THE STERADIAN TRAIL: BOOK #0 OF THE INFINITY CYCLE (23 page)

56

V
enus came for his laptop like a debt collector at eight o’ clock; only the kidney gougers were missing. Chander had left for work, Meenakshi was making breakfast, the maid Vatsala was doing the dishes and gossiping with her, but Divya showed no signs of even getting up from bed.

Meenakshi let Venus in and shook Divya awake. ‘Look at him and look at you! He’s woken up early in the holy month and come wearing a bright namam on his forehead and here you are, still sleeping. Shame! Embarrassing!’

Wily Meenakshi kept Venus occupied with a piping hot cup of coffee he couldn’t put his lips to for another ten minutes.

The first thing Divya did upon waking up was put on her glasses and check out both the computers. She was delighted when she saw that both sets of programs had finished running and dumped something in the output files. She skimmed through them but they looked a little too garbled to make sense in one glance. She decided to study them in detail after a cup of coffee.

‘Did you stay up all night or what?’ Venus asked Divya when she strolled into the living room with her cup.

‘Yeah, something like that,’ Divya said.

‘Did the database help?’

‘I don’t know,’ Divya said. ‘The programs have just dumped something into the output files; I just saw them. But I can’t tell anything in one glance. Need to take a close look. Do you want to join me?’

‘What will I know?’ Venus said. But he followed her into her room.

‘Why do you have to come so religiously like this?’ Divya asked in a whisper. ‘All this show just to give me a bad name.’

‘No, I really wake up at four and go to the temple at five every morning.’

‘Four, really?’ Divya said. ‘What for?’

‘I have to go to America, don’t I?’ Venus said.

Divya looked through the output files on her PC first . . .

But nothing concrete about the pattern had come out of the programs. There were way too many possibilities and the programs just couldn’t narrow them down.

She turned to the laptop and spent some time reading through the outputs there . . .

But they too seemed to be of no avail.

‘This is of no use,’ she threw up her hands and said. ‘I give a list with nineteen, no eighteen cities, and the program comes back with twenty more. Rather than simplifying things, it’s making them more complex. I can’t even see what the connection is between the eighteen cities, how am I going see the connection between forty cities?’

Venus sidled up to Divya and tried to look at the output, but she pretty much monopolized the laptop; he couldn’t read much in the glare from his angle. ‘I thought your data mining programs were going to identify the common attributes?’

‘Yeah, they did,’ Divya said with an edge. ‘Guess what great insights they came up with?’

‘What?’

‘There are Indians living in these cities, both male and female. And, oh yeah, children, both boys and girls. All of them have bus stops, phone lines, electricity supply, houses, schools, post offices, telegraph offices, temples, telephone exchanges, hospitals, fire departments, water supply, government offices . . .’ she rattled off from the screen.

Venus did not remember all nineteen places on the list, but he remembered some. Something Divya said seemed to make a ping in his brain. ‘Can I have a look?’ he said.

‘By all means,’ Divya said and pushed the laptop towards him.

Venus took his time reading through the output, his face turning more serious. ‘Where’s the other file? Can you pull it up?’ he said.

‘What other file?’ Divya asked.

‘The file with the output of the other twenty places?’

‘I closed it. Give me a sec.’ Divya dragged the laptop towards her and dredged it up.

When she pushed the laptop back towards him, he said, ‘Can you show me your original list again?’

Divya hunted it down and gave it to him.

Venus scanned through the two files on the computer and the list on paper, switching back and forth between the three.

Unable to bear his silence, Divya asked, ‘What? You’re not saying anything . . .’

‘No, don’t disturb,’ Venus said, a finger raised theatrically, and turned back to the computer with an intense frown on his face.

After what seemed like ages, Divya saw his face muscles relaxing. The wrinkles on his forehead vanished and a knowing smile lit up his face.

‘What?’ she asked.

‘I’ll tell you, but first tell me what I’ll get in return?’ Venus said. ‘What’s in it for me?’

‘Anything you want. But only if you are right. Okay?’

‘Yeah, only if I am right.’

‘What do you want?’

‘Why don’t you surprise me?’ said Venus.

‘How do you want to be surprised?’

‘Can you even hear what you’re saying?’ Venus said to Divya. ‘Go get some sleep.’

‘Tell me!’

‘Okay,’ Venus said. ‘First tell me where does this list come from? How did you get it?’

Divya stared at him for a moment. ‘I can’t tell you that.’

Venus thought for a second. ‘Okay, let me ask you something, just say if it’s right or not,’ he said. ‘Is there an Iyengar or Vaishnavite involved here somewhere?’

