"Good night, Lucinda. Sleep well."

"Good night, Cass. You sleep well, too. I love you."

XXIX.

The Argument from Rigid Designators Cass came down the next morning at seven, still wet from his shower, anxious that Azarya be on time for his appointment with Gabriel Sinai. He wanted the boy to have a good breakfast, too. The door to the spare bedroom was open. Cass walked over to it and saw that the bed was neatly made. In the bathroom, the bath towel was still damp from the boy's shower. But he was gone, no signs of his having had a glass of juice or milk. Cass imagined that either Azarya wanted to get out before Pascale and Cass woke up so that he wouldn't get in their way, or that he was too excited to stay put.

Cass was disappointed. He had woken eager to come down and talk to Azarya. He'd given him a key to the house so he wouldn't have to worry about the boy's having to wander around until somebody got home.

Azarya called Cass at his office during the day to say that Professor Sinai wanted to take him to the Harvard Hillel that night for dinner, and would that be okay? Cass assured him it would be, but again was disappointed-stupidly, of course, since Azarya had come here to spend time not with Cass and Pascale but with Professor Sinai.

Azarya had asked Cass whether there was a time by which he ought to be home, and Cass had said no, he should feel free to come and go as he wanted. That's why he had given him the key.

"But you have to be careful. Not all parts of Cambridge are safe. It's not like New Walden."

Azarya assured him, telling him that Professor Sinai was going to drive him home.

Azarya came back a little before midnight. Cass didn't have to ask him how his day had gone. His flushed face said it all. He began by apologizing for the late hour.

"We lost track of the time."

"Are you tired now, Azarya? Do you want to go to bed, or do you want to stay up and talk a little?"

"If you're not too tired, it would be wonderful to talk. I'm too excited to sleep."

"It was that good?"

They sat at the table, and Cass went to the refrigerator to get some water, juice, and fruit and laid it out, his instincts telling him that this was the thing to do.

"Better. How good I can't describe. When I tried to put into words something, Professor Sinai knew already what it was before I'd said two syllables, and he had the perfect formulation ready for it. He speaks in music. Mathematical music. He wasn't teaching today, and he thought I should see what the classes at MIT are like. I sat in on a class on topology, which was wonderful, and then another class on modern philosophy that was also wonderful."

"Did you and Professor Sinai talk about your future?"

"He wants me to come to MIT next year. We didn't talk that much about it. We were too busy speaking math."

"You're not too young?"

"He did mention the William James Sidis rule. Do you know who is this William James Sidis? Professor Sinai was vague on the details."

"He's the cautionary tale of how not to raise your prodigy. He was the son of two doctors, and according to legend taught himself eight languages by the age of eight and lectured on four-dimensional bodies when he was eleven. He graduated from Harvard at sixteen, burned out early, spent his adult life doing menial jobs and collecting subway transfers, and would run screaming if anyone mentioned mathematics to him."

"That would explain it. He said there's an unofficial rule at MIT, that they call the William James Sidis rule, not to accept kids who are too young, that just because a student is ready to do advanced math doesn't mean he's mature enough to live away from home and go to college."

"That makes sense."

"But I'll be seventeen next year, an old man compared to William James Sidis. Professor Sinai doesn't think there will be a problem, even though my education has been what he's kind enough to call 'unconventional.' "

"What do you call it?"

Cass knew he was pushing, asking such a direct question, but it seemed to him that Azarya wanted to talk about this subject. He was right.

"I call it nonexistent."

"Do you really think so? You've been studying your whole life."

"What I've been studying isn't going to help me with anything I'm interested in knowing."

"What are you interested in, besides math?"

"I hardly even know enough to know what I'm interested to know. I've only tried to teach myself mathematics. I haven't had time for much else, with all the studies heaped on me. I know nothing about your field, psychology. I'm interested in your specialty."

"The psychology of religion?"

"Yes. It interests me very much. So tell me, since this is your area, why do people the world over and in all times have such strong inclinations to believe what they have no evidence for, and to believe it so strongly that they shape their entire lives around it?"

Cass was floored.

"You think religious beliefs have no evidence?"

Azarya laughed. "Wait a minute. I've heard about you psychologists always answering a question with another question."

"That's a different kind of psychologist. A psychotherapist."

