The Compleat McAndrew

SIXTH CHRONICLE: The Invariants of Nature

“I must say it was a surprise to me that you came here at all,” Van Lyle said pleasantly. “You really have to hand it to the Director. Anna Griss predicted all of this, you know — the effect of the announcement, McAndrew’s arrival, and then yours. Very perceptive of her. But, then, isn’t that exactly why she has the job of Administrator, and we do not?”

He was standing in front of a huge pair of metal doors, checking a set of dials built into the frame. On the other side of them lay the processing vats, where all organic tissues — muscles, bones, nails, skin and hair — were dissolved to basic biotic molecules. Warning signals were splashed all over the chamber, and on both the doors: CONTROLLED ACCESS — DANGER, CORROSIVE GASES AND LIQUIDS — DO NOT PROCEED WITHOUT PROTECTIVE SUITS — OFFICIAL DEPARTMENT REPRESENTATIVES ONLY PERMITTED BEYOND THIS POINT.

Van Lyle turned to me questioningly. “Impressive, wouldn’t you say? Don’t be coy, Captain. I’d really like to hear your opinions on all this.”

I rolled my eyes at him. I was sitting upright in a metal wheelchair. My wrists and elbows were bound to the chair arms with broad fiber tape, the sort that is hard to unstick and just about impossible to break. My lower legs were lashed to the chair’s metal struts with the same material. A broad sticky strip of it covered my face, from just below my nose to the point of my chin.

“Ah, I see the problem,” Lyle went on. “But are you ready to talk nicely now, and not make a fuss?”

I nodded — one of the few degrees of freedom available to me.

Van Lyle nodded back. “Very good! And just in case you feel tempted to change your mind, let me point out that it would be quite pointless. This part of the installation is all automated. No one is here but the two of us.”

He came across to me and touched one end of the tape that covered my mouth. But instead of pulling it loose, he paused to run his fingers along one side of my nose, and back down the other.

“What a nice, shapely adornment,” he said. “Not at all like mine, eh? Before we finish, we’ll have to do something about that.”

I hadn’t realized until that moment just how much he hated me. His nose was bent and slightly flattened, detracting from his rugged blond good looks. The mouth beneath the crooked nose twisted with anger as he ripped the tape away from my mouth.

I worked my lips against each other, wincing. A layer of skin had been torn away by the super-adhesive tape, along with every fine hair on my face. I felt a trickle of blood down my chin.

The less discussion of noses, though, the better. I had broken Van Lyle’s, half a light-year away from Sol, when he wouldn’t take his lecherous hands off me. That had been long ago, but unfortunately he didn’t seem willing to forget it.

“You know McAndrew,” I said. “All it took was the right word, and he was ready to head for Earth. Nothing that I said could stop him from coming.”

“So I understand.” Lyle nodded. “But you, Jeanie — surely you’re much more sophisticated than that? I would have bet money against you following him down here.”

Van Lyle’s calling me Jeanie made my flesh crawl, but he was right. I didn’t have the excuse that Mac had, the siren song, the magic words that had left him helpless: a new invariant of nature.

“You don’t understand,” I said. “I’ve spent half my life chasing after Mac when he got into trouble. By now it’s second nature. But usually it’s to some place halfway to the stars — not a trip down to Earth.”

I had no real interest in telling any of this to Van Lyle, true as it might be. I was merely stalling, postponing the moment when he would tape my mouth again and carry out the next stage of the proceedings. I had little doubt what that was going to be. Lyle hadn’t hauled me down to this processing plant, far offshore and a hundred meters beneath the surface of the sea, just to show off the advanced technology of Earth’s Food Department.

It was also a very bad sign that he had mentioned the name of Anna Griss. In the past he had always refused to admit that he worked for her.

I wondered what he was waiting for now. It shows how desperate I was feeling, but I actually hoped he might be planning another shot at raping me. Let him do anything — anything that might provide enough time for help to arrive, or give me a thin chance of resistance. That was better than being strapped in the wheelchair, able only to move my head and trunk from side to side.

I didn’t have much hope. This wasn’t my environment, it was theirs. I might have an edge in deep space, but down on Earth, Van Lyle and Anna Griss held home field advantage.

And suddenly I had no hope at all. Because I heard the steel doors at the back of the chamber open, the ones through which I had been wheeled in. There was the squeak of unoiled bearings, and a few seconds later another wheelchair was rolled alongside mine.

McAndrew sat in it, his legs and arms tied to the chair’s metal struts, not by sticky tape but by thick, knotted cords. His mouth was not covered.

He stared across at me miserably. “I’m sorry, Jeanie,” he said. “I really am. This is all my fault, every bit of it.”

I tried to smile at him, and winced at raw, stripped skin. My lips began to bleed again. “Don’t feel bad, Mac,” I mumbled. “If it’s your fault, it’s my responsibility.”

It had started at the Penrose Institute, over a month ago. I had been on the way home after a routine Europan delivery run. Orbital geometries happened to be favorable, so it was the most natural thing in the world for me to drop in on McAndrew. The Institute, after a disastrous couple of years of bureaucratic rule, was once more under the steady but informal guiding hand of old Dr. Limperis, dragged out of retirement to put things right. I wanted to see how everything was going, and renew old acquaintances.

I headed straight for Mac’s working quarters. He was not there. Instead, Emma Gowers was loafing in his favorite chair and staring at a display.

“Off in the communications center,” she said. “He’ll be back in a few minutes. You might as well wait here.” She was as blond, beautiful and blowzy as ever. And presumably as brilliant. She was the Institute’s resident expert on multiple kernel arrays.

“Is he all right?” I asked. Mac usually had to be dragged out of his own office, unless he was off somewhere running an experiment.

“Oh, he’s fine.” Emma pushed her mass of blond hair higher on her head. “But you know McAndrew. He’s got another pet project going. You can hardly talk to him any more.”

I nodded. It was the most natural thing in the world to find McAndrew in the grip of a new scientific obsession. He would be delighted to see me, I knew that. But he might also be only vaguely aware of my presence.

