‘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?
And then there will be the times when I see you laughing. Like the time you’ll be playing with the neighbor’s puppy, poking your hands through the chain-link fence separating our back yards, and you’ll be laughing so hard you’ll start hiccuping. The puppy will run inside the neighbor’s house, and your laughter will gradually subside, letting you catch your breath. Then the puppy will come back to the fence to lick your fingers again, and you’ll shriek and start laughing again. It will be the most wonderful sound I could ever imagine, a sound that makes me feel like a fountain, or a wellspring.
Now if only I can remember that sound the next time your blithe disregard for self-preservation gives me a heart attack.
After the breakthrough with Fermat’s principle, discussions of scientific concepts became more fruitful. It wasn’t as if all of heptapod physics were suddenly rendered transparent, but progress was steady. According to Gary, the heptapods’ formulation of physics was indeed topsy-turvy relative to ours. Physical attributes that humans defined using integral calculus were seen as fundamental by the heptapods. As an example, Gary described an attribute that, in physics jargon, bore the deceptively simple name ‘action,’ which represented ‘the difference between kinetic and potential energy, integrated over time,’ whatever that meant. Calculus for us; elementary to them.
Conversely, to define attributes that humans thought of as fundamental, like velocity, the heptapods employed mathematics that were, Gary assured me, ‘highly weird.’ The physicists were ultimately able to prove the equivalence of heptapod mathematics and human mathematics; even though their approaches were almost the reverse of one another, both were systems for describing the same physical universe.
I tried following some of the equations that the physicists were coming up with, but it was no use. I couldn’t really grasp the significance of physical attributes like ‘action’; I couldn’t, with any confidence, ponder the significance of treating such an attribute as fundamental. Still, I tried to ponder questions formulated in terms more familiar to me: what kind of worldview did the heptapods have, that they would consider Fermat’s principle the simplest explanation of light refraction? What kind of perception made a minimum or maximum readily apparent to them?
Your eyes will be blue like your dad’s, not mud brown like mine. Boys will stare into those eyes the way I did, and do, into your dad’s, surprised and enchanted, as I was and am, to find them in combination with black hair. You will have many suitors.
I remember when you are fifteen, coming home after a weekend at your dad’s, incredulous over the interrogation he’ll have put you through regarding the boy you’re currently dating. You’ll sprawl on the sofa, recounting your dad’s latest breach of common sense: ‘You know what he said? He said, “I know what teenage boys are like.”’ Roll of the eyes. ‘Like I don’t?’
‘Don’t hold it against him,’ I’ll say. ‘He’s a father; he can’t help it.’ Having seen you interact with your friends, I won’t worry much about a boy taking advantage of you; if anything, the opposite will be more likely. I’ll worry about that.
‘He wishes I were still a kid. He hasn’t known how to act toward me since I grew breasts.’
‘Well, that development was a shock for him. Give him time to recover.’
‘It’s been years, Mom. How long is it gonna take?’
‘I’ll let you know when my father has come to terms with mine.’
During one of the videoconferences for the linguists, Cisneros from the Massachusetts looking glass had raised an interesting question: Was there a particular order in which semagrams were written in a Heptapod B sentence? It was clear that word order meant next to nothing when speaking in Heptapod A; when asked to repeat what it had just said, a heptapod would likely as not use a different word order unless we specifically asked them not to. Was word order similarly unimportant when writing in Heptapod B?
Previously, we had focused our attention only on how a sentence in Heptapod B looked once it was complete. As far as anyone could tell, there was no preferred order when reading the semagrams in a sentence; you could start almost anywhere in the nest, then follow the branching clauses until you’d read the whole thing. But that was reading; was the same true about writing?
During my most recent session with Flapper and Raspberry I had asked them if, instead of displaying a semagram only after it was completed, they could show it to us while it was being written. They had agreed. I inserted the videotape of the session into the VCR, and on my computer I consulted the session transcript.
I picked one of the longer utterances from the conversation. What Flapper had said was that the heptapods’ planet had two moons, one significantly larger than the other; the three primary constituents of the planet’s atmosphere were nitrogen, argon, and oxygen; and 15/28ths of the planet’s surface was covered by water. The first words of the spoken utterance translated literally as ‘inequality-of-size rocky-orbiter rocky-orbiters related-as-primary-to-secondary.’
Then I rewound the videotape until the time signature matched the one in the transcription. I started playing the tape, and watched the web of semagrams being spun out of inky spider’s silk. I rewound it and played it several times. Finally I froze the video right after the first stroke was completed and before the second one was begun; all that was visible on-screen was a single sinuous line.
Comparing that initial stroke with the completed sentence, I realized that the stroke participated in several different clauses of the message. It began in the semagram for ‘oxygen,’ as the determinant that distinguished it from certain other elements; then it slid down to become the morpheme of comparison in the description of the two moons’ sizes; and lastly it flared out as the arched backbone of the semagram for ‘ocean.’ Yet this stroke was a single continuous line, and it was the first one that Flapper wrote. That meant the heptapod had to know how the entire sentence would be laid out before it could write the very first stroke.