Gardan’s Steelyard: A rule of thumb attributed to Fraa Gardan (-1110 to-1063), stating that, when one is comparing two hypotheses, they should be placed on the arms of a metaphorical steelyard (a kind of primitive scale, consisting of an arm free to pivot around a central fulcrum) and preference given to the one that “rises higher,” presumably because it weighs less; the upshot being that simpler, more “lightweight” hypotheses are preferable to those that are “heavier,” i.e., more complex. Also referred to as Saunt Gardan’s Steelyard or simply the Steelyard.

— THE DICTIONARY, 4th edition, A.R. 3000

Very comfortable, as I saw when I came up the steps and pushed the door open (again fighting the sense that I was a trespasser). ROF carpenters had been at work furnishing the stone shell with wooden floors and paneled walls. Actually “cabinet-makers” was a fairer description than “carpenters” for avout who chose woodworking as their avocation, and so the place was all fitted and joined to tolerances that Cord might have envied. It was mostly one great cubical room, ten paces square, and lined with books. To my right a fire burned on a hearth, to my left, clear northern sky-light rushed in through a bay window so large that it formed a sort of alcove, as broad, round, and comfortable as Arsibalt, who sat in the middle of it reading a book so ancient he had to handle the pages with tongs. So he had not seen me tree-climbing after all. I could have slunk away. But now I was glad I hadn’t. It was good to see him here.

“You could be Shuf himself,” I said.

“Ssh,” he commanded, and looked about the place. “People will be cross if you talk that way. Oh, all the orders have their special hideaways. Islands of luxury that must make Saunt Cartas roll over in her chalcedony sarcophagus.”

“Pretty luxurious, that, come to think of it-”

“Come off it, it’s cold as hell in the winter.”

“Hence the expression ‘cold as Cartas’s-’”

“Ssh,” he said again.

“You know, Arsibalt, if the Edharian chapter has a luxurious hideaway, they’ve yet to show it to me.”

“They are the odd ones out,” he said, rolling his eyes. He looked me up and down. “Perhaps when you have attained more seniority-”

“Well, what are you, at the age of nineteen? The FAE of the Reformed Old Faanians?”

“The chapter and I have become most comfortable with each other in, yes, a short time. They support my project.”

“What-reconciling us with the Deolaters?”

“Some of the Reformed Old Faanians even believe in God.”

“Do you, Arsibalt? All right, all right,” I added, for he was getting ready to shush me for a third time. He finally began to move. He took me on a little tour, showing me some of the artifacts of the Dowment’s halcyon days: gold drinking-cups and jeweled book-covers now preserved under glass. I accused his order of having more of the same hidden away somewhere for drinking out of, and he blushed.

Then, as all this discussion of utensils had put him in mind of food, he shelved his book. We left Shuf’s Dowment behind us and began walking back for the midday meal. We had both skipped Provener, a luxury that was possible only because some younger fraas had begun to spell us winding the clock a few days a week.

When we gave up altogether on clock-winding, which would happen in two or three years, each of us would have enough free time to settle on an avocation-something practical that one could do to help improve life at the concent. Between now and then, we had the luxury of trying different things just to see how we liked them.

Fraa Orolo, for example, and his ongoing conversation with the library grape. We were too far north. The grapes were not happy. But we did have a south-facing slope, between the page trees and the outer wall of the concent, where they deigned to grow.

“Beekeeping,” Arsibalt said when I asked him what he was interested in.

I laughed at the image of Arsibalt enveloped in a cloud of bees. “I always thought you’d end up doing indoor work,” I said, “on dead things. I thought you’d be a bookbinder.”

“At this time of year, beekeeping is indoor work on dead things,” he pointed out. “Perhaps when the bees come out of hibernation I won’t favor it so much. How about you, Fraa Erasmas?”

Though Arsibalt didn’t know it, this was a sensitive subject. There was another reason you needed an avocation: so that if you turned out to be incapable of doing anything else, you could give up on books and chalk halls and dialog and work as a sort of laborer for the rest of your life. It was called “falling back.” There were plenty of avout like that, making food, brewing beer, and carving stone, and it was no secret who they were.

“You can pick some funny thing like beekeeping,” I pointed out, “and it’ll never be anything more than an eccentric hobby-because you’ll never need to fall back. Not unless the ROF suddenly recruits a whole lot of geniuses. For me the odds of falling back are a little greater and I need to pick something I could actually do for eighty years without going crazy.”

Arsibalt now blew an opportunity to assure me that I was really smart and that this would never happen. I didn’t mind. After my rough conversation with Tulia six weeks ago I was spending less time agonizing and more time trying to get things accomplished. “There are some opportunities,” I told him, “making the instruments on the starhenge work the way they’re supposed to.”

“Those opportunities would be much brighter if you in fact had access to the starhenge,” he pointed out. It was safe for him to talk this way since we were sloshing through leaves and no one was near us, unless Suur Trestanas was hiding in a leaf pile with a hand cupped to her ear.

I stopped and raised my chin.

“Are you expecting an Inquisitor to fall out of a tree?” Arsibalt asked me.

“No, just looking at it,” I said, referring to the starhenge. From here, on this little rise, we had a good view of it. But nestled as we were in the coppice, we’d be difficult to make out from the Mynster and so I felt comfortable taking a long look. The twin telescopes of Saunts Mithra and Mylax were in the same position where they had rested during the three months or so we’d been locked out: slewed around to aim at the northern sky.

“I was thinking that if Orolo was using the M amp; M to look at something they didn’t want him to see, then we might get some clues from where he pointed it the last day he had access to it. Maybe he even took some pictures that night, yet to be seen.”

“Can you draw any conclusions from where the M amp; M is pointed now?” Arsibalt asked.

“Only that Orolo wanted to look at something above the pole.”

“And what is above the pole? Other than the pole star?”

“That’s just it,” I said. “Nothing.”

“What do you mean? There must be something.”

“But it messes up my hypothesis.”

“What, pray tell, is that? And can you explain it as we walk toward a place that is warm and has food?”

I started moving my feet again, and talked to the back of Arsibalt’s head as I let him break trail through the leaves. “I had been guessing it was a rock.”

“Meaning an asteroid,” he said.

“Yeah. But rocks don’t come over the pole.”

“How can you say such a thing? Don’t they come from all directions?”

“Yeah, but they mostly have low inclinations-they are in the same plane as the planets. So you’d look near the ecliptic, which is what we call that plane.”

“But that is a statistical argument,” he pointed out. “It could simply be an unusual rock.”

“It fails the Steelyard.”

“Saunt Gardan’s Steelyard is a useful guideline. All sorts of real things fail it,” Arsibalt pointed out, “including you and me.”

Orolo sat with us. It was the first time I’d talked to him in ages. He sat where he could gaze out a window at the mountains, in much the same mood as I’d been looking at the starhenge a few minutes earlier. It was a clear day, and the peaks were all standing out, seeming as if they were close enough to throw stones at. “I wonder what the seeing will be like tonight on top of Bly’s Butte,” he sighed. “Better than here, anyway!”

“Is that the one where the slines ate Saunt Bly’s liver?” I asked.

“The same.”

“Is that around here? I thought it was on another continent or something.”

“Oh no. Bly was a Saunt Edhar man! You can look it up in the Chronicle-we have all of his relics salted away somewhere.”

“Do you really mean to suggest that there’s an observatory there? Or are you just pulling my leg?”

Orolo shrugged. “I’ve no idea. Estemard built a telescope there, after he renounced his vow and stormed out the Day Gate.”

“And Estemard is-”

“One of my two teachers.”

“Paphlagon being the other?”

“Yes. They both got fed up with this place at about the same time. Estemard left, Paphlagon went into the upper labyrinth one night after supper and then I didn’t see him for a quarter of a century, until-well-you know.” A thought occurred to him. “What were you doing during Paphlagon’s Evocation? At the time, you were still a guest of Autipete.”

Autipete was a figure of ancient mythology who had crept up on her father as he lay sleeping and put out his eyes. I had never heard Suur Trestanas referred to this way. I bit my lip and shook my head in dismay as Arsibalt blew soup out his nostrils. “That is not fair,” I said, “she’s only following orders.”

Orolo squared off to plane me. “You know, during the Third Harbinger it was quite common for those who had committed terrible crimes to say-”

“That they were just following orders, we all know that.”

“Fraa Erasmas is suffering from Saunt Alvar’s Syndrome,” Arsibalt said.

“Those people during the Third Harbinger were shoving children into furnaces with bulldozers,” I said. “And as far as Saunt Alvar goes-well, he was the sole survivor of his concent in the Third Sack and was held captive for three decades. Locking the door to the telescopes for a few weeks doesn’t really measure up, does it?”

Orolo conceded the point with a wink. “My question stands. What did you do during Voco?”

Of course I’d have loved to tell him. So I did-but I made it into a joke. “While no one was looking, I ran up to the starhenge to make observations. Unfortunately, the sun was out.”

“That damned luminous orb!” Orolo spat. Then something crossed his mind. “But you know that our equipment can see some things during the daytime, if they are very bright.”

Since Orolo had decided to play along with my joke, it would not have been sporting for me to drop it at this point. “Unfortunately the M amp; M was pointed in the wrong direction,” I said. “I didn’t have time to slew it around.”

“The wrong direction for what?” Orolo asked.

“For looking at anything bright-such as a planet or…” I faltered.

Jesry sat down at an empty table nearby, facing me and Orolo, and remained still, ignoring his food. If he’d been a wolf his ears would have been erect and swiveled toward us.

Orolo said, “Would it be too much trouble for you to bring your sentence to a decent conclusion?”

Arsibalt looked as rattled as I felt. This had started as a joke. Now, Fraa Orolo was trying to get at something serious-but we couldn’t make out what.

“Aside from supernovae, very bright objects tend to be nearby-within the solar system-and things in the solar system are, by and large, confined to the plane of the ecliptic. So, Fraa Orolo, in this absurd fantasy of me running to the starhenge to look at the sky in broad daylight, I’d have to slew the M amp; M from its current polar orientation to the plane of the ecliptic in order to have a chance of actually seeing anything.”

“I just want your absurd fantasy to be internally consistent,” Fraa Orolo explained.

“Well, are you happy with it now?”

He shrugged. “Your point is well reasoned. But don’t be too dismissive of the poles. Many things converge there.”

“Like what? Lines of longitude?” I scoffed.

Arsibalt, in similar spirit: “Migratory birds?”

Jesry: “Compass needles?”

Then a higher-pitched voice broke in. “Polar orbits.”

We turned and saw Barb coming toward us with a tray of food. He must have been listening with one ear as he stood in line. Now he was giving the answer to the riddle in a pre-adolescent voice that could have been heard from Bly’s Butte. It was such an odd thing to say that it had turned heads all over the Refectory. “By definition,” he continued, in the singsong voice he used when he was rattling off something he had memorized from a book, “a satellite in a polar orbit must cross over each of the poles during each revolution around Arbre.”

Orolo stuffed a piece of gravy-sopped bread into his mouth to hide his amusement. Barb was now standing right next to me with his tray a few inches from my ear, but he made no move to sit down.

I had the feeling I was being watched. I looked over at Fraa Corlandin a few tables distant, just in the act of glancing away. But he could still hear Barb: “A telescope aimed north would have a high probability of detecting-”

I yanked down on a loose fold of his bolt. One arm dropped. All the food slid to that end of his tray and threw it out of balance. He lost control and it all avalanched to the floor.

All heads turned our way. Barb stood amazed. “My arm was acted on by a force of unknown origin!” he stated.

“Terribly sorry, it was my fault,” I said. Barb was fascinated by the mess on the floor. Knowing by now how his mind worked, I rose, squared off in front of him, and put my hands on his shoulders. “Barb, look at me,” I said.

He looked at me.

“This was my fault. I got tangled up with your bolt.”

“You should clean it up, if it was your fault,” he said matter-of-factly.

“I agree and that is what I shall do now,” I said. I went off to fetch a bucket. Behind me I could hear Jesry asking Barb a question about conic sections.


Calca: (1) In Proto-and Old Orth, chalk or any other such substance used to make marks on hard surfaces. (2) In Middle and later Orth, a calculation, esp. one that consumes a large amount of chalk because of its tedious and detailed nature. (3) In Praxic and later Orth, an explanation, definition, or lesson that is instrumental in developing some larger theme, but that, because of its overly technical, long-winded, or recondite nature, has been moved aside from the main body of the dialog and encapsulated in a footnote or appendix so as not to divert attention from the main line of the argument. -THE DICTIONARY, 4th edition, A.R. 3000

One form of drudgery led straight into another as Suur Ala helpfully reminded me that it was my day to clean up the kitchen following the midday meal. I hadn’t been at it for long before I noticed that Barb was in there with me, just following me around, making no move to help. Which irked me at first: yet another case of his almost perfect social cluelessness. But once I got over that, I decided it was better that way. Some things were easier to do alone. Communicating and coordinating with others was often more trouble than it was worth. Many tried to help anyway because they thought it was the polite thing to do, or because it was an avenue for social bonding. Barb’s thinking wasn’t muddled by any such considerations. Instead, he talked to me, which in my view was preferable to being “helped.”

“Orbits are about as much fun as what you are doing,” he observed gravely, watching me get down on my knees and reach elbow-deep into a grease-choked drain.

“I gather that Grandsuur Ylma has been teaching you about such things,” I grunted. Drain-cleaning made it easy to hide my chagrin. I hadn’t learned about orbits until my second year. This was Barb’s second month.

“A lot of xs and ys and zs!” he exclaimed, which forced a laugh out of me.

“Yes,” I said, “quite a few.”

“You want to know what’s stupid?”

“Sure, Barb. Lay it on me,” I said, hauling a fistful of vegetable trimmings up out of the drain against the back-pressure of twenty gallons of dammed-up dishwater. The drain gargled and began to empty.

“Any sline could stand out on the meadow at night and see some satellites in polar orbits, and other satellites in orbits around the equator, and know that those were two different kinds of orbits!” he exclaimed. “But if you work out the xs and ys and zs of it, guess what?”

“What?”

“They just look like a lot of xs and ys and zs, and it is not as obvious that some are polar and some are equatorial as it would be to any old dumb sline looking up into the sky!”

“Worse than that,” I pointed out, “staring at the xs and ys and zs doesn’t even tell you that they are orbits.”

“What do you mean?”

“An orbit is a stationary, stable thing,” I said. “The satellite’s moving all the time, of course, but always in the same way. But that kind of stability is in no way shown by the xs and ys and zs.”

“Yeah! It’s like knowing all of the theorics only makes us stupider!” he laughed excitedly, and cast a theatrical glance over his shoulder, as if we were up to something incredibly mischievous.

“Ylma is having you work it out in the most gruesome way possible,” I said, “using Saunt Lesper’s Coordinates, so that when she teaches you how it’s really done, it’ll seem that much easier.”

Barb was dumbfounded. I went on, “Like hitting yourself in the head with a hammer-it feels so good when you stop.” This was the oldest joke in the world, but Barb hadn’t heard it before, and he became so amused that he got physically excited and had to run back and forth across the kitchen several times to flame off energy. A few weeks ago I would have been alarmed by this and would have tried to calm him down, but now I was used to it, and knew that if I approached him physically things would get much worse.

“What’s the right way to do it?”

“Orbital elements,” I said. “Six numbers that tell you everything that can be known about how a satellite is moving.”

“But I already have those six numbers.”

“What are they?” I asked, testing him.

“The satellite’s position on Saunt Lesper’s x, y, and z axes. That’s three numbers. And its velocity along each one of those axes. That’s three more. Six numbers.”

“But as you pointed out you can look at those six numbers and still not be able to visualize the orbit, or even know that it is an orbit. What I am telling you is that with some more theorics you can turn them into a different list of six numbers, the orbital elements, that are infinitely easier to work with, in that you can glance at them and know right away whether the orbit goes over the poles or around the equator.”

“Why didn’t Grandsuur Ylma tell me that to begin with?”

I couldn’t tell him, because you learn too damned fast. But if I tried to be overly diplomatic, Barb would see through it and plane me.

Then I had an upsight: it was my responsibility, just as much as it was Ylma’s, to teach fids the right stuff at the right time.

“You are now ready to stop working in Saunt Lesper’s Coordinates,” I announced, “and begin working in other kinds of spaces, the way real, grown-up theors do.”

“Is this like parallel dimensions?” said Barb, who apparently had been watching the same kinds of speelies as I had before coming here.

“No. These spaces I’m talking about aren’t like physical spaces that you can measure with a ruler and move around in. They are abstract theorical spaces that follow different rules, called action principles. The space that cosmographers like to use has six dimensions: one for each of the orbital elements. But that’s a special-purpose tool, only used in that discipline. A more general one was developed early in the Praxic Age by Saunt Hemn…” And I went on to give Barb a calca* about Hemn spaces, or configuration spaces, which Hemn had invented when he, like Barb, had become sick of xs and ys and zs.

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