Easier said than done, with only a rough estimate of the object’s size and mass to work with. But the ship calculated a cone of possible trajectories and matched it against the other objects it had monitored, then superimposed the likely paths. The result was inconclusive, but Turk saw what I saw: the most likely trajectories all intersected at the Arch of the Hypotheticals.

“What’s that mean?” Turk asked.

I didn’t know. But the sun was coming up and the nearest leg of the Arch would soon be visible from where we hovered. Turk aimed the window so we could see it.

The Arch of the Hypotheticals had been and would forever be the largest artificial structure ever to contact the surface of the Earth. Its apex was higher than the atmosphere and the base of it was embedded deep in the planet’s mantle. It straddled the Indian Ocean like a wedding band dropped edge-up into a shallow pond. The fraction of it we could see from where we circled above the clouds looked like a silver thread laced into the yellow fabric of the dawn. “Focus on the peak of it,” I told Turk, “and amplify the image.”

He struggled with the interface but eventually succeeded. Because he had configured the display as a window, we seemed to zoom suddenly and dangerously close to the upper reaches of the Arch. The image wavered, distorted by the intervening atmosphere; then the one-dimensional thread acquired width and became a ribbon. In reality it was many miles wide.

The most detailed telescopic images of the Arch, beginning back in Turk’s day, had never revealed even the slightest imperfection in its surface. Until now. Now the ribbon was visibly flawed. The smoothly curving edge of it was ragged and sawtoothed. “Amplify it another times-ten,” I said, though we were approaching the limits of the aircraft’s optical functions.

Another vertiginous leap forward. The image writhed and twisted until the ship applied corrective algorithms.

And I gasped. The Arch was worse than merely imperfect. Visible cracks ran across it. There were gaps where immense pieces of it had calved away.

That was what had been coming out the sky: pieces of the Arch the size of small islands, some of them moving at only a little less than orbital velocity, burning on re-entry and spending their enormous kinetic energy in the Earth’s dead oceans or on its lifeless continents.

It should have been impossible. But it happened again as we watched. A dark crack widened and expanded and intersected another, and suddenly a piece of the Arch separated and began to fall. It moved with the elephantine grace of its own inertia, and I guessed it might circle the planet a couple more times before it began its final burn and tumble.