"Like your mother. She's more that kind of psychologist. You're more a scientist, doing research on how people think. I know a little about your work. I've asked your mother. She sent me one of your journal articles, 'Self-Definition and Religious Identification.' I liked it a lot. I liked the concept of a rigid designator. It made a lot of things clear for me."

"I borrowed it from the philosophers."

A rigid designator is a term that designates the same object in all possible worlds which makes it different from a mere description. So, for example, "Pascale Puissant's husband" is a description that refers to Cass Seltzer, but it didn't have to. It's not a rigid designator. There are logically possible worlds in which Cass was currently a bachelor or was currently married to somebody else. But "Cass Seltzer" is a rigid designator, as are all proper names. Rigid designators pick out an individual-that very thing and nothing else. One can even say, "Suppose that Cass Seltzer wasn't named 'Cass Seltzer,'" and that proposition has meaning because the first use of "Cass Seltzer" is a rigid designator. Terms that aren't rigid designators are called "non-rigid designators" or, more whimsically, "flaccid designators."

"That's another subject I know nothing about. Philosophy. I loved sitting in on that class. It was all arguments and proofs, almost like math. I'm going to have a lot of catching up to do when I get to MIT."

"So you've decided, then. You're coming here."

"I should have said 'if I get to MIT.' At one point today it seemed perfectly clear. Professor Sinai had explained something to me that I had been confused about, and the thought came to me, how can you not take the opportunity to study with a gaon like this?" Azarya had used one of the Hebrew terms for "genius"-there are several-to describe Gabriel Sinai. Looking at him, Cass had the vivid memory of that little boy standing on the tish, trying to point his Hasidim's eyes at the proof that he was seeing, that same smile on his face.

"It was the first time you spoke to somebody who could understand you."

"Not the first time, no. The first time was Roz and you. But it's been a while." He said this softly and with a self-deprecating smile.

"If it makes your decision any easier, you ought to know that I would love for you to live with us if you come to MIT. It will be less strange than if you stay in a dorm."

"You open your home to me as if I were your son. How can I express how that makes me feel?" He managed to do it, with his eyes and the heat that rose in his cheeks. "Perhaps it will be. But, you know, I don't think I would feel strange at MIT. I maybe think I would feel less strange at MIT than I feel in New Walden."

Cass looked at Azarya's face, which was struck open with his confession.

"For how long has it been like this for you?"

"My Bar Mitzvah. That's when I remember feeling afraid for my future. That's when I saw clearly what I mean for the Valdeners."

"You became a man, according to the tradition."

"Yes, that's one tradition I had no trouble with."

"You still keep all the laws?"

"Yes, why not? I'd have to make a big effort not to, living in New Walden. It's not the laws that bother me. They're second nature." He thought for a moment. "One has to live some way, so why not that way? Professor Sinai is observant, but it doesn't stop his mind. He's not a Valdener. He's not the son of the Valdener Rebbe, with a whole community of people who mention him in their every prayer. It's foolishness, their prayers, I know that. Still, how can I not feel the burden of so many prayers? Every time I hear how they call me, Azarya ha-kodesh, Azarya the holy one, it sounds like shovels of dirt on a coffin."

Cass looked at him, taken aback by the note of melodrama. In addition to everything else that Azarya was, he was also an adolescent. Cass found this touching, just as he'd been touched by the small Azarya waving bye-bye.

"The problem is that 'Valdener MIT math student' is not a rigid designator. There are many possible worlds in which it doesn't pick me out."

"Is 'son of the Valdener Rebbe' a rigid designator?"

