It seemed an odd word to use, "partner", as if we were discussing a business relationship rather than one that involved the messy business of s.e.x and the hard duty of raising children.
"I well, hmm. No, not really. I was going to get married, but it wouldn"t have worked. I"m probably better off alone."
The Doctor sat up abruptly. "Yes, well, that"s my view too. Now, can you remember the numbers or will you have to go through the decoded messages again first?"
I looked at him then, and knew something had been lost. He was looking straight past me. He had, quite deliberately, closed the door on the more intimate sort of friendship that normally comes about between two people, after a period of time: he was letting me know that our relationship would be limited to what was that strange, cold term he had used? A partnership yes, that was it. A business partnership.
I thought then that there were many things that the Doctor did not understand that in some ways he did not truly connect with the human world. In retrospect, it occurs to me that, in addition to this, he was trying to be kind. The grey, aching years since VE Day have taught me too much about the separation of business and pleasure, in fact, about the separation of all parts of our lives into little fissured compartments. Only that way is there any happiness for the truly adult man: secured away from the pain of real life, hidden in the backstreets of Manchester I"m sorry. I mustn"t let my present predicament weigh down this story. I was younger then, and still believed in the possibility of a whole happiness, a home-andtwo-children life that could not be divided. Even the debacle with my fiancee, Joan, had not taught me the futility of believing that a man such as myself was ent.i.tled to that happiness.
So, though I was disappointed at the Doctor"s rejection of my offer of emotional intimacy, I didn"t let it spoil the evening: I remember we stood arm in arm on the iron balcony, both of us quite drunk, and in breach of the blackout (which was not strictly enforced in Paris the French apparently thought their capital city led a charmed life). I remember, too, the light from our window catching the face of a man in a doorway on the street two floors below. I recognised the features, despite the dim, long-shadowed light, as those of Mr White.
He shrank back, and I wondered if he was spying on us, though it seemed a silly enough thing to do from the damp street when he could have listened from the corridor outside, or perhaps even concealed a microphone in the room. But I quickly enough saw the real reason for his watch, in the profiled face of a sharp-featured and rather pretty woman, with a tall hat of the sort fashionable in my mother"s day, and coiffured black hair. She was half turned away, cowering against the wall.
"Don"t worry!" White"s voice. "They won"t say anything!"
But the woman scuttled away out of the light, her heels clicking on the pavement.
I noticed that the Doctor was staring, following her movement even though he couldn"t see her any more. At the corner, a flicker of light showed her grey coat, moving.
He stared after her long after she had gone. In the street below, White had vanished.
"What is it?" I asked the Doctor.
He didn"t speak. He looked shocked, afraid, rather as he had sounded after hearing the partly decoded message in Bletchley. He didn"t scream, but his knuckles were bloodless as they gripped the black iron railing.
"It? I don"t know. I hoped it had gone away," he muttered after a while. "But it will never leave me. Never."
"What won"t?" I asked, confused: it wasn"t clear what "it" he was talking about. When he didn"t reply, I asked, "Did you know that woman?"
"No," he said. "I didn"t. Not yet. But we will, Alan, we will."
Chapter Five.
Let me tell you how I destroyed mathematics.
I wrote one major paper before the war it took me over a year, and was called "Computable Numbers". In this paper I described my now-famous (or infamous) Universal Machine, the "computer" which can, by reading and writing from a paper tape, perform any mathematical operation as a series of simple steps. That concept has since found practical application with valves and wire replacing much of the paper, for the sake of speed and efficiency but it was not an essential part of the point I was making, more a way of demonstrating it.
The paper was an attempt to overturn David Hilbert"s contention that "all problems are solvable". What I needed to show was that there are problems that can"t be solved at all, however much time or information you have. To do this I needed, first, to show that the process of solving a problem within any logical mathematical system could be reduced to a finite series of simple, mechanical steps, and, second, to show that there were results that could not be found using these steps, no matter how they were applied. Exactly how I did this was a complex process, requiring many pages of reasoned argument, but in the end the result stood, and continues to stand. In essence, by using reasoned steps I had proved that the process of using reasoned steps will not solve all problems. This is not the same thing as saying that there are some things "beyond" reason, and especially it doesn"t mean that anything that feels comforting, regardless of whether or not it can be proven, must be true that way lies madness. Nonetheless I had established that mathematics contains undecidable problems, and therefore cannot solve all problems.
The only other way I know of getting the answer is guessing, and I think this is what the Doctor did to break what we later came to call the Dresden Code.