I sat down next to Emma. “What is it this time?”

“There’s talk of a new fundamental invariant. I’m skeptical, frankly, but he’s a believer — at least enough to want to check it out for himself.”

“Educate me, Emma. What do you mean, a fundamental invariant?”

Simple explanations were not Dr. Gowers’ forte. She frowned at me. “Oh, you know. Things that don’t change under transformation. Like the determinant of a linear system under orthogonal rotation, or the Newtonian equations of motion with a Galilean transformation, or Maxwell’s equations with a Lorentz transformation.”

It’s an odd thing about Emma Gowers. Her own taste in men is for primitive specimens, dim and hairy objects who apparently decided to stop evolving somewhere in the early Pleistocene. Yet she insisted on assuming that McAndrew and I were on the same intellectual plane, just because we were long-time intimates.

“Uh?” I wanted to say; but I was saved from new admissions of stupidity and ignorance by McAndrew’s own bustling arrival.

“Using my chair and my data banks again, Emma,” he said. “Out, out, out.” And then to me, as though we had not been separated for months, “Jeanie, this is perfect timing.”

Most people think that I tolerate behavior in McAndrew that I would never stand in any other human being, just because he’s a genius. He is that, the best combination of theorist and experimenter to arise in physics since Isaac Newton — at least, that’s what those few equipped to make the evaluation all tell me. But genius has nothing to do with my own tolerance of Mac, or his of me.

I can’t do better than to say that we click. We are very different, but we touch at just enough points to make us stick.

McAndrew puts it differently. “A hydrogen bond,” he has said to me, often enough to make it irritating. “Not an ionic bond, that’s all set and rigid, or even a covalent bond, where things are actually shared. No. We’re a hydrogen bond, loose and fluid and easy-going.”

I’ll just say that we like each other. And if he thinks I’m so dim that everything he says to me about science has to be deliberately “dumbed down,” and if I think he is so wrapped up in abstractions that he ought not to be allowed outside in the real world without a keeper — well, that’s acceptable to both of us.

This time he responded to my hug, but in an automatic and absent-minded way. “If you’re heading inward,” he went on, “as I suspect you are, then I’ll hitch a ride with you.”

The space structure that houses the Penrose Institute is mobile, and at the time of my visit it was again drifting free, well outside the orbit of Mars. But inward? Mac’s interests usually lay well beyond the edge of the Solar System.

“To Earth,” he explained. And, as my eyebrows rose, “Och, don’t worry, I’m not asking you to come with me. Drop me off at a libration point, Jeanie. That will do fine.”

He knew my aversion to Earth, overcrowded and noisy and smelly. But I had always thought that he shared it, and he and I had other good reasons to avoid going there. One of Earth’s most powerful people was Anna Griss, former head of Earth’s Food Department, and now Administrator of the full Food and Energy Council. Mac had cut off her arm with a power laser, out in the Oort cloud. It had been done with the best of intentions, and it had saved her life; but I knew Anna. She would not have forgotten, or forgiven.

As for me, I had been a target for her hatred since the same trip, perhaps even more so, because I had challenged her authority — and proved her wrong.

It’s no surprise that there are people like Anna Griss in the world. There always have been. Go back fifty thousand years, to a time when most of us were just grubbing along, looking for a decent bush of ripe berries or a fresher lump of meat. A few, like McAndrew, were busy inventing language or numbers, or painting the walls of the cave. And some, just a handful but too many in every generation, were seeking an edge over the rest of us: Water access, or mating rules, or restricted entry to heaven. No matter how few they were, Anna Griss would have been one of them.

So McAndrew knew very well what I was driving at when I stared at him and said, “Earth? Do you think that’s a good idea?”

“It’s a must,” he said. “I’m going to visit the Energy Council. To be specific, I’m going to the laboratory of Ernesto Kugel, where there is evidence that something wonderful has been discovered: a new Invariant of Nature.”

You could hear the capital letters.

“Told you so,” said Emma Gowers. And she stood up, tugged her short dress down as close to her dimpled knees as it would go, and swept out.

If McAndrew’s words were designed to impress me, they failed.

“Mac,” I said. “With me, three invariants and a dollar will get you a cup of coffee.”

“You’re a barbarian, Jeanie,” he said amiably. “I’m just using the term that Kugel used: a new invariant of nature. Would it help if I rephrased that, and said that he claims to have found an important new conservation law?”

It did help, because I have been around McAndrew for a long time. But it didn’t help much.

“New, how?” I asked. “I mean, I know that energy is conserved, and momentum is conserved—”

“In a closed system.”

“In a closed system, fine. But how can there be a new conservation law?”

“Well, that’s where things get interesting. Now and again, physicists realize that certain things that they used to think of as independent are actually different aspects of the same thing. For example, a few hundred years ago, heat and motion and light used to be thought of as quite separate entities. But then, after lots of work by people like Rumford and Joule and Kelvin, scientists realized that those separate things were all forms of energy. And though different types of energy can be converted, one to another, they decided that the total could never be changed. That was the principle of conservation of energy.

“Starting with the work of chemists like Lavoisier, people also observed that mass is conserved, too, in every form of physical and chemical reaction. So you had conservation of energy, and you had conservation of mass. But the big breakthrough came in 1905, when Einstein showed that mass and energy are equivalent, and that their total is the thing that is conserved, rather than either one. And he also showed that it didn’t matter which reference frame you use for the measurements. The energy-momentum four-vector is invariant. That single principle helped to unify the whole field of physics.

“The same thing happened with angular momentum. For a while it looked as though it wasn’t conserved in nuclear reactions. But then workers in quantum theory found that an internal angular momentum had to be added to the picture for many particles — spin — and after that angular momentum became a fully conserved quantity. That, too, was a terrific generalizing idea. Did you know that in 1931 Pauli deduced the existence of a new particle, the neutrino, just because the principles of conservation of energy and of angular momentum required that it exist?”

“I did know that, Mac” — once — “and you haven’t answered my question. I realize very well that there are conservation principles. But how can there possibly be a new one?”

