He pressed the button. For the tenth time, the grinning figure in red danced away across the screen and waved his good-bye.
“Any ideas?” When it was not form-change theory, Bey was ready to admit that Aybee had the better chance of deciding what was going on. Sylvia might return at any moment, and Bey wanted to have a lot of his thinking done before he encountered a farmer.
“Too many ideas.” Aybee scowled at him. “It’s not a well-posed problem.”
“You don’t think he means what he says? That he’s a man with negative entropy.”
“I’m sure he isn’t. For a start, negative entropy has no physical meaning.” Aybee made a rude noise at the display and turned it off. “ ‘Negentropic’ just refers to something that decreases the entropy of a system. So a Negentropic Man ought to be a man who reduces entropy.”
“But what exactly is entropy?” Leo Manx had been listening carefully while the conversation made less and less sense to him. “Remember, I’m supposed to send a report back to Cinnabar Baker. I can’t send her your gibberish about negentropy. She’d jump all over us.”
“Hey, is it my fault if you’re a dummy?” Aybee looked down his nose at Leo. “I’ll give you a bunch of entropy definitions. You can pick any one you like. And don’t blame me if you’re wrong, because I sure as hell don’t know how the word is being used here. Oldest use: entropy in thermodynamics. Entropy change was defined as the change in the heat in a system, divided by its temperature. Can a process involving heat transfer be run backward? If not, the entropy of the system must increase. Rudolph Clausius knew that nearly four hundred years ago. He pointed out that entropy tends to go on increasing in any closed system. If the universe is a closed system, its entropy must increase. So then the universe is running down to a state of maximum disorganization, and we’ll all end up in uniform-temperature soup.”
“But we’re talking about a man here, not a universe.”
“I know that, Leo. Hold on a minute, I’m getting there. Remember, this is complicated stuff. We don’t want to make it so easy it’s meaningless. Einstein said it right: Things should be as simple as possible—but not simpler. Maybe our Negentropic Man has something to do with thermodynamic entropy, maybe not. Entropy number two: Ludwig Boltzmann found a statistical definition of entropy in terms of the number of possible states of the atoms and molecules of a system. He showed that it produced the same value as the thermodynamic one, provided the system has a whole lot of possible states.”
“How do we decide which definition we want?”
“We can’t—not yet. We keep going, then we’ll play pick and choose. Entropy number three: in information theory. Fifty years after Boltzmann, Claude Shannon wanted to know how much information a message channel could carry. He found it depended on a particular mathematical expression. The formula was the same as Boltzmann’s entropy formula, except for a sign change, so Shannon called the thing he calculated the entropy of the transmitted signal. That confused the hell out of people. The information-theory entropy is a maximum when the information carried is as much as you can get with a given channel.”
“Aybee, you’re not helping. Three forms of entropy—and not one of them intelligible. Why don’t people use clearly defined terms?”
“Hey, I understand them fine. We’re lucky there’s only four to pick from. Do you have any idea how many different things the word ‘conjugate’ can mean in mathematics? One more to go. Kernels have entropy. Even a nonrotating kernel—a Schwarzschild black hole—has an entropy. Two hundred and fifty years ago, Jakob Bekenstein pointed out that the area of a kernel’s event horizon can be exactly equated to an entropy for the black hole.”
“But we have to pick one of your four definitions! Aybee, how can we possibly do it? They’re all totally different.”
“No. They sound it, but they all tie together through the right mathematics. The mathematics of ensembles, it’s called. As for deciding which one we ought to be thinking about… don’t ask me. Spin a coin. Thermodynamic entropy, statistical mechanics entropy, information theory entropy, kernel horizon entropy—which one is Wolfman’s buddy talking about? We don’t know. But there’s more. Before you spin that coin, let me give you the other half of it. You see, the universe moves to higher values of thermodynamic entropy—that’s Clausius, and the Second Law of Thermodynamics. But life—any life, from us to bacteria and single-celled plants—is different—”
Aybee was interrupted as Sylvia Fernald hurried into the room, grabbed his arm, and began to pull him at once toward the door. “They’ll meet with us,” she said. “But we have to do it right this minute, before they change their minds. Come on.”
She led the way for Aybee and Leo, leaving Bey floundering along behind. The others were expert at moving in low gravity. He still rolled and yawed and missed handholds. He reached the chamber half a minute after the others and looked around for the elusive farmers.
The room was dark and divided in two by a wall of ribbed black glass. As Bey stepped forward, dim ceiling lights came on and the glass wall lightened to full transparency. On the other side of the partition, shrouded in white garments that left only dark pairs of eyes, two human figures became visible.
“Five minutes,” a deep, whispering voice said. Cowls were pushed back to reveal smooth skulls and nervous skeletal faces. “We promised at most five minutes.”
“Did you see your people in the form-change tanks?” Bey asked at once.
“I did,” the taller figure said. The deep voice was expressionless. “I found them.”
“Were they alive?”
“Already dead. According to the temperature monitors, already cold. They must have been dead for at least a day.”
“And no emergency signal was sent from the tanks?”
“Nothing. All indicators showed normal.”
“Has anything like this happened before? Something maybe less extreme?”
There was a pause while the two farmers turned to look at each other. “Tell them,” the second figure said. It was a woman.
“I think we must.” The man turned back to Bey. “We had noticed some peculiarities. Nothing serious, nothing that was not corrected on a second attempt with the form-change equipment. We considered calling for help, but after a vote we decided against the intrusion. Our colleagues who died took part in and approved of the decision.”
“You know when the problem began,” Bey said rapidly. The two farmers were beginning to move about uneasily. “Can you relate it to anything else that happened here on the farm? Any visitor? Any change in procedures?”
There was another pause—precious seconds of interview time slipping away. “The problems began six months ago,” the woman said. “There have been no visitors to the farm in more than a year. New form-change equipment was delivered to us at that time, but it performed perfectly for many months.”
“How about unusual events? Did anything odd happen six months ago?”
“Nothing,” the man answered. “There were automated deliveries to us, but that is usual. There were cargo shipments from here to the harvester, as always.”
“And there were—” the woman began.
“No,” the man interrupted. He reached out a hand, shielding the woman’s eyes from the four visitors but being careful not to touch her.
“I must tell. Two of us are dead because we valued privacy above their lives. It must not happen again.” The woman moved so that she could see Bey. Her voice was shaking. “Six months ago, some of us began to see things when we were out on the farm. Apparitions. Things that could not be real.”