. At first the artist wept, but she pulled herself together as she had always done, and thought of the many lives her lover had lived. It occurred to her in a flash of inspiration that she would spend the rest of her one life painting those lifetimes.

  At last, the artist said to her lover’s grave, where she came with flowers the day af
ter the interment, at last the solitude we had both sought is mine.

  The Third Account

  Reports of a third impossible machine come from the Western Sahara, although there have been parallel, independent reports from the mountains of Peru and from Northern Ireland. A farmer from the outskirts of Lima, a truck driver in Belfast, and an academic from the University of Bamako in Mali all report devices that, while different in appearance, seem to have the same function. The academic from Mali has perhaps the clearest account.

  She was an archeologist who had obtained her Ph.D. from an American university. In America she had experienced a nightmarish separateness, the like of which she had not known existed. Away from family, distanced by the ignorance and prejudices of fellow graduate students, a stranger in a culture made more incomprehensible by proximity, separated from the sparse expatriate community by the intensity of her intellect, she would stand on the beach, gazing at the waters of the Atlantic and imagining the same waters washing the shores of West Africa. In her teens she had spent a summer with a friend in Senegal, her first terrifying journey away from home, and she still remembered how the fright of it had given way to thrill, and the heart-stopping delight of her first sight of the sea. At the time her greatest wish was to go to America for higher education, and it had occurred to her that on the other side of this very ocean lay the still unimagined places of her desire.

  Years later, from that other side, she worked on her thesis, taking lonely walks on the beach between long periods of incarceration in the catacombs of the university library. Time slipped from her hands without warning. Her mother passed away, leaving her feeling orphaned, plagued with a horrific guilt because she had not been able to organize funds in time to go home. Aunts and uncles succumbed to death, or to war, or joined the flood of immigrants to other lands. Favorite cousins scattered, following the lure of the good life in France and Germany. It seemed that with her leaving for America, her history, her childhood, her very sense of self had begun to erode. The letters she had exchanged with her elder brother in Bamako had been her sole anchor to sanity. Returning home after her Ph.D., she had two years to nurse him through his final illness, which, despite the pain and trauma of his suffering, she was to remember as the last truly joyful years of her life. When he died she found herself bewildered by a feeling of utter isolation even though she was home, among her people. It was as though she had brought with her the disease of loneliness that had afflicted her in America.

  Following her brother’s death, she buried herself in work. Her research eventually took her to the site of the medieval University of Sankore in Timbuktu, where she marveled at its sandcastle beauty as it rose, mirage-like, from the desert. Discovering a manuscript that spoke in passing of a fifteenth century expedition to a region not far from the desert town of Tessalit, she decided to travel there despite the dangers of political conflict in the region. The manuscript hinted of a fantastic device that had been commissioned by the king, and then removed for secret burial. She had come across oblique references to such a device in the songs and stories of griots, and in certain village tales; thus her discovery of the manuscript had given her a shock of recognition rather than revelation.

  The archeologist had, by now, somewhat to her own surprise, acquired two graduate students: a man whose brilliance was matched only by his youthful impatience, and a woman of thirty-five whose placid outlook masked a slow, deep, persistent intelligence. Using a few key contacts, bribes, promises, and pleas, the archaeologist succeeded in finding transportation to Tessalit. The route was roundabout and the vehicles changed hands three times, but the ever-varying topography of the desert under the vast canopy of the sky gave her a reassuring feeling of continuity in the presence of change. So different from the environs of her youth—the lush verdure of south Mali, the broad ribbon of the Niger that had spoken to her in watery whispers in sleep and dreams, moderating the constant, crackly static that was the background noise of modern urban life. The desert was sometimes arid scrubland, with fantastic rock formations rearing out of the ground, and groups of short trees clustered like friends sharing secrets. At other times it gave way to a sandy moodiness, miles and miles of rich, undulating gold broken only by the occasional oasis, or the dust cloud of a vehicle passing them by. Rocky, mountainous ridges rose on the horizon as though to reassure travelers that there was an end to all journeys.

  In Tessalit the atmosphere was fraught, but a fragile peace prevailed. With the help of a Tuareg guide, an elderly man with sympathetic eyes, the travelers found the site indicated on the manuscript. Because it did not exist on any current map, the archaeologist was surprised to find that the site had a small settlement of some sixty-odd people. Her guide said that the settlement was in fact a kind of asylum as well as a shrine. The people there, he said, were blessed or cursed with an unknown malady. Perhaps fortunately for them, the inhabitants seemed unable to leave the boundary of the brick wall that encircled the settlement. This village of the insane had become a kind of oasis in the midst of the armed uprising, and men brought food and clothing to the people there irrespective of their political or ethnic loyalties, as though it was a site of pilgrimage. Townspeople coming with offerings would leave very quickly, as they would experience disorienting symptoms when they entered the enclosure, including confusion and a dizzying, temporary amnesia.

