Quantum Patterns

By the middle of August the Core, too, had started returning answers before Ananya had finished asking.

On the Saturday she came home at two in the morning with her head ringing and lay on top of the sheet with her shoes still on until the crows started on the neem.

It was Vikram's idea, the way all the good ideas in the family were his and all the bad ones were too.

"Nanna hasn't left this house since Bonalu," he said at breakfast on Sunday, to his dosa. "Not counting Somajiguda. Somajiguda is not leaving the house, Somajiguda is punishment. Today we are taking him to Golconda."

"Golconda is a fort, ra," said Ananya, who had slept three hours. "The whole point of a fort is that people like us can't get in."

"The Qutb Shahis didn't have me." He flexed an arm that had carried nothing heavier than a gaming laptop since 2019. From the bedroom Nanna called, "I heard that," in the voice of a man who was already looking for his good shirt.

So at five in the evening the three of them were at the Fateh Darwaza, the Victory Gate, its teak doors studded with iron spikes at the height of an elephant's forehead, and Nanna's chair was stuck in a crack in the Qutb Shahi paving, and a thin old guide with a laminated government ID on a string had attached himself to them for a hundred rupees. Vikram put his shoulder to the chair and lifted the small wheels out of the crack. They went in under the gate into the cool, where it smelled of bat and old lime mortar and somebody's chilli bajji.

Just inside, under the dome, the guide planted his feet on a worn patch of floor. He raised his hands and clapped once.

It went up into the dome and came down wrong. Too loud, too near, as if the clap had been handed back to him.

"Up there," the guide said, and pointed through an arch at the pavilion of the Bala Hissar, black against a sky going orange. "One kilometre. The guard hears this clap. No telephone, no WhatsApp. Only architecture."

Nanna looked up at the hill. Three hundred and eighty steps, many of them boulders someone had once agreed to call a step. Nobody said anything about the chair.

"Go," he said to her. "You go up. I'll clap."

"Nanna—"

"Call Vicky when you're there." He was already rolling himself back to the guide's worn patch, not looking at her. "I want to see if a fluids man can still send something up a hill."

She went up. He had asked for so little in ten years that anything he asked for was a command.

The climb took twenty-five minutes. The city came up round her, and far off, the towers of the Financial District, where somewhere under the ground a point of light was sitting in the dark, being held.

At the top the wind was strong and smelled of dust. She stood on the pavilion's edge and rang Vikram.

"She's there," she heard him say, and then, to Nanna, "go, go, go."

She took the phone away from her ear so that she wouldn't cheat.

For a second there was only wind, and then it came up out of the fort below her: a clap. Small, clean, like a single drop landing on a steel plate in another room. Her father's hands. A kilometre away and a hundred metres down, it arrived in one piece.

She stood on the top of Golconda and cried, briefly and without any fuss, the way you sneeze.

When she came down it was nearly dark, and he was holding his palms up, curved, as if carrying an invisible bowl.

"Did you hear?"

"I heard."

"Good. Look." He held the bowl up to her. "A flat wall throws a sound wherever it likes. Wasted. A curve takes every piece of it and sends them all to one place at the same time, so they add." His fingertips came together, not quite touching. "It doesn't get louder, beta. It just doesn't get lost."

"Like a lens."

"Like a lens." He dropped his hands into his lap. "A curved wall is a promise to a sound. It says: I'll bring you to one place."

He bent to his bag for his water, and his shoulder caught, and she saw the pain go across his face. He unzipped the back pocket anyway and took out a maroon ledger with a cloth spine, the kind kirana shops sold, fat with use.

"You know about systems," he said. "Tell me I'm a fool." And he gave it to her.

She knew his careful Kanpur hand before she knew she was reading: fountain pen, date and time, then A. in the left column, L. in the right, both ruled in pencil.

25 July. A. worked late, happy, "coherence absurd." L. did not know me for twenty minutes.

2 Aug. L. in pūjā room 3:20, chanting, did not know me. Second tablet at 4.

3 Aug. Sunday. A. at home all day. Tired, flat, did nothing. L. made pesarattu. Sang. Asked after the Kanpur milkman's daughter.