We spent three days in that Paris hotel. French soldiers brought sheaves of paper thick with numbers each morning, and the Doctor and I studied them, looking for patterns. The Doctor talked a good deal, of syntax, of codes, of "number plans". I followed very little of it, and yet I was sure that at some level much of it made sense: for the first time in my life I began to have some idea of how an ordinary person might feel when I talked of the higher realms of mathematics. Sometimes I had the sense that whole new fields of endeavour, as radical as the calculus, or the theory of sets, was being implied by what he said at others, he seemed to be talking the purest nonsense.
But he got the answers.
At first they were only the vaguest concepts, outlines of meaning, but then the Doctor made a breakthrough. I"m still not sure how he did it, but in the centre of the message itself he found a translation table, containing German words and the sounds of the "artificial" language, both of course translated into lengthy numerical codes. This made it possible to turn some of the "words" in the rest of the message into German, without having to understand the sounds at all.
From this point my experience with ENIGMA became useful. In the early days, many messages had been decoded because we knew roughly what they said: things like meteorological reports, for example, contain certain words in certain positions, and it was easy enough to run a decoding machine through all the possibilities until the answers made sense. Here, we could do it without recourse to a machine, because the table was quite small: only one hundred and forty-five words carried "translations" in the code. Because of the method of encoding as discrete particles of sounds the "translations" were very long, but their patterns were easy enough to find. Within a few hours we had decoded all that part of the message that had German translation.
There was quite a lot of it that we couldn"t decipher: the entire first minute was untranslated. But then came a part that was reasonably clear.
The exiles... resume their status according to procedure [meaningless word/s]. Rejoin from Dresden. Two [meaningless word/s] to remove. Uncertain location. Use local [meaningless word/s]. War and soldiers. Many weapons. Distrust available.
I felt a sense of triumph, if anything more intense than when the ENIGMA code had first been broken, even though I wasn"t more than ten per cent responsible for the work. I think I was proud of the Doctor of his mind, which was clearly extraordinary. It was a curious thing, almost a relief, to discover that I had at last met someone cleverer than myself.
"We"ll have to go there."
That was the Doctor"s immediate verdict, and he stuck to it in the face of my bemus.e.m.e.nt, White"s outraged stare and Elgar"s hearty laughter.
"Look er Doctor," said Elgar, when he had recovered. "I understand something about operating behind the lines, you know, and it"s not a good idea. Not for you. What we need you for is to break as much of the code as possible, so that anybody who does go behind the lines will be as well-briefed as possible. Mr Turing, you understand this, surely?"
I glanced at the Doctor. I could see a level of emotion building in his face that might lead to another Byronic fit such as that which had got us thrown out of the Crown. I didn"t know what effect it might have on White: I doubted it would impress Elgar. If I didn"t do something to stop the performance, we might both end up back at Bletchley, having achieved nothing we couldn"t have done by staying there.
I didn"t want to go back.
I said, "I understand that the Doctor and I can"t just go to Dresden. But I know why the Doctor needs to go."
"And why is that?" Elgar"s question was unexpectedly sharp, and White"s blue hawk eyes were searching my face.
Of course, I had no idea why the Doctor wanted to go. I merely wanted to calm him down by giving him a chance to elaborate.
"Doctor, you"d better explain to them," I said.
The Doctor appealed to White. "You"ve talked about affinities. You"ve released me from custody twice on the strength of an "affinity" between us."
I saw Elgar shake his head, but he said nothing.
"Now believe me when I say that I have an affinity with the makers of this message. I can"t say what it is. There"s something that they have that I haven"t met in in a long time. I want to see them."
White seemed about to say something, but Elgar got in first. "These seem to me like selfish reasons, Doctor." His bluff Colonel Blimp manner had entirely disappeared: his voice was cold, distant, judgemental. Even White seemed a little surprised.
"I can find out their secrets!" promised the Doctor. "Who they are, where they"re going, whether they will affect the course of the war!"
"Can you really?" Elgar again: the question sharp, biting.
"Steady on," said White. "The Doctor may be on to something. You can"t just a.s.sume he"s raving he"s broken their code, after all. He may well have something "
"He can"t go to Dresden, White, and that"s final." Elgar looked as if he"d like to say more, but didn"t want to say it in front of the Doctor and me.
The Doctor spoke up again. "I need to go. Please. I need to see them." His gaze was impa.s.sioned, his eyes watery, almost spilling tears.
