down a cylinder filled with mercury-we stole the idea from John Wilkins, founder of the Royal Society, who came up with it three hundred years ago, except he was going to use air instead of quicksilver. I-excuse me, Lawrence, did you say you had been working on them?'
'I did the same thing with tubes. Valves, as you would call them.'
'Well that's all well and good for you Yanks,' Alan says, 'I suppose if you are infinitely rich you could make a BURY/DISINTER system out of steam locomotives, or something, and retain a staff of thousands to run around squirting oil on the squeaky bits.'
'The mercury line is a good idea,' Waterhouse admits. 'Very resourceful.'
'Have you actually gotten BURY and DISINTER to work with
'Yes. My DISINTER works better than our shovel expeditions,' Lawrence says. 'Did you ever find those silver bars you buried?'
'No,' Alan says absently. 'They are lost. Lost in the noise of the world.'
'You know, that was a Turing test I just gave you,' Lawrence says.
'Beg pardon?'
'This damned machine screws up your voice so bad I can't tell you from Winston Churchill,' Lawrence says. 'So the only way I can verify it's you is by getting you to say things that only Alan Turing could say.'
He hears Alan's sharp, high-pitched laugh at the other end of the line. It's him all right.
'This Project X thing really is appalling,' Alan says. 'Delilah is infinitely superior. I wish you could see it for yourself. Or hear it.'
Alan is in London, in a command bunker somewhere. Lawrence is in Manila Bay, on the Rock, the island of Corregidor. They are joined by a thread of copper that goes all the way around the world. There are many such threads traversing the floors of the world's oceans now, but only a few special ones go to rooms like this. The rooms are in Washington, London, Melbourne, and now, Corregidor.
Lawrence looks through a thick glass window into the engineer's booth, where a phonograph record is playing on the world's most precise and expensive turntable. This is, likewise, the most valuable record ever turned out: it is filled with what is intended to be perfectly random white noise. The noise is electronically combined with the sound of Lawrence's voice before it is sent down the wire. Once it gets to London, the noise (which is being read off an identical phonograph record there) is subtracted from his voice, and the result sent into Alan Turing's headphones. It all depends on the two phonographs being perfectly synchronized. The only way to synchronize them is to transmit that maddening buzzing noise, a carrier wave, along with the voice signal. If all goes well, the opposite phonograph player can lock onto the buzz and spin its wax in lockstep.
The phonograph record is, in other words, a one-time pad. Some where in New York, in the bowels of Bell Labs, behind a locked and guarded door stenciled PROJECT X, technicians are turning out more of these things, the very latest chart-topping white noise. They stamp out a few copies, dispatch them by courier to the Project X sites around the globe, then destroy the originals.
They would not be having this conversation at all, except that a couple of years ago Alan went to Greenwich Village and worked at Bell Labs for a few months, while Lawrence was on Qwghlm. H.M. Government sent him there to evaluate this Project X thing and let them know whether it was truly secure. Alan decided that it was-then went back home and began working on a much better one, called Delilah.
What the hell does this have to do with dead Chinese abacus slaves?
To Lawrence, staring through the window at the spinning white-noise disk, the connection could hardly be clearer. He says, 'Last I spoke to you, you were working on generating random noise for Delilah.'
'Yes,' Alan says absently. That was a long time ago, and that whole project has been BURIED in his memory storage system; it will take him a minute or two to DISINTER it.
'What sorts of algorithms did you consider to create that noise?'
There is another five-second pause, then Alan launches into a disquisition about mathematical functions for generating pseudorandom number sequences. Alan had a good British boarding-school education, and his utterances tend to be well-structured, with outline form, topic sentences, the whole bit:
PSEUDO-RANDOM NUMBERS
I. Caveat: they aren't really random, of course, they just look that way, and that's why the pseudo
II. Overview of the Problem
A. It seems as if it should be easy
B. Actually it turns out to be really hard
C. Consequences of failure: Germans decrypt our secret messages, millions die, humanity is enslaved, world plunged into an eternal Dark Age
D. How can you tell if a series of numbers is random
1, 2, 3, . . . (A list of different statistical tests for randomness, the advantages and disadvantages of each)
III. A bunch of stuff that I, Alan Turing, tried
A, B, C, . . . (A list of different mathematical functions that Alan used to generate random numbers; how almost all of them failed abjectly; Alan's initial confidence is replaced by surprise, then exasperation, then despair, and finally by guarded confidence as he at last finds some techniques that work)
IV. Conclusions
A. It's harder than it looks
B. It's not for the unwary
C. It can be done if you keep your wits about you
D. In retrospect a surprisingly interesting mathematical problem deserving of further research
When Alan finishes with this perfectly structured whirlwind tour of the Surprising World of Pseudo- Randonmess, Lawrence says, 'How about zeta functions?'
'Didn't even consider those,' Alan says.
Lawrence's mouth drops open. He can see his own semitransparent reflection in the window, superimposed on the spinning phonograph, and he sees that he has got a sort of mildly outraged look on his face. There must be something conspicuously nonrandom about the output of the zeta function, something so obvious to Alan that he dismissed it out of hand. But Lawrence has never seen any such thing. He knows that Alan is smarter than he is, but he's not used to being so desperately far behind him.
'Why. . . why not?' he finally stammers.
'Because of Rudy!' Alan thunders. 'You and I and Rudy all worked on that damn machine at Princeton! Rudy knows that you and I have the knowledge to build such a device. So it is the first thing that he would assume we would use.'
'Ah.' Lawrence sighs. 'But leaving that aside, the zeta function might still be a good way of doing it.'
'It might,' Alan says guardedly, 'but I have not investigated it. You're not thinking of using it, are you?'
Lawrence tells Alan about the abaci. Even through the noise and the buzz, he can tell that Alan is thunderstruck. There is a pause while the technicians at each end flip over their phonograph records. When the connection is reestablished, Alan's still very excited. 'Let me tell you something more,' Lawrence says.
'Yes, go ahead.'
'You know that the Nipponese use a plethora of different codes, and we still have only broken some of them.'
'Yes.'
'There is an unbroken cipher system that Central Bureau calls Arethusa. It's incredibly rare. Only thirty- some Arethusa messages have ever been intercepted.'
'Some company code?' Alan asks. This is a good guess; each major Nipponese corporation had its own code system before the war, and much effort has gone into stealing code books for, and otherwise breaking, the Mitsubishi code, to name one example.
'We can't figure out the sources and destinations of Arethusa messages,' Lawrence continues, 'because they use a unique site code system. We can only guess at their origins by using huffduff. And huffduff tells us that most of the Arethusa messages have originated from submarines. Possibly just a single submarine, plying the route between Europe and Southeast Asia. We have also seen them from Sweden, from London, Buenos Aires, and Manila.'
