Once she understood that the behavior of the water-gates was orderly and predictable, it was not long before she was able to program their behavior and locate the bugs that the dark knight had introduced into the system. Soon water was flowing through the irrigation system again, and the famine was relieved.
The people who lived in this castle were grateful, which she had expected. But then they put a crown on her head and made her their ruler, which she had not expected.
On some reflection, though, it only made sense. They would die unless their system functioned properly. Princess Nell was the only person who knew how it worked; she held their fate in her hands. They had little choice but to submit to her rule.
So it went, as Princess Nell proceeded from castle to castle, inadvertently finding herself at the helm of a full-fledged rebellion against King Coyote. Each castle depended on some kind of a programmable system that was a little more complicated than the previous one. After the Castle of the Water-gates, she came to a castle with a magnificent organ, powered by air pressure and controlled by a bewildering grid of push-rods, which could play music stored on a roll of paper tape with holes punched through it.
A mysterious dark knight had programmed the organ to play a sad, depressing tune, plunging the place into a profound depression so that no one worked or even got out of bed. With some playing around, Princess Nell established that the behavior of the organ could be simulated by an extremely sophisticated arrangement of water-gates, which meant, in turn, that it could just as well be reduced to an unfathomably long and complicated Turing machine program.
When she had the organ working properly and the residents cheered up, she moved on to a castle that functioned according to rules written in a great book, in a peculiar language. Some pages of the book had been ripped out by the mysterious dark knight, and Princess Nell had to reconstruct them, learning the language, which was extremely pithy and made heavy use of parentheses. Along the way, she proved what was a foregone conclusion, namely, that the system for processing this language was essentially a more complex version of the mechanical organ, hence a Turing machine in essence.
Next was a castle divided into many small rooms, with a system for passing messages between rooms through a pneumatic tube. In each room was a group of people who responded to the messages by following certain rules laid out in books, which usually entailed sending more messages to other rooms. After familiarizing herself with some of these rule-books and establishing that the castle was another Turing machine, Princess Nell fixed a problem in the message-delivery system that had been created by the vexatious dark knight, collected another ducal coronet, and moved on to castle number six.
This place was entirely different. It was much bigger. It was much richer. And unlike all of the other castles in the domain of King Coyote, it worked. As she approached the castle, she learned to keep her horse to the edge of the road, for messengers were constantly blowing past her at a full gallop in both directions.
It was a vast open marketplace with thousands of stalls, filled with carts and runners carrying product in all directions. But no vegetables, fish, spices, or fodder were to be seen here; all the product was information written down in books. The books were trundled from place to place on wheelbarrows and carried here and there on great long seedylooking conveyor belts made of hemp and burlap. Book-carriers bumped into each other, compared notes as to what they were carrying and where they were going, and swapped books for other books. Stacks of books were sold in great, raucous auctions-and paid for not with gold but with other books. Around the edges of the market were stalls where books were exchanged for gold, and beyond that, a few alleys where gold could be exchanged for food.
In the midst of this hubbub, Princess Nell saw a dark knight sitting on a black horse, paging through one of these books. Without further ado, she spurred her horse forward and drew her sword. She slew him in single combat, right there in the middle of the marketplace, and the book-sellers simply backed out of their way and ignored them as Princess Nell and the dark knight hacked and slashed at each other. When the dark knight fell dead and Princess Nell sheathed her sword, the commotion closed in about her again, like the waters of a turbulent river closing over a falling stone. Nell picked up the book that the dark knight had been reading and found that it contained nothing but gibberish. It was written in some kind of a cipher.
She spent some time reconnoitering, looking for the center of the place, and found no center. One stall was the same as the next. There was no tower, no throne room, no clear system of authority. Examining the market stalls in more detail, she saw that each one included a man who did nothing but sit at a table and decipher books, writing them out on long sheets of foolscap and handing them over to other people, who would read through the contents, consult rule-books, and dictate responses to the man with the quill pen, who enciphered them and wrote them out in books that were then tossed out into the marketplace for delivery. The men with the quill pens, she noticed, always wore jeweled keys on chains around their necks; the key was apparently the badge of the cipherers' guild.
This castle proved fiendishly difficult to figure out, and Nell spent a few weeks working on it. Part of the problem was that this was the first castle Princess Nell had visited that was actually functioning as intended; the dark knight had not been able to foul the place up, probably because everything was done in ciphers here, and everything was decentralized. Nell discovered that a smoothly functioning system was much harder to puzzle out than one that was broken.
In the end, Princess Nell had to apprentice herself to a master cipherer and learn everything there was to know about codes and the keys that unlocked them. This done, she was given her own key, as a badge of her office, and found a job in one of the stalls enciphering and deciphering books. As it turned out, the key was more than just a decoration; rolled up inside its shaft was a strip of parchment inscribed with a long number that could be used to decipher a message, if the sender wanted you to decipher it. From time to time she would go to the edge of the market, exchange a book for some gold, then go buy some food and drink.
On one of these trips, she saw another member of the cipherer's guild, also taking his break, and noticed that the key hanging around his neck looked familiar: it was one of the eleven keys that Nell and her Night Friends had taken from the Faery Kings and Queens! She concealed her excitement and followed this cipherer back to his stall, making a note of where he worked. Over the next few days, going from stall to stall and examining each cipherer, she was able to locate the rest of the eleven keys. She was able to steal a look at the rule-books that her employers used to respond to the encoded messages. They were written in the same special language used at the previous two castles.
In other words, once Princess Nell had deciphered the messages, her stall functioned like another Turing machine. It would have been easy enough to conclude that this whole castle was, like the others, a Turing machine. But the Primer had taught Nell to be very careful about making unwarranted assumptions. Just because her stall functioned according to Turing rules did not mean that all of the others did. And even if every stall in this castle was, in fact, a Turing machine, she still could not come to any fixed conclusions. She had seen riders carrying books to and from the castle, which meant that cipherers must be at work elsewhere in this kingdom. She could not verify that all of them were Turing machines.