We passed through a domain of libraries. The books were densely packed, and, as you see in some academic archives, the shelf units ran on rails: in a whole room there would be only enough space for a single passageway between a pair of shelves, and you would have to turn a little handle to make the shelves roll back and forth until you got the access you wanted. There was a lot of material. Farther on there were rooms more like museum departments, which contained what looked like extremely ancient manuscripts, scrolls and clay tablets, all held in air-conditioned isolation and low light, many of them in the drawers of glass-topped cabinets.

This area was the scrinium, said Rosa, the Order’s term for the monumental internal record center that had now been turned outward to fuel the Internet genealogy business. Rosa showed me cabinets full of somewhat dog-eared index cards. There was so much material, she said, that even the indices had an index. We passed a computer center, where great mainframes hummed behind sealed windows. I got a fresh sense of the power and wealth of this place.

Before we left the scrinium Rosa gave me a small hardback book. It turned out to be the story of Regina, our Roman British ancestress—“A more complete biography than of anyone else in the ancient world, even the Caesars,” Rosa said. “Bedtime reading.”

A little farther on, to my surprise, we came to classrooms, where children, mostly girls, sat in neat rows, or worked in groups at desks, or labored over baffling-looking experiments in a science.

Rosa told me that few of these pupils belonged to the Order. Offering quality education to outsiders had been the Order’s earliest significant money earner—earliest in the Order’s terms, I learned, meaning ‘fifth century after Christ.’ She said they even had accounting records that went back that far, though the earliest entries were of limited use: they predated the invention of the double-entry bookkeeping system by the best part of a millennium.

“How inconvenient,” I murmured.

In one place there was even a small theater, where a group of young teenagers was rehearsing a play.

Schools. A theater. A play. And all of this, remember, dug deep into the ground below four levels of Catacombs.

Again we walked on.

In that first visit I didn’t even come close to figuring out the geography of the Crypt. The place isn’t designed to give you long vistas and perspectives anyhow; it’s designed to disorient, to make you forget where you are.