The Last Theorem

18 COMPANY

On the seventh day of Ranjit’s stay with the Vorhulsts the butler announced another visitor, and it was Myra de Soyza. “Am I intruding, Ranjit?” she asked at once. “Aunt Bea said I could look in on you as long as I didn’t keep you from resting.”

Actually he had in fact been resting, and Myra de Soyza was certainly keeping him from it. He didn’t want to say that and did his best to manufacture conversation. “What are you doing now?” he asked. “I mean, are you still at the university?”

She wasn’t. Hadn’t been since that sociology class they had shared; had in fact just come back from a postdoc session (postdoc! He had had no idea how far up the academic ladder she had climbed) at MIT in America, and naturally he asked, “Studying what?”

“Well…artificial intelligence, more or less.”

He decided to ignore the cryptic “more or less.” “So how’s artificial intelligence doing?”

She grinned at last. “If you mean how close are we to getting a computer to have a reasonable chat with us, terrible. If you go back to the kinds of artificial intelligence projects that the people who started the field were trying to solve, not bad at all. Did you ever hear of a man named Marvin Minsky?”

Ranjit consulted his memory and came up empty. “I don’t think so.”

“Pity. He was one of the best minds ever to try to define what thought was, and to find ways of getting a computer to actually do something you could call thinking. He used to tell a story that cheers me up sometimes.” She paused there, as though unsure of her audience’s interest. Ranjit, who would have taken pleasure in hearing her announce train delays or closing stock prices, made the right sounds, and she went on. “Well, the thing is that in the beginning of AI studies, he, and all the other pioneers, too, considered pattern recognition as one of the hallmarks of AI. Then pattern recognition got solved in a rather everyday way. Checkout counters in every supermarket in the world began reading the prices of every item from bar codes. So what happened? AI simply got redefined. Pattern recognition got left out of the recipe because they’d solved that one, even if the computers still couldn’t make up a joke or figure out from the way you looked that you had a hangover.”

Ranjit said, “So can you get a computer to make up a joke now?”

She sat up. “I wish,” she said moodily. And then she sighed. “Actually, my main interest isn’t in that kind of thing anymore. It’s more in applications. Autonomous prostheses, mostly.” Then she changed expression, and the subject. Without warning she asked, “Ranjit, why do you keep covering your mouth like that?”

It was a more personal question than he had expected from her. He was, however, quite aware of the way his hand kept covering his face. She persisted. “Is it your teeth that bother you?”

He conceded, “I know what I look like.”

“Well, so do I, Ranjit. You look like an honest, decent, and extremely intelligent man who hasn’t gotten around to letting a dentist repair his bite.” She shook her head at him. “It’s the easiest thing in the world, Ranjit, and you will not only look better, you’ll chew better.” She stood up. “I promised Aunt Bea that I wouldn’t stay longer than ten minutes, and she promised me that I could ask you if you wanted to swim in the ocean for a change. On Nilaweli beach. Do you know where that is? We’ve got a little beach house there, so if you’d care to…”

Oh, yes, Ranjit would care to. “We’ll work it out,” she said, and surprised him by giving him a hug. “We missed you,” she said, and then drew back to look at him. “Gamini said you asked him about his old girlfriend. Do you have any of that kind of question for me?”

“Uh,” he said. And then, “Well, yes, I suppose you mean about that Canadian.”

She grinned. “Yes, I suppose I do. Well, the Canadian was in Bora-Bora, last I heard, where they were building an even bigger hotel. But that was long ago. We don’t keep in touch.”

Ranjit hadn’t even known that Gamini and Myra were aware of each other’s existence, much less that they were apparently on easy chatting terms. That wasn’t all he hadn’t known. His density of visitors was getting more so, with the lawyer from Dr. Bandara’s office coming in with more documents to sign—“It’s not that your father’s estate is at all complicated,” he told Ranjit apologetically. “It’s just that you were reported missing and somebody in the bureaucracy interpreted that to mean presumed dead. So we have to clear that up.”