"Yes. It is. I had to be my father's son, or I wouldn't be me. I am Azarya ben Rav Bezalel. It's a rigid designator. Just as my father is rigidly Rav Bezalel ben Rav Yisroel. It was Rav Yisroel, my grandfather, who came to America in 1933, saving the few Valdeners he could. He built New Walden for them so that they could insulate themselves against the corruptions of America. He tried as best he could to duplicate Valden as it had been before it was destroyed. When you live in New Walden, then the old Valden is always in your mind. You go to the shul in New Walden and you are thinking of the old shul. That's where the Germans packed all the remaining Valdeners, left behind when Rav Yisroel came to America, before they set it on fire. And my grandfather was rigidly Rav Yisroel ben Rav Eliezer. Rav Eliezer, my great-grandfather, was rigidly Rav Eliezer ben Rav Bezalel. He had an older brother, Rav Azarya ben Rav Bezalel, who died the same year as his own father, and so Rav Eliezer ben Rav Bezalel became the Rebbe. Rav Eliezer ben Rav Bezalel is known as 'der shvagte Rebbe,' the silent Rebbe. He had a saying: 'Man shvagt un man shvagt. Dernoch riet men abisl un man shvagt vater.' 'We stay silent and we stay silent, and then we rest a little and we stay silent.' He's always been one of my favorite ancestors because of that. I think maybe he was a mathematician himself, to have had such a fine idea of paradox. Rav Bezalel, my great-great-grandfather, was rigidly Rav Bezalel ben Rav Itzikil. Rav Itzikil ben Rav Yosef, my great-great-great-grandfather, was the Borshtchaver Rebbe's son, but he married the Valdener Rebbe's daughter, Sura Sima, so Rav Itzikil ben Rav Yosef was the son-in-law of Rav Azarya ben Rav Yisroel, who was my great-great-great-great-grandfather. And Rav Azarya ben Rav Yisroel was a direct descendant of ha-Rav Yisroel ben Eliezer, as he was rigidly designated, but whose many non-rigid designations include der heyliger Ba'al Shem Tov, the holy Master of the Good Name."

They stared at each other over the dining-room table. Cass wished he were that other sort of psychologist, the kind that knows the right thing to say to a young person caught as Azarya was caught.

"But a name's being a rigid designator doesn't make the decision for you, does it?"

"No." He paused for a while, staring into space. Again, Cass remembered his own exalted vision that night at the Rebbe's tish, when he thought he'd caught a glimpse of what the world must look like to Azarya. "But if not rigid designation, then what does make the decision?"

"You. Only you."

"It's never only you. Not when your 'ben's iterate back to the Ba'al Shem Tov."

"But you also have a link to others. To Professor Sinai. And to his teacher and the teacher of the teacher, maybe going back to Gauss or Dedekind, or Euler or Archimedes. That's also a long chain of links going back in time. And it has more to do with you, with who you really are, than your connection with the Ba'al Shem Tov, rigid designator or no."

Azarya shrugged in a Hasidic way, his palms turned upward. "Maybe you're right. Anyway, if nothing else, I have this week."

"I think you're being, if anything, too philosophical here. Rav Hillel said, 'If I'm not for myself, then who will be for me?'"

"'And if I'm only for myself, then what am I?'"

"'And if not now, when?'"

"I know the formula, but I can't see my way clear to the solution. I try out every permutation, and nothing comes out right. How can that be? How can there be no solution? The only thing I seem to be able to prove is that there is no solution. No matter how many different ways I attack it, that's as far as I get. If I leave New Walden, I break the heart of every Valdener Hasid, a community that remade itself through the efforts of my grandfather, who did what he could to save a few, and it wasn't enough, which is what he was crying out the hour that he died. He was calling out by name Valdeners that he had left behind. I break the heart of my father, whom I love more than anything in the world. So that has impossible consequences and can be ruled out. So I stay. But if I stay, then I have no more days like I did today. I live among people who love me more than they love themselves, who think I'm their messenger to der Abishda, who will grab someday for the shirayim on my plate, and I'll never be able to share a single thought with them. I'll live the life of my father, and of his father before him, and of all the fathers who lived only to repeat the lives of their fathers. Where's the sense in that? How can one choose such a meaningless life? So I leave. And so it goes. Going to a university is necessary but impossible. Staying in New Walden is impossible but necessary."

"Azarya, do you know what you are? Has anyone ever told you? Do you understand why a man like Gabriel Sinai is so eager to bring you to work with him?"

"You don't need to tell me that I'm special. All my life, that's all that I've heard. All my life, the community has kvelled at my every word."

"But not for the right reasons, Azarya. Not because of who you are but because of your bloodline."

"Not because of who I am." He smiled ruefully. "I guess that's the question. Who am I?" He shrugged. "When my designator is rigidly picking me out in other possible worlds, what's it coming up with? What's the part that can go and what's the part that can't?"

It was extraordinary how young Azarya could still look, when the clarity in his eyes was overtaken by a helpless wonder and his mouth quaked.

"You're the boy who proved at six years old that there's no largest prime number. I can't imagine what you've proved since then. I can't imagine what you could go on and prove. You talk about your responsibilities to the Valdeners. Don't you have a responsibility to human understanding?"