14 Aug. A. home 4:10, very happy. "The machine is finding things by itself, Nanna." L. awake at 3, chanting fast, "like running". Forgot the word for the neem. Pointed.

16 Aug. L. chanting from midnight. Could not stop it. A. home 2.

She turned the pages under the sodium lamp. Her good days and her mother's bad ones, side by side, two waves on a tank. Where one rose, the other fell. He had ruled the columns and written no conclusion under them.

She took out her phone and photographed the August page, flash off, the book flat on her knee in the Victory Gate with the tourists clapping and clapping behind her, and then she photographed it again, because the first one had his thumb in it.

"Nanna," she said.

He held out his hand. It was held out for the ledger, but it was open over the phone too, and for a second she thought he would ask for both. He took the ledger in both hands and zipped it back into the pocket. The phone he left her.

"It's a log," he said. "When a system misbehaves you keep a log. That's all."

"It's a log of me."

"It's a log of everybody, beta. I'm in it too, I just don't write myself down." He looked up the hill at the dark pavilion where she had stood. "Small sample. Confounds everywhere. A frightened old man will find a pattern in rice."

"You're not old."

"I'm not frightened either," he said, and took a long drink of water, and behind them somebody's child clapped under the dome, and up on the Bala Hissar, where nobody was listening, the stones received it anyway.

On Sunday there was no run, because Sharath had said the Core needed a night off and she suspected he meant her, and so at a quarter to ten Ananya was at home in Tarnaka with her feet on the rexine sofa and her mother's head on her shoulder, watching TV9.

Nanna had gone to bed with his maroon register under the pillow. Vikram had dropped them at the gate and gone back to the office. Amma had eaten half a chapati at dinner, and taken her tablets, and said "It's nice" about the dal in a voice like a radio in another flat. Her phone lay face up on the sofa arm, lighting now and then. On the colony group a forward about lemon water curing dengue had sat unanswered since Thursday, and under it Padma from next door had written, Lakshmi garu?? No link today??

"The Quantace CSR hospital network marks six years today," said the anchor, a woman with lipstick the colour of a traffic cone. There was Sharath, on a stage with a lamp in front of him, lighting the wicks one by one with a long taper, looking out at the hall over the flames as if he were counting the people in it.

Ananya felt her own face go warm, which was ridiculous. She reached for the remote.

Amma's head came up off her shoulder. She did not turn it. She only lifted it, and her eyes were clear. Ananya had not seen them clear since June.

"The boy from the hospital," Amma said. It was the other voice: low, and slow, with a kind of patience in it that had nothing to do with her, like a well answering a stone. "He's still carrying her."

"Amma?"

"Carrying her. All this time. Nobody told him to put her down."

"Who, Amma? Carrying who?"

But her mother had already lowered her head again, into its old place, and when Ananya said "Amma" once more she said, in her ordinary voice, sleepily, "Mm? Is it over, the news?" and did not know what she had said, and Ananya could not ask her to.

At half past ten Vikram came in smelling of the Gachibowli flyover, diesel and rain.

"Sleeping on duty," he said. "I'll report you to your Sir."

"Report me. He'll give me a car."

"He already gave you a car. With a driver who says Madam."

She laughed, properly, and Amma smiled in her sleep at the sound of it. Vikram's thumb was working at the strap of his laptop bag, back and forth, a thing he had done since he was nine and lying about cricket.

"Akka." He waited until she looked at him. "Your Core. Does it ever do things at night? By itself?"

She thought of a golden point humming a hair off the beat.

"It's a fridge, Vicky. It does what fridges do. Why?"

For a moment he kept looking at her. Then he smiled.

"Nothing. Our clocks went funny on Friday night. Karthik says it's the auth server's sixth sense." He went to bed, and she sat on with Amma asleep against her and the photograph of the August page on her phone.

At midnight she sat at her desk under Nanna's slide rule with the phone propped against the lamp and the laptop open beside it, and did what she would have done with anyone else's data. Left, his hand. Right, hers.

2 Aug. L. in pūjā room 3:20, chanting, did not know me. She scrolled the job log back to the first of August. NSD_7v_trst run_at 03:17. Friday night into Saturday; Nanna dated by the morning, as he dated milk bills. Three minutes: the time it took a man in a wheelchair to wake, hear, and find his watch.