“I can give you two possible answers to that. The first is that the physical laws of the universe, as we already know them, admit some conserved quantity that we simply haven’t recognized yet.”

“Isn’t that unlikely?”

“You might think so, after all the time and effort we’ve put into searching for that sort of invariance principle, for the past hundred and fifty years, with nothing to show for it. But there’s another possible answer, one that at first doesn’t sound much more likely. It could be that Ernesto Kugel’s lab has discovered a new fundamental form of physical law.”

McAndrew was starting to make sense to me, which should have been a tipoff right there that something was about to go wrong. Usually, the longer that we talk, the more confused I become.

“You mean, a new force? Something like discovering gravity for the first time?”

“That will do nicely. We happen to have been aware of gravity for as long as humans existed, and we’ve had theories of it for over five hundred years. We’ve known the electromagnetic force for three centuries, and the strong and weak forces that govern nuclear interactions for just a couple. But gravity is actually a very weak force, something we only feel because very large bodies are involved. Suppose that we had evolved as tiny creatures, no bigger than fleas, in the middle of an energetic plasma? Then gravity wouldn’t have much immediate effect on our lives. We’d have learned about electromagnetism early, but we might still not know about gravity.”

I was finally getting the head-swirling buzz that usually accompanied a McAndrew explanation. “But we didn’t evolve smaller than fleas, in the middle of a plasma.”

“No. But different environments make it easy to detect different forces.”

“But less than a year ago you were telling me that the place to look for new laws of nature is out in deep space where we’ve never been, out where the sun and planets don’t interfere with observations.”

“I did say that. But suppose I’m wrong. Wouldn’t that be exciting, Jeanie? A new law of nature, sitting there under our noses all this time, and detectable down on the surface of Earth.”

And there you had it. Most people hate to learn that they are wrong. Not McAndrew. When he’s proved wrong, he’s ecstatic. It means he’s learned something new, and that’s his main reason for existence.

But I still hated the idea that he’d be going to Earth. “This Ernesto Kugel. If he’s in the Energy Department, that means he works for Anna Griss.”

“So?”

“Do you know him?”

“Not personally. But I know his work, very well. Ernesto Kugel built the Geotron.”

Capital letters again. I resisted the urge to be distracted by that. “Is he the sort of person you believe might make a fundamental new discovery?”

“Oh, no.”

“Well…”

“Not him. He’s an engineer — and a first-rate one — but he’s no physicist. Someone in his lab would have done the work. Someone I don’t know. Kugel would probably put his own name on the report just to make people pay attention.”

“But surely you don’t think that some total unknown would have come up with a big scientific breakthrough?”

“Jeanie, the big breakthroughs always come from some total unknown. And genius can pop up anywhere. Kugel got lucky.”

“Maybe. But Kugel works for Anna Griss, and she hates your guts. Don’t you remember what you did to her?”

“Ah, away with you.” He ran his fingers through his thinning hair. “Jeanie, I’m sure that’s all long forgotten. The invitation to visit Kugel’s lab was approved by Anna. She signed off on it.”

“Did she?” I said. “Well, of course that makes everything fine, doesn’t it?”

I should have known better. Irony is totally wasted on McAndrew.

He beamed at me. “I knew you’d see it my way when you had the facts, Jeanie. How soon can we leave?”

I think my inner voices are pretty good when it comes to warning of trouble. The problem is, I don’t always listen to them.

This time I allowed another event to occupy my mind when I ought to have been worrying about McAndrew’s visit to Earth. In my own defense, I must say that the intrusion came from outside. When the linked spheres of the Assembly were halfway to Earth, with Mac and me cozy in the Control Section, I received a message from Hermann Jaynsie at the United Space Federation Headquarters.

It was long and wordy, because Hermann is long and wordy, but I can boil it down. It said, in essence, “What the devil did you do, Captain Roker, on your last cargo haul from the Jovian system to Earth? We thought we had a deal with them for four billion tons of vegetable foodstuffs, grown in our Europan ocean farms. Now Earth is telling us they don’t want to take delivery of any more shipments.”

The lightspeed round-trip travel time to USF Headquarters was seven minutes, so I couldn’t exactly chitchat back and forth. But I did send him a pretty long reply, which again can be boiled down to, “Damned if I know, Hermann. They seemed happy enough with what I dropped off last time.”

My livelihood wasn’t hurt by the cancellation of a food supply contract with Earth; but my ego was, and I spent a good deal of time fuming. Was it Anna Griss, getting at me in a remarkably indirect way? I knew she was capable of subtle malice. But I still looked for a more logical explanation. I couldn’t see even Anna risking Earth’s food supply just to get at me.

I had no intention of going to Earth, or wasting another minute thinking of Ernesto Kugel and his mysterious invariant. So when we arrived at the Colony drop-off point, where the Assembly would be moored until its next trip out, McAndrew and I went our own ways. He headed down on a shuttle, as excited as a child on his way to a birthday party. I mothballed the ship, and handed it over to the local USF maintenance crew.

That took me three days. And then on the fourth morning, without thinking about what I was doing, I found myself aboard a shuttle vessel.

Heading for Earth.

I had been given a number to reach McAndrew, and I forwarded a message to tell him that I was on the way, and when and where I would arrive. I didn’t ask, but I rather hoped he might be waiting for me.

He wasn’t. And it was one of life’s less pleasant experiences to pass through entry formalities, search for Mac’s face, and see Van Lyle waiting for me on the other side of the barrier.

“Captain Jeanie Roker.” He reached out and took my hand. “It’s been a while.”

I shook his hand, but my feelings must have showed on my face, because he laughed and said, “Don’t say anything. You did what you did, and I thoroughly deserved it. Let bygones be bygones.”

But he touched his fingertips to his bent nose.

I said, “McAndrew—”

“Is having too much fun, Captain, to tear himself away from the Geotron facility. He asked me to come to the port, and take you there to join him.”

It sounded awfully plausible. But I couldn’t put the past behind me as easily as he claimed to have done. “Professor McAndrew asked you to come and meet me?”

