But within the first year of his happiness, the engineer noticed something troubling. Watching his wife, he would sometimes see her cheek acquire the translucency of an oasis under a desert sky. Looking into her eyes, he would feel as though he was traveling through a cosmos bright with stars. These events would occur in bursts, and after a while she would be restored to herself, and she would pass a hand across her forehead and say, I felt dizzy for a moment. As time passed, her face seemed to resemble more and more the fuzzy, staccato images on an old-fashioned television set that is just slightly out of tune with the channel. It occurred to him that he had, despite his best intentions, created a weapon after all.
So one cold winter night, he crept out of the house to the shed and uncovered the machine. He tried to take it apart, to break it to pieces, but it had acquired a reality not of this world. At last he spoke to it: You are a pile of dust! You are a column of stone! You are a floor tile! You are a heap of manure! But nothing happened. The machine seemed to be immune to its own power.
He stood among the goats, looking out at the winter moon that hung like a circle of frost in the sky. Slowly it came to him that there was nothing he could do except to protect everyone he loved from what he had created. So he returned to the house and in the dim light of a candle beheld once more the face of the woman he loved. There were fine wrinkles around her eyes, and she was no longer slim, nor was her hair as black as it had once been. She lay in the sweetness of sleep and, in thrall to some pleasant dream, smiled in slumber. He was almost undone by this, but he swallowed, gritted his teeth, and kept his resolve. Leaving a letter on the table, and taking a few supplies, he wrapped up the machine and walked out of the sleeping village and into the Gobi, the only other place where he had known stillness.
The next morning his wife found the letter, and his footprints on the frosty ground. She followed them all the way to the edge of the village, where the desert lay white in the pale dawn. Among the ice-covered stones and the frozen tussocks of brush, his footsteps disappeared. At first she shook her fist in the direction he had gone, then she began to weep. Weeping, she went back to the village.
The villagers never saw him again. There are rumors that he came back a few months later, during a dust storm, because a year after his disappearance, his wife gave birth to a baby girl. But after that he never returned.
His wife lived a full life, and when she was ready to die, she said goodbye to her daughter and grandchildren and went into the desert. When all her food and water were finished, she found some shade by a clump of brush at the edge of a hollow, where she lay down. They say that she felt her bones dissolving, and her flesh becoming liquid, and her hair turning into wind. There is a small lake there now, and in its waters on a cold night, you can see meteors flashing in a sky rich with stars.
As for the engineer, there are rumors and folk legends about a shaman who rode storms as though they were horses. They say he ventured as far as Yakutsk in Siberia and Siena in Italy; there is gossip about him in the narrow streets of old Istanbul, and in a certain village outside Zhengzhou, among other places. Wherever he stopped, he sought village healers and madmen, philosophers and logicians, confounding them with his talk of a machine that could blur the boundary between the physical realm and the metaphoric. His question was always the same: How do I destroy what I have created? Wherever he went, he brought with him a sudden squall of sand and dust that defied the predictions of local mete-orologists, and left behind only a thin veil of desert sand flung upon the ground.
Some people believe that the Mongolian engineer is still with us. The nomads speak of him as the kindest of shamans, who protects their gers and their animals by pushing storms away from their path. As he once wandered the great expanse of the Gobi in his boyhood, so he now roams a universe without boundaries, in some dimension orthogonal to the ones we know. When he finds what he is seeking, they say, he will return to that small lake in the desert. He will breathe his last wish to the machine before he destroys it. Then he will lay himself down by the water, brushing away the dust of the journey, letting go of all his burdens. With his head resting on a pillow of sand, still at last, he will await his own transformation.
The Second Account
At the edge of a certain Italian town, there is a small stone church, and beside it an overgrown tiled courtyard, surrounded entirely by an iron railing. The one gate is always kept locked. Tourists going by sometimes want to stop at the church and admire its timeworn façade, but rarely do they notice the fenced courtyard. Yet if anyone were to look carefully between the bars, they would see that the tiles, between the weeds and wildflowers, are of exceptional quality, pale gray stone inlaid with a fine intricacy of black marble and quartz. The patterns are delicate as circuit diagrams, celestial in their beauty. The careful observer will notice that one of the tiles in the far left quadrant is broken in half, and that grass and wildflowers fill the space.
The old priest who attends the church might, if plied with sufficient wine, rub his liver-spotted hands over his rheumy eyes and tell you how that tile came to be broken. When he was young, a bolt from a storm hit the precise center of the tile and killed a man sweeping the church floor not four yards away. Even before the good father’s time, the courtyard was forbidden ground, but the lightning didn’t know that. The strange thing is not so much that the tile broke almost perfectly across the diagonal, but that one half of it disappeared. When the funeral was over, the priest went cautiously to the part of the railing nearest the lightning strike and noted the absence of that half of the tile. Sighing, he nailed a freshly painted NO ENTRY sign on an old tree trunk at the edge of the courtyard and hoped that curious boys and thunderstorms would take note.
It wasn’t a boy who ignored the sign and gained entry, however—it was a girl. She came skipping down the narrow street, watching the dappled sunlight play beneath the old trees, tossing a smooth, round pebble from hand to hand. She paused at the iron railing and stared between the bars, as she had done before. There was something mesmerizing about that afternoon, and the way the sunlight fell on the tiles. She hitched up her skirts and clambered over the fence. Inside, she stood on the perimeter and considered a game of hopscotch.
But now that she was there, in the forbidden place, she began to feel nervous and to look around fearfully. The church and the street were silent, drugged with the warm afternoon light, and many people were still at siesta. Then the church clock struck three, loudly and sonorously, and in that moment the girl made her decision. She gathered her courage and jumped onto the first tile, and the second and third, tossing her pebble.
Years later she would describe to her lover the two things she noticed immediately: that the pebble, which was her favorite thing, having a fine vein of rose-colored quartz running across it, had disappeared into thin air during its flight. The next thing she noticed was a disorientation, the kind you feel when transported to a different place very suddenly, as a sleeping child in a car leaving home awakes in a strange place, or, similarly, when one wakes up from an afternoon nap to find that the sun has set and the stars are out. Being a child in a world of adults, she was used to this sort of disorientation, but alone in this courtyard, with only the distant chirping of a bird to disturb the heat-drugged silence, she became frightened enough to step back to the perimeter. When she did so, all seemed to slip back to normality, but for the fact that there was the church clock, striking three again. She thought at the time that perhaps the ghosts in the graveyard behind the church were playing tricks on her, punishing her for having defied the sign on the tree.
But while lying with her lover in tangled white sheets on just such an afternoon many years later, she asked aloud: What if there is some other explanation? She traced a pattern on her lover’s back with her finger, trying to remember the designs on the tiles. Her lover turned over, brown skin flushed with heat and spent passion, eyes alive with interest. The lover was a Turkish immigrant and a mathematician, a woman of singular a
ppearance and intellect, with fine eyes and deep, disconcerting silences. She had only recently begun to emerge from grief after the death of her sole remaining relative, her father. Having decided that the world was bent on enforcing solitude upon her, she had embraced loneliness with an angry heart, only to have her plans foiled by the unexpected. She had been unprepared for love in the arms of an Italian woman—an artist, at that—grown up all her life in this provincial little town. But there it was. Now the mathematician brushed black ringlets from her face and kissed her lover. Take me there, she said.
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 after 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 archaeologist who had obtained her PhD 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.
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