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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.'

XII

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.

Mackie read:

Ah child! Bound in time's tapestry, and yet you are born free Come, let me sing to you of what there is and what will be, Of all men and all gods, and of the mighty emperors three…

'We don't know how much was lost, and how much has been garbled in the repeated transcriptions. We don't even know the purpose of the deflection, if it was a deflection. Geoffrey speculated it had something to do with the Emperor Constantine.'

'Constantine? He was centuries later. What's he got to do with the price of fish?' He glanced down the lines again.

Remember this: We hold these truths self-evident to be -

I say to you that all men are created equal, free

Rights inalienable assured by the Maker's attribute

Endowed with Life and Liberty and Happiness' pursuit.

O child! thou tapestried in time, strike home! Strike at the root!

Hmm. I'm blowed if that doesn't sound familiar.'

She smiled. 'An American would recognise the reference straight away.'

'Ah. Let me see if I can remember. "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. The Declaration of Independence.'

'Right-'

'Good Lord.' The implications seemed to hit him then, and he sat silently for a heartbeat. 'I think I'm going to have something eke to keep me awake at night, apart from Godel's banishment of time… So a modern figure sent this back to pre-Roman Britain? Why? To establish democratic values back in the Iron Age?'

'Maybe. But, Tom, the important question is not why but who.'

'Ben's friend Rory O'Malley, perhaps.'

'Yes. O'Malley was an idealistic Irishman who was a great admirer of the US. And he was a lapsed Catholic. He had grown up amid a lot of religious sectarian tension. In the US, before he went to Spain, where he met Ben, he wrote a whole series of articles attacking the Church's oppressive nature, and the evils done in the name of organised religion.'

'Hmm. Wasn't Constantine responsible for the establishment of Christianity as the Roman state religion?'

'He was indeed. You can see there's a tenuous case to be made that the Nectovelin document was authored by O'Malley, in order to deflect Constantine's establishment of the Church. He even sent it back to 4BC, the year Christ was born, to establish the link with Christianity.'