'But that seemed a bit arbitrary to Godel; he wasn't reassured. So he – and we think in collaboration with Kamen – dug into Einstein's mathematics. I admit I'm winging it a bit here; Godel hasn't actually written up his results formally, and until he does we're all a bit in the dark. But what he seems to be trying to do is to find a description of a possible universe, consistent with Einstein, in which there could be no cosmic time.'
'And he's found one.'
'I'm afraid so. He says that if the universe rotated, in a grand and global way, it would be possible for me to fly around it in some super Spitfire – heading off into the future, but at last arriving in the past.'
'So time travel would be possible in such a universe.'
'Well, that's the implication you and I would naturally draw. I think Godel, however, doesn't care about time travel. He's a logician; he's simply trying to establish a contradiction. For you see if there is no global time in his model universe, you can't assume a global time exists in ours, for there is no difference in principle between the universes. And so our sense of inner time, our most basic apprehension of the universe, is actually an illusion.' His eyes were unfocused. 'Must say that when I lie awake at night, this sort of stuff scares me more than all the Panzers in Germany. Poor old Godel.'
'But what we have to be concerned about,' Mary said, 'is the practical application.'
'Quite.' He tinkered with his pipe, tucking the last strands of his precious tobacco into place, and lit it. She'd observed this sort of finicky fiddling in smokers ever since tobacco had gone on the ration. He blew smoke up towards the ceiling. 'Now we must come back to Ben Kamen again – and having led you off into the depths of time and space, I'm going to ask you to take another leap in the dark. For at Princeton Ben developed yet another new set of ideas, with a student called Rory O'Malley…
'Look, Godel's theory suggests that a path might exist between present and past – between this room, say, and the Roman fort of AD 200 from whose ruins it was built. The question is, how do you find your way along that path? Have you ever heard of a writer called John William Dunne?'
'I think so,' Mary said. 'Something to do with J.B. Priestley?'
Dunne was British, an aeronautical designer. He had served as a soldier, and was invalided out of the Boer war. He had become interested in the perception of time, having had, he believed, a glimpse of the future through a dream.
Mackie waved a hand, a bit dismissively. 'Sort of half-baked stuff that becomes fashionable from time to time in certain arty circles, playwrights and novelists and that sort of crew. That's why you connect him with Priestley, I imagine. But what gives Dunne's work credibility is a patina of science. He was an engineer. So he is methodical even about his dreams; he derives statistics about them; he couches his ideas in language that sounds almost Einsteinian. Dunne says essentially that when we sleep we come untethered in time. He imagines time as an extra dimension, a landscape you can go exploring. Some remember what they see during their dream journeys, some don't. And some may be able to direct where their dreaming selves travel.'
It felt very strange to Mary to hear these ideas expressed by a serious middle-aged man in a sober Navy uniform.
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.'