14 Aug. L. awake at 3, chanting fast, "like running". job 14Aug 02:38, ended 03:31. Three o'clock sat inside it like a stone in a mango.

16 Aug. L. chanting from midnight. Could not stop it. A. home 2. She did not need the log for that one. She had pressed the key herself at 23:58, with nobody told, and come home at two to a house that was, she remembered now, not dark: the pūjā-room bulb on, the door pulled to. She had walked past it to bed, because it was only Amma.

She checked the other way. The third of August: no job in the log, and Amma had made pesarattu and sung.

Three pairs. Small sample, confounds everywhere; she could hear him say it. She did not go and wake him. He had given her the book so that she could tell him he was a fool, and she could not, and she would not say the other thing to him until she had tried to break it.

At half past one she gave up on sleep and dragged Ajji's chest out from under the bed.

Under the red silk, in the sandalwood, were the twenty-two Osmania exercise books in Ajji's small upright hand. In June she had leafed through them looking for comfort and found only arithmetic.

Pingala's Meru, the triangle the rest of the world called Pascal's, carried to the sixteenth row; the seventeenth ruled and empty but for the 1s at either end, because anyone could fill those. A ghana pāṭha schedule with one syllable missing in every eighth cycle and a small circle in its place: a carpenter's mark. Leave this hole open.

Everywhere, a structure walked right up to the edge of its own completion and then was told, on purpose, to wait.

She had spent the whole summer teaching a machine to find endings.

"Ayyo," she said, to nobody, and laughed, and put her hand over her mouth, because it was a quarter to three and the walls in Tarnaka were thin. Every blank cell was a job, and the job was to keep it blank.

Under the notebooks was her own, where she had put it back in June: spiral-bound, a Magadheera sticker half peeled off, fifteen-year-old Ananya's attempt to map laghu and guru onto nested functions, and the margin note in her teenage round hand:

Doesn't converge. Pattern suggests solution but function never terminates.

She read it three times and heard, at last, what she had missed for fourteen years: both could be true of something that converged. Chaitin had written the third thing down in the seventies. She wrote it under her teenage self's note, in her adult hand, which was smaller and less sure of itself.

Ω = Σ 2^(−|p|), summed over every program p that halts

[Every term brings you closer. None of them tells you how close.]

The halting probability: the chance that a program typed out at random ever stops. It converges, God knows it converges, but no rule could ever tell you how fast, so you could add for the life of the universe and never be entitled to say nearly there.

And hers? Her run logs had an order: first pure information, then the fridge itself, the pulse tube settled into one clean mode. Everything in the world that held its shape held it because the way down was hard to find. And since the Pingala schedule the Core had leaked nothing to the world around it. Nothing was watching it. A place with no watcher keeps no record of before and after, so it has no arrow of time, and if the universe were ever going to get good at search, it would start in a pocket like that.

You can't mine the ground state. Unless it isn't the ground state.

She made it give her a number. Empty space had a floor too, the lowest it could settle to, and nobody had proved ours was the bottom one. If the space round the golden point sat in a deeper vacuum than the rest of the universe, the wall between them was a wall that moved: Coleman, 1977, a bubble of true vacuum that, once big enough to live, grew outward at very nearly the speed of light. Sub-Level 5 of PJS Tower to this room in Tarnaka: nineteen kilometres as the crow flew. She divided by c.

Sixty-three microseconds.

A nerve impulse from Amma's fingertip took ten thousand microseconds to reach her brain. Amma, asleep in the next room with her mouth open, would not have time to feel her own hand. Nanna would not finish a breath. The crows on the neem would not have time to lift.

She was frightened, and still she was proud: the point had held for two weeks, and she was the only person alive who knew how.

At four in the morning, lying on the floor with Ajji's blank cells round her, she opened the run calendar and deleted Wednesday's slot. If she was wrong, nothing would happen. If she was right, nothing would happen to the Core either. It was Amma she would be watching.

