“Not understand,” he said in his minimalist way.

She flicked a command into her voicewriter and said, “Think of a sentence like this one, only the parts don’t relate in a straight-line sequence.” Her voicewriter noted this down as she spoke. “So my previous sentence could read,” she said, adjusting the voicewriter screen again to redeploy the sentence, “Parts straight-line sequence sentence, one that doesn’t previous relate like.”

A trick, but it worked. He stared at the screen. “Ah, I… think I see. To unwrap the above line and make sense of it, you need a mapping function. Noun, veerb, object—”

She nodded, wondering what her smart systems would make of veerb, a pronunciation nuance. “Now expand that idea to whole paragraphs, and then to whole idea groups. The weave of them would be complex, and would not convey a simple logic.”

He blinked. “Ah.”

“There are various conventions about how to represent numbers—for example, least significant digit first versus most significant digit first—and remember, aliens won’t know that U+FFFE is a guaranteed nonassigned codepoint.”

He looked disgusted. “What?”

“Maybe I’m more of a nerd than I know. Anyway, what the ‘natural’ order is to represent a sequence, whether signal-on represents one or zero—if, say, we restrict our aliens to binary—nobody knows. Mathematics may be universal, but transmittable representations are not.”

“But binary has own logic.” He spread his hands, as if this was obvious. And of course, it was. Zero and one, you needed no more.

“You know more trans-group math than you let on,” she said, in what she hoped was a nerdy, coy tone.

“I never show all my cards.” He grinned, and launched into a little song:

“A problem worthy of attack

Proves its worth by fighting back.”

“Sounds like a march,” she said.

“Was trying for ‘Battle Hymn of the Republic.’ ” A sly grin. “Grandiose.”

“Look, becoming a SETI Librarian for the money and the fame is like becoming a Jesuit for the kinky sex. I know that.”

“Ambition is good,” he said enigmatically.

She decided to bring up a dicey issue. “Look, I’ve seen your background. Damned impressive. Why be here, when you could do so much elsewhere?”

To her surprise he sprang to his feet—overshooting, springing a meter high in the low grav. Coming down, he paced back and forth, face a clown mask of bright-eyed wonder. “Why didn’t I think of that? Here I am, yes?—wasting my golden years on this dangerous dustball, all messed up with mysterious smart plants? When I could, with just a little thought, be seeking and striving! Putting my shoulder to the wheel—or is it my face to the grindstone?—for betterment! Plus that of all mankind. I’ll bet I could write a billion bucks a year in overscale insurance on asteroid shipments. Pull a big oar in the flagship of life! Exercise impressive skill set. Or wait, maybe it isn’t too late—do you think? I could race back Earthside, find the little woman, get in with MegaCorp or Solaristics, go to executive lunches, nod soberly at board meetings, make money while I sleep! Why, the opportunities—thanks so much for finally pointing me in right direction!”