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“My point is this: their motive might not be to trade, but that doesn’t mean that we cannot conduct trade. We simply need to know why they’re here, and what we have that they want. Once we have that information, we can begin trade negotiations.

“I should emphasize that our relationship with the heptapods need not be adversarial. This is not a situation where every gain on their part is a loss on ours, or vice versa. If we handle ourselves correctly, both we and the heptapods can come out winners.”

“You mean it’s a non-zero-sum game?” Gary said in mock incredulity. “Oh my gosh.”

* * *

“A non-zero-sum game.”

“What?” You’ll reverse course, heading back from your bedroom.

“When both sides can win: I just remembered, it’s called a non-zero-sum game.”

“That’s it!” you’ll say, writing it down on your notebook. “Thanks, Mom!”

“I guess I knew it after all,” I’ll say. “All those years with your father, some of it must have rubbed off.”

“I knew you’d know it,” you’ll say. You’ll give me a sudden, brief hug, and your hair will smell of apples. “You’re the best.”

* * *

“Louise?”

“Hmm? Sorry, I was distracted. What did you say?”

“I said, what do you think about our Mr. Hossner here?”

“I prefer not to.”

“I’ve tried that myself: ignoring the government, seeing if it would go away. It hasn’t.”

As evidence of Gary’s assertion, Hossner kept blathering: “Your immediate task is to think back on what you’ve learned. Look for anything that might help us. Has there been any indication of what the heptapods want? Of what they value?”

“Gee, it never occurred to us to look for things like that,” I said. “We’ll get right on it, sir.”

“The sad thing is, that’s just what we’ll have to do,” said Gary.

“Are there any questions?” asked Hossner.

Burghart, the linguist at the Ft. Worth looking glass, spoke up. “We’ve been through this with the heptapods many times. They maintain that they’re here to observe, and they maintain that information is not tradable.”

“So they would have us believe,” said Hossner. “But consider: how could that be true? I know that the heptapods have occasionally stopped talking to us for brief periods. That may be a tactical maneuver on their part. If we were to stop talking to them tomorrow—”

“Wake me up if he says something interesting,” said Gary.

“I was just going to ask you to do the same for me.”

* * *

That day when Gary first explained Fermat’s Principle to me, he had mentioned that almost every physical law could be stated as a variational principle. Yet when humans thought about physical laws, they preferred to work with them in their causal formulation. I could understand that: the physical attributes that humans found intuitive, like kinetic energy or acceleration, were all properties of an object at a given moment in time. And these were conducive to a chronological, causal interpretation of events: one moment growing out of another, causes and effects created a chain reaction that grew from past to future.

In contrast, the physical attributes that the heptapods found intuitive, like “action” or those other things defined by integrals, were meaningful only over a period of time. And these were conducive to a teleological interpretation of events: by viewing events over a period of time, one recognized that there was a requirement that had to be satisfied, a goal of minimizing or maximizing. And one had to know the initial and final states to meet that goal; one needed knowledge of the effects before the causes could be initiated.

I was growing to understand that, too.

* * *

“Why?” you’ll ask again. You’ll be three.

“Because it’s your bedtime,” I’ll say again. We’ll have gotten as far as getting you bathed and into your jammies, but no further than that.

“But I’m not sleepy,” you’ll whine. You’ll be standing at the bookshelf, pulling down a video to watch: your latest diversionary tactic to keep away from your bedroom.

“It doesn’t matter: you still have to go to bed.”

“But why?”

“Because I’m the mom and I said so.”

I’m actually going to say that, aren’t I? God, somebody please shoot me.

I’ll pick you up and carry you under my arm to your bed, you wailing piteously all the while, but my sole concern will be my own distress. All those vows made in childhood that I would give reasonable answers when I became a parent, that I would treat my own child as an intelligent, thinking individual, all for naught: I’m going to turn into my mother. I can fight it as much as I want, but there’ll be no stopping my slide down that long, dreadful slope.

* * *

Was it actually possible to know the future? Not simply to guess at it; was it possible to know what was going to happen, with absolute certainty and in specific detail? Gary once told me that the fundamental laws of physics were time-symmetric, that there was no physical difference between past and future. Given that, some might say, “yes, theoretically.” But speaking more concretely, most would answer “no,” because of free will.

I liked to imagine the objection as a Borgesian fabulation: consider a person standing before the Book of Ages, the chronicle that records every event, past and future. Even though the text has been photoreduced from the full-sized edition, the volume is enormous. With magnifier in hand, she flips through the tissue- thin leaves until she locates the story of her life. She finds the passage that describes her flipping through the Book of Ages, and she skips to the next column, where it details what she’ll be doing later in the day: acting on information she’s read in the Book, she’ll bet $100 on the racehorse Devil May Care and win twenty times that much.

The thought of doing just that had crossed her mind, but being a contrary sort, she now resolves to refrain from betting on the ponies altogether.

There’s the rub. The Book of Ages cannot be wrong; this scenario is based on the premise that a person is given knowledge of the actual future, not of some possible future. If this were Greek myth, circumstances would conspire to make her enact her fate despite her best efforts, but prophecies in myth are notoriously vague; the Book of Ages is quite specific, and there’s no way she can be forced to bet on a racehorse in the manner specified. The result is a contradiction: the Book of Ages must be right, by definition; yet no matter what the Book says she’ll do, she can choose to do otherwise. How can these two facts be reconciled?

They can’t be, was the common answer. A volume like the Book of Ages is a logical impossibility, for the precise reason that its existence would result in the above contradiction. Or, to be generous, some might say that the Book of Ages could exist, as long as it wasn’t accessible to readers: that volume is housed in a special collection, and no one has viewing privileges.

The existence of free will meant that we couldn’t know the future. And we knew free will existed because we had direct experience of it. Volition was an intrinsic part of consciousness.

Or was it? What if the experience of knowing the future changed a person? What if it evoked a sense of urgency, a sense of obligation to act precisely as she knew she would?

* * *

I stopped by Gary’s office before leaving for the day. “I’m calling it quits. Did you want to grab something to eat?”

“Sure, just wait a second,” he said. He shut down his computer and gathered some papers together. Then he looked up at me. “Hey, want to come to my place for dinner tonight? I’ll cook.”