On Monday Lakshmi did not take her tablets. Krishna found the new strip that evening back in the drawer with the steel tumblers, every blister full, and when he held it up she said, "The house is too quiet, Krishna," as if that answered it. In bed he took the register from under his pillow and wrote:

18 Aug. L. put the new strip back in the drawer, full. Said the house was too quiet.

He did not show it to Ananya. She had photographed enough.

The flower man came down their lane in Tarnaka at seven every morning on a black Atlas cycle, singing the same two words at the same three gates, "Malle poolu," with the second word dropping off a little cliff at the end. On the Tuesday after Golconda Krishna had himself wheeled out to meet him. He had bought his wife jasmine every day of their marriage that he could reach a flower man, the one extravagance of a careful man.

Lakshmi was sitting on the step under the neem with her tea, in her old cotton nightie with a towel over her shoulders, hair still wet. She had been quiet since Sunday: not the thin quiet of the tablets but a listening quiet, as if somebody were talking in the next house and she was trying to catch the words.

"Here," he said, and held the string out to her across his knees.

She took it and smiled at him the old way, one side of her mouth first. Then she looked up into the neem. "Krishna, it's less detailed. Like somebody has drawn it well. Very good drawing. But drawn."

He was a fluids man. He looked at the thousand serrated edges moving against the white sky, and they moved. Only, perhaps, now that she had said it, a little together, the way a crowd moves when the police have put up barricades.

He did not say that. He said, "Smell your flowers."

She lifted the string to her face and breathed in, eyes closed. He waited for the small hum in the nose that meant it was good.

It didn't come.

She breathed in again, harder, and pressed the flowers to her nose so hard that a bud broke and left a wet white smear on her lip.

"I can't," she said. "I know what it smells like, Krishna. Milk sweets, and a little bit like a baby's head. I can say all of it. I just can't get it." She held the string out at arm's length. "Here. You."

He smelled it. Jasmine, so sweet it was almost rude, the smell of every wedding and every temple queue and every bus in April.

"Is it there?"

"It's there."

She did not cry. She pinned the string into her wet hair above the left ear with a clip from her pocket, as Ajji had taught her as a girl. "Then I'll wear it for you, and you can smell it for me. Fair?"

"Fair."

The flower man rang his cycle bell once and pushed off. "Malle poolu," he sang at the next gate, and Krishna found himself listening to be sure that the second word fell a little differently from the last time.

It did.

On Wednesday she came home at six, which had not happened since June, and heard Amma before she saw her: in the kitchen, singing.

Not the japa. The real song, the Ghantasala one she sang over the tawa, badly, with her own words where she had lost the real ones, the spatula conducting. She turned round and said, "Look who remembered she has a house," and pinched Ananya's cheek with oily fingers, and it was so entirely her mother that Ananya had to go and wash her face.

They ate together, the four of them. Amma called Vikram Manager-garu and asked whether the girl from Karthik's wedding had a name or only an Instagram, and Nanna laughed till his back hurt. At ten Amma went to bed humming. Ananya sat at her desk with the run calendar open on its empty Wednesday and let herself think it: there, then.

At 11:45 the pūjā-room door clicked to.

It began low, the short japa, Ajji's hour. She waited for it to stop, as it stopped on ordinary nights, after ten minutes, after twenty. It did not stop. It did not quicken either. It went on at the pace of somebody walking a long way, and Ananya sat on her bed with her back against the wall the pūjā room shared and listened through the plaster, and did not go in. She told herself it was method: if she went in, she would be part of the measurement. It was also that she had never once sat with Ajji for it, and did not know how you began.

Her phone said 04:02. Her mother was still going, the way Ajji had on her bad nights, the voice worn down to breath.

At seven there was a message from Nag. Point drifted 03:52. Recovered 04:10. Not fully. ? —N.V. The overnight trace showed it plainly: two weeks of a held thing, and then, on the night she had held back, a slip off its axis and a hum a hair off the pulse tube's beat, as if a hand had loosened.

She opened the run calendar and booked the Core for Friday night.

The trap had shown her what stopping did: the point came loose with Amma still inside it.

