Titus scratched his head. ‘Here we go again … Dare I ask, why not?’

‘The trouble is, Titus,’ the ColU said, ‘some scholars have always believed that nature does not contain infinities. Infinities are just a useful mathematical toy invented by humans, with no correspondence to reality. Unlike the number three, say, which maps on to collections of three objects: three people, three potatoes …’

Stef said, ‘Infinities can make sensible questions meaningless. Titus, start with the number one.’

‘I think I can grasp that.’

‘Add another one.’

‘I have two.’

‘Subtract one.’

‘I have one again.’

‘Add one.’

‘Two.’

‘Subtract one.’

‘One!’

‘Add one!’

‘Two!’

‘Subtract one!’

‘One!’

She held up her hands. ‘OK, that’s enough. You get the idea. Now if I asked you to stop doing that after some finite number of steps – twelve or twenty-three or five hundred and seventy-eight – what answer would you get?’

‘That’s easy. Either two or one.’

‘Definitely one or the other?’

‘Of course.’

‘But if I asked you to go on for ever, what answer would you end up with?’

‘I – ah … Oh.’

‘You see?’ Stef said. ‘The answer can’t be determined. The question becomes absurd, once you bring infinity into it.’

Titus said, ‘I can feel my brain boiling like the water in that pot.’

‘Physics – my philosophy – is about asking sensible questions and expecting sensible answers. About being able to predict the future from the past. When you bring in infinities, sensible questions have dumb answers. The whole system breaks down.’

The ColU said, ‘So the point is, the multiverse – the collection of the universes we visit – must be finite. Because nature won’t allow infinities.’

Mardina scowled. ‘Well, so what? What do I care if there is one reality, or ten or twenty or a million?’

Stef said, gently but persistently, ‘It matters because a finite multiverse has an edge. And if one of the member universes should encounter that edge …’ She looked into the pot of water, and pointed out one largish bubble slowly migrating from the boiling centre towards the side of the clay pot. ‘Watch.’ When the bubble reached the edge, it popped, vanishing as if it had never existed.

The ColU said, ‘Given that one simple fact – that the multiverse must be finite – and knowing how old the universe is, or was in the age we came from – it has always been possible to make an estimate of how long the universe was going to last. How long it was likely to be before we hit the multiverse wall. Probabilistic only, but …’

Titus snapped, ‘How long, then?’

The ColU said, ‘My latest estimate, based on my inspections of the sky as far back as our time on the Malleus Jesu, is three and a half billion years after the age of mankind.’

Titus shook his head, growling under his breath. ‘An absurd number.’

‘Not to an astrophysicist,’ Stef said with a smile. ‘That is, a philosopher who knows the stars, Titus. In my culture we were pretty sure that the universe was a bit less than fourteen billion years old. So why should the universe last longer than a few billions more? You see? Not trillions or hundreds of trillions of years, or beyond the age of proton decay … In my culture we used to call this the Doomsday Argument. Why should the future be so dissimilar to the past? Shouldn’t we expect to find ourselves somewhere in the middle of the life span of the universe, not in its first few instants?’

Mardina was touching her belly again, as if trying to shield her baby from all this. ‘Three point five billion years. You’re saying the universe will die, three point five billion years after the year I was born. If I understand these numbers at all – that’s still an immense stretch of time.’

‘Of course,’ Stef said. ‘But here’s the catch, Mardina. We have been brought to the end of that stretch. That’s what we’ve determined – what the ColU has established definitively from his study of the sky.’

‘It isn’t just the ageing of the stars, the position of the galaxies,’ the ColU said. ‘That would be enough for a rough estimate. There are also distortions in the background glow of the sky, the fading relic of the Big Bang explosion. Distortions caused by events from the future.’

Titus tapped the pot with a fingernail. ‘Because of the proximity of this wall of yours.’

‘Which is a tremendously energetic horizon that sends back signals, back through time. Signals that show up as distortions in the background radiation. That is why I am able to be so precise. This, the age in which we find ourselves, is the End Time—’

‘I don’t want to hear it.’ Mardina stood, suddenly, pulling away from Beth, the weight of her blankets almost making her stumble into the fire. ‘I don’t want to hear any more.’ She clamped her hands over her ears, and stomped out.

Beth half-rose. ‘She needs her boots, her cloak if she’s going out there—’

‘No.’ Chu was already on his feet, and grabbing his own boots. ‘Let me. It is our problem.’

Titus nodded. ‘Let him go. It will be harder for them, to be so young, to have to face this. We must let them find their way.’

Beth longed to go after her daughter, but she made herself sit still. ‘You’re a wise man, Titus Valerius.’

He smiled, looking tired. ‘No. Just an old one, and a survivor. So, Collius. Here we are in the far future, as I understand it. How long until we encounter this – edge?’

The ColU said simply, ‘A year. No more.’

Titus nodded. ‘And what then? What will happen?’

Stef said, ‘A wall of light.’

Titus heaved a huge sigh. ‘Very well. From the ethereal to the practical. Shall we consider our route for tomorrow? And then we all need sleep, if Morpheus grants it tonight.’

CHAPTER 68

The antistellar was the place where all the gravity-train tunnel mouths converged.

At the final destination, as the rest of the party went through the by-now practised routine of grappling their sled-cart out of the frictionless tube, Stef walked forward, away from the tunnel. The ice under her booted feet was concrete-hard but ridged, crumpled, wind-scoured – evidently old – and was not slick, maybe it was too cold for that; the footing was good. Once, back in her original timeline, she’d skimmed in space over the polar caps of Mars, which were very old accretions of water ice, the deepest layers perhaps a couple of million years old. The ice under her feet now might be a thousand times older than that. She really had been brought to an antique time, an old universe.

And the dark side cold itself – she seemed to remember that too, from her first experience here. This point furthest from the warmth of the star was the centre of a hemisphere of endless night, of ice and dark. Yet there was a limit to the cold, even here; some warmth at least washed around the world from the day side. It was evidently a survivable cold. Still, her breath steamed, and the frigid air plucked at her lungs and nose and eyes.

As she walked she could clearly see, by the light of an Andromeda reduced to a bloated sunset sitting on the horizon, more tunnels, dark gashes in the ground: a network of tunnels lacing this chill hemisphere of the planet, and all converging here, at the antistellar, at this point of geographic symmetry.

And at the precise antistellar point itself, the place all the tunnels seemed to be pointing to – something was there, a kind of flattened dome from which came a glow of pale light, with structures dimly visible within.

Earthshine. It had to be him.

Stef walked back to her companions. By now they had the cart set up on its runners, ready for the final haul over the ice to the dome. The ColU was in its pack on Chu’s back. Mardina, more visibly pregnant every day despite her layers of cold-weather clothing, stood at Chu’s side, their gloved hands locked together, breath wreathed around their faces.