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now is to accept the women’s famine. That works well enough, so why not let it be?
    “Let me try this,” Carlo pleaded. If he had no other choice he could work on his own, but everything would be easier with the support of his former mentor and his team. “What’s the worst that can happen? We learn something useless about the reproductive cycle in voles?”
    Tosco said, “The worst thing would be if the harvest fails, and you start wishing you’d persisted with your last career. But if you really believe you have the patience to carry this through—”
    “I’m certain of that,” Carlo insisted.
    Tosco looked skeptical, but he was done with arguing. He said, “How can I turn down an agronomist who’s willing to step off his pedestal and rejoin his old friends?”

    It was Carlo’s turn to travel down the axis, to meet his co in the new home she’d made for herself. Most of his friends had told him that a partial separation sounded like the worst of both worlds, but he’d studied the numbers from the last census. Total separation was a bad idea: it left women at an elevated risk of spontaneous fission, and no amount of holin could eliminate that entirely. But living together and relying on willpower alone to delay reproduction was even worse; more than half the recorded births in those circumstances had come earlier than planned. The trick was to let your co’s body know that you hadn’t abandoned her—that if it waited, her children would be cared for—while doing all you could to minimize the risk of delivering on that promise prematurely.
    Carla wasn’t home when he arrived at the apartment. The moss-light was enough for him to see his way around, so he didn’t light a lamp. He’d brought four loaves for them to share, for the evening meal and breakfast; he packed them away in the empty cupboard.
    Passing the entrance to the bedroom, he saw a spare tarpaulin floating in the air, suspended against the weak gravity by a faint updraft from a cooling vent.
    When he heard the guide rope twanging in the corridor he went to the doorway and parted the curtains. Carla saw him and chirped excitedly. “Get ready to hear some good news,” she said.
    “What—you’ve won a place on the Gnat ?”
    “That would be something.” She followed him back into the apartment. “But this is better.”
    Carlo lit a lamp in the front room, then clung to the rope beside her as she described her tarnishing experiment. She’d had to refresh his hazy memories of Nereo’s force and Yalda’s puzzles countless times before, so he knew she’d forgive him if he didn’t immediately grasp the significance of the results.
    “Five to four,” he said. “What’s so special about that?”
    “A ratio of small integers isn’t likely to be a coincidence,” Carla replied. “If it was dozens and something to dozens and something else, that would be meaningless, but this suggests very strongly that the numbers in the ratio really are lurking in the physics itself. Four of something, then five of something… the transitions mark a kind of succession.”
    Carlo could only understand physics by translating it into geometry; he started raising undulating lines on his chest. “So can I draw it like this, fitting different numbers of cycles into the same amount of time?”

    “No, no, no!” Carla chided him. “You’ve got it backward!”
    “What’s wrong?” he asked. “Doesn’t that give a five to four frequency ratio?”
    “It does,” she conceded. “But I’m working on the assumption that the frequency goes down as the associated integer goes up, and you’ve described the opposite trend. Going your way, there’d be another transition at a higher frequency—‘frequency six’, out in the infrared—beyond which mirrors would start tarnishing at an even greater rate. The trouble with that is, if the pattern in tarnishing rates held up then Marzio’s mirrors would have needed re-polishing after a couple of stints,