It hit Divya like a punch in the face. ‘WHAT!’ she gasped. ‘Huh . . . huh . . . how?’ she stuttered.

Venus pumped his fist and crowed in delight. ‘Yes!’

Venus was definitely on to something and it sent a thrill down Divya’s spine. Her pulse started racing and she asked, ‘How could you tell?’

‘It’s all right here,’ Venus said, pointing at the screen, the smile refusing to go away.

‘What is it about?’ Divya said.

‘Well, it’s about . . . you,’ Venus said.

Divya crinkled up her face.

‘Your very name says it all and you didn’t even see it,’ Venus said.

57

D
ivya looked even more puzzled now. ‘My name?’

‘Yeah, your name,’ Venus said.

‘You mean Divya?’

‘Do you have any other name?’

‘Shut up, monkey,’ Divya said. ‘Tell me, does it mean something?’

‘Now that I think about it, yes. Divya means divine. The two words may actually come from the same root,’ the student of Norman Lewis said.

‘But what is the connection to Iyengars?’

‘Divya Desams. Heard of them?’

Divya looked blank. ‘No,’ she said. ‘What the hell is that?’

‘Not hell, heaven,’ Venus said. ‘They’re the most sacred Vishnu temples of all. There are 108 of them . . . That’s the common attribute of the nineteen places on the list. All of them are near Divya Desam temples; they’re the major towns near them.’

‘Common attribute to eighteen places or all nineteen?’ Divya asked. ‘I had taken out Nepal in my input file because your database covered only India.’

‘All nineteen,’ Venus said. ‘One of the 108 Divya Desams, the Salagrama temple, is in Nepal. That’s why it’s on the list.’

‘What’s so special about the Divya Desam temples? I mean, of all the thousands of Vishnu temples in the country?’

‘These are the temples mentioned in the
Divya Prabhandham
, so they’re special,’ Venus said.
Divya Prabhandham
was a collection of four thousand Tamil hymns on Vishnu sung by twelve saints called the Alwars. ‘All orthodox Vaishnavites, Iyengars especially, try to visit all the temples at least once in their lifetime. In olden days they used to go on a long pilgrimage. On foot.’

‘Oh . . . my . . . God!’ Divya said.

‘Exactly,’ Venus said.

Divya didn’t even register it. She made a lunge for the PC and frantically pulled up the web browser.

‘What are you doing?’ Venus asked.

‘Before I do anything I want to first confirm what you’re saying is right.’

‘What? You trust Google over an Iyengar like me?’ Venus said, pointing to his forehead.

‘No, I just want to check if these nineteen places cover all the Divya Desam temples.’

‘They won’t cover all 108,’ Venus said. ‘Only 106.’

‘What do you mean?’

‘Two Divya Desam temples are not on this earth,’ Venus said.

Divya gave him a puzzled look.

‘They are in the heavens,’ Venus said. ‘One is Parkadal or Kshir Sagara, the Milk Ocean, and the other is Vaikundam where Vishnu hangs out with Lakshmi. You can’t go there in this life or in this body. The belief is that if you visit the 106 temples on this earth, you will be automatically taken to the other two in heaven when your life ends.’

‘Okay, let’s just see if these nineteen places cover the 106 temples on earth then,’ Divya said.

‘You need to make one little correction in your list,’ Venus said.

‘What?’

‘When it says North Madurai, it doesn’t mean North Madurai, it means Madurai in North India, which is Mathura,’ Venus said. ‘That could be why your program didn’t spell it out explicitly.’

She trawled the net and pulled up the names and locations of the 108 temples and transferred them onto a spreadsheet. The good Iyengar that he was, Venus was more familiar with them, so he took over from her and began checking them off against her list.

The check marks kept piling up on the spreadsheet and Divya found herself throbbing with excitement.

But Venus’s brow knitted in concern before long.

‘Divvy, I think something’s wrong somewhere,’ he said.

‘What?’

‘The numbers don’t add up,’ Venus said. ‘The nineteen places account for only ninety-five Divya Desam temples. The town with the other eleven temples is missing from the list.’

Divya only had to think for a second. ‘Let me guess, are the eleven temples located in and around Kumbakonam? Is Sri Sarangapani temple one of them?’

‘What!’ It was Venus’s turn to be surprised now. ‘How did you know?’

‘Oh Venus, you don’t know what you have done!’ Divya leapt up in joy and was about to give him a hug when Vatsala made a strategic entrance into the room, holding a broom and a dustpan. Divya checked herself and stepped away.

