“The basic CTC program has three steps. When the processor starts, the first step is to check the time register. If a signal has been received—if the solution to the problem is already in memory—then stop. If not, we go to step two, which says to carry out the calculation by brute force, however long it takes. When the answer is finally derived, we go to step three: go back in time, deliver the solution and mark the time register.”

Luru nodded. “So the timeline is redrafted. In the first draft timeline, the problem is solved by brute force. In the final version of the timeline, the answer is sent back through time to the moment when the question is posed. So it isn’t necessary to run the computation at all.”

“That’s correct.”

Luru sighed. “The joy of time-travel paradoxes. You can get the answer to a problem without needing to work it out! But there must be a good deal more to your design. Your closed-timelike-curves must be pretty short.”

“Actually just milliseconds.”

“Surely you can solve no problem which would take longer to solve than that length of time.”

Torec smiled, her confidence growing. “No. By breaking a problem down into pieces you can solve anything.” She described how the problem was broken up into a hierarchy of nested subcomponents. At the base level were calculations so trivial they could be handled within the processor’s short CTC periods. The answers were passed back in time to become the input for the next run-through, and so on. That way an answer was assembled piece by piece and looped back repeatedly to the zero instant, until the overall problem was resolved. “The technical challenge is actually decomposing the problem in the first place, and controlling the information flow back up the line,” she said.

Luru laughed, an odd, hollow sound. “You’re computing with multiple time loops, and you think that’s the only challenge? Ensign, you’re a true pragmatist. . . . I think it’s nearly time.”

Over the glittering, much-patched array of the prototype processor, the bots hovered, utterly motionless against the greater lunar stillness. Behind the prototype, the blank Virtual screen hovered, waiting to display the solution.

The last seconds wore away.

And at zero, the screen filled with a molecular diagram. Just like that, with no time elapsed. It was almost anticlimactic, Torec thought.

There was utter silence on the common loops; nobody moved, none of the techs or the observers from the Navy or the Ministry, not even a bot. But on the screen the diagram whirled, as it was ferociously analyzed for verification. After ten seconds, the screen turned green, and numerical results scrolled over its surface.

Torec didn’t need the details, nor would she have understood them; she just knew what that green color meant. “Lethe,” she whispered. “We did it.”

There was a howling. She turned and saw Commissary Nilis capering barefoot on the surface of the Moon. Some transmission glitch was pixellating his image, and his voice sounded feathery, remote.