Instead of answering, Lyle took a palm-sized phone from his pocket and tapped in a string of numbers. “Four one seven,” he said into the unit. After a few seconds’ pause he handed me the phone.

I found myself staring into the tiny screen at a familiar high-cheekboned face. His wispy hair was sticking up in little random spikes, and his color was a fraction ruddier than usual. I couldn’t see his fingers, but I could bet that he was cracking the joints.

“Jeanie,” he said, as soon as he saw me. “I didn’t expect to hear from you until you arrived at the Geotron. What’s wrong? Are you having problems getting underwater?”

Underwater? But it was McAndrew, without a doubt. McAndrew live, healthy, unrestrained, and by the look of it having the time of his life. He actually did not sound too thrilled by the news of my arrival.

“No problems,” I said. “I touched down just a few minutes ago.”

“Right then. I’ll have to go. We’re very busy here.” And his picture promptly vanished. The phone link disconnected.

That was the genuine McAndrew, without a doubt, and he was clearly all right. The smart thing to have done at that point would have been to apologize to Van Lyle for my rudeness, plead prior job commitments off Earth, and turn right around and head back to space. Instead I handed the little phone back, sighed, and said, “Before I make a complete fool of myself, tell me one thing. What is a Geotron, and where is a Geotron?”

Van Lyle stared at me. I think I had actually managed to surprise him.

“You’re asking me what a Geotron is?”

“I am.”

“But didn’t Professor McAndrew explain to you?”

“He would have done — if I had given him half a chance.”

“Well… I’m not a scientist, as you know very well.”

“Nor am I. That ought to make things easier for both of us.” We started walking toward a sleek high-speed aircar, as Van Lyle said, “Well, you know what neutrinos are, don’t you?”

“Yes. They’re elementary particles, with no charge, and a tiny rest mass. Their discovery was predicted by Pauli in 1931, because they were needed to preserve the laws of conservation of energy and angular momentum.”

That was gross intellectual dishonesty, and I knew it. But Lyle didn’t. He looked quite impressed.

“Right,” he said. “All they have are spin and energy. And they don’t interact much with ordinary matter, uness they have very high energy. That makes them the devil to detect. A free neutrino can easily pass right through the Earth. But sometimes that can be an advantage. Like if you want to do down-deep exploration. And you decide to build a Geotron.”

He explained the rest of it as we took off and he flew us west at Mach Ten. The staff of Earth’s Food and Energy Council had done all the easy exploration of Earth’s interior that they could do — which meant prospecting to about twenty kilometers down. Now they were forced to search deeper, or else be dependent on off-planet resources. The Geotron was nothing more than a huge kind of X-ray machine, for examining the inner structure of the Earth. But instead of X-ray radiation, which would penetrate no more than a few feet, the machine generated tight beams of high-energy neutrinos. They could be sent in any direction. They passed right through the middle of the Earth, scattering off structures in the interior, and emerged at points around the world where their numbers were measured. Then a very fancy set of computer programs took the information on the detected neutrinos and used that to deduce the interior structures that they had encountered in their path from the Geotron to the detection chambers.

“Looking for primordial methane, as the primary target,” Lyle explained. “Pockets of compressed methane left over from the time of the Earth’s formation, and still trapped deep inside.”

“To use as fuel?”

“Lord, no. Methane’s far too valuable an organic material to burn — even if the laws permitted it. We use it for complex hydrocarbon synthesis.”

“Have you been finding any?”

“More than you would believe.”

It occurred to me that I had an explanation to offer Hermann Jaynsie for Earth’s lack of interest in the food supply contracts. There would never be a shortage of nitrogen on Earth, with an atmosphere that was nearly eighty percent that gas. If they now had enough hydrocarbons, and enough energy, elemental food synthesis would be a snap.

The most surprising thing was Van Lyle’s willingness to tell all this to me, an outsider. Didn’t Earth’s Food and Energy Council care any more who knew what? Or were there missing pieces that were not being mentioned?

“I understand the Geotron,” I said. “But what was that about being underwater?”

“Well, you don’t think we’d put it on land, do you? Solid surface is too precious. We put it on the seabed.” And then, when I looked puzzled. “Captain Roker, just how big do you think the Geotron is?”

“I’ve no idea.”

“Then I’ll tell you. The main ring is forty kilometers across.”

Forty kilometers. A long day’s walk. Or in this case, a long day’s swim.

“So it was built on the Malvinas’ continental shelf,” he went on. “Where there’s a lot of available seabed, and the water is only fifty to a hundred meters deep.”

“Malvinas?”

“Off the east coast of Patagonia. We’ll be there in half an hour. Then you can see it for yourself.”

In the next few minutes I learned that the Malvinas’ coastal zone was now Earth’s hottest development area, site not only of the Geotron but also of the world’s most modern food facilities and genetic laboratories; all, naturally, off-shore, in the shallow seas that ran for hundreds of kilometers east of the mainland.

And while Lyle talked, I struggled to remember where Patagonia was. Southern hemisphere? Definitely. South America? Probably. It occurred to me that although I could quote the size and approximate orbital parameters for every major body from Mercury to the edge of the Oort cloud, I did not know the geography of Earth.

We were flying near the edge of the atmosphere. I stared up at the familiar black sky, with the brightest stars showing, then turned my eyes down to wisps of white cloud, with far below them the alien sea.

I felt, as usual when I was on Earth, a long way from home.

Our descent to the Geotron did nothing to ease my feeling of alienation. I had not realized that our aircar was amphibious, until we were skimming a few feet above long, rolling waves. We touched down, planing across the surface in a cloud of spray. Lyle took his hands off the controls.

And instead of bobbing on the rollers, we kept descending. After a few moments of panic, while the water level rose past the windows and plunged us into a green gloom, I realized that the aircraft was not only an amphibian, it was also a submersible. I could hear the thrum of engines aft, and see the yellow beams of light that lit the way ahead and behind us for many meters.

“Lights for passenger viewing only,” explained Lyle. “Just so you can enjoy the sights. I haven’t been controlling the craft since we touched down on the waves. We’ll be homed in to the Geotron facility automatically — sonic control, of course, not radio. Radio signals won’t travel through water.”