But Elgar was unmoved. "No, no, and no," he said, fierce, but almost smiling now, as if the Doctor"s ridiculous insistence had become a joke.
This put-down had the effect of ending the interview quickly, and without a fit of madness from my friend. But I could see that the Doctor"s emotions were still running high. As soon as the door had closed behind us, I suggested that we go out and get drunk.
By the end of our second bottle of wine, the Doctor had worked his way through anger, disgust, maudlinity and wild talk of impossible schemes to travel to Dresden on our own. At last his mood settled and he seemed ready to tell me why meeting this group of dissident Germans, refugee Jews or escaped prisoners of war was so important to him.
"Well, first of all, they"re none of those," he said, referring to the above three categories, which I had just mentioned. "People like that wouldn"t have the resources or the need to make up a whole new language and a complicated radio code to escape."
"Admittedly it"s overcomplex," I said, "but people often do things in an overcomplicated way. Mathematical proofs, for instance, often contain more lines than are strictly needed to show "
"How many times do I have to tell you, Alan? This isn"t mathematics! This is real life, with real people suffering!" He banged his fist on the table at the end of each sentence, making both bottle and gla.s.ses vibrate.
I wondered how excited he might get, whether he might get us thrown out once more. As calmly as I could, I said, "I realise that, Doctor. I think that "real suffering" is all the more reason why they might do something that you and I, sitting at this rather cosy table in this rather warm cafe on the right side of the lines, might regard as too complicated. They may be frightened confused they may not even know that the war"s as good as over "
"Oh, I think most people know that." The Doctor met my eyes and gave a curious half-smile, and I realised then that he was quite consciously using an old trick of conversation arguing with everything I said to keep me away from the subject I most wanted to discuss.
I half smiled back. "Come on, Doctor, you can tell me. Who do you think these people are, and why do you think you know them?"
"Not just them. The woman too. And I don"t know. I really don"t know. It"s something I feel, but don"t remember. Can you understand that?"
I was puzzled, and my face must have shown it, because he reached out and grabbed my hand.
"It"s like walking into a room full of people, say the dining room at the hotel, and you know just know know that you"re familiar with some of the people there. You can"t put a name to them, but you can recognise them, and you can see that they can recognise you. You played a game together, once, and you can still feel the rules of that game, though you can"t remember ever playing it, or what the results were. And you know it was the best game you ever played, the most exciting, the most exhilarating, and at the same time the most frightening, but you don"t want to play it again, not with these people, not now, because " He turned away. The waitress was pulling long, rattling blackout curtains along the wide windows of the cafe. I glanced at my watch and saw that it was late afternoon: the day almost gone. that you"re familiar with some of the people there. You can"t put a name to them, but you can recognise them, and you can see that they can recognise you. You played a game together, once, and you can still feel the rules of that game, though you can"t remember ever playing it, or what the results were. And you know it was the best game you ever played, the most exciting, the most exhilarating, and at the same time the most frightening, but you don"t want to play it again, not with these people, not now, because " He turned away. The waitress was pulling long, rattling blackout curtains along the wide windows of the cafe. I glanced at my watch and saw that it was late afternoon: the day almost gone.
"Because?" I prompted after a while.
The Doctor only shrugged, whispered, "I can"t remember."
I offered him more wine. He picked up the gla.s.s, sniffed at it, swirled it vigorously, sniffed some more, though it was only the most ordinary vin rouge vin rouge. He looked up at last, with a gleam of merriment in his eye, and the clouds on his face quite lifted.
"I"m sorry, Alan, this must be getting very boring for you. My entire conversation must seem to consist of "I don"t know" and "I"ve forgotten". Let me tell you something I can can remember!" He swigged back the gla.s.s of wine as if it were water, then went on. "I tried to join the RAF, you know. In 1940, when they needed all the pilots they could get. Whatever Mr Churchill said, I could see I remember!" He swigged back the gla.s.s of wine as if it were water, then went on. "I tried to join the RAF, you know. In 1940, when they needed all the pilots they could get. Whatever Mr Churchill said, I could see I knew knew how desperate the situation was. And I knew I could pilot an aircraft with very little training. But they wouldn"t let me do it." how desperate the situation was. And I knew I could pilot an aircraft with very little training. But they wouldn"t let me do it."
"Why not?" It struck me that the Doctor was possibly too old: he looked older than I was perhaps forty and whilst I didn"t know what RAF policy was on pilots I suspected that anyone over thirty-five would not normally be considered.