They grabbed the laptop and shifted into the living room, giving Vatsala all the privacy she needed to clean the room.

‘Are you going to tell me what this is about?’ Venus asked.

‘Just give me some more time,’ Divya said. She was sleepless and tired but there was no hiding that euphoria. The glow on her face said it all.

‘Can I take my laptop and go now? It’s almost nine o’ clock.’

‘Sure, but meet me in the lab around lunchtime. Or I’ll come and look for you. We’ll go out for lunch today. My treat.’

‘And a movie in the afternoon?’ Venus said.

Divya shot that down.

‘No, I’d rather crash at home,’ she said. ‘I didn’t even get three hours of sleep.’

~

Once Venus left, Divya had her tiffin – pongal with tomato chutney – and began organizing her thoughts. She went through all the material one more time. She could now use the numeric labels in the notebook to verify certain things. She didn’t have time to write a program, but there was no need. She could do it manually with a calculator or spreadsheet in a few minutes . . .

Janaki Ammal’s interview too started making more sense now and she began underlining some of the relevant sections in the transcript. As she was doing that, she remembered something . . . the original audio-file. Nancy was going to upload it on Joshua’s homepage by Monday, US time. It was Tuesday in India now.

She went to Joshua’s website and there it was, the MP3 . . .

58

H
alf past ten, Lakshman’s office. Divya had promised to report at ten but there was no sign of her.

But Lakshman, well trained in the Indian school of philosophy on timeliness and punctuality, wasn’t unduly bothered. Besides, the day had started on an upbeat note for him and he wasn’t going to spoil it worrying over Divya’s arrival. Though Urmila had overheard their discussion with Banerjee from the vantage point of the room upstairs and picked up enough pointers about the incident on the bridge, she hadn’t hauled him over the coals for it. Her brother Parasuram was visiting the city on some business and had arrived at the house last evening, a few days later than planned originally. She was busy catching up with him and had very little time for her husband. Parasu was going to stay for a few more days and there was no way she would create a scene in front of him. All Lakshman had to do was to avoid getting caught alone with her and rubbing his sprained shoulder in front of her. If he behaved like a good boy with his brother-in-law and refrained from going on a binge with Joshua when he was around, there was even a good chance that she would forget or forgive his escapade, or at least let him off lightly. He did an extra round at the stadium in the
morning and arrived at the office oozing optimism and pulsating with positivity.

But Joshua was not in such perky spirits. He had spoken to Becky and Katie last night and he was told in no uncertain terms that they were both dying go back home. He didn’t even tell them about the skirmish on the bridge but even without that their restlessness was unbearable. It rubbed off on him as well. He had a disturbed sleep and woke up early in the morning and arrived ahead of time at Lakshman’s office. The delay in Divya’s arrival only made his restlessness worse. He excused himself from Lakshman and decided to go downstairs and get a breath of fresh air.

Durai had gone to the campus canteen and the cop Michael was sprawled out in the car – as much as he could in an Expanzo, getting some sleep. Joshua began pacing the entrance, trying to calm himself by browsing the notice boards.

Ten minutes passed and a Scooty Dopplered to a stop near the building, promptly waking up Michael. He sat up with a start, saw who was coming and then slumped back in the car seat.

Divya saw Joshua prowling in the corridor and wished him good morning. He wished her back and shepherded her straight to Lakshman’s office.

It didn’t take Divya more than a few minutes to leave Joshua slumping back in his chair, stunned into silence. It didn’t even seem like he was paying attention to her after that. He just sat frozen in his chair like a sculpture. Lakshman didn’t quite comprehend it; he gave Divya a patient hearing and asked: ‘So what you’re saying is, Ramanujan developed a combinatorial algorithm to help pilgrims make travel plans?’

‘Yes sir,’ Divya said. ‘He not only worked on combinatorial problems like partitions, he was also good at solving these kinds of practical problems. He even used to help his headmaster in school, in coming up with timetables and assigning teachers to classes.’

‘Really?’ Lakshman said. ‘Where did you see that?’

‘It’s mentioned in his biography. Even Janaki Ammal refers to it in the interview.’

She pulled out the printout from her bag and shuffled through the sheets. ‘Here, sir.’

She placed the sheaf on the desk midway between Joshua and Lakshman, but only Lakshman seemed interested; Joshua was still in a daze.

She had underlined the relevant sections and Lakshman ran his eyes through them.

His schoolteachers used to like him a lot. He would help his school headmaster with writing timetables.

He scrolled further down and there was another.

