[Question] 1 [belongs to] [prime numbers]

[Answer 1] [correct] [good]

[Answer 2] [incorrect] [good]

[Answer 3] [delta]

"Again, that’s gibberish," he said. "One either is or isn’t prime. And, well, it is, isn’t it? I mean, a prime is a number that’s only evenly divisible by itself or one, right?"

"Is that what they taught you at Humberside Collegiate? We used to define one as a prime; you’ll see it called such in some old math books. But these days, we don’t.

Primes are generally thought of as numbers that have precisely two whole-number factors, themselves and one. One has only one whole-number factor, and so isn’t a prime."

"Seems rather arbitrary," said Don.

"You’re right. It is a debatable point. One is definitely an odd-ball as primes go. And two — well, it’s not an odd-ball; it’s an even-ball. That is, it’s the only even prime number. You could just as arbitrarily define the set of primes as all odd numbers that have precisely two whole-number factors. If you did it that way, then two isn’t a prime."

"Ah."

"See? That’s what they’re conveying. Delta is a symbol that means, I think, ‘It’s a matter of opinion.’ Neither answer is wrong ; it’s just a matter of personal preference, see?"

"That’s fascinating."

She nodded. "Now, the next part of the message is really interesting. Elsewhere, they established symbols for ‘sender’ and ‘recipient’ — or ‘me,’ the person sending the message, and ‘you,’ the person receiving it."

"Okay."

"And with those," said Sarah, "they get down to the nitty gritty. Look at this." Her display changed:

[Question] [good] : [bad]

[Answer] [sender] [opinion] [good] ›› [bad]

"See? The question is, what’s the relationship between good and bad. And the response from the sender, who had said previously, when discussing factual matters, that good is the opposite of bad, now says something quite a bit more interesting: good is much greater than bad — a significant philosophical statement."

" ‘Does not your sacred book promise that good is stronger than evil?’ "

Sarah felt her eyes go wide. "You’re quoting the Bible?"

"Um, actually, no. That’s Star Trek. Second season, ‘The Omega Glory.’ " He shrugged sheepishly. " ‘Yes, it is written: good shall always destroy evil.’ "

Sarah shook her head in loving despair. "You’ll be the death of me yet, Donald Halifax."

"McGavin Robotics," said a crisp, efficient female voice. "Office of the president."

For once, Don wished he did have a picture phone; for all he knew, he was talking to a robot. "I’d like to speak to Cody McGavin, please."

"Mr. McGavin is unavailable. May I ask who’s calling?"

"Yes. My name is Donald Halifax."

"May I ask what this is about?"

"I’m the husband of Sarah Halifax."

"Ah, yes. The SETI researcher, no?"

"That’s right."

"What can I do for you, Mr. Halifax?"

"I need to talk to Mr. McGavin."

"As you might imagine, Mr. McGavin’s schedule is very full. Perhaps there’s something I can help you with?"

Don sighed, beginning to get it. "How many layers deep am I?"

"I’m sorry?"

"How many layers between you and McGavin? If I give you a message, and you decide it’s worth passing on, it doesn’t go to McGavin, does it?"

"Not normally, no. I’m the receptionist for the president’s office."

"And your name is?"

"Ms. Hashimoto."

"And who do you report to?"

"Mr. Harse, who is the secretary to Mr. McGavin’s secretary."

"So I have to get through you, then the secretary’s secretary, then the secretary, before I get to McGavin, is that right?"

"We do have to follow procedures, sir. I’m sure you understand that. But of course things can be escalated quickly, if appropriate. Now, if you’ll just tell me what you need…?"

Don took a deep breath, then let it out. "Mr. McGavin paid for my wife and me to undergo rejuvenation treatments — you know, rollbacks. But it hasn’t worked for my wife, only for me. The doctor from Rejuvenex says nothing can be done, but maybe if she had a request directly from Mr. McGavin. Money talks. I know that. If he indicated he was dissatisfied, I’m sure—"

"Mr. McGavin has had a full report on this."

"Please," Don said. "Please, my wife… my wife is going to die."

Silence. His words were probably more brutally honest than the receptionist to the secretary to the secretary to the president was used to hearing.

"I am sorry," Ms. Hashimoto said with what sounded like genuine regret.

"Please," he said again. "Surely whatever report he’s seen came from Rejuvenex, and they’ve doubtless put a spin on it. I want him to understand what we — what Sarah — is going through."

"I’ll let him know you called."

No, you won’t, he thought, you’ll just pass it on to the next layer. "If I could just talk to Mr. McGavin, just for a minute. I just…" He hadn’t begged for anything for decades — not since…

It hit him, just then. It hit him like a sucker punch to the gut.

Forty-five years ago. The oncology ward at Princess Margaret. Dr. Gottlieb talking about experimental therapies, about things that were new and untested.

And Don begging her to try them on Sarah, to try anything that might save her. The details were lost to time, but he did now recall the interferon treatment, not approved for use in the States. Gottlieb might have agreed to try it because of his begging, his insistent demands that she do everything that might help.

The experimental treatment had failed. But now, four decades on, its lingering effects were blocking another treatment, all — he swallowed hard — because of him.

"Mr. Halifax?" said Ms. Hashimoto. "Are you still there?"

Yes, he thought. Yes, I’m still here. And I’ll still be here for years to come, long after Sarah’s gone. "Yes."

"I do understand that you’re upset, and, believe me, my heart goes out to you. I’ll flag this double-red. That’s the best I can do. Hopefully someone will get back to you shortly."

Just as he had all those many years ago, when Sarah had been trying to translate the first Dracon message, Don stopped by from time to time to see how she was faring with decrypting the current one. But instead of working at the university, she was struggling with this one in the study — the upstairs room that had once been Carl’s.

The Dracons’ original message, the one picked up in 2009, had been divided into two parts: a primer, explaining the symbolic language they were using, and the meat of the message — the MOM, as it rapidly came to be known — which used those symbols in baffling ways. But eventually Sarah had figured out the purpose of the MOM, and a reply had been sent.

This second message from the aliens also had two parts. But in this case, the beginning was the explanation of how to decrypt the rest, assuming the right decryption key could be provided, and the rest, well, that was anybody’s guess.

Because it was encrypted, not even a single symbol that had been established in the original message was visible in the second part of this one.

"Maybe the aliens are responding to one of the unofficial responses," Don said, late one evening, leaning against the study’s doorway, hands crossed in front of his chest. "I mean, even before you sent the official reply, didn’t thousands of people send their own unofficial responses to the Dracons?"

Sarah looked ancient, almost ghostly, in the glow from her magphotic monitor, her thin white hair backlit from his perspective. "Yes, they did," she said.