Krishna had heard it too. He had lain in the dark from a quarter to twelve with his hand on the register under the pillow, and when the pūjā-room door opened at last and Lakshmi lay down beside him with her feet as cold as the floor, he waited until her breathing evened and then switched on the small torch and wrote:

20 Aug. A. home early. No run. L. sang in the kitchen, the real song. Japa from 11:45 till after four.

At breakfast Ananya came in with her phone in her hand and her face set, and he knew the face. She had booked something. She did not say what, and he did not ask.

He had a sentence ready. He had been polishing it since Golconda: a column is not a cause. He opened his mouth and shut it, because she was the one in this house who knew about causes, and he was the one who had handed her the book.

When she had gone he opened the register on the table and wrote it at the foot of the August page instead, small, under the ruled columns where he had never put a conclusion: A column is not a cause. Then, because he was an honest man, he added a question mark.

On Thursday Sharath came down to the Sanctum at six and said, "Have you eaten today?" and when she had to think about it, he said, "Come. My mother will be offended if I let you starve in my building."

The car went south, over the Musi at Nayapul, and stopped where the lane off Shah Ali Banda got too narrow for it. Farooq bhai's shop at the corner with Thums Up in a chest cooler, and Farooq bhai himself shouting, "Aao, sahab, aao, today you brought company!" so that every door in the lane found a reason to be open.

His mother's house was one room and a kitchen with a blue door. A cot, a steel almirah, a jeweller's calendar, a television under a lace cloth. Sumathi Shetty was standing in the doorway with a ladle.

She looked at Ananya's feet first, then her face, then her son.

"Yehich ladki?" she said. "This is the scientist?"

"Amma, this is Dr. Ananya Nayagiri."

"I know who she is, you told me four times on the phone. Doctor, doctor." She took Ananya's wrist in a hand that was all knuckle and heat. "Come inside, amma, sit. You are too thin. His whole building is thin people." To her son, without looking round: "Chappal outside, sahab."

He was already taking them off.

She sat Ananya on the cot and put a steel plate in her lap before she had finished sitting: rice, and khatti dal sour with Lalitamma's tamarind, bright with chilli oil, curry leaves fried black. Sharath was given a plate too, and sat on a plastic stool with his knees near his ears and ate like a man who had been hungry since 1999.

Halfway through, a big man in a checked lungi and a white skullcap walked in without knocking, said "Salaam, Sumathi amma," and ate four puris standing up. "Imran," said Sumathi. "Two doors down. Eats here, sleeps there." He told Ananya that if she ever needed anything in the Old City she should come to his stall at the Laad Bazaar end of the Chowk, attar and phone recharges, opposite the bangle shops: ask anyone for Imran bhai. Then he kicked a pistachio-green Chetak four times until it agreed.

Sumathi turned to her son with the ladle raised. "Yeh ladki tereku kaiku jhelti hai? You make her work at night, na? You made your sister work at night also. Maths, maths, three o'clock you are shouting in this room, Priya, look, look, and the whole lane cannot sleep."

"Amma, she made me work at night."

"She was twelve!"

"She was merciless," he said, and for the first time since Ananya had known him he smiled with no calculation in it at all, a boy's smile, with tamarind on his lip.

Later, carefully, Ananya asked what Priya had been like, and Sumathi talked plainly, as if Priya had only moved to Dubai.

"Clever. Too clever. Skipped two classes and came in his class and beat him every exam. And naughty. Never gave a straight answer in her life. When she was nine she ate all the laddus I made for Lalitamma's daughter's function. Twenty laddus. I said, Priya, who ate the laddus? Straight face, she says to me, 'Amma, who counted them?'"

Ananya choked on her water.

"Her father laughed so much he fell off this cot. He said, that girl will never let a question die a natural death."

Sharath was looking at his plate. His ears had gone red.

"Show her the books, Amma."

"You show."

"Amma."

So Sumathi got up, her knee refusing, and unlocked the almirah with a key on a thread round her neck. From under a pile of folded school uniforms that a mother had not given away, she lifted out a bundle of long notebooks tied with a pink ribbon gone grey.

"Careful. The pages are going."

Ananya held the first one open on her knees. PRIYA SHETTY, IX-B, in a round confident hand that grew smaller and quicker as it went, while the maths grew stranger.