“How far is it?”

“Just a couple of kilometers. There was no point in landing too far away, but the final approach is interesting.”

We had been angling steadily downward. The natural sunlight was vanishing, breaking to cloudy patches of darkening green. Shoals of silver-green fish and what looked like endless thousands of purple squids darted through the beams of our headlights. Then they too were gone, and I had my first sight of Earth’s sea-floor, a smooth grey-brown carpet of fine sediments that swirled up like an ominous mist behind us in the wake of our propulsion jets.

That alien fog made me uneasy. I was much comforted when the huge silver wall of the outer Geotron ring appeared ahead, and we moved to an underwater docking. That felt quite familiar to me. An inward pressure of seawater replaced the space environment’s outward pressure against vacuum, but the same sort of locks were needed. And once we were inside, we could have been in any controlled one-gravity environment between the Vulcan Nexus and the Hyperion Deep Vault.

Van Lyle led the way through the set of connected chambers that formed the control nexus for the Geotron. Other maintenance areas were spaced all around the rim of the main rings, a couple of kilometers apart. After a final up-and-down ride over the top of the inner ring, we were finally spilled by a moving stairway into a big square room, partitioned off into dozens of small work cubicles.

McAndrew sat in one of them with a man and a woman in their early twenties. His shoes and socks were off and he was staring at a listing that filled the whole of the cubicle wall. He looked well, was obviously unrestrained, and gave every impression of a man totally at home and thoroughly enjoying himself.

“There he is,” said Lyle. “I was wondering, why does he take his shoes and socks off when he’s working?”

“In case he needs to count to more than ten.” But I didn’t know the real answer, any more than Lyle did, and I had known Mac for a long time. At least he wasn’t cracking his toe joints at the moment.

We walked forward. Mac saw me first, and stood up. “Jeanie! This is Merle Thursoe and Tom O’Dell. We’re setting up a really great experiment.”

He nodded to me, almost dismissively, and turned back to the display. Then something — maybe my snort of anger — must have told him that this wouldn’t quite do for someone who had come so far to see him.

“Tom, Merle,” he said, “would you carry on without me for a few minutes?” And then, turning back to me and standing up, “Jeanie, I don’t think you know Ernesto Kugel. Come on. You have to meet him.”

He walked me right through the complicated center of the room, to a cubicle no bigger or better furnished than any of the others. Sitting at a desk there, facing outward, was a serious little man wearing a formal black suit, white shirt, and dark blue neckerchief. A matching blue rose adorned his lapel.

“Director Ernesto Kugel.” McAndrew was at his most formal. “May I present Captain Jeanie Roker.”

Kugel stood, came around his desk, and bowed, giving me a splendid view of the top of a hairless scalp as smooth and white and round as an ostrich egg. His whole head was free of hair, except for the neatly trimmed black moustache on his upper lip. I decided that nature could never have created the effect. Ernesto Kugel had worked on it.

I was all set to dislike the man, when he straightened up and took my hand.

“I am delighted to meet you, Captain Roker,” he said, in a deep, smooth voice. “Professor McAndrew told me that you are most competent. What he did not mention is that you are also elegant and beautiful.”

I stared at him. “Does that line work often?”

He gazed back, unblinking and unashamed, his brown eyes as bright and lively as a bird’s. “Not so often.” He suddenly smiled, and it transformed his face. “But let us say, it works often enough.”

“And I suppose that joking about it works, too?”

“Sometimes. Most times. And if it does not” — he shrugged — “what harm has been done? God made two sexes, Captain Jeanie — and luckily that was exactly the right number.”

I suddenly found it impossible to dislike him at all. We stood grinning at each other, until McAndrew said, “I want a word in private. Just the three of us.”

“Of course.” Kugel nodded his head toward the cubicle. “But this is as private as we get. I believe it is bad if I hide myself away from where the real work is done. Bad for my staff — and worst of all for me.” Kugel waved to us to sit down. His desk was as neat and organized as Mac’s was usually messy.

McAndrew didn’t waste any time. “Ernesto, I could explain our discussions to Captain Roker — to Jeanie. But I would feel much more comfortable if you were to do that.”

“Of course.” Kugel leaned toward me, and spoke in his low, confidential voice. “You should sleep with him, you know. You two should have children.”

I turned on McAndrew. “You brought me in here, just to hear a proposition on your behalf? You ought to be old enough to handle your own public relations.”

“That’s not what I meant!” Mac waved at the other man. “Keep going, Ernesto.”

“Of course.” Kugel was chuckling to himself. “What I mean, Captain Jeanie, is that the man standing before you, Arthur Morton McAndrew, is a great genius. His genes, and your genes, should be preserved and cherished. I knew his reputation long before he came here, but now I realize that he is one of the immortals.”

“But I’m not fit to carry Dr. Kugel’s coat, when it comes to large-scale engineering,” McAndrew added. Praise of his abilities makes him terribly uncomfortable.

I sighed. It was obviously a mutual admiration society. Apparently I had travelled the distance from Moon to Earth, just to hear the two of them compliment each other.

“But to be specific,” Kugel said, after a long pause in which they sat nodding and smiling. “Before Professor McAndrew’s arrival, I and my staff had operated the Geotron for three months. In all that time, we had observed an inexplicable loss of neutrinos. We know how many the machine produces. And we know how many we are finding, in each of our mobile detectors. From that it is a simple calculation to estimate the total number escaping over the whole of the Earth’s surface. There were too few of them, less than we were creating — and not by a number within the reasonable bounds of statistical error. There were far too few. For a long time we thought that it must be a matter of phase changes, or instrument calibration. Finally we decided that could not be the case.

“We had no explanation. Until two of my brightest young staff, Thursoe and O’Dell, became involved.”

“Jeanie met them both,” McAndrew said.

