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With Heptapod B, I was experiencing something just as foreign: my thoughts were becoming graphically coded. There were trance-like moments during the day when my thoughts weren’t expressed with my internal voice; instead, I saw semagrams with my mind’s eye, sprouting like frost on a windowpane.

As I grew more fluent, semagraphic designs would appear fully formed, articulating even complex ideas all at once. My thought processes weren’t moving any faster as a result, though. Instead of racing forward, my mind hung balanced on the symmetry underlying the semagrams. The semagrams seemed to be something more than language; they were almost like mandalas. I found myself in a meditative state, contemplating the way in which premises and conclusions were interchangeable. There was no direction inherent in the way propositions were connected, no ‘train of thought’ moving along a particular route; all the components in an act of reasoning were equally powerful, all having identical precedence.

A representative from the State Department named Hossner had the job of briefing the U.S. scientists on our agenda with the heptapods. We sat in the videoconference room, listening to him lecture. Our microphone was turned off, so Gary and I could exchange comments without interrupting Hossner. As we listened, I worried that Gary might harm his vision, rolling his eyes so often.

‘They must have had some reason for coming all this way,’ said the diplomat, his voice tinny through the speakers. ‘It does not look like their reason was conquest, thank God. But if that’s not the reason, what is? Are they prospectors? Anthropologists? Missionaries? Whatever their motives, there must be something we can offer them. Maybe it’s mineral rights to our solar system. Maybe it’s information about ourselves. Maybe it’s the right to deliver sermons to our populations. But we can be sure that there’s something.

‘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 creating 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.