And then there were the police. Not that anybody was filing any charges against Ranjit himself. De Saram made sure of that, before he would allow any questioning at all. But they had loose ends to tie up about the piracy, and Ranjit was the only one who could help tie them.

Then there was the question of Myra de Soyza’s “autonomous prostheses,” whatever they were. His data searches were of limited help. True, they coached him to the right spelling, but what had AI to do with artificial limbs or hearing aids?

Beatrix Vorhulst helped him out there. “Oh, they’re not talking about smart wooden legs, Ranjit,” she told him. “It’s more subtle than that. The idea is to manufacture a lot of really tiny robots that they inject into your bloodstream, and they’re programmed to recognize and destroy, say, cancer cells.”

“Huh,” he said, considering the idea and liking it. It was, of course, the exact right kind of project to interest Myra de Soyza. “And these little robots, are they working out?”

Mevrouw Vorhulst gave him a sad little smile. “If they’d had them a few years ago, I might not be a widow today. No, they’re still just hopes. There just isn’t the funding for the research—even Myra has been waiting and waiting for her own project to be funded, and it just doesn’t happen. Oh, there’s plenty of money for research—as long as what is being researched is some kind of a weapon.”

When at last Ranjit was able to take Myra de Soyza up on her invitation, Beatrix Vorhulst was happy to provide him with a car and driver. When they were well along the road to the beach, he began to recognize landmarks. He and Gamini had of course checked this beach out in their exploration of everything the area had to offer. Not much had changed. The beaches still had their quota of good-looking young women in trivial bathing costumes, of which there were quite a few.

Ranjit had no idea what the de Soyza beach house would look like, until the driver pointed it out: tile roof, screened lanai around the door, nicely planted with bright flowers. It was only when the door opened and Myra de Soyza came out, wearing a light robe over a bikini that was fully as fashionable, and trivial, as any other along the beach, that he was sure he was in the right place.

Then not quite so sure, because right behind her was a five-or six-year-old girl. Ranjit experienced a quick, dismaying reality shift.

Six-year-old girl?

Myra’s?

Had he been gone quite that long?

He hadn’t. Ada Labrooy was the child of Myra’s sister, now seriously pregnant with another and for that reason quite happy to grant her daughter’s wish to spend as much time as possible with her favorite aunt. Myra herself was happy to have Ada there, not least because Ada’s mother had sent along Ada’s nanny to make sure the child was no inconvenience. When Ranjit had changed and been anointed with UV-repellent cream by Myra, which in itself was one of his nicer recent experiences, the two of them minced across the hot sands to the pleasingly cool waters of the gulf.

What was most wonderful about a Sri Lankan beach, apart from the company, was that the water deepened so gradually. Many dozens of meters from the shoreline he could still stand up straight.

He and Myra didn’t go much farther than waist-deep, and they didn’t swim as much as they happily threw themselves about in the water. Ranjit didn’t resist the temptation to show how far he could swim underwater—nearly a hundred meters; a lot less than he had done as a teenager near Swami Rock, but still enough to get compliments from Myra, which was what the purpose had basically been.

The shrewdness of Myra’s deal with the nanny then became evident. By the time they were showered and changed, a pleasant luncheon had been laid out for them. When they finished with that, the nanny took Ada away for a nap, and herself away to wherever it was she went when not visibly on duty.

By and large, that was one of the pleasantest parts of the day for Ranjit. However, when Myra announced that she really needed to put in the exercise of at least a couple hundred yards of actual swimming—and, no, Ranjit shouldn’t come with her, because he needed to keep his time in bright sunlight down to a safe minimum until his skin got used to the stuff again—he was comfortably aware that she would be back. And for the last twenty minutes or so he had been beginning to wonder if he had properly expanded one of Sophie Germain’s terms.