“Then you must know, Captain, that both of them are far brighter than I. They proposed a specific physical reason for the absence of neutrinos, arguing by analogy to the conserved vector current theory of Feynman and Gell-Mann. That would imply the existence of a new kind of weak force, and a new physical invariant. It was speculative, but I thought it looked very interesting. I mentioned the work and the theory in my weekly report of activities to the Food and Energy Council. I did not expect that it would receive external circulation — until the sudden arrival of Professor McAndrew’s request to visit the Geotron facility, and review the evidence.”

He turned to Mac. “Now I think that you should continue.”

“Well…” McAndrew became uneasy. “I don’t like to criticize other people’s work, you know, and the O’Dell and Thursoe theory is highly ingenious; but it did occur to me that there could be a simpler explanation.”

“You knew it,” Kugel said flatly. “Knew it before you ever left the Penrose Institute.”

“No. Everything depended on the experimental results.” McAndrew turned back to me. “You see, Jeanie, the Geotron had been operating at a very precise and very high neutrino energy, a domain that to my knowledge had not been explored before in any detail. It seemed to me that the explanation for the loss of neutrinos could be something as simple as resonance capture. Certain materials, common in Earth’s interior, may have a very high capture cross-section for neutrinos of the Geotron energy. And that could account for the observed difference between production and detection. It would also be a most important scientific discovery, because such a resonance is not predicted by current theories.”

“Mph,” I said. It meant, Mac, I have now heard more than I wish to know about lost neutrinos.

But McAndrew, as it turned out, was close to the end. “And there’s a very simple way to tell if I’m right,” he said. “In less than twelve hours we can do an experiment with a modulated Geotron energy, far from possible resonance, and get an instant neutrino count. That’s what O’Dell, Thursoe, and I have been working on. And we are just about ready for final set up.”

As I said, I’ve known McAndrew for a long time; long enough to interpret what he had just told me: he was all ready to do a neat physics experiment, and for the next half day nothing in heaven or earth would budge him from the Geotron facility.

That conviction was at once reinforced by Ernesto Kugel.

“You are of course welcome to remain here during the experiment,” he said to me placatingly. “On the other hand, one of the Administrator’s own staff members suggests that you might find a visit to our new food production plant, a few kilometers away, much more intriguing. He would be happy to serve as your escort.”

“More than happy.” And dead on cue, Van Lyle was standing at the entrance to the cubicle. “Ready when you are, Captain Roker.”

It was all fine — and all just a little bit too pat.

“I need to go to the bathroom,” I said, “before we leave.”

“Sure.”

Inside the stall I sat down on the toilet seat, put my head in my hands, and thought.

I was uncomfortable. What was the source of my discomfort? Nothing that I could put a name on, except that maybe the leopard had changed his spots a little too completely. This Van Lyle was not the Van Lyle I had known.

But what then were the dangers? Nothing that I could think of.

I was being paranoid. I went back out. I gave McAndrew a farewell hug, while Ernesto Kugel looked on approvingly. But as I was doing it I whispered in Mac’s ear, “I’m going to look at the food production center with Van Lyle. If I’m not back in twelve hours, you come after me.”

McAndrew is not good at this sort of thing. “What?” he said loudly.

“You heard.” I did not raise my voice. “See you soon — I hope.”

Earth is an amazing place. It’s a spent force, a used-up relic, a crusted dinosaur that the rest of the System looks back on and shakes its head.

But it doesn’t know that — or at least it won’t admit it.

The Malvinas’ food production facility was astonishing. On the seabed, powered by abundant fusion energy and with nothing but the raw elements as working material, the production center was making foodstuffs as good as any I’d tasted through the whole system. No wonder that Earth, with a ten thousand year supply of primordial methane promised by Ernesto Kugel, wanted to renege on supply contracts. It had little interest in what it saw as extortion from the Outer System.

Earth looked like — dare I say it? — the planet of the future.

Maybe it was that, the total unreality of the experience, that made me lower my guard. Lyle and I were walking through a chamber where vat after vat of synthesized milk and beef extract stood in ferment.

“We’ll visit the organic recycling center next,” he said. “But first, smell this.” We paused in front of an open container, much smaller than the others. “It is Roquefort cheese. Synthesized, but you’d never know it. Lean over, stick your head in, and take a good sniff. Then I’ll give you a taste.”

I leaned over the tub. And I passed out cold, without ever knowing that I had gone.

When I came to I was in a wheelchair, bound but not yet gagged. Lyle was standing at my side.

“Ah, there you are, Jeanie,” he said in a cheerful voice. “Back with us at last. Are you ready for action?”

My head reeled, and a cloying smell was still in my nostrils. How long had I been out? I didn’t know, but it felt like an age. McAndrew might arrive at any moment. I had to think, and I had to survive until that happened.

“I don’t know what you’re up to,” I said, “but I know it won’t work. They’ll come after me.”

“Will they now?” Lyle cocked his head politely. “Don’t take this wrong, Jeanie, but I think you are mistaken. Though I have to say that I am looking forward to the appearance of Professor McAndrew. The show wouldn’t be the same without him. I also think it would be better for the time being if your mouth were taped, just in case.” And a minute later, “I must say it was a surprise to me that you came here at all.”

That, I think, is just where we came in. And a couple of minutes later it was Mac’s arrival in a second wheelchair, pushed by Anna Griss herself, that sent me to a final misery.

“Mac,” I whispered, after he had been rolled up alongside me. I was already full of an awful suspicion. “Where are the others?”

“Others?” He frowned at me, high forehead wrinkling. “Others? I came by myself.”

McAndrew had done what I asked him to do — literally. He had come after me. Alone.

Well, at least there were few illusions left. And when Anna Griss came forward to stand in front of us, there were none. She was, as ever, elegantly dressed, carefully made up, and totally self-confident. She stared at us for a few seconds without speaking. At me, I would suggest, with a total cold hatred; at McAndrew, as at a wayward child who despite the best of advice has gone terribly and incorrigibly wrong.

“It took a while, didn’t it?” she said. “How long has it been since the Oort cloud? But it finally worked out all right. I knew it would.”

“You won’t get away with this, you know,” I said. “People know where McAndrew is. They know where I am.”

