The upper reaches of this tower—the place where it devolved into piers and pinnacles, the highest part, in other words, that you could get to without ladders and mountaineering equipment—was at about the same altitude as the Warden Regulant’s headquarters. It sported one of the most elaborate works of stone-carving in the whole concent, a sort of cupola/tower/walk-through statue depicting planets and moons and some of the early cosmographers who had studied them. Built into the middle of this was a portcullis: a grid of bars that could be cranked up and down. At the moment, it had been drawn up out of the way, giving us the freedom to attack yet another stair. This one was cut right into the top of a flying buttress. It would take us up and inwards to the Præsidium. If the portcullis had been closed, we’d have had nowhere else to go, unless we wanted to cross over a sort of bridge into the Warden Regulant’s quarters.

Cord and I passed through the cupola, moving slowly so that she could take in the carvings and the mechanism. Then we were on our way up. I let her go ahead of me so that she could get an unobstructed view, and so that I could steady her if she got dizzy. For we were high above the ground here, climbing over the curve of a stone buttress that seemed about as thick as a bird’s bone when you looked at it from the ground. She gripped the iron banisters with both hands and took it slowly and seemed to enjoy it. Then we passed through an embrasure (sort of a deep complicated Mathic archway), built into the corner of the Praesidium at about the level of the belfries.

From here there was only one way up: a series of stairs that spiraled up the inside of the Præsidium just within its tracery walls. Few tourists were game for that much climbing, and many of the avout were extramuros, so we had the whole Præsidium to ourselves. I let her enjoy the view down to the chancel floor. The courts of the Wardens, immediately below us, were cloister-shaped, which is to say that each had a big square hole in the middle where the Præsidium shot through it, lined with a walkway with sight-lines down to the chancel and up to the starhenge.

Cord traced the bell-ropes up from the balcony and satisfied herself that they were in fact connected to a carillon. But from here it was obvious that other things too were connected to the bells: shafts and chains leading down from the chronochasm, where automatic mechanisms chimed the hours. It was inevitable that she’d want to see this. Up we went, trudging around like a couple of ants spiraling up a well shaft, pausing now and then to catch our breaths and to give Cord leisure to inspect the clock-work, and to figure out how the stones had been fitted together. This part of the building was much simpler because there was no need to contend with vaults and buttresses, so the architects had really gotten out of hand with the tracery. The walls were a fractal foam of hand-carved, interlocking stone. She was fascinated. I couldn’t stand to look at it. The amount of time I had spent, as a fid, cleaning bird droppings off this stone, and the clock-works inside…

“So, you can’t come up here except during Apert,” she asserted at one point.

“What makes you think that?”

“Well, you’re not allowed to have contact with people outside your math, right? But if you and the One-offs and the Hundreders and Thousanders could all use this stairway any time you wanted, you’d be bumping into each other.”

“Look at how the stairway is designed,” I said. “There’s almost no part of it that we can’t see. So, we just keep our distance from each other.”

“What if it’s dark? Or what if you go to the top and bump into someone at the starhenge?”

“Remember that portcullis we went through?”

“On top of the tower?”

“Yeah. Well, remember there’s three more towers. Each one has a similar portcullis.”

“One for each of the maths?”

“Exactly. During the hours of darkness, all but one of them is closed by the Master of the Keys. That’s a hierarch—a deputy of the Warden Regulant. So on one night, the Tenners might have sole access to the stair and the starhenge. Next night it might be the Hundreders. And so on.”

When we reached the altitude where the Century weight was poised on its rail, we paused for a minute so that Cord could look at it. We also looked out through the tracery of the south wall to the machine hall where she worked. I retraced my morning’s walk, and picked out the house of Jesry’s family on the hill.

Cord was still looking for flaws in our Discipline. “These wardens and so on—”

“Hierarchs,” I said.

“They communicate with all of the maths, I guess?”

“And also with the Ita, and the Sæcular world, and other concents.”

“So, when you talk to one of them—”

“Well, look,” I said, “one of the misconceptions people have is that the maths are supposed to be hermetically sealed. But that was never the idea. The kinds of cases you are asking about are handled by disciplined conduct. We keep our distance from those not of our math. We are silent and hooded when necessary to avoid leakage of information. If we absolutely must communicate with someone in another math, we do it through the hierarchs. And they have all sorts of special training so that they can talk to, say, a Thousander in a way that won’t allow any Sæcular information to pass into his mind. That’s why hierarchs have those outfits, those hairstyles—those literally have not changed in 3700 years. They speak only in a very conservative ancient version of Orth. And we also have ways to communicate without speech. So, for example, if Fraa Orolo wishes to observe a particular star five nights in a row, he’ll explain his plan to the Primate, and if it seems reasonable, the Primate will direct the Master of the Keys to keep our portcullis open those nights but leave all the others closed. All of them are visible from the maths, so the Millenarian cosmographers can look down and see how it is and know that they won’t be using the starhenge tonight. And we can also use the labyrinths between the maths for certain kinds of communication, such as passing objects or people back and forth. But there’s nothing we can do to prevent aerocraft from flying over, or loud music from being heard over the walls. In an earlier age, skyscrapers looked down on us for two centuries!”

That last detail was of interest to Cord. “Did you see those old I-beams stacked in the machine hall?”

“Ah—were those the frames of the skyscrapers?”

“It’s hard to imagine what else they’d be. We have a box of old phototypes showing those things being dragged to our place by teams of slaves.”

“Do the phototypes have date prints?”

“Yeah. They’re from about seven hundred years ago.”

“What does the landscape in the background look like? A ruined city, or—”

She shook her head. “Forest with big trees. In some of those pictures they are rolling the beams over logs.”

“Well, there was a collapse of civilization right around 2800, so it all fits together,” I said.

The chronochasm was laced through with shafts and chains that in some places converged to clock-movements. The chains that led up from the weights terminated up here in clusters of bearings and gears.

Cord had been growingly exasperated by something, and now, finally, she let it out: “This just isn’t the way to do it!”

“Do what?”

“Build a clock that’s supposed to keep going for thousands of years!”

“Why not?”

“Well, just look at all those chains, for one thing! All the pins, the bearing surfaces, the linkages—each one a place where something can break, wear out, get dirty, corrode…what were the designers thinking, anyway?”

“They were thinking that plenty of avout would always be here to maintain it,” I answered. “But I take your point. Some of the other Millennium Clocks are more like what you have in mind: designed so that they can run for millennia with no maintenance at all. It just depends on what sort of statement the designer wanted to make.”