For the Greek's love she gave away her heart

Her father, crown and homeland.

They stopped to rest on Naxos

She woke up alone upon the strand

The sails of her lover's ship descending

Round the slow curve of the earth. Ariadne

Fell into a swoon on the churned sand

And dreamed of home. Minos did not forgive her

And holding diamonds in the pouches of his eyes

Had her flung into the Labyrinth.

She was alone this time. Through a wilderness

Of blackness wandered Ariadne many days

Until she tripped on the memory.

It was still wound all through the place.

She spun it round her fingers

Lifted it from the floor

Knotted it into lace

Erased it.

The lace made a gift for him who had imprisoned her.

Blind with tears, he read it with his fingers

And opened his arms.

The answer came back much too quickly, and it was the same answer as always: "I do so envy your skill with words. Now, if you do not object, let us turn our attention to the inner workings of the Turing machine."

She had made it as obvious as she dared, and the Duke still hadn't gotten the message. He must be a machine.

Why the deception?

Clearly, the mechanical Duke desired for her to learn about the Turing machines. That is, if a machine could ever be said to desire something.

There must be something wrong with the Duke's programming. He knew there was something wrong with it, and he needed a human to fix it.

Once Nell had figured these things out, the rest of the Castle Turing story resolved itself quickly and neatly. She slipped out of her cell and stealthily explored the castle. The soldiers rarely noticed her, and when they did, they could not improvise; they had to go back to the Duke to be reprogrammed. Eventually, Princess Nell found her way into a room beneath the windmill that contained a sort of clutch mechanism. By disengaging the clutch, she was able to stop the Shaft. Within a few hours, the springs inside the soldiers' back had all run down, and they had all stopped in their tracks. The whole castle was frozen, as if she had cast an enchantment over it.

Now roaming freely, she opened up the Duke's throne and found a Turing machine beneath it. On either side of the machine was a narrow hole descending straight through the floor and into the earth for as far as her torch light could illuminate it. The chain containing the Duke's program dangled on either side into these holes. Nell tried throwing stones into the holes and never heard them hit bottom; the chain must be unfathomably long.

High up in one of the castle's towers, Princess Nell found a skeleton in a chair, slumped over a table piled high with books. Mice, bugs, and birds had nibbled away all of the flesh, but traces of gray hair and whiskers were still scattered around the table, and around the cervical vertebrae was a golden chain bearing a seal with the T insignia.

She spent some time going through the Duke's books. Most of them were notebooks where he would sketch the inventions he hadn't had time to build yet. He had plans for whole armies of Turing machines made to run in parallel, and for chains with links that could be set in more than two positions, and for machines that would read and write on two-dimensional sheets of chain mail instead of one-dimensional chains, and for a three-dimensional Turing grid a mile on a side, through which a mobile Turing machine would climb about, computing as it went.

No matter how complicated his designs became, the Duke always found a way to simulate their behavior by putting a sufficiently long chain into one of the traditional Turing machines. That is to say that while the parallel and multidimensional machines worked more quickly than the original model, they didn't really do anything different.

One afternoon, Nell was sitting in her favorite meadow, reading about these things in the Primer, when a riderless chevaline emerged from the woods and galloped directly toward her. This was not highly unusual, in and of itself; chevalines were smart enough to be sent out in search of specific persons. People rarely sent them in search of Nell, though.

The chevaline galloped at her full-tilt until it was just a few feet away, and then planted its hooves and stopped instantly– a trick it could easily do when it wasn't carrying a human. It was carrying a note written in Miss Stricken's hand: "Nell, please come immediately. Miss Matheson has requested your presence, and time is short."

Nell didn't hesitate. She gathered her things, stuffed them into the mount's small luggage compartment, and climbed on. "Go!" she said. Then, getting herself well situated and clenching the hand-grips, she added, "Unlimited speed." Within moments the chevaline was threading gaps between trees at something close to a cheetah's sprint velocity, clawing its way up the hill toward the dog pod grid.

From the way the tubes ran, Nell guessed that Miss Matheson was plugged into the Feed in two or three different ways, though everything had been discreetly hidden under many afghans, piled up on top of her body like the airy layers of a French pastry. Only her face and hands were visible, and looking at them Nell remembered for the first time since their introduction just how old Miss Matheson was. The force of her personality had blinded Nell and all the girls to the blunt evidence of her true age.

"Please let us be, Miss Stricken," Miss Matheson said, and Miss Stricken backed out warily, strewing reluctant and reproving glances along her trail.

Nell sat on the edge of the bed and carefully lifted one of Miss Matheson's hands from the coverlet, as if it were the desiccated leaf of some rare tree. "Nell," Miss Matheson said, "do not waste my few remaining moments with pleasantries."

"Oh, Miss Matheson-" Nell began, but the old lady's eyes widened and she gave Nell a certain look, practiced through many decades in the classroom, that still had not lost its power to silence.

"I have requested that you come here because you are my favorite student. No! Do not say a word," Miss Matheson admonished her, as Nell leaned her face closer, eyes filling with tears. "Teachers are not supposed to have favorites, but I am approaching that time when I must confess all my sins, so there it is.

"I know that you have a secret, Nell, though I cannot imagine what it is, and I know that your secret has made you different from any other girl I have ever taught. I wonder what you suppose you will do with your life when you leave this Academy, as you must soon, and go out into the world?"

"Take the Oath, of course, as soon as I reach the age of eligibility. And I suppose that I should like to study the art of programming, and how ractives are made. Someday, of course, after I have become one of Her Majesty's subjects, I should like to find a nice husband and perhaps raise children– "

"Oh, stop it," Miss Matheson said. "You are a young woman– of course you think about whether you shall have children– every young woman does. I haven't much time left, Nell, and we must dispense with what makes you like all the other girls and concentrate on what makes you different."

At this point, the old lady gripped Nell's hand with surprising force and raised her head just a bit off the pillow. The tremendous wrinkles and furrows on her brow deepened, and her hooded eyes took on an intense burning appearance. "Your destiny is marked in some way, Nell. I have known it since the day Lord Finkle-McGraw came to me and asked me to admit you– a ragged little thete girl– into my Academy.