“I’m sure they do,” said Anna Griss. “But accidents happen, don’t they? A tour of the recycling facility, an unfortunate entry into a clearly forbidden area…”

“You’re a monster.”

“Thank you. But I don’t think I need to listen to that sort of thing. And I don’t need to watch it.” She turned to Lyle. “Put the gag back on the mouthy one. She talks too much. Then finish both of them. Before you do that, I need one more word with you. I’ll be outside.”

Typical Anna. She wouldn’t watch, she wouldn’t listen; so if there ever were an investigation, for any reason, she could proclaim her innocence. Hear no evil, see no evil.

She left. But Van Lyle was still there, and he was more than enough. He walked forward, sticky tape in his hand, and stood in front of me.

“It will be nice to hear you scream, Jeanie,” he said quietly. “I won’t be able to give you all that you deserve, the thing I’d really like to give you. We don’t have time for that. But I can’t wait to hear you grovel. I want to hear you beg, Jeanie.”

“Maybe you will.” I made my voice quiver. “And maybe you won’t.” He was moving closer. “But if you tape my mouth, you’ll never hear anything from me. Ever. So go ahead.”

He hesitated. “You’ll beg all right,” he said, “and you’ll grovel. Trust me, Jeanie. You’ll plead, and you’ll beg, and you’ll scream. Just you wait.”

He left the room. But he had not taped my mouth.

Mac’s wheelchair stood right next to mine. “Don’t move,” I said, and I leaned as far over to the left as I could. I could get my mouth down to the cords that bound his right hand — just.

Undoing knots in thick cord may sound easy. It isn’t, especially when you can’t see what you’re doing, you’re in a desperate hurry, and you have to work only with your mouth. The lips are very sensitive organs, but we are visual animals. I felt with my tongue and lips, tugged and twisted with my teeth, and was convinced that I was getting nowhere.

I forced myself to remain calm, to be patient, to pull gently instead of tearing and biting. McAndrew did not move, even when my teeth were catching more of his flesh than the cords.

It took forever before I felt the first loosening, a knot responding to my quivering mouth. But then it came faster. The second knot seemed easy. At last Mac’s right hand was free.

“Right,” he grunted. “I’ll have us out in a minute.” He reached across to his other hand, with the loose bonds still on his right wrist. As he worked on his left hand, I craned my head around to watch for the return of Van Lyle.

“Getting it,” Mac said at last. But his legs were still tied when I saw the door opening.

“No more,” I whispered. The two of us sat frozen as Van Lyle walked again in front of us. Mac had left the cords around both wrists, and his forearms rested on the arms of the wheelchair. It looked as though he was securely tied, hand and foot. As for me, I was still taped like a trussed chicken, arms and legs.

“So, Jeanie,” Lyle said. “You don’t know if you’ll ask for mercy, eh? Well, I ought to tell you that Dr. Griss left the final steps in my hands. How you go is completely up to me — and to you. Quick and easy, or slow and hard. Do you think you can persuade me to be nice to you? Let’s find out.”

He moved behind me and pushed my wheelchair forward. Then he came past me, to the panel that controlled the great double doors.

“Take a look at this, Jeanie.”

The doors slid open. Pungent fumes rose from the pit that was revealed before me, searing my throat. I saw a great pond of dark liquid, just beyond the doors and a few feet down.

“Ten seconds in there,” Lyle said conversationally, “and you’d be choking. Half a minute, and your skin would start to peel off. But we don’t have to rush everything like that. You can be dipped in and out like a bit of beef fondue, a toe or a foot or a hand at a time, as often and as slow as I choose to do it. Would you like to beg now, Jeanie? Or would you like to take your trial dip this very minute? Or maybe you would like me to be really merciful, and knock you unconscious first?”

I could hardly move, but I jerked and screamed and writhed against the tapes, making as much noise as I possibly could. Lyle laughed delightedly. Between us we were making a frightful din. How much of my screaming was genuine panic? I don’t know, but I’m sure a good deal of it was, because my chair was rolling steadily closer to the edge without being pushed. There was a small lip at the very brink of the pit, but it might not be enough to halt the forward motion.

I was an arm’s length from death — the chair nearing the edge — Van Lyle walking by my side and peering at my face, savoring my expression.

Then, from behind — at last — came the squeak of unoiled wheels.

Before Van Lyle could move, McAndrew was on him. Mac had freed his legs and was out of the wheelchair. Smarter than I would have been, he came forward in one silent rush, pushing the wheelchair in front of him like a ram. The edge of the seat caught Lyle behind the thighs at knee level. He fell backward into a sitting position. Before he could cry out he was at the edge. He and the chair went right on over. There was a scream and a great splash. McAndrew halted at the brink, staring down.

“Mac!” I screamed. I was still rolling.

He half-turned and threw himself in front of my wheelchair, stopping it with his own body. At the very edge, we both peered into the pit.

Lyle had gone in flat and facedown. He rose to the surface in a cloud of steam, screaming and clawing at his eyes. As we watched, his hair and skin began to smoke and frizzle. His arms waved and thrashed down on either side of him. Then he went under again.

The vat was more corrosive than Lyle had suggested. Twice more he rose, howling in agony. But the liquid must have reached his lungs. By the time he went under for the last time he was silent, a dark-green mass that was already losing its human form.

And while Van Lyle was dying, McAndrew kept tearing at the tapes that held me. I think it was the only thing that kept him from plunging in himself to try to help.

The tapes were strong, and Mac’s hands were trembling. It was two more minutes before I could stand up, advance shakily to the brink, and peer down into the choking green fumes. I saw a dark vat, with sluggish ripples moving across the surface. About ten feet away from the edge floated an amorphous rounded lump.

“Don’t look,” McAndrew said. “He’s dead.”

“Of course he is. But it was his own damned fault.”

I don’t know how angry I sounded, but Mac winced. “Come on, Jeanie,” he said. “It’s over now. Let’s get out of here.”

“It’s not.” And then, when he stared at me. “It’s not over. Not yet. Come on, Mac. I may need help.”

