But as we watched the AI-5 chase the mirage, there was no sign of an end, no slowdown at all.

  “I’m hungry,” I said. “Want a pizza?”

  He nodded without looking at me. I got up, went out into the hall, and called it in from the wall phone. Then I alerted the security guard downstairs and asked him to leave it out on a cart in front of our workroom.

  “We may have to stop it,” I said hours later, “even if it’s close to completion.” Though the pizza had been very bad, I thought as I eyed the empty boxes on the cart, a full stomach had taken some of the romance out of what we were doing. “We can’t tie up all this power and time indefinitely. It’s using more every minute, and it’ll be my ass if we can’t justify it.”

  “No!” Witter shouted maniacally. “It may be very close.”

  I burped, waiting for my heartburn to subside. The AI-5 hummed along.

  “We can continue from this point onward at another time,” I insisted.

  “Be quiet!”

  I reached over to stop the run. Felix grabbed my hand and pinned it to the panel.

  “What’s wrong with you?” I demanded.

  “Just a few minutes more,” he said, fixing me with his mismatched eyes. “We’re at the edge of a major discovery!”

  “Felix, this can’t be done.” I struggled to free myself, but his strength was that of a true believer.

  “Be still, you fool,” he said harshly. “Don’t you see? This will be the culmination of our careers. We’ll never match this no matter how hard we work. Gödel is one of the supreme monuments of mathematics, marking the limits of human minds. If we topple him . . .”

  “You may not like what you get,” I said, twisting my arm. “If his proof is right, then mechanism is false and minds are not machines. They escape the completeness of the purely mechanical. But if Gödel is wrong, then we’re automatons! I’d rather not know.”

  He shook his head. “There’s even more to it than that, Bruno.”

  “What?” I was breathing very hard, unable to free myself.

  “We’re opening up the very vitals of reality.”

  I had to laugh. “By manipulating man-made symbolic structures? You need a bucket of cold water to soak your head in. Let me go!”

  “Completion may be only a few minutes away. Do you want to stop and then wonder what might have been?” He tightened his grip.

  “But you can’t know how far along it is.”

  He let go of my hand and seemed to cool down, and I found I didn’t have the heart to reach over and stop the run.

  “You’re right,” he said, “I’m sorry. It probably is all for nothing.”

  I massaged my hand. The AI continued its work run. “Don’t feel too bad about it,” I managed to say. “It was a nice idea, but it had to confirm Gödel. I’m glad we’re not machines.”

  He was shaking his head. “You don’t understand. There’s no reason to fear that. It’s not a problem.”

  “What isn’t?”

  “Free will,” he said as the AI-5 stopped its run.

  Witter and I looked at each other, then at the main screen. It read:

  SYSTEM CAPABLE OF GENERATING

  ARITHMETIC COMPLETE

  “It’s a mistake of some kind,” I said. Something strange seemed to pass across my eyes. I sat back, expecting to lose consciousness as the tension got to me.

  “Maybe,” Witter was saying, “but we can test to see if it’s a mistake.”

  “How?” I heard myself ask, even though I knew the answer.

  “By trying to make a true statement that is not provable in the system. As long as the AI can show us that we can’t make such a statement by proving it, then the system is complete.”

  The room went black for a second. “But maybe we can’t make such a statement,” I said.

  “We can try,” he answered.

  We tried for the next twelve hours. I was relieved that our prime AI was no longer running a huge power draw. Witter brought a smaller AI on-line and had it question the alleged complete system achieved by the AI-5. It failed to come up with a single true proposition that was not provable in the complete system.

  “There’s no question about it,” Felix said finally.

  “There’s only one thing left to do,” I replied. “We’ve got to run the whole thing again.”

  Witter looked at me, smiled strangely, then sat down and gave the command.

