I finished his thought for him. “When one of them left behind a dog.”

“I guess that could be.”

“And the signals they were trying to send out . . .”

“Were the ghost signals. The prayers. They wanted to send them as far out into space as they could.”

“Where there are more repeaters to send them even farther. Or—just like Ravenette said—a vast network of energy waves.”

We both fell silent for a moment as we considered the fact that perhaps we had just stumbled upon the solution to the mystery that had plagued Avi, but in which he had also, however unwittingly, apparently played a role. On many levels, this scenario was difficult for me to accept.

“I don’t know,” I said to Jack. “It seems a little primitive, doesn’t it? I mean, they’re using radio waves and a repeater built from a kit you could order from the back of a catalogue? Shouldn’t they be using interstellar wormhole-piercing light rays or something like that?”

“You’re asking me?” Jack said. “I haven’t got the slightest idea what they should be using. But I guess radio makes sense. That’s more or less what astronomers have always expected to hear if another civilization ever decided to make contact, for example. Radio is an easy technology to discover. And if you keep boosting radio waves with a repeater, then they can probably travel through space for an infinite distance, for an infinite amount of time.”

I picked up another one of the photocopies and examined it, and as I did, I had the sensation, real or imagined, of feeling a little light go on in some tiny compartment in a cabinet in the storeroom of my memory. The picture of the card I held in my hand showed a jolly-looking, bearded leprechaun in a green jacket, wearing pointy green shoes, with a big grin on his face. The only unusual thing about the otherwise familiar depiction of this particular creature of folklore was, like the smiling penguin, that he was wearing a pair of oversize headphones that covered his ears. Above his head, in bright green letters, were written the words, “Hello from the Emerald Isle.” Looking at this fellow, I felt like I was gazing at the face of a long-lost friend, because I remembered him. This had been one of my favorite postcards in Avi’s album. For the longest time, I had no idea that the Emerald Isle referred to Ireland. I thought it was a special place you could visit where bright green gems would wash up on the beach like seashells.

“What do you think happened to the repeater?” I asked Jack.

“Who knows? If it was up on the roof of . . . what was that place called where you used to go?”

“The Sunlite Apartments.”

“Right. So maybe if it was on the roof of the Sunlite Apartments, Avi did take it down at some point—maybe to repair it. Or maybe, after your mother died and your family stopped going out to Rockaway, he just relocated it and let someone else in the DX club maintain it. Or it was destroyed in a storm and no one replaced it. All we really know, I guess, is that it isn’t where it’s supposed to be anymore. At least, where it works for your radioman.”

All this time, Jack had been standing next to me, watching as I paged through the photocopies of the QSL cards. Suddenly, he lowered himself into a chair and said, simply, “Wow.”

“What?” I asked.

He shook his head. “I guess it just hit me,” he said. “I talk about this stuff all the time on the radio. Aliens, alternate universes, you name it. But that’s just . . . talk. This is real, isn’t it?”

“Tell me it isn’t,” I said, “and I’ll try to believe you.”

“I can’t,” Jack replied, “because I’ve got this picture in my head now. I think your friend is a member of another distance listening club. Only in his club, the members’ idea of distance is . . . well, a lot farther than ours. And there’s something else.” Jack pointed at the computer where the image of the Haverkit repeater was still displayed; a black rectangle with silvery metal mountings hovering in cyberspace. “This is a D model, 3689D,” he said, emphasizing the letter that ended the model number.” That means duplex. A duplex repeater uses two radio frequencies. The designated output frequency retransmits a signal, but there’s also a frequency dedicated to recognizing an incoming signal. In other words, it seems like your radioman and his—well, what should we call them? Friends? Colleagues? Fellow workers? Whoever they are, they seem to be hoping for an answer.”

That was about the first thing either of us had said this morning that actually didn’t seem so peculiar to me. “I guess that’s what everyone expects when they pray.”

A sort of faraway look came over Jack’s face, like he was trying to find a clear line of sight from a distant spot where he really had to focus in order to see what was ahead. Finally, he said, “You want to give it back to him. The repeater.”

“If I don’t, he’ll never leave me alone.”

“And you have an idea of how we would make this hand-off?”

“I think so. I think you just gave it to me. You said, ‘maybe for something to exist where the radioman is, it also has to exist here.’ Well, what if the opposite is also true? He’s in a room that exists wherever he is but I know where that room exists here. The building where we stayed in Rockaway is still standing. So . . .”

Jack nodded, understanding what I meant. We had both already accepted so many bizarre ideas as possibilities—even facts—that I didn’t really have to explain this one any further. “Okay,” he said and turned back to the computer. He started jumping around different websites again, going from auction sites to online electronics stores to message boards filled with technical information about radio parts. He spent some time scrolling through these and then announced, “I can’t find a duplex Haverkit repeater anywhere. But I have another idea. Maybe I could build one. I mean, they were kits; they were meant for people to put together themselves. I think I can buy most of the parts and probably even an old schematic.”

“You really think you can?”

“I should be able to. I told you a long time ago, Laurie—I’m a radioman myself.”

It only took Jack about fifteen minutes to find a blueprint for building the repeater on a site that archived Haverkit manuals, and he soon became absorbed in looking for the parts. Some components he was able to find, some he left messages about in chat rooms for radio buffs, asking if he could substitute one thing he couldn’t locate for another that he could. I sat beside him for a while, watching him as he went about his online search, but then I decided to go home. I hadn’t had much sleep; I was tired and I was supposed to work that evening so I wanted to go back to my apartment and try to nap for a while.

We said good-bye, clearly back on our old, steady footing. Jack said he’d be in touch and I headed out, meaning to start off on the long walk to the subway. But maybe just out of mental exhaustion, or maybe something else—who knows?—I found myself wandering in the opposite direction, toward the waterfront, which was just a few blocks away. Here, the landscape was dominated by huge cranes meant to lift containers on and off the barges that floated them in from the huge ships anchored somewhere off in deeper water, though few were still in operation. Rust was creeping up the steel feet of these monster-like structures; rot had pulled down whole sections of the nearby piers that stretched into the water of the oily shipping channel.

I sat down at the edge of a dock supported by moss-covered pilings. Mindlessly, I looked off toward the towers of Manhattan, standing like a cluster of shadowy obelisks against a backdrop of vast white sky. It was a cool day, neither summer nor fall, with no wind, no clouds, and seemingly, no sun, just that sheet-colored sky, stretching from horizon to horizon above the calm, colorless water.