"Believe me, human understanding will continue without Azarya Sheiner. The Valdeners are a different story."

"But should they continue? It's a harsh question, I know, harshly put."

"Yes. Harsh."

"But, Azarya, you don't seem to shy away from questions. So answer this one for me: Why should the Valdeners continue with their superstitions and their insularity and their stubborn refusal to learn anything from outside? Why is that something to perpetuate?"

"I was hoping that maybe you could help me answer that. Because that is your specialty, psychology of religion, no?"

"No. This question is meant for you alone, Azarya."

"As I've always feared," he said softly.

"Let's think about it together, then. Let's say you leave and the community suffers for a while, then disintegrates and disperses to other Hasidic groups; maybe even-because of the trauma of your leaving-the members become assimilated into the modern world. Tell me what's lost? A few fewer false beliefs knocking about in the world? The Valdeners end up being like my mother and me? Is that so bad?"

Azarya stared down at the table a while before he spoke.

"It's tragic, a diminishment, when a people goes out of existence, a way of life, a culture, a language." He spoke slowly, either from emotion or because he was thinking out his line of reasoning as he went. "But that's not even the heart of it. No. The heart of it is the story of this people, my people, my Valdeners. You are who you are." Cass saw with horror that Azarya's eyes were welling. "Had my grandfather Rav Yisroel ben Rav Eliezer not fought with all his life to bring over as many Valdeners as he could in 1939, then there would be none living now, and even so he wept on his deathbed for the lives he hadn't saved. That bloodline that every Valdener child can recite as easily as Shema Yisroel"-"Hear O Israel," the iconic Jewish prayer-"would have ended in that burning shul if not for him. So how can I, Azarya ben Rav Bezalel ben Rav Yisroel ben Rav Eliezer, decide to be the executioner now? How can it be by my hand?"

He's sixteen, Cass was thinking. Look at the quantities of agonized thought he's poured into his paradox, and look at the living agony twisting itself out on his face right now, welling over in his eyes and making his upper lip tremble.

It was enough for one night, more than enough, and Cass said so. As they were getting up from the table, he couldn't help putting his hand gently on Azarya's shoulder, remembering, as he did so, how the Valdeners had kissed their prayer shawls and touched the child with them as if he were a living Torah as he was bounced around on his dancing father's back.

"Azarya, I'm sorry. I shouldn't have pushed you so hard."

"It's for me wonderful to be able to share this with somebody. It's a gift that you are taking my decision so seriously. Often I think maybe I'm taking it too seriously myself, that the world will go on whatever Azarya Sheiner decides to do. Still, a person takes his life seriously. A person has to live his life. Who else's life is he supposed to live? Maybe together we'll figure out how something that's necessary but impossible can happen. We'll collaborate on a solution."

"It would be an honor to be your collaborator. And we'll bring Professor Sinai on board, too, as a collaborator. Why don't you bring him here tomorrow for dinner? I've still got piles of food from Tirza's Batampte Kitchen. I'd like to meet the man whom Azarya Sheiner calls a gaon."

Pascale was up in her study and Cass was in the kitchen, warming up the barbecued chicken and the potato kugel, when an excited Azarya arrived home with a burly man in heavy black-framed eyeglasses, his wavy black hair awkwardly mounding on random places of his head. He had the shy, uncomfortable grin that had probably not been revised since he was a child. He wore a green flannel shirt and an air of unkemptness, but it was hard for Cass to take him in because of a transformed Azarya beside him, holding three bunches of green-tissue-wrapped tulips in one hand and a bottle of wine in the other.

Before Cass had gotten a word out, Pascale came sashaying into the room, balanced on a spiky pair of red shoes that matched her lipstick. Her long black hair, the color of the rest of her outfit, was piled high on her head. She stopped cold at the sight of them.

"But is it you?" she asked Azarya with the directness of a small child, and he laughed.

"But where are your"-she curled her index fingers beside her ears- "your baguettes a cheveux?"

Azarya, who didn't know French but couldn't help getting Pascale's drift, pointed to the Red Sox baseball cap he was wearing. He lifted it off his head with a flourish, and two dark-blond payess came flopping down.

Pascale shrieked with laughter, which cracked them all up, Gabriel Sinai joining in with a high whinnying noise.