I ran back, through the sequence of chambers that threaded the food production facility like beads on a necklace. Anna Griss sat at a table in the third one, calmly reading. She had just enough time to cry out in surprise before I reached her.

I lashed out and caught her with my fist high on the left cheek. While she was still reeling backward, partly stunned, I grabbed her in a neck lock.

“Come on, Mac. Help me. Back to the vats.”

He wasn’t much use, but it didn’t matter. My own adrenaline level was so high, I could easily have carried her all the way myself. She was faintly struggling when I thrust her into the remaining wheelchair. The sticky tape that had held me was no good any more, but the cords that had bound Mac were enough to tie her.

I wheeled her to the very edge, so that the acrid corrosive vapors filled her throat and mine.

“That’s Van Lyle down there.” I pointed to the sodden green hulk, floating almost submerged. “You’re going after him.”

“Ohmygod. No, no.” She was panting, shaking her head with its newly disordered hair and smudged make-up. “Don’t push me over. Don’t kill me. Please.”

“You were ready enough to see us killed. Here you go, Anna Griss.” I tilted the chair far forward, so that all that held her from the vat were her bonds. “This is what people get who mess around with me. You’re dead.”

I put my face close to hers. She was too frightened for tears, but her staring eyes were watering in the poisonous fumes.

“Say your prayers,” I whispered. “Say goodbye.”

“No. Oh, please.” She was straining back, away from the deadly vat. “Don’t. I’ll do anything. Anything!”

“Jeanie!” cried McAndrew.

“Shut up, Mac. This is between me and her.”

I moved the chair back a couple of feet and walked around in front of it to gaze into her eyes. “Look at me, Anna Griss. I’m not going to kill you — this time. But one more problem with you and you’re dead. Do you understand? If the sight or sound or smell of you crosses my path again, ever, I’ll come after you. And I’ll get you. Don’t ever doubt that. I’ll get you.”

She did not speak, but she nodded. I turned to McAndrew.

“I think she has the message. If she annoys either of us again, she’ll be pig feed. Come on, Mac.”

“You can’t just leave her! She might go over the edge.”

“If she goes, she goes.” I grabbed his arm. “No big loss. But you and I are leaving. Come on.”

He kept turning to look at her, but he allowed me to lead him away. I did not look back.

“You wouldn’t have, would you?” he said at last, when we had walked through half a dozen chambers. “You wouldn’t have killed her, no matter what she did.”

It was obvious what he wanted to hear. “No. I wouldn’t have killed her.”

“Then why did you do all that, threatening her?”

“Because I had to. I might as well ask, why did you push Van Lyle over.”

“But he was going to kill you! I didn’t think — I just did it. Like you when you were screaming, going toward the pit. You just did it. What a bit of luck that was, Lyle leaving your mouth untaped! Otherwise you’d not have been able to scream, and when I ran at him he would have heard me coming.”

I don’t usually care what credit I get. But that was a bit too much.

“Mac,” I said. “Listen to me. I’m going to tell you something about the invariants of nature. You have yours for physics and mathematics, determinants and momentum and conserved vector currents. And I have mine — the invariants of human nature: Love, and jealousy, and fear, and hate. Van Lyle was a cruel, sadistic bastard. He was like that when we first met him, he was like that out in the Oort cloud, and he was still like that until the moment he died. He couldn’t change his nature. I deliberately told him that I wouldn’t be able to beg and scream and grovel with my mouth taped. After that there was absolutely no way he’d muzzle me — no matter what Anna Griss told him to do. He wanted to see my terror, and hear my screams. And so I had the chance to free you.”

McAndrew is an innocent soul. He was shocked silent by what I said. Finally he sighed, and muttered, “Maybe you’re right. But I don’t see why you did that to Anna Griss.”

“I had to — because in her own way, she’s no different from him. She has her own invariants: power, and control, and fear. Anna won’t hold back on revenge to be nice to anyone. She’ll go on, as far as she can go, until she’s stopped. You and I have just stopped her. But we could never have done that by persuasion, or logic. She had to look death in the face for herself, and stare right down his black gullet.”

“She could still cause us trouble. She could come after us, on Earth or off it.”

“She could, but she won’t. She’d like to get us, but she’ll remember that pit. Anna understands power. If her people tried and failed again, she knows I’ll come after her. The pleasure of finishing me isn’t worth the risk.”

“Are you sure?”

“Yes, I am. Mac, trust me. If I don’t question your spinors and twistors and calibration of optical scalars, you shouldn’t second guess me on Anna Griss.”

“So you think it’s safe to go back to the Geotron, and see how the experiments came out? I left before the results were in, you see, because of what you said to me.”

He was returning to normal. Which is to say, totally abnormal.

I sighed. “Sure. We can go to the Geotron.”

That sounded like the end of it, but it wasn’t. We were in the submersible, cruising back to Ernesto Kugel’s lab, while I wondered what story I was going to tell. Probably I’d say nothing. I’d pretend I had a nice pleasant tour, and leave it to Anna Griss to tell it otherwise.

Then McAndrew started up again.

“Jeanie. You really wouldn’t have killed her, would you? No matter what.”

I reached out and stroked his cheek. “Of course not. But can we drop it now? You and I ought to be celebrating our survival. Maybe we ought to act on Ernesto Kugel’s suggestion — his first one.”

It came out as flat and artificial as it sounds, and it didn’t fool McAndrew for one moment. He gave me a wary, weary look, and leaned back in his seat. But it did accomplish my objective. It shut off a line of conversation that I was afraid to pursue.

Because one thing I’ve learned in life is that a person never knows her own invariants. I thought I knew the answer to McAndrew’s question, but I wasn’t positive. That terrible rage, the all-consuming fury that I felt when Anna Griss was poised on the edge of the pit… if she had been a little more resistant, just a little tougher and more defiant — then who knows what I would have done?

Not I.

But one thing I did know for sure. I was not going to discuss that sort of thing with McAndrew. Ever.

He’s a dear, and he’s super-smart, and in almost every way I can think of he is wonderful. But he’s also like most people who spend their lives studying the nature of the Universe.

He can only take a tiny little bit of reality.