  As the AI-5 began its second run at Gödel, Witter turned to me and said, “Funny about determinism. I always think of it as stuff outside me, pushing at my skin. But I feel free inside. When that second run finishes, we’ll be certain that we’re living in a hard determinism. No choice is our own, if we’ve understood the word correctly. Even our decision to run the AI-5 again was not made freely. We’re automatons. No avoiding the conclusion, Bruno.”

  He was baiting me, I was sure. “But we resist the notion. Doesn’t that suggest something?”

  He shrugged. “That we’re free in our minds but not in our actions. We can envision alternatives, but whichever one we pick is determined, right up through an infinite future.”

  “Witter, I thought you were intelligent. There can’t be such a thing as unconditioned freedom. There are always initial conditions—necessary and sufficient conditions for every choice. Otherwise we could perform miracles, make happen things that are uncaused. The existence of free will cannot violate causality.”

  He grimaced at me and I felt stupid. “Yeah, I know all that. But do we have the freedom to choose between alternatives?”

  “I think we do. Physical conditions make us both the determined and determinators in our own right. Things affect us and we affect them. Determinism goes right down into us, into our consciousness and will, and we send it back out. I couldn’t prove it to you without a physiologist, though.”

  The AI-5 was still running its second completion smoothly. If it succeeded, then it might be that we were living in a universe where even choice among alternatives was an illusion.

  Witter looked at me suddenly. “I wonder if our running this program can have an effect on the universe we live in?”

  “What are you talking about?” I asked. He seemed to have a mind like a break dancer.

  “Maybe our attempting what Gödel said was impossible can change the universe?”

  “I don’t think so, Felix. But there are other things you might like to consider.”

  He took a deep breath. “What’s that?”

  “Well, we began with the idea that no finitary deductive system can complete a rich, self-consistent system. But what if the AI-5 is not a finitary deductive system? Assume it can work outside the limits of the human mind, which is all that Gödel may have charted. It was all he could demonstrate because he had only his own mind to work with.”

  Witter nodded. “I see what you mean. If our AI reaches completion, then it follows, perhaps, that it’s not a finitary deductive system, and we can draw no conclusions about the nature of the universe.”

  I smiled. “Right. And we don’t have to worry about being automatons, or that our sense of inner freedom is a mirror trick of some kind. Free will is a special case of determinism. It’s determinism from the inside. The means of determinism are also those of free will.”

  Witter was watching the screen with a worried look on his face, as if he now expected the AI to fail. It didn’t matter one way or the other, if what I had said was true.

  “Unconditioned free will would be omnipotence,” I continued, “and that’s an absurd state to be in. No law, no causal structures. It’s just a conceptual extreme, like infinities.”

  “Something is working against us,” Witter said softly.

  “What do you mean?”

  He gripped the panel. “It won’t come out the same way twice,” he replied.

  “You’re still mistaking the maps for reality,” I said.

  “Look at the time, you fool! It’s almost as long as before. If the AI doesn’t repeat its completion in the same time, it will run on forever.”

  “So what. We have the first completion in memory, step by step, for whatever it’s worth.”

  He swiveled his chair and glared at me. His eyes were bloodshot and had dark circles around them. The whole experiment, I saw, was eating up his entire energy. “You don’t see, do you?” he said. “You think in terms of tricks of language, ways of speaking . . . you can’t imagine worlds dying and others supplanting them. You don’t give a damn about anything except apportioning time and keeping other administrators happy.”

  “What are you talking about, Felix? I’m here with you, and we’re doing what you wanted. Have you lost your mind?” I almost felt hurt, as if he were questioning my loyalty.

  He pointed to the clock on the wall. “Look, time’s up and our AI is still running.”

  “So what? It was a fluke the first time, a mistake. You can’t beat Gödel, and it wouldn’t matter if you could.”

  He laughed. “You still don’t see!”

  “No, I don’t.”

  The AI-5 was still running.

  “It will run forever this time. Our decision to run the experiment puts us at a great juncture between possible universes. We collapsed the wave function reaching our minds.”

