he come from money? What was he working on? I never understood. He always seemed to me like some kind of stranded time traveler, from an era when you really could get away with just being good at conversation—”
“Time traveler. Funny that you say that.” Jacob shook extra sugar onto the dregs of his iced tea and then slurped at it. “Ilan may have been right about you. Though honestly I could never see it myself. Well, I need to get going.”
“Why do you have to be so obscure?” I asked. “Why can’t you just be sincere?”
“Sincere. Huh. Let’s not take such a genial view of social circumstances so as to uphold sincerity as a primary value,” he said, with affected distraction, stirring his remaining ice with his straw. “Who you really are—very bourgeois myth, that. Obviously an anxiety about social mobility.”
I could have cried, trying to control that conversation. Maybe Jacob could see that. Finally, looking at me directly, and with his tone of voice softened, he said, “I really am very sorry for you to have heard like this.” He patted my hand in what seemed like a genuine attempt at tenderness. “I imagine I’ll make this up to you, in time. But listen, sweetheart, I really do have to head off. I have to pick my wife up from the dentist and my kid from school, and there you go, that’s what life is like. I would advise you to seriously consider avoiding it—life, I mean—altogether. I’ll call you. Later this week. I promise.”
He left without paying.
He had never called me sweetheart before. And he’d never so openly expressed the opinion that I had no life. He didn’t phone me that week, or the next, or the one after that. Which was OK. Maybe, in truth, Jacob and I had always disliked each other.
•
I found no obituary for Ilan. If I’d been able to find any official trace of him at all, I think I might have been comforted. But he had vanished so completely that it seemed like a trick. As if for clues, I took to reading the New York Post. I learned that professional wrestlers were dying mysteriously young, that baseball players and politicians tend to have mistresses, and that a local archbishop who’d suffered a ski injury was now doing, all told, basically fine. I was fine, too, in the sense that every day I would get out of bed in the morning, walk for an hour, go to the library and work on problem sets, drink tea, eat yogurt and bananas and falafel, avoid seeing people, rent a movie, and then fall asleep watching it.
One afternoon—it was February—a letter addressed to Ilan showed up in my mailbox. It wasn’t the first time this had happened; Ilan had often, with no explanation, directed mail to my apartment, a habit I’d assumed had something to do with evading collection agencies. But this envelope had been addressed by hand.
Inside, I found a single sheet of paper with an elaborate diagram in Ilan’s handwriting: billiard balls and tunnels and equations heavy with Greek. At the bottom it said, straightforwardly enough, “Jacob will know.”
This struck me as a silly, false clue—one that I figured Jacob himself had sent. I believed it signified nothing. But. My face flushed, and my heart fluttered, and I felt as if I were a morning glory vine in bloom.
I set aside my dignity and called Jacob.
Without telling him why, assuming that he knew, I asked him to meet me for lunch. He excused himself with my-wife-this, my-daughter-that; I insisted that I wanted to thank him for how kind he’d always been to me, and I suggested an expensive and tastelessly fashionable restaurant downtown and said it would be my treat. He again said, No.
I hadn’t thought this would be the game he’d play.
“I have something of Ilan’s,” I finally admitted.
“Good for you,” he said, his voice betraying nothing but a cold.
“I mean work. Equations. And what look like billiard ball diagrams. I really don’t know what it is. But, well, I had a feeling that you might.” I didn’t know what I should conceal, but it seemed like I should conceal something. “Maybe it will be important.”
“Does it smell like Ilan?”
“I think you should see it.”
“Listen, I’ll have lunch with you, if that’s going to make you happy, but don’t be so pathetic as to start thinking you’ve found some scrap of genius. You should know that Ilan found your interest in him laughable and that his real talent was for convincing people that he was smarter than he was. Which is quite a talent, I won’t deny it. But other than that, the only smart ideas that came out of his mouth he stole from other people, usually from me, which is why most everyone, although obviously not you, preferred me—”
Having a “real” life seemed to have worn on Jacob.
At the appointed time and place, Ilan’s scrawl in hand, I waited and waited for him. I ordered several courses but ate only a little side of salty cucumbers. Jacob never showed. Maybe he hadn’t been the source of the letter. Or maybe he’d lost the spirit to follow through on his joke, whatever it was.
•
A little detective work on my part revealed that Ilan’s diagrams had something to do with an idea often played with in science fiction, a problem of causality and time travel known as the grandfather paradox. Simply stated, the paradox is this: if travel to the past is possible—and much in physics suggests that it is—then what happens if you travel back in time and set out to murder your grandfather? If you succeed, then you will never be born, and therefore you won’t murder your grandfather, so therefore you will be born, and will be able to murder him, et cetera, ad paradox. Ilan’s billiard ball diagrams were part of a tradition (the seminal work is Feynman and Wheeler’s 1949 Advanced Absorber Theory) of mathematically analyzing a simplified version of the paradox: imagine a billiard ball enters a wormhole, and then emerges five minutes in the past, on track to hit its earlier self out of the path that sent it into the wormhole in the first place. The surprise is that just as real circles can’t be squared, and real moving matter doesn’t cross the barrier of the speed of light, the mathematical solutions to the billiard ball–wormhole scenario seem to bear out the notion that real solutions don’t generate grandfather paradoxes. The rub is that some of the solutions are exceptionally strange and involve the balls behaving in extraordinarily unlikely, but not impossible, ways. The ball may quantum tunnel, or break in half, or hit up against its earlier self at just such an angle so as to enter the wormhole in just such a way that even more unlikely events occur. But the ball won’t, and can’t, hit up against its past self in any way that would conflict with its present self’s trajectory. The mathematics simply don’t allow it. Thus no paradox. Science fiction writers have arrived at analogous solutions to the grandfather paradox: murderous grandchildren are inevitably stopped by something—faulty pistols, slippery banana peels, their own consciences—before the impossible deed can be carried out.
Frankly, I was surprised that Ilan—if it was Ilan—was any good at math. He hadn’t seemed the type.
Maybe I was also surprised that I spent so many days trying to understand that note. I had other things to do. Laundry. Work. I was auditing an extra course in Materials. I can’t pretend I didn’t harbor the hope that eventually—on my own—I’d prove that page some sort of important discovery. I don’t know how literally I thought this would bring Ilan back to me. But the image that came to me was that of digging up a grave.
I kind of wanted to call Jacob just to say that he hadn’t hurt my feelings by standing me up, that I didn’t need his help, or his company, or anything.
•
Time passed. Then one Thursday—it was August—I came across two (searingly dismissive) reviews of a book Jacob had written called Times and Misdemeanors. I was amazed that he had completed anything at all. And frustrated that “grandfather paradox” didn’t appear in the index. It seemed to me implied by the title, even though that meant reading the title wrongly, as literature. Though obviously the title invited that kind of “wrongness.” Which I thought was annoying and ambiguous in precisely a Jacob kind of way. I bought the book, but