"I didn"t have any nationality papers. I couldn"t prove I was a British subject."
"And are you?"
He shrugged. I frowned: despite all he had said, I hadn"t until that moment realised his loss of memory was so complete, but the lost expression on his face, the slight nod to my raised eyebrows, told me it was so.
"I"m sorry. That must have been very distressing."
He didn"t say anything.
"It probably makes you all the more glad to be able to serve now."
He shook his head. "You don"t understand. I"ve always had a role a function to perform. Only twice in the last fifty years have I felt the way I should feel "
He stopped, took a startled intake of breath and stared transfixed. It was almost as if he had been physically trapped in some clear, fast-setting liquid, like an insect cast in amber. The effect was so alarming that I thought, at the very least, that someone must have walked in. I looked over my shoulder but saw only the almost empty cafe, the bar girl standing with folded arms over the counter, probably waiting for us to go.
"What"s the matter?" I asked.
He leaned forward and whispered, "I"ve just remembered something."
Then, without warning, he got up and left, banging the door behind him. I would have followed, but I had to pay for our drinks first: besides, I didn"t expect him to go far. But, by the time I got outside, I looked up and down the quiet street and could see no trace of him.
I searched for the Doctor for a while, then the light began to fade so I made my way back towards the hotel. There was another cafe on the way, with some tables outside despite the chilly season. At one of the tables sat Colonel Elgar, with his back to me, and the woman who had been with White last night at least, I was reasonably sure. Surely no two people could have that same coiffure, that same sharp profile.
She didn"t recognise me, and Elgar didn"t see me. I was stepping up towards him I did not imagine that there was anything unusual about the situation and was all ready to say "h.e.l.lo" when I heard Elgar ask, "How much does he know about the Doctor?"
I froze, and very quickly turned away, shuffling through the doorway to the interior of the cafe. I was lucky, in that there was no window: I could stand here, with the door ajar, and there was little chance that Elgar would see me, yet I could hear them both fairly clearly. It did not occur to me until afterwards that I was spying.
"Well Greene is completely persuaded that he"s good." The woman spoke with a strange accent: middle-European, perhaps, but with an odd overtone I hadn"t heard before. In addition, there was something unusual about the voice itself: it was pinched, constrained, as if she were an actress "doing" an accent and doing it badly rather than speaking in her natural voice. The words themselves meant little to me: I didn"t know who Greene was at this point.
The conversation that followed, when Elgar pressed for details, was very strange.
"He isn"t from here," she said. "It"s possible that he thinks he is, but he isn"t. That"s obvious. I should see him for myself I could come to the hotel, perhaps?"
"You"re the only first-generation we"ve got."
A slightly petulant note entered her voice. "This is precisely why I need to see him myself."
"And if he"s what you think he is?"
"I don"t know what I think he is. Yet."
I could have been listening to the Doctor. I had a strange, lurching sensation in my brain, as if I had entered a children"s game, an Alice-inWonderland world where the rules of life had changed to a sort of nonsense, and everyone had lost their memory and replaced it with a series of giant playing cards, the meaning of most of which they had forgotten. I would not have been surprised to see a giant white rabbit hopping through the misty twilight outside.
"Very well," said Elgar to the woman. "Come to the hotel the day after tomorrow."
She stood up then, and for a moment I saw something that wasn"t quite a woman, more like an image of a woman, an Art Deco swirl of half-metallic colour, a face, a coiffure.
I think that was the first time that I realised if only for a moment that something entirely beyond my reasoning was involved in this problem, something I would never quite grasp or understand. Even the shock of her next words couldn"t drive away the otherworldliness of the moment.
She said, "Remember, though, my curiosity is of secondary importance. If you think for a moment that he will be able to prevent the execution of our mission, he should be destroyed."
Chapter Six.
Elgar left a couple of minutes after the woman, and I went back to the hotel, confused and rather afraid. Elgar was clearly a traitor. White, too, had been involved with the woman, though I suspected that White"s involvement had been no more than an a.s.signation of a romantic nature. Still, there was the possibility that both of them were in on it. But what was "it"? The woman hadn"t seemed German, and it was surely inconceivable that any non-German would choose to work for the n.a.z.is at this late stage in the war, when they were so evidently the losing side. It occurred to me that the French Resistance might be running this operation, trying to get some advantage over the British, now that they were free of the Germans: but I hardly thought they would kill for it, as the woman had suggested. So who? The Russians? The Doctor had spoken Russian once, hadn"t he?