But as the game progressed, he found himself drawn more and more into all the problems going around his mind, despite himself. And he kept wondering if Bob Manthorpe had called him back yet. He’d phoned him first thing this morning and left a message.

As Kaplan and he changed ends, Ollie stopped by his bag to have a swig of water and glance at his phone, on silent. No messages. It was now 1.15 p.m. and the retired vicar had not called him back. Hopefully he would sometime this afternoon.

He kept his concentration focused enough to win the first set, narrowly, on a tie-break. He lost the second 4 – 6, got whopped 0–6 on the third and was 0–3 down in the fourth when their time was finally up.

Before showering and changing, they went to the bar. Ollie ordered pints of lime and lemonade and some sandwiches for them. Then they carried them over to a table, sat and caught up on each other’s news.

‘You were doing really well in the first set,’ Kaplan said. ‘Then you kind of lost the plot. I guess it was superior play that made you realize you really didn’t have a chance, heh-heh.’

Ollie glanced at his phone and saw there was still no returned call from Manthorpe. He grinned, downed a large gulp of his drink, then wiped the back of his mouth with his hand. ‘I’ve just got a shitload of stuff on my mind at the moment,’ he said. ‘Sorry if my game was rubbish.’

‘It’s always rubbish.’

‘Sod you!’

Kaplan grinned. ‘So what’s on your mind?’

Kaplan worked in the Artificial Intelligence faculty at Brighton University. He had a number of theories that had always seemed to Ollie to be on the wild side of science, but he never dismissed anything. One of Kaplan’s interests, and the topic of a book he had written, which had been published by a respected academic imprint, was whether a computer could ever appreciate the taste of food, laugh at a joke or have an orgasm.

‘What’s your view on ghosts, Bruce?’ he asked him, suddenly.

‘Ghosts?’ the professor repeated, quizzically.

‘Do you believe they exist?’

‘Absolutely, why wouldn’t they?’

Ollie looked at him, astonished. ‘Really?’

‘I think you’ll find a lot of mathematicians and physicists – like me – believe in them.’

‘What’s your theory – I mean – what do you think they are?’

‘Well, that’s the ten-gazillion-dollar question.’ He laughed again, the short, nervous, ‘Heh-heh’ laugh he regularly made, like a nervous tic. ‘Why are you asking?’

‘I think our new house may be haunted.’

‘I can’t remember – did you say it had a tennis court?’

‘No, but there’s plenty of room for one.’

‘Going to put one in?’

‘Maybe. A lot of maybes at the moment.’

‘And you have a ghost, you think? A smart or a dumb ghost?’

‘There’s a difference?’ Ollie considered Bruce to be super-intelligent and he liked that the scientist always had an unusual – and often unique – perspective on almost any topic they ever discussed.

‘Sure! A big difference. Want to tell me about this ghost?’

Ollie told him about the bed turning round, about the spheres, the apparition that Caro and Jade had seen and all the other strange events that had happened. Kaplan listened, nodding his head constantly. When he had finished, Ollie asked him, ‘So what do you make of all that?’

Kaplan removed his towelling headband and held it up. ‘Do you know what Einstein said about energy?’

‘No.’

‘He said energy cannot be created or destroyed, it can only be changed from one form to another.’ Making a show of it, he squeezed his headband until droplets fell from it on to the white surface of the table. ‘See those droplets? That water’s been around since the beginning of time. In one form or another molecules of it might have passed through Attila the Hun’s dick when he was taking a piss, or gone over the Niagara Falls, or come out of my mother’s steam iron. Heh-heh. Every molecule in them has always existed, and always will. Boil one and it turns to steam and goes into the atmosphere; then it’ll return with a bunch of others as mist or rain one day, somewhere; it’s never going to leave our atmosphere. No energy will or can – you with me?’

‘Yes,’ Ollie said, dubiously.

‘So if you stick a knife through my heart now, killing me, you can’t kill my energy. My body will decay, but my energy will remain behind – it will go somewhere – and re-form somewhere.’

‘As a ghost?’ Ollie asked.

Kaplan shrugged. ‘I have theories about memory – I’m doing research into it right now – I think it’s a big part of consciousness. Our bodies have memory – keep doing certain movements in certain ways – certain stretches – and our bodies find them increasingly easier, right? Fold a piece of paper and the crease remains – that’s the paper’s memory. So much of what we do – and the animal kingdom does – is defined by memory. If a person spends a long