  “What are you saying?” I demanded.

  “Proving that our universe was deterministic threw us into a freer one. Gödel proved his work in the wrong universe. Here the AI will run forever. But if we stop it and start again, something even stranger might happen.”

  “You’re off the deep end now,” I said, feeling sorry for him.

  “We might be moving across a whole series of universes, drawing closer to the unconditional omnipotence that has the true freedom to be everything . . .”

  “Yeah, and can’t become anything in particular. That’s what I was saying. Witter, wake up. We have the other program. Go see for yourself. That system completed. In this one there’s obviously some kind of difficulty. Neither result means a thing. Get that through your stupid head!” Mathematicians were all idealists to some degree or another, always secretly believing in the literal existence of infinities, numbers, and tortured geometries. Witter was no exception.

  He shook his head and smiled. “There’s nothing in the memory, Bruno. See for yourself. Go ahead, punch it up.”

  I leaned forward and typed in the command. Nothing came up. I went into search mode. Still nothing.

  “We’ve left that universe behind,” Witter said.

  “It’s got to be here,” I said.

  The screen remained blank.

  “You erased the memory!” I shouted.

  “I did not,” he replied softly, and I knew he was telling the truth.

  I glanced at the food cart; it winked out of existence.

  “Did you see that?” I asked.

  “Bruno!” Witter shouted. “We’ve escaped a totalitarian cosmos. We’re free!”

  “Relatively,” I said, shaken.

  He looked at me strangely, and I saw that both his eyes were now brown. As the AI-5 continued its endless run into a free infinity, I feared what we would find when we went outside. . . .

  1986

  Stooges

  Curly and friends make, a comic comeback. But they may—nyuk, nyuk, nyuk—want more than laughs.

  Curly Howard’s history flashed up on my screen when I entered his fingerprints. I told Ned, my station manager.

  “Manny, Moe, and Jack have been dead for years,” he said.

  “No, no, you’re thinking of the Pep Boys,” I replied.

  “They owned an auto service dealership in southern California. This is Curly Howard of the Three Stooges. It was a comedy act. Films and television.”

  “What?”

  “I’ve got him in the lockup. Prints don’t lie.”

  “Oh.” He scratched his bald pate as if he’d hidden something there and was now searching for it.

  “Yeah, you see it’s the name Moe in both the Three Stooges and the Pep Boys that leads to the confusion.”

  “You wouldn’t be kidding me, would you, Felix?”

  “About the Pep Boys?”

  “No, about the guy you have.”

  “Run it and see for yourself,” I said sourly.

  He looked at me wonderingly. “Records in D.C. gotta be wrong. Don’t worry, it’ll straighten out. What’s he in for?”

  “Vandalism. Slapped a bust of Einstein right off its pedestal in the lobby of the Main Library. Ruined my day off.”

  “That’s too bad,” Ned said, “for a reader like yourself.”

  He wandered away.

  Of course, I was something of a secret fan, from long before the Stooge films started coming back on video cassettes. I felt embarrassed at times; it was hard to accept that so many people had my lack of taste. But it wasn’t just a fad with me. I was used to watching a reel or two before the news, while eating my lonely guy’s dinner. I’d woo woo once or twice, get in a few nyuk nyuks, just to help my digestion. A cop for NYPD needs all the help he can get.

  It couldn’t be a look-alike, I told myself again as I stared at the picture on the screen. The man I had brought in was as pale as the old photo—black stubble on a shaved head, demonic eyes to match, fat; in other words, a dirty tennis ball in a gym shirt.

  “Nice seeing you . . . alive,” I managed to say as he danced around the bust of Einstein.

  “It’s great!” he had piped back, clawing his face.

  The great Stooge himself, long dead, had stroked the bust until Albert went to pieces on the hard floor.

  There was a loud rap on my office door the next morning, two hours before Curly Howard’s arraignment.

  “Come in!”

