– – – the

– – – – (not used; possibly alan?)

– – – – – of

If that was right, then the message was HELLO I AM THE DUKE OF TURING, which was interesting, since the giant fellow in the armor had previously identified himself as such, and she deemed it unlikely that he would be sending her a message by this route. This must have come from someone else calling himself the Duke of Turing– perhaps a real, living human being.

A few years ago Nell could have relied on it. But in recent years the Primer had become much subtler than it used to be, full of hidden traps, and she could no longer make comfortable and easy assumptions. It was just as likely that this chain had descended straight from the throne room itself, and that the mechanical Duke was, for some unfathomable reason, trying to dupe her. So while she was happy to respond to this message in kind, she intended to take a guarded approach until she had established whether the sender was human or mechanical.

The next part of the message was GIVE– – -CHAIN– – – -TUG-– – – – -ANSWER. Assuming that four horizontal marks stood for alan and six stood for to, this was GIVE THE CHAIN A TUG TO ANSWER.

Nell began to flip the toggles on the chain, erasing the message from this personage calling himself the Duke and replacing it with I AM PRINCESS NELL WHY DID YOU IMPRISON ME. Then she gave the chain a tug, and after a moment it began to withdraw from her cell. A few minutes later, back came the message: WELCOME PRINCESS NELL LET US DEVISE A MORE EFFICIENT MEANS OF COMMUNICATION followed by instructions on how to use a more compact system of toggles to represent numbers, and how to convert the numbers into letters and punctuation marks. Once this was settled, the Duke said I AM THE REAL DUKE. I CREATED THESE MACHINES, AND THEY IMPRISONED ME IN A HIGH TOWER FAR ABOVE YOU. THE MACHINE CALLING HIMSELF THE DUKE IS MERELY THE LARGEST AND MOST SOPHISTICATED OF MY CREATIONS.

Nell responded, THIS CHAIN WEIGHS HUNDREDS OF POUNDS. YOU MUST BE STRONG FOR A HUMAN.

The Duke responded YOU ARE A SHARP ONE PRINCESS NELL! THE FULL WEIGHT OF THE CHAIN IS ACTUALLY SEVERAL THOUSAND POUNDS, AND I MANAGE IT BY MEANS OF A WINCH LOCATED IN MY ROOM AND DERIVING ITS MOTIVE POWER FROM THE CENTRAL SHAFT.

Night had long since fallen on the meadow. Nell closed the Primer, packed up her basket, and returned home.

She stayed up late into the night with the Primer, just as she had when she was a small child, and as a result was late for church the next morning. They said a special prayer for Miss Matheson, who was at home and said to be feeling poorly. Nell called on her for a few minutes after the service, then went straight back home and dove into the Primer again.

She was attacking two problems at once. First, she needed to figure out how the lock on the door worked. Second, she needed to find out whether the person sending her the message was human or mechanical. If she could be confident that he was a human, she could ask him for assistance in opening the lock, but until she had settled this issue, she had to keep her activities a secret.

The lock only had a few parts that she could observe: the crank, the bolt, and a pair of brass drums set into the top with digits from 0 to 9 engraved in them, so that by spinning different ways, they could display all the integers from 00 to 99. These drums were in almost constant motion whenever the crank was turning.

Nell had managed to detach several yards of chain from the one that she was using to converse with the Duke, and so she was able to feed different messages into the lock and see what result they had.

The number on the top changed with every link that went into the machine, and it seemed to determine, in a limited way, what the machine would do next; for example, she had learned that the number happened to be 09, and if the next link in the chain was in the vertical position (which the Duke referred to as a one), the drums would spin around and change the number to 23. But if the next link was, instead, a zero (as the Duke referred to links with horizontal toggles), the number drums would change to 03. But that wasn't all: In this case, the machine would, for some reason, reverse the direction in which the chain was moving through the machine, and also flick the toggle from zero to one. That is, the machine could write on the chain as well as read from it.

From idle chitchat with the Duke she learned that the numbers on the drums were referred to as states. At first she did not know which states led to other states, and so she wandered aimlessly from one state to the next, recording the connections on scratch paper.

This soon grew to a table listing some thirty-two different states and how the lock would respond to a one or a zero when it was in each of those states. It took a while for Nell to fill out all the blank spaces in the table, because some of the states were hard to get to-they could be reached only by getting the machine to write a certain series of ones and zeros on the chain.

She would have gone crazy with ones and zeros were it not for the frequent interruptions from the Duke, who evidently had nothing better to do than to send her messages. These two parallel courses of inquiry occupied all of Nell's free time for a couple of weeks, and she made slow but steady progress.

"You must learn how to operate the lock on your door," the Duke said. "This will enable you to effect an escape and to come and rescue me. I will instruct you."

All he wanted to talk about was technology, which wouldn't help Nell in figuring out whether he was a human or a machine.

"Why don't you pick your own lock," she responded, "and come and rescue me? I am just a poor helpless young thing all alone in the world, and so scared and lonely, and you seem so brave and heroic; your story really is quite romantic, and I cannot wait to see how it all comes out now that our fates have become intertwined."

"The machines placed a special lock on my door, not a Turing machine," responded the Duke.

"Describe yourself," Nell wrote.

"Nothing special, – I'm afraid," wrote the Duke. "How about yourself?"

"Slightly taller than average, flashing green eyes, raven hair falling in luxuriant waves to my waist unless I pin it up to emphasize my high cheekbones and full lips. Narrow waist, pert breasts, long legs, alabaster skin that flushes vividly when I am passionate about something, which is frequently."

"Your description is reminiscent of my late wife, God rest her soul."

"Tell me about your wife."

"The subject fills me with such unutterable sadness that I cannot bear to write about it. Now, let's buckle down to work on the Turing machine."

Since the prurient approach had dead-ended, Nell tried a different tack: playing stupid. Sooner or later, the Duke would become a little testy. But he was always terribly patient with her, even after the twentieth repetition of "Could you explain it again with different words? I still don't get it." Of course, for all she knew, he was upstairs punching the walls until his knuckles were bloody and simply pretending to be patient with her. A man who'd been locked up in a tower for years would learn to be extremely patient.

She tried sending him poetry. He sent back glowing reviews but declined to send her any of his own, saying it wasn't good enough to be committed to metal.

On her twentieth day in the dungeon, Princess Nell finally got the lock open. Rather than making an immediate escape, she locked herself back in and sat down to ponder her next move.

If the Duke was human, she should notify him so that they could plan their escape. If he was a machine, doing so would lead to disaster. She had to figure out the Duke's identity before she made another move.She sent him another poem.