A staircase in pencil, each step labelled with a question, why?, why that?, who's asking?, and at the bottom, where it should have landed, a blank, and in the blank a tiny girl sitting cross-legged, keeping it open.

Ananya turned a page and went cold.

She had seen this before. Not something like it; this. A nested bracket structure spiralling inward, each loop feeding its output back as the next loop's question, with the same peculiar notation for the feed-back, an arrow with a small circle at its tail. It had been on the whiteboard in the Sanctum since before she arrived in June, in a hand she had assumed was Nag's.

"Fifteen," Sumathi said, watching her face. "She was fifteen when she did that one. Her teacher said it was nonsense. He" (a nod at her son) "said it was not nonsense. They fought. Then she got sick."

Ananya looked up at Sharath. He was sitting very still on the stool with his hands between his knees, and he was looking at the notebook in her lap as she had looked up at the Bala Hissar: a place a person had once been standing.

He's still carrying her, Amma had said on Sunday night, with her eyes clear, to a television. Ananya had put it down to the tablets.

She had meant, all evening, to be careful. The car outside was his and the driver was his; bringing her here was a move. Knowing that did not help her keep her distance from the man on the plastic stool in his mother's kitchen. He had loved a girl who answered every question with a question, and had never, in twenty-three years, been told to put her down.

"She was brilliant," she said.

"She was better than brilliant," said Sharath. "She was annoying."

His mother hit him on the shoulder with the ladle, and he let her, and the tube light buzzed, and in the next house someone's pressure cooker whistled three times, unevenly, and a baby answered it.

He dropped her in Tarnaka at 21:40. The dashboard had said it would be 21:40:16 when they left Shah Ali Banda, and when the driver pulled up at the neem the clock on the dash read 21:40:16, and Sharath watched her walk to her gate without looking back.

Then he said, "The Tower," and closed his eyes, and touched the crescent behind his right ear twice.

Communion was like putting your hand into water exactly the temperature of your hand. Then the signal phases at Mettuguda, Secunderabad, Begumpet arrived in him as a kind of posture. Tonight, for the first time, the corridor ran itself. Every ETA on every phone between Paradise and Gachibowli was correct to the second. He could feel them landing, one after another: arrived, arrived, arrived.

"Sir, traffic is too good," said the driver, who was from Karimnagar and did not trust good things.

Sharath found that he was smiling.

Anna.

He did not turn his head. The voice came from behind his eyes, where the graphacer lit the corridor, and it was hers: her voice at fifteen, a little hoarse, the Old City in the vowels.

Anna. She's the one.

"You saw her," he said. His own voice was a whisper. The driver, who had been told long ago to hear nothing, looked at the road.

I saw her read my books. She knew the arrow. She knew what it was for.

"She's frightened."

She'll come. Warm. Certain. She's the one, anna. You don't have to look any more.

He sat with that for three signals. All green. Some very old part of him, the part that had sat in the OGH general ward counting the monitor's beeps, wanted to ask her the thing he always asked: how do you know? He had asked her that once about a proof, at this age, and she had grinned at him across the cot and said, how do you know I know?

He didn't ask. He was afraid that she would simply tell him.

Something warm ran over his lip. He touched it and his fingers came away dark, and a drop fell onto his white cuff and spread there into a small circle, exact as a compass could make it.

The driver passed back a box of tissues without looking. Sharath tipped his head back against the seat and watched the flyover lights go over the roof, and every one of them arrived precisely when he knew it would.

It was nearly one when Ananya came home on the Friday, and she did not knock on his door, but he heard her in the kitchen humming, and heard her laugh out loud once at something on her phone, and he knew.

Lakshmi had been asleep since ten. Earlier, at dinner, she had found their wedding photograph on the showcase, the black-and-white one from the Kanpur hall, and brought it to the table and asked who the nice young couple were. He had told her. The garlands. Her uncle crying. The power going off in the middle of the muhurtham and the priest carrying on in the dark, and the whole hall laughing, and his hand finding hers under the cloth.

He took the register from under his pillow and unscrewed the pen. Through the window the neem moved every leaf at once, in a wind he could not feel. He did not write a conclusion. He wrote:

22 Aug. A.'s best run. L. could not remember our wedding. I told her. She said, "That's a lovely story."