Грегори Бенфорд - Not One of Us - Stories of Aliens on Earth

I’ll stop in my tracks. “Excuse me? I am not the hired help, nor am I some mutant relative for you to be ashamed of.”

“But Mom, I can’t let anyone see you with me.”

“What are you talking about? I’ve already met your friends; they’ve been to the house.”

“That was different,” you’ll say, incredulous that you have to explain it. “This is shopping.”

“Too bad.”

Then the explosion: “You won’t do the least thing to make me happy! You don’t care about me at all!”

It won’t have been that long since you enjoyed going shopping with me; it will forever astonish me how quickly you grow out of one phase and enter another. Living with you will be like aiming for a moving target; you’ll always be further along than I expect.

Ilooked at the sentence in Heptapod B that I had just written, using simple pen and paper. Like all the sentences I generated myself, this one looked misshapen, like a heptapod-written sentence that had been smashed with a hammer and then inexpertly taped back together. I had sheets of such inelegant semagrams covering my desk, fluttering occasionally when the oscillating fan swung past.

It was strange trying to learn a language that had no spoken form. Instead of practicing my pronunciation, I had taken to squeezing my eyes shut and trying to paint semagrams on the insides of my eyelids.

There was a knock at the door and before I could answer Gary came in looking jubilant. “Illinois got a repetition in physics.”

“Really? That’s great; when did it happen?”

“It happened a few hours ago; we just had the videoconference. Let me show you what it is.” He started erasing my blackboard.

“Don’t worry, I didn’t need any of that.”

“Good.” He picked up a nub of chalk and drew a diagram:

“Okay, here’s the path a ray of light takes when crossing from air to water. The light ray travels in a straight line until it hits the water; the water has a different index of refraction, so the light changes direction. You’ve heard of this before, right?”

I nodded. “Sure.”

“Now here’s an interesting property about the path the light takes. The path is the fastest possible route between these two points.”

“Come again?”

“Imagine, just for grins, that the ray of light traveled along this path.” He added a dotted line to his diagram:

“This hypothetical path is shorter than the path the light actually takes. But light travels more slowly in water than it does in air, and a greater percentage of this path is underwater. So it would take longer for light to travel along this path than it does along the real path.”

“Okay, I get it.”

“Now imagine if light were to travel along this other path.” He drew a second dotted path:

“This path reduces the percentage that’s underwater, but the total length is larger. It would also take longer for light to travel along this path than along the actual one.”

Gary put down the chalk and gestured at the diagram on the chalkboard with white-tipped fingers. “Any hypothetical path would require more time to traverse than the one actually taken. In other words, the route that the light ray takes is always the fastest possible one. That’s Fermat’s Principle of Least Time.”

“Hmm, interesting. And this is what the heptapods responded to?”

“Exactly. Moorehead gave an animated presentation of Fermat’s Principle at the Illinois looking glass, and the heptapods repeated it back. Now he’s trying to get a symbolic description.” He grinned. “Now is that highly neat, or what?”

“It’s neat all right, but how come I haven’t heard of Fermat’s Principle before?” I picked up a binder and waved it at him; it was a primer on the physics topics suggested for use in communication with the heptapods. “This thing goes on forever about Planck masses and the spin-flip of atomic hydrogen, and not a word about the refraction of light.”

“We guessed wrong about what’d be most useful for you to know,” Gary said without embarrassment. “In fact, it’s curious that Fermat’s Principle was the first breakthrough; even though it’s easy to explain, you need calculus to describe it mathematically. And not ordinary calculus; you need the calculus of variations. We thought that some simple theorem of geometry or algebra would be the breakthrough.”

“Curious indeed. You think the heptapods’ idea of what’s simple doesn’t match ours?”

“Exactly, which is why I’m dying to see what their mathematical description of Fermat’s Principle looks like.” He paced as he talked. “If their version of the calculus of variations is simpler to them than their equivalent of algebra, that might explain why we’ve had so much trouble talking about physics; their entire system of mathematics may be topsy-turvy compared to ours.” He pointed to the physics primer. “You can be sure that we’re going to revise that.”

“So can you build from Fermat’s Principle to other areas of physics?”

“Probably. There are lots of physical principles just like Fermat’s.”

“What, like Louise’s principle of least closet space? When did physics become so minimalist?”

“Well, the word ‘least’ is misleading. You see, Fermat’s Principle of Least Time is incomplete; in certain situations light follows a path that takes more time than any of the other possibilities. It’s more accurate to say that light always follows an extreme path, either one that minimizes the time taken or one that maximizes it. A minimum and a maximum share certain mathematical properties, so both situations can be described with one equation. So to be precise, Fermat’s Principle isn’t a minimal principle; instead it’s what’s known as a ‘variational’ principle.”

“And there are more of these variational principles?”

He nodded. “In all branches of physics. Almost every physical law can be restated as a variational principle. The only difference between these principles is in which attribute is minimized or maximized.” He gestured as if the different branches of physics were arrayed before him on a table. “In optics, where Fermat’s Principle applies, time is the attribute that has to be an extreme. In mechanics, it’s a different attribute. In electromagnetism, it’s something else again. But all these principles are similar mathematically.”

“So once you get their mathematical description of Fermat’s Principle, you should be able to decode the other ones.”

“God, I hope so. I think this is the wedge that we’ve been looking for, the one that cracks open their formulation of physics. This calls for a celebration.” He stopped his pacing and turned to me. “Hey, Louise, want to go out for dinner? My treat.”

I was mildly surprised. “Sure,” I said.

It’ll be when you first learn to walk that I get daily demonstrations of the asymmetry in our relationship. You’ll be incessantly running off somewhere, and each time you walk into a door frame or scrape your knee, the pain feels like it’s my own. It’ll be like growing an errant limb, an extension of myself whose sensory nerves report pain just fine, but whose motor nerves don’t convey my commands at all. It’s so unfair: I’m going to give birth to an animated voodoo doll of myself. I didn’t see this in the contract when I signed up. Was this part of the deal?