He had just about convinced himself there had been no mistake when little Ada came back from her nap. She looked around for her aunt, but was sufficiently reassured when Ranjit waved an arm in the direction of where Myra’s arms and kicks were propelling her along.

Then Ada got herself a fruit juice and sat down to oversee whatever it was that Ranjit was doing.

By and large Ranjit preferred to be unwatched during his tussles with mathematics. Ada, however, seemed to have her own rules of audienceship. She didn’t wail about being kept on the beach, wasn’t even morose about it. When Ranjit bought her an ice from one of the beach’s wandering vendors, she ate it slowly, her eyes fixed on the things he was writing in his notebook. When she finished, she ran down to the water’s edge to wash the stickiness off her fingers before she asked politely, “Can I see what you’re doing?”

By then Ranjit was quite reassured about his use of the Germain formulation. He opened the notebook on the table before him, interested to see what she would make of the Germain Identity.

She studied the line of symbols for a moment, then announced, “I don’t think I understand that.”

“It’s difficult,” Ranjit agreed. “I don’t think I can explain it to you just now, either. However—”

He paused, examining her. She was a lot younger than Tiffany Kanakaratnam, of course, but then she had the advantage of a better educated and more sophisticated family. “Maybe I can show you something,” he said. “Can you count on your fingers?”

“Of course I can,” she said, just one moiety of courtesy short of indignation. “Look,” she said, raising one finger at a time. “One, two, three, four, five, six, seven, eight, nine, ten.”

“Yes, that’s very good,” Ranjit said, “but you’re only counting up to ten. Would you like to know how to count to one thousand and twenty-three?”

By the time he finished showing the child the all-fingers-extended binary representation of 1,023, Myra was back from her swim and listening as intently as Ada.

When he was done, the child looked at her aunt, now toweling her hair dry. “That’s quite good, don’t you think, Aunt Myra?” And to Ranjit, “Do you know any other tricks?”

Ranjit hesitated. His one other trick he had never even shown to Tiffany Kanakaratnam, but Myra was in this audience.

“Actually,” he said, “I do,” and moved off the boarded part of the bungalow’s lanai so he could scratch a circle in the sand:

“That’s a rupee,” he said. “Well, of course it’s really just a picture of a rupee, but let’s say it’s a real coin. If you flip it, there are two possible ways it can come down, either as heads or as tails.”

“Or, if it fell in the sand, it could land on edge,” Ada said.

He looked at her, but the child Ada’s expression was innocent. “So we don’t flip on the beach. We flip on a craps table in the casino. Now, if you flip two coins—”

“—each of the coins can come down either heads or tails. That means there are four possible outcomes. They can be heads-heads, heads-tails, tails-heads, or tails-tails. While if there are three coins—”

“—there are eight possibilities: heads-heads-heads, heads-heads-tails, heads—”

“Ranjit,” Myra interrupted him, smiling but with the faintest hint of annoyance in her voice, “Ada does know what two to the third power is.”

“Well, of course she does,” he said meekly. “Now, here’s the thing. You take this stick and draw in as many more coins to the line as you want to. I won’t look. Then when you’re done, within ten seconds or less, I will undertake to write down the exact number of possible outcomes if that number of coins are flipped. And,” he added, holding up one finger, “just to make it more interesting, what I’m going to do is let you cover up as many of the coins as you like, from either end of the line, so I won’t be able to tell how many coins are there.”

Ada, who had been listening carefully, said, “Wow. Can he do that, Aunt Myra?”

Myra said firmly, “No. Not if he doesn’t peek or cheat in some other way.” Then, to Ranjit, “You aren’t going to peek?”

“No.”

“And you won’t know how many coins are actually in the row?”

He pursed his lips. “I didn’t say anything about what I would know… but, no, I won’t.”

