Mackie ploughed on, 'It was Rory O'Malley who introduced these ideas of Dunne's to Ben Kamen. Now, Ben may have such a facility, this "dream precognition. Or he may not – interestingly he seems to deny it himself.' He looked at her. 'Perhaps you can see where I'm going with this.'

She nodded. 'If you put it together – Godel shows that paths from the present to the past may exist. And Dunne argues that it might be possible to explore such paths.'

'To dream yourself from present to past – and perhaps to do a bit of mucking about when you get there. We don't think it would be possible with this method to travel to the past, but you could perhaps send back information – perhaps in the form of a dream or a vision implanted in another wandering soul.'

Which, she reflected with growing excitement and dread, was exactly how many of the historical 'deflections' in the testimony of Geoffrey Cotesford were supposed to have originated.

'But it would take a Ben Kamen to do it, perhaps,' Mackie said. 'A man who has, or may have, both this peculiar precognitive facility, and the brains to understand Godel's mathematical solutions.' Mackie smiled. 'It's a wonderful idea, isn't it, to be able to run around in future and past, as freely as one runs as a child loose in a meadow of grass?'

'Wonderful, yes,' Mary said. 'But is it true?'

'We have reason to believe the Nazis take it seriously. Indeed they killed for it.'

Mary was shocked. 'Who was responsible?'

'Actually not a German. A British woman called Julia Fiveash. Holds a rank in the SS. Took part in the invasion – on the German side.'

'I know,' Mary said. 'I met her.'

'Did you, by God?' Mackie listened as she told him the story of how she had run into Fiveash at Battle, with her accomplice Josef Trojan. 'Well, that could be useful. Very nasty piece of work, that young lady. And now,' he said, 'we believe they are at a Nazi research centre at Richborough. And that's where they've taken Ben. He managed to hide away in the POW camp for the best part of a year, it seems. But at last they flushed him out.'

'And that's why you say the situation is becoming urgent – why you contacted me now.'

'Yes. For, you see, if they have Ben, they may have everything they need to make their wretched scheme work – if there's anything in it at all.' He stood up, holding his pipe. 'I feel a bit stale, do you? I could do with a walk, I think. And there's something else I should show you of what we're doing here…'

He led her to what appeared to be a converted barn; it was stone-built, and she wondered if this was the building with the Roman god built into its wall, but Mackie didn't mention it. Inside, the barn seemed to have been converted into a workshop, the walls panelled with whitewashed wood, and a bright light glowed from bulbs suspended from the ceiling; Mary surmised the fort must have its own generator, for no mains electricity bulb burned so bright these days. 'We do try to keep this place clean,' murmured Mackie. 'All the small parts, you know…'

The centrepiece of the room was a table bearing an elaborate mechanical device, a rectangular array screwed together from fine strips of green-painted metal, with tiny pulleys and gears and motors and threads of string – and, in one corner, two discs of what looked like ground glass. Elaborate graphs had been prepared on drafting tables, set up under the lights for visibility. It was all very complicated, but toy-like, like a model of something else rather than anything significant in itself. But it was being taken very seriously, Mary realised. Around the walls were shelves bearing spare parts, and racks of tiny screwdrivers and spanners.

Mackie asked, 'Any idea what you're looking at?'

Mary shrugged. 'Some kind of game?'

'Not exactly, but you're close. Mary, we live in a mathematical age – indeed, this is a mathematical war. And we need new mathematical techniques to cope with it all. There is a class of analyses based on differential equations, which-'

'Please, Captain. Godel and his undecidability are enough for me for one day.'

'Quite so. Look – let's suppose you want to compute the trajectory of a shell from a new breed of gun. Very necessary for firing tables, as you can imagine. Now you can list the impulse of the propellant, the angle of the barrel, gravity, air resistance and so forth. But to work out how the shell will fly you must put all that together, step by step, mapping the trajectory as a whole.'

'And that's what this thing does, right?'

'We call it a differential analyser. It's a sort of mechanical brain, if you will. You can input your requirements by using this stylus – you see, you manually push it along the curves, here. The motion is transmitted through these levers and gears and so forth to the glass discs; roughly speaking the spinning of those discs is a model of the variables of interest – I mean, the numbers that describe the shell trajectory, or whatever.'

'All right. So what's it doing here?'

'Well, Einstein's equations of general relativity are just another example of a set of differential equations. It's fiendishly difficult to extract any kind of analytical solution from them. And if you do need to extract solutions of Godel's kind, describing trajectories from present to past-'

'Oh. You'd need a machine like this.'

'We know that Kamen and O'Malley had access to an analyser in Princeton. And we believe, though we aren't sure, that Fiveash and her Nazi companions are building such a device at Richborough. We, or the mathematical boffins I recruited to work on this, thought we should study Godel's solutions ourselves, if we were to try to make sense of it all. Hence the beast you see before you.'

'Kind of Rube Goldberg, isn't it?' Mary longed to touch the gadget, to pull the little levers and turn the pulleys. 'Did you have to get these teeny tiny parts specially made?'

'Actually no. They come from a kit called Meccano.'

'A kit?'

'A construction kit for boys.'

'A toy? You made your calculating machine from a toy?'

He coughed. 'Rather embarrassing to have to admit that to an American – but, yes, afraid so. Rather British, don't you think? Of course it will make it all the more satisfying if we were to beat the bad guys with it.' He rubbed his hands together. 'Let's go back to the office, and you can tell me all about the history you've dug up.'

Back in Mackie's kitchen-study she opened her briefcase and spread the contents over the table.

'It begins again with Ben Kamen. When he arrived in England he did a bit of research himself – he is a bright boy – and came up with a medieval study of historical anomalies.'

'You're kidding.'

'Nope. He got to know Gary, and found out that his mother was a specialist in the period, and as soon as he met me he got me started on it.'

Kamen had found a memoir by a fifteenth-century monk called Geoffrey Cotesford. She raised a scrap of paper and read out: "'Time's Tapestry: As mapped by myself, that is Cotesford. "In which the long warp threads are the history of the whole world; and the wefts which run from selvedge to selvedge are distortions of that history, deflected by a Weaver unknown; be he human, divine or satanic…"'

'Deflections of history,' murmured Mackie.

'Yes. Suggestive, isn't it? Cotesford believed he had lived through one such attempted deflection himself, and had been made aware of others. He did some research – he was a Franciscan monk, a scholar, and he knew what he was doing. Plus he had access to sources, such as from the Muslim libraries in Spain, which have now been lost to us. This is a sound piece of work, considering.

'In all he found evidence of six deflections. He went right back to a prophecy supposedly intoned right here at Birdoswald by a Briton some decades before the Roman invasion of the country. It's called the Prophecy of Nectovelin. That's the one I've concentrated on first. Nectovelin itself is lost, at least the original. But Geoffrey was able to find extracts from it, in an old Moorish library in Toledo. Just a few lines – here.' She passed him a paper.