Many people in Kumbakonam used to know him. Someone or the other would always come looking for him. If they ask him to give tuitions to children, he would help them. If they ask him how to go on a pilgrimage, he would help also.

‘I think some of the things she said got lost in translation, sir,’ Divya said. ‘It’s much clearer in the audio-file.’

Joshua finally stirred in his seat. ‘What!’ he said, flinching. ‘You’ve listened to the interview?’

‘Yes sir, I listened to it this morning, that’s why I was late,’ Divya said. ‘It’s already uploaded on your homepage. That’s
what helped me convince myself that I was seeing what I was seeing.’

Lakshman looked stunned for a second and then reached out to the mouse and keyboard. Soon the old frail voice of Janaki Ammal quivered out of the speakers and filled the air.

Lakshman turned up the volume to the max.

It was an old recording and there was a persistent hiss in the background punctuated by occasional grating and squeaking, but there was no mistaking what she was saying. Lakshman and Divya listened intently.

Janaki Ammal spoke a brahmin dialect of Tamil, not just any brahmin dialect but that of Iyengars, one suffused with baroque Tamil phrases in addition to Sanskrit terms. Lakshman, who was never fully at ease with the brahmin idiom or dialect, especially as spoken by someone from the old school, had to think hard to puzzle out what she was saying. He was better now than he was back in the Eighties, but even so, he couldn’t grasp some of the nuances in her speech.

‘Here, sir, it’s coming,’ Divya alerted Lakshman when the relevant segment was approaching.

Lakshman summoned every bit of concentration he was capable of and listened.

A lot of people in Kumbakonam knew about him. So many people would come to the house to visit him. Some people would ask him to give private tuitions to their children. He would gladly oblige. Some Vaishnavites came home once and asked him to tell them a shortcut to go on a pilgrimage to all the Divya Desam temples. He spent a lot of time helping them.

Lakshman asked her to play back the segment once again. There was no mistaking what she was saying.

‘What is it?’ asked Joshua.

‘Sloppy translation. My mistake,’ Lakshman said and explained it to him.

‘But still,’ Lakshman said, ‘108 temples, 106 on earth, two up in the skies somewhere . . . I can’t imagine how Jeffrey managed to make sense of all this. Even I am hearing about it for the first time. Did you know all this before, Divya?’

‘No sir,’ Divya said.

‘Then how did you figure it out now?’ Lakshman asked. ‘I don’t think your programs are
that
smart.’

‘No sir, it wasn’t the programs,’ Divya said. ‘It was a guy in Civil who told me: Venu Sampath. I talked to him when I was having trouble making sense of the output files.’

‘My God!’ Lakshman said.
So that’s how Jeffrey figured it out?
It hit Lakshman like a bolt of lightning. Narasimhan Thathachari. The very name said it all. It couldn’t get any more Iyengar than that.

‘Were you able to reverse engineer the algorithm?’ Lakshman asked Divya.

‘No sir, that’s impossible, for me at least,’ Divya said, a touch embarrassed. ‘We don’t have any sense of the termination criteria, sir; the last pages are missing. The programs couldn’t go further without them. Those people knew what pages to remove, sir; they’ve taken away the crucial sections, so even if someone else found the notebook, they can’t do much with it.’

Lakshman still didn’t seem to have gotten it and Joshua decided to step in. ‘Okay, you don’t have the algorithm, but could you figure out which mathematical problem it’s aimed at solving?’ he asked Divya.

This was the moment she had been waiting for. The revelation about Divya Desams, she owed entirely to Venus. But this one was her own.

‘I think so, sir,’ Divya said. ‘The pilgrims want to start from Kumbakonam, travel to nineteen other cities to worship at all the Divya Desam temples and finally return to Kumbakonam. They want to know what sequence to follow so they can complete the pilgrimage as quickly as possible. Since there are nineteen cities to visit, there are nineteen factorial or trillions of possibilities; the problem is figuring out which of them is the best. This is nothing but the classical Travelling Salesman Problem, sir. You explained it to me after your presentation last week; it has no mathematical solution and even the world’s most powerful computers cannot handle that kind of exponential growth in complexity.’

Joshua had seen it coming minutes after Divya walked into the room. But Lakshman had not been so quick on the uptake. Divya drove the point home in plain and simple English.

Ramanujan had an algorithm for the Travelling Salesman Problem!

Given that it was about twenty years before the coinage Travelling Salesman Problem took hold in the 1930s he would have probably called it the Vishnu Pilgrim Problem or something close to it.

It descended upon Lakshman like a ton of bricks, leaving him reeling.