'But not when anyone's looking,' said the Doctor. 'It only happens when no one can see how it's done.'

'But why?' asked Martha.

'Oh really, dear,' said Mrs Wingsworth. The mechanics of these things are so terribly vulgar.'

'Exactly,' said the Doctor. 'It's all part of the well-mannered service. Isn't it, Gabriel?'

They all turned to the robot. His blank, metal head reflected their faces back at them. 'There are protocols, Mr Doctor,' he said.

'You don't really understand it yourself, do you?' said the Doctor, gently.

'I . . .' began Gabriel. 'The logic is impaired.'

'Yes,' said the Doctor. 'That's the problem, isn't it? You're struggling to make sense of it. The whole starship is.'

'What?' said Martha. 'The starship is thinking?'

'Well, yeah,' said the Doctor. 'Kind of. We can have the philosophy later, but basically it responds to stimuli the best way it can, just like the rest of us. And sometimes we think about it and sometimes we just respond.'

'You mean it's like breathing,' said Martha. 'You can control your breathing consciously, but mostly you don't really think about doing it.'

'That's true of the Balumin, too, dear,' said Mrs Wingsworth. 'Although my cousin Sandy makes a great kerfuffle about how you should always control your breathing. She was into all that sort of thing: crystals, coloured smoke...'

'I can hold my breath,' said Archibald proudly. 'For when we go swimming.'

'I think we've established the analogy,' said the Doctor impatiently, always eager to get back to the mystery. 'Now, this ship is going round and round in circles, isn't it? So every day's the same and no one dies for good.'

'It's a time loop,' said Martha. 'Like in that film, Groundhog Day.'

'Huh,' said Archibald. 'Groundhogs are bad. They take our stuff.'

'Yes, it is a bit like the film,' said the Doctor. 'Just without all the dancing at the end. And it's not a complete loop. Things don't all go back to the beginning at midnight, they jump back bit by bit. Which suggests the loop is broken somewhere. And we kind of skip over the gap.'

'That's bad, isn't it?' said Martha, seeing the look in his eyes.

'Yes,' he said. 'A closed loop just runs and runs for ever. But with a gap in it, every time it goes round there's something a bit different. You have a scar, you don't have a scar. The badgers come back with new earrings.' He grinned. 'See it didn't try to make another TARDIS key. Probably couldn't understand it. But anyway, all the time it's making things better again, it needs energy. A lot of energy.'

'But how?' said Martha. 'What's keeping it all together?'

'There are protocols, Ms Martha,' said Gabriel. But he did not explain any further.

'Yes, there are protocols,' said the Doctor. 'The Starship Brilliant doesn't fly through what you think of as reality, Martha. Think of where we are right now as a sort of sea of dreams. And when it's flying normally it needs to get itself back out of that and into the "real" universe. So, as well as the experimental drive itself, it must also be able to twist reality a bit.'

'It was all in the brochure, dear,' said Mrs Wingsworth.

'That doesn't sound good,' said Martha. 'You're not supposed to change reality, are you?'

'Well, usually you're all right if you only twist it a bit,' said the Doctor. 'The TARDIS has to be able to warp things about to get in and out of the Vortex. That's your top-end of the clever scale. A ship like this one has just got to make sure the ship holds together and everyone comes out the far end the same shape as when they went in.' He shook his head. 'Though you should see what happens to people when they travel about a lot. Long-term exposure to non-reality, that can be a bit weird.'

'But that's not what's happening here, is it?' said Martha.

'No,' said the Doctor. 'It's working all-out to hold everything together. The Brilliant has a rough idea of how things are meant to be, and it tries to keep them like that. And it's got protocols to look after the passengers and make sure they are safe. So it's restocking the nibbles and bringing you back to life. And all in the most discreet of ways, so you don't quite notice.'

'The service has been exemplary,' agreed Mrs Wingsworth.

'Thank you, Mrs Wingsworth,' said Gabriel. 'I shall pass on your kind words to the captain.'

'The captain,' said the Doctor. 'I should have a word with him, too.'

'I regret to say that the captain cannot meet with passengers at the present time, Mr Doctor,' said Gabriel. 'I would be happy to pass on any message to her.'

'Gabriel,' said the Doctor, 'if I don't speak to the captain myself, the whole ship is in danger. It's only a matter of time before you exhaust the energy available and the Brilliant just explodes. And there'll be no more miraculous resurrections then.'

Gabriel considered carefully. 'You believe the passengers are at risk, Mr Doctor?' he said.

'Yes,' said the Doctor.

'Very well,' said Gabriel. 'Please accompany me.'

They followed the robot – left, left again and then right, and up the wide staircase into the dining room. Martha could hear the tentacled aliens yammering away to each other over in the cocktail lounge, oblivious to any danger. A thought struck her.

'Where are Jocelyn and Dashiel?' she asked the Doctor.

'Dash is sleeping,' Archibald told her, eager to be helpful.

'Yeah,' said the Doctor, 'had a nasty bang on his head. Now, we're up here, aren't we?'

He led them off to the side of the dining room and into an area of the ship that clearly wasn't for passengers. There was no wood panelling or plush carpets but whitewashed walls and thick metal. It felt more like the kind of sailing ships Martha had seen in films. They clanged up the steep metal staircase onto the upper level and into a cramped space where the ship's crew appeared to hang out. There were posters on the walls of the tiny sleeping spaces, young and pretty humans waving in 3D.

But Martha had been in the accommodation blocks of hospitals, where the doctors and nurses lived. Her first thought was how tidy these sailors must be. They didn't have books and clothes and DVDs littered all over the floor. She assumed they had to keep their quarters tidy as part of the job. Then she saw the great gash in the ship's metal wall and its cause, the sharp-nosed little space car in the middle of the deck. Everything that hadn't been bolted down had been sucked out into space before the Brilliant could seal the hole. She felt a pang of horror at the thought of the sailors who must have died at the same time.

'That's you, is it?' she asked Archibald sourly.

'Yeah,' he replied, but he could not meet her eye. For a moment she felt guilty for being so mean to him. Then she remembered what he'd done to her – the icy pain of the blade as it went through her – and to the other people on board.

'He is trying to be a better badger, dear,' Mrs Wingsworth told her. 'But you have to remember how he's been brought up. I doubt he's been to public school.'

'Went to Eton Nine,' said Archibald. 'S'on an asteroid.'

Mrs Wingsworth quivered with amazement, her long tentacles up to her mouth. 'Really, dear?' she said.

'Yeah,' said Archibald. 'Burnt it down, took the gold.'

'Well that's something of a relief,' said Mrs Wingsworth.

'Is it?' asked Martha. 'I don't see how.'

'Well, dear,' laughed Mrs Wingsworth. 'I was worried for a moment he'd been admitted as a pupil. You know how standards are slipping.'

They followed the Doctor and Gabriel along through the passageway. The small sleeping areas got slightly bigger as they went, and Martha realised they had started in the area for the lowest officers and were now walking up through the ranks. Gabriel opened a heavy door into a chamber full of little rooms, and Martha could see how much better the Brilliant's officers had it. They had proper quarters, with beds and wardrobes and desks.