“Then it’s impossible,” she declared. But when Ranjit invited her to put him to the test, she made him turn around and set Ada to watch his eyes to see that he wasn’t making use of some accidental window that could serve as a mirror. Then she swiftly smoothed most of the coins out of existence, leaving just three. She winked at Ada, and then draped her beach towel so that it covered two of the remaining three, and also covered a full meter of no coins at all—

—and said, “You’re on.”

Ranjit turned slowly, as though he had all the time in the world, while Ada squealed, “Hurry, Ranjit! You only have ten seconds! Or five, now. Or maybe only two—”

He gave the child a smile. “Don’t worry,” he admonished. He leaned forward and for the first time glanced at where the row of circles had been, took the stick, and at one end of the row scratched a straight line. Then, as he was removing Myra’s towel, he said, “There’s your answer,” and grinned. “Huh,” he said, admiring the result. “Very clever.” He waited for a reaction from Myra to the drawing in the sand—

Myra stared in puzzlement for a moment, and then her expression cleared. “Oh my God! Yes! It’s the binary number for—wait a minute—for the decimal number eight! And that’s the right answer, too!”

Ranjit, still grinning, nodded and turned to Ada, now a little apprehensive. Should he explain again how binary notation worked—1, 10, 11, 100 for one, two, three, four? He hesitated.

But the child’s lips had broken into a smile. “You didn’t say you were going to go binary, Ranjit, but then you didn’t say you weren’t, either, so I guess that’s all right. It’s a good trick.”

She delivered her verdict with enough adult gravity to sustain Ranjit’s smile. His curiosity was piqued, though. “Tell me something, Ada. Do you really know what binary numbers are?”

She became mock-indignant. “But of course I do, Ranjit! Don’t you know who Aunt Myra made my parents name me after?”

Myra was the one who responded to Ranjit’s puzzled look. “I’m guilty,” she admitted. “When my sister and her husband couldn’t agree on a name for the baby, I suggested Ada. Ada Lovelace was my heroine and role model, you know. All of my friends fixated on women like Shiva or Wonder Woman or Joan of Arc, but the only woman I wanted to be just like when I grew up was Countess Ada Lovelace.”

“Countess—” Ranjit began, and then snapped his fingers. “Of course! The computer woman in, when was it, the 1800s? Lord Byron’s daughter, who wrote the first computer program ever for Charles Babbage’s calculating machine!”

“That one, yes,” Myra agreed. “Of course, that machine never got built—they didn’t have the technology—but the program was good. She’s why they named the software language Ada.”

The daily beach drive had become a fixed date, and then Ranjit thought of a way to make it even better. De Saram had opened a line of bank credit for him, based on the anticipation of his father’s estate, which meant not only that he then had an actual bank account with actual rupees in it that he could spend, but meant he had a credit card as well. Ranjit had noticed the beachside restaurants up above the tree line, and decided to take Myra to dinner.

His driver stopped at one of the restaurants along the road, but when Ranjit opened the door to investigate, the smells were not encouraging. The second he tried was better. He actually went inside, got a menu, sniffed thoughtfully, and told the person who gave him the menu that he’d probably be back, but he made no promises about when. But in the third, Ranjit got a menu but hardly looked at it. The aroma from the kitchen, the way the few diners were lingering over their tea and sweets…Ranjit inhaled deeply and made a reservation. And when he issued the actual invitation to Myra, she looked uncertain for only a moment, and then said, “Of course. It would be lovely.”

Which meant Ranjit had only the day to get through before he could have the pleasure of being the one who provided something for her.

Ada wasn’t there, so they actually swam together, farther out than usual, and when they came back, they dressed and sat with drinks on the lanai, idly talking. Well, Myra was doing most of the talking. “It used to be a lot livelier here,” she said, gazing out over the nearly empty sand. “When I was tiny, there were two deluxe hotels right down the beach, and a lot more restaurants.”

Ranjit looked at her curiously. “You miss the lively times?”

