Cordelia was looking dazed, left behind. Vikram ducked out from the clutter he'd created, leaving the rest of them to try to make sense of it. He took Cordelia's hands and they waltzed across the scape together. "The central mystery of quantum mechanics has always been: why can't you just count the ways things can happen? Why do you have to a.s.sign each alternative a phase, so they can cancel as well as reinforce each other? We knew the rules for doing it, we knew the consequences - but we had no idea what phases were, or where they came from." He stopped dancing, and conjured up a stack of Feynman diagrams, five alternatives for the same process, layered one on top of the other. "They're created the same way as every other relationship: common links to a larger network." He added a few hundred virtual particles, crisscrossing between the once-separate diagrams. "It's like spin. If the networks have created directions in s.p.a.ce that make two particles' spins parallel, when they combine they'll simply add together. If they're anti-parallel, in opposing directions, they'll cancel. Phase is the same, but it acts like an angle in two dimensions, and it works with every quantum number together: spin, charge, colour, everything - if two components are perfectly out-of-phase, they vanish completely."

Gisela watched as Cordelia reached into the layered diagram, followed the paths of two components, and began to understand. They hadn't discovered any deeper structure to the individual quantum numbers, as they'd hoped they might, but they'd learnt that a single vast network of world lines could account for everything the universe built from those indivisible threads.

Was this enough for her? Her original, struggling for sanity back in Athena, might take comfort from the hope that the Dive clone had witnessed a breakthrough like this - but as death approached, would it all turn to ashes for the witness? Gisela felt a pang of doubt herself, though she'd talked it through with Timon and the others for centuries. Did everything she felt at this moment lose all meaning, just because there was no chance to carry the experience back to the wider world? She couldn't deny that it would have been better to know that she could reconnect with her other selves, tell all her distant family and friends what she'd learnt, follow through the implications for millennia.

But the whole universe faced the same fate. Time was quantised; there was no prospect of infinite computation before the Big Crunch, for anyone. If everything that ended was void, the Dive had merely spared them the prolonged false hope of immortality. If every moment stood alone, complete in itself, then nothing could rob them of their happiness.

The truth, of course, lay somewhere in between.

Timon approached her, grinning with delight. "What are you pondering here by yourself?"

She took his hand. "Small networks."

Cordelia said to Vikram, "Now that you know precisely what phase is, and how it determines probabilities ... is there any way we could use the experimental beams to manipulate the probabilities for the geometry ahead of us? Twist back the light cones just enough to keep us skirting the Planck region? Spiral back up around the singularity for a few billion years, until the Big Crunch comes, or the hole evaporates from Hawking radiation?"

Vikram looked stunned for a moment, then he began launching software. Sachio and Tiet came and helped him, searching for computational shortcuts. Gisela looked on, light-headed, hardly daring to hope. To examine every possibility might take more time than they had, but then Tiet found a way to test whole cla.s.ses of networks in a single calculation, and the process sped up a thousandfold.

Vikram announced the result sadly. "No. It's not possible."

Cordelia smiled. "That's all right. I was just curious."