  A tall, grey-haired man entered, opening his coat as he sat down before me. “I’m from Washington.” He flashed his ID. “Lieutenant, tell me why you punched up a dead man’s records.” He sounded almost apologetic. “Your chief told me I could ask you about it.”

  “Because he’s alive,” I said, feeling grumpy. “What’s your name again?”

  “Max Karinthy,” he answered nasally. “On what charge is he being held?”

  “Vandalism. He broke a bust of Einstein in the public library.”

  His thin lips held a restrained smile, making me feel better about him. “Let’s have a look,” he said, standing up.

  I took him down to Cell Block A. “There,” I said, pointing at Curly. I’d put him in with two burglars I knew, so he’d be safe, but clearly they hadn’t gotten along with him. Both were in the left corner, looking a bit frightened.

  Curly came to the bars and dog-barked at us. We stared at him. He gave us a shy look and said, “Aw, come on, fellas, let me out. This ain’t fun anymore.”

  “It is him,” Max said softly.

  “You a fan, too?” I asked.

  He bit his lower lip. “Listen, I have the papers to hold him indefinitely. Move him to a quiet hotel at once. And shut up about it. That’s a National Security Order. Understand?”

  I swallowed hard. “Yes, sir. But what’s up?”

  His blue eyes seemed kindly. “Don’t worry, you’ll find out.”

  “It’s a freak of some kind, isn’t it?” I offered. “One in a billion for the prints to match. Or someone went to a lot of trouble to make himself over with surgery. You know a lot more than you’re saying, don’t you?”

  Curly was staring at us reproachfully through the bars.

  “For now, think of him as a kind of Stooge fan,” Max said mysteriously, smiling.

  “Hey, Felix!” Joey the burglar shouted at me. “When you gonna get this nut off us?”

  They couldn’t break his identity. Even the dental records were perfect. “Which makes it even more certain that he’s a fake,” Max said, leaning back in the chair behind my desk.

  “So tell me what you know,” I said, staring out into the evening. “Is he a wealthy fan who had the money to transform himself? You’ve hinted at that.”

  “We’ll have to interrogate him,” Max replied, ignoring my question.

  I smiled. “Sure, lots of luck.”

  “You’re going to be working on this with me, Felix.”

  “Why me?” I asked apprehensively. “I’m just a city cop. My chief would rather you just took him away.”

  “I feel I can trust you, you’re a Stooge fan, and you’re single, so you don’t have to go home at all. No telling where this might lead. You’re transferred for as long as this takes.”

  “So fill me in!”

  “Don’t get so irritated, Felix, you’ll see. The fewer people who know the truth now the better. Trust me.”

  “What truth? You probably don’t know a thing.” I put my feet up on the edge of my desk. “You watch the Stooges much, Max?”

  He looked at me calmly. “Lately. All ninety-seven episodes with Curly.”

  “And?”

  “Well, I can see that our Curly is in character.”

  “That’s all?”

  He shrugged. “Nothing else in those films concerns this case.”

  “But did you laugh at the routines?”

  “What has that got to do with anything? Look, I’ve got to make some calls. You and I will be going it alone with him tonight.”

  His evasiveness was irritating. I could still see Curly’s pleading eyes staring at me through the bars. I had to make sure that nothing bad would happen to him, so I went with Max to the hotel.

  “You can’t be Curly Howard,” Max insisted.

  “Why not?” He jumped up from his chair and clucked at him.

  I sat back on the hotel sofa.

  “Because your physical was too perfect!” Max shot back.

  “So what! My mutter brought me up healthy!” He beamed at us with pride. His tongue flicked across his lips as he looked at Max with expectation. Max didn’t answer. We weren’t being very good straight men.

  “Okay,” I said finally, “where’s your brutters—I mean brothers—I mean Larry and Moe?”

  He patted his stubble and seemed genuinely puzzled. His eyes closed as he searched for an answer. Something else besides Curly seemed to be at work.