“Oh, not really. I like it peaceful, the way it is. But my parents used to go dancing there, and now there’s nothing.”

Ranjit nodded. “The Boxing Day tsunami,” he said wisely.

But she was shaking her head. “Long before that,” she said. “It was 1984. The beginning of the civil war. Some of the first battles were fought right here, Sea Tigers making a landing so they could launch an attack on the airport. The army took the hotels over as firing positions, so the Tigers took care of the hotels. My parents were right here, couldn’t get away until things calmed down a little and the roads reopened. My mom said the tracers were like a fireworks display, screaming in from the assault boats and back out from the hotels. They called it ‘the entertainment.’”

Ranjit wanted to make a response but didn’t know how to do it. Not in words, maybe. What he really wanted to do was put an arm around her. He settled for a sort of first step, putting his hand over hers as it rested on the arm of her chair.

She didn’t seem to mind. “The ruined old buildings were still there while I was growing up,” she said. “You know what finally took care of them? That was the tsunami. Otherwise I think they’d still be right there.”

She turned toward him, smiling…and looking quite a lot as though she wanted to be kissed.

He put it to the test.

It turned out that his estimate had been correct. She had. And she was the one who took his hand and led him back into the beach house, with that welcoming couch, just right for two, and Ranjit discovered that sexual intercourse with a woman was not only a good thing in itself, but was several times better when the woman was someone you liked, and respected, and really wanted to spend a lot of time in the company of.

And then there was the dinner that he hosted, and that was great, too. So all in all that day on the beach was a great success, and Myra and Ranjit at once made plans to do it again. Often.

It didn’t quite work out that way, though, because the very next day something happened to change their plans.

Ada Labrooy was with them that day, and so was her nanny, who kept giving sidelong glances at Myra and Ranjit, convincing Ranjit that what the two of them had done was written all over their faces. It was a perfectly normal day, though—if you didn’t count that when he arrived, Myra kissed him on the lips instead of the usual cheek—until they were back from their outing in the water, and wearing their robes and helping themselves to their drinks.

And then Ada saw something. Hand shading her eyes from the sun, she asked, “Is that that man who works for the Vorhulsts again?”

And when Ranjit stood up to get a better look, yes, it was the Vorhulst butler, moving a great deal faster than Ranjit had ever seen him move before, and holding a sheaf of papers clenched tightly in one hand. He seemed excited. Not just excited, impatient to get the pages to Ranjit, so that he was still five or six meters away when he called, “Sir! I think this may be what you’ve been waiting for!”

And it was.

Well, it sort of was. Well, what it was was a lengthy analysis of Ranjit’s paper, or actually five different analyses of the paper, each apparently written by a different (but unnamed) person, and what they’d done—in exacting and almost unreadable detail—was go over every last passage that Ranjit himself had already found to contain a mistake or an unclarity. Plus, they’d found no fewer than eleven other passages that needed cleaning up just as much but that Ranjit hadn’t caught in his own reading. There were forty-two sheets of paper in all, each densely written over with words and equations. As Ranjit quickly scanned each one and hurried to the next, he passed the sheets to Myra, his frown getting deeper with every page. “Holy gods,” he said at last, “what are they saying? Are they just telling me all the reasons they have for rejecting the bloody thing?”

Myra was biting her lip as she reread the final page for the fourth or fifth time. Then a smile broke through. She handed the page back to Ranjit. “Dear,” she said—in the excitement of the moment neither of them noticed that she had never used that word to him before—“what’s the very last word at the end of the message?”

Ranjit snatched the page from her. “What word?” he demanded. “You mean at the very bottom here? Where it says ‘Congratulations’?”

“That is exactly what I mean,” she informed him, the smile now broad and tender and in every way exactly the best kind of smile he could ever have wished for from Myra de Soyza. “Have you ever heard of anyone being congratulated for a failure? They’re publishing your paper, Ranjit! They think you’ve finally done it!”