Got some typing time in. There's a lot more to transcribe, though.
Kate
"I am going to make a prediction"
Everyone looked up; this was probably the first time Kate had said something in one of these conferences without being asked a direct question since they had been convened.
"If, from here, we take one transit of half charge, JJ223, AF017, GC504 and follow it with a sixty-three percent AL552, BC087, EF324 we will detect the beacon we left two transitions ago, and I will get a Nobel prize."
"You've solved it?" The captain was up and moving towards her immediately, but his intended hug was thwarted by Penny getting in first.
"No, captain, I have not 'solved it'. I have developed an equation of the fourteenth order that, in certain circumstances allows for a solution. This happens to be one of those circumstances and, if it works out, we will be able to plan our transits so as to remain in them in the future, and always have alternative return paths. Not the great revelation they've been waiting for, but significantly better than nothing. And, obviously, I could be completely wrong."
A thousand races of sheave travellers had sought the philosopher's stone, and her voice betrayed no more excitement than at a medical examination. Surely she must feel something?
"I am essentially defining a plane cutting through a four dimensional overspace, and simplifying our transitions to remain within it. It was fortunate that our two previous transitions were in the same defined plane, so I worked out two more in the same surface. I predict that this way it will never be possible to return to a point of departure in fewer than four, and no more than twelve transitions without subloops. But we have to do the test first; it could be that my model does not correspond to reality.
Perhaps this dry, analytic tone was the equivalent of excitement for her. She'd already said more words than she normally managed in a total trip, and her voice revealed the tiniest tenuous trace of animation.
"Of course we'll do the test. Even if we weren't searching at random…" there was a cough from the historian, but he didn't contradict the captain "it would be worthwhile, and, as it is, we've got nothing to lose, and a lot to gain."
Penny was prised off, and cheerfully hugged others, squealing "She did it! Special case or not, she did it!" and everyone in the room was congratulating her.
"Easy, easy, must test it first. Is good mathematics but physics less certain." Her accent had thickened; she wasn't used to being the centre of attention in anything but mathematicians' conventions. "Maybe those clowns in Brussels not so stupid after all to say I should travel. But if this works out I can leave and you'll have space for another useful crew member."
"You want to leave?" It was Erik who spoke, but it could have been anyone there "Has anyone been suggesting that you don't pull your weight? If so this should prove to him that he is totally wrong."
"No, everyone has been very good. And I find I like being part of a team, even if the transitions are hard to enjoy. Is probable I would never have come up with this simplification if not actually aboard, if sat at home thinking. Penelope's readings were critical in mapping displacements, even if she don't turn out empirical route map. But once base equation is in computer, Penny can do the calculations well as I; any one can do, computer does work, operator optimises. No need for me, get someone who's good for ship, come and visit when you're home. I get bigger flat, 'nother cat, everyone welcome."
The chorus of "You're a Heinliner", you can't get away that easily", "You'll need us to push you into generating the general solution, otherwise someone else'll get the credit", "No way; you're one of us, now" and other, less coherent messages in the same vein washed over her like warm bathwater, relaxing and comforting.
She'd never been part of a community before; mathematicians don't team up like some other specialities. Most of those here didn't understand a word she'd explained, but they thought of her as one of them. And these were not stupid people; in their own fields they were top, and they thought of her as one of them. Was happy-making feeling, no? So why eyes leaking, why sniffling like first day at school?
They all stood back, slightly embarrassed except for Penny, who regained her role as official hugger. The ice-maiden melted, the machine feels; what more marvels would this trip bring?