  Thanks to her study of the medieval manuscript, the archaeologist had some idea of what to expect, although it strained credulity. She and her students donned metal caps and veils made from steel mesh before entering the settlement with gifts of fruit and bread. There were perhaps thirty people—men and women, young and old—who poured out of the entrance of the largest building, a rectangular structure the color of sand. They were dressed in ill-fitting, secondhand clothing, loose robes and wraparound garments in white and blue and ochre, T-shirts and tattered jeans—and at first there was no reply to the archaeologist’s greeting. There was something odd about the way the villagers looked at their guests—a gaze reveals, after all, something of the nature of the soul within, but their gazes were abstracted, shifting, like the surface of a lake ruffled by the wind. But after a while a group of people came forward and welcomed them, some speaking in chorus, others in fragments, so that the welcome nevertheless sounded complete.

  “What manner of beings are you?” they were asked after the greetings were done. “We do not see you, although you are clearly visible.”

  “We are visitors,” the archaeologist said, puzzled. “We come with gifts and the desire to share learning.” And with this the newcomers were admitted to the settlement.

  Within the central chamber of the main building, as the visitors’ eyes adjusted to the dimness, they beheld before them something fantastic. Woven in complex, changing patterns was a vast tapestry so long that it must have wrapped around the inner wall several times. Here, many-hued strips of cloth were woven between white ones to form an abstract design the like of which the newcomers had never seen before. People in small groups worked at various tasks—some tore long lengths of what must have been old clothing, others worked a complex loom that creaked rhythmically. Bright patterns of astonishing complexity emerged from the loom, to be attached along the wall by other sets of hands. Another group was huddled around a cauldron in which some kind of rich stew bubbled. In the very center of the chamber was a meter-high, six-faced column of black stone—or so it seemed—inlaid with fine silver lacework. This must, then, be the device whose use and function had been described in the medieval manuscript—a product of a golden period of Mali culture, marked by great achievements in science and the arts. The fifteenth century expedition had been organized in order to bury the device in the desert, to be guarded by men taking turns, part of a secret cadre of soldiers. Yet here it was, in the center of a village of the insane.

  Looking about her, the archaeologist noticed some odd things. A hot drop of stew fell on the arm of a woman tending the cauldron—yet as she cried out, so did t
he four people surrounding her, all at about the same time. Similarly, as the loom workers manipulated the loom, they seemed to know almost before it happened that a drop of sweat would roll down the forehead of one man—each immediately raised an arm, or pulled down a headcloth to wipe off the drop, even if it wasn’t there. She could not tell whether men and women had different roles, because of the way individuals would break off one group and join another, with apparent spontaneity. Just as in speech, their actions had a continuity to them across different individuals, so as one would finish stirring the soup, the other, without a pause, would bring the tasting cup close, as though they had choreographed these movements in advance. As for the working of the loom, it was poetry in motion. Each person seemed to be at the same time independent and yet tightly connected to the others. The archaeologist was already abandoning the hypothesis that this was a community of telepaths, because their interactions did not seem to be as simple as mind reading. They spoke to each other, for one thing, and had names for each individual, complicated by prefixes and suffixes that appeared to change with context. There were a few children running around as well: quick, shy, with eyes as liquid as a gazelle’s. One of them showed the travelers a stone he unwrapped from a cloth, a rare, smooth pebble with a vein of rose quartz shot through it, but when the archaeologist asked how he had come by it they all laughed, as though at an absurdity, and ran off.

  It was after a few days of living with these people that the archaeologist decided to remove her metal cap and veil. She told her students that they must on no account ever do so—and that if she were to act strangely they were to forcibly put her cap and veil back on. They were uncomfortable with this—the young man, in particular, longed to return home—but they agreed, with reluctance.

  When she removed her protective gear, the villagers near her immediately turned to look at her, as though she had suddenly become visible to them. She was conscious of a feeling akin to drowning—a sudden disorientation. She must have cried out because a woman nearby put her arms around her and held her and crooned to her as though she was a child, and other people took up the crooning. Her two students, looking on with their mouths open, seemed to be delineated in her mind by a clear, sharp boundary, while all the others appeared to leak into each other, like figures in a child’s watercolor painting. She could sense, vaguely, the itch on a man’s arm from an insect bite, and the fact that the women were menstruating, and the dull ache of a healing bone in some other individual’s ankle—but it seemed as though she was simultaneously inhabiting the man’s arm, the women’s bodies, the broken ankle. After the initial fright a kind of wonder came upon her, a feeling she knew originated from her, but which was shared as a secondhand awareness by the villagers.