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.