At the Presidence, going in the main entrance worked much better than going through the visitor's center. Apparently sometimes people put up signs as much for their own reasons as for those of the readers. Nyssa was shown by one of those pages that walked on their corners to a cafeteria, where she was invited to serve herself as much as she liked from a buffet of the oddest things. There was a tureen of magnetic field soup, and a tall glass of barometric readings. There was a pot of spectrometer data, a dish of galvanometer output, and, most popularly, a plate of calorimeter figures; by the time Nyssa reached these there was only one left.
Nyssa didn't know what she liked out of these things so she loaded up her tray with a little of each and found herself partial enough to her forkful of radar blips and her cup of rain gauge that she went back for seconds of those until she was full. Then her escort page led her to the Precedent's office.
It was full of books, so to pass the time she looked at them. He had books on every kind of science, from archaeology to zoology and everything in between. He had books on places people had been - memoirs and travelogues from places Nyssa had never heard of and a few she had. He had atlases, he had cookbooks for the strange sort of fare they ate in Percepolis (on the cover of one was a mouthwatering braised anemometer rotation) and he had books about politics and statecraft and music and art, though they were odd ones with titles like "Natural Experiments in Planned Economy" and "An Inquiry into the Appeal of Certain Chords" and "Seventeen Studies on Aesthetics in Various Populations".
Nyssa pulled down an atlas, to compare against her map, which she'd been updating periodically as she traveled. She'd gotten a few things wrong, she found, and had just pulled out her pencil to make corrections when it occurred to her that just because this map looked very fancy and was much more complete than hers didn't mean it was more accurate. Maybe this map had been made by someone like the Cartographer she had first met, and the pretty illuminations and detailed labeling and precise distances were all made up to be impressive. Maybe it wasn't, but she should at least ask the Precedent how good his map was and how he knew it was good before she replaced hers entirely.
She put the atlas back, and found Pomodoro a book on the history of the duration of the second, which sounded like the sort of thing it would like; it blobbed onto the book, ringing cheerfully. Nyssa was scanning the titles of a section on historiography when the Precedent arrived.
"Hello, hello," he said. "What did you say your name was?"
"Nyssa," she said.
"That's what I'd heard, but you always want independent verification if you can get it."
"Are those maps any good?" she asked, pointing at the atlas.
"They were good when they were new, but they're old, now," he told her. "It's gotten too dangerous for most people to want to travel over not-recently-charted wilderness double-checking this and that. I wouldn't trust them, no, not in their particulars. Anyway. So you have a secret weapon with which to rescue Wonder, and you want some additional less secret items from me to help you do that."
"Yes, Mister Precedent," Nyssa replied.
"Well. I do have a couple of things that might be helpful, although I can give you no guarantee - the Valley of Error is treacherous."
Nyssa swallowed. "I understand. I think getting Wonder back sounds really important."
"It is, it is... everything was so much better when she was here," he sighed. "We saw more, we put together the things we learned into more interesting and useful shapes, we were all happier in good times and more determined in the bad times... yes, we certainly need Wonder. The first thing I have to offer you is this." He pulled open a tile of the office floor, which proved to be a trap door with a compartment underneath. From this compartment he produced a monocle. "A lens," he said. "Hold it to your eye and look through it, and you will not see things as they really are - at least, not more than you normally do, which is less than you think - but the lens will make clear to you in what ways what you see is distorted. You'll need to rely on your own brain to correct for that, but once you know which twists to untwist, it all becomes much easier."
"Thank you," Nyssa said, taking the lens and tucking it into a pocket of her bag.
"And secondly," said the Precedent, reaching back into the compartment, "I offer you this, my old crown. I no longer need it, as it was a symbol of the office of the King and I now accomplish its job differently, with elections and polls instead of the wisdom of crowns. But you may find it convenient. Did you know, Nyssa, that if you have five hundred people look at a jar of pebbles - so many pebbles that not a single person can count them, in such a large jar that they cannot even guess just how big around it is - and every single one of those people guesses at how many pebbles there are, and then you take the average of their guesses, it will be very nearly right? The crown will do that for you - ask it any question while you wear it on your head, and it will make hundreds of guesses, all wrong in different ways, and tell you the average, which is often very nearly right. You do know what an average is?"
"I'm afraid I don't quite remember," admitted Nyssa.
"Well," said the Precedent, "it's good that you know you don't know, because otherwise you'd never find out. It's a matter of statistics - one place where Qed's interests and mine tend to overlap - and it goes like this." He rummaged in his desk, found a bag of sand like the one that spilled from the pendulum in the pendulum room, and also a rectangular box, one that might have been used to package a fancy pen but was now empty. He made six different heaps of sand in the box, one next to the other, some tall and some short. "These heaps are all different sizes, as you can see," he said. "And their average size is what happens when you do this..." He swept his hand across the tops of the tallest piles so that they collapsed onto their shorter neighbors and spread into a uniform flatness of sand. "And then divide by how many piles there were to begin with. You see?"
"Yes, I think so," said Nyssa.
The Precedent placed his old crown on Nyssa's head, where it was heavy and sat slightly askew on her curls. "There you go, then you understand how it works. That's always important for making good use of any tool. Now, don't follow the wisdom of crowns off a cliff. You must always use your own judgment too."
"I understand," Nyssa said seriously.
"There's a good girl," said the Precedent. "Is there anything else I can do for you?"
"I could use some packed-up food," she said. "I really liked the radar blips in the cafeteria."
"Hmm, radar blips are pretty tasty but I don't think they'd better go gallivanting about the countryside, there have been wars started that way," he replied. "How about some things they don't have in the cafeteria? Pyrometer data to keep you warm on chilly nights! Brix refractometry for dessert! And odometer numbers, to always know how far you've come."
"That sounds delicious," said Nyssa.
"Excellent. I'll have the kitchens send it up. You have your own transportation?"
"I have a curiosipede," Nyssa said proudly.
"Exquisite. Those used to be more commonplace," sighed the Precedent. "But they've been falling out of fashion, ever since... well, ever since Wonder was banished. I hope you can bring her back, Nyssa. She's very sorely missed."
"I hope so too."
And Nyssa packed up her snacks in her bag, collected Pomodoro to put on her shoulder again, got back on her curiosipede, and zoomed out of the Percepolis city center, out through its suburbs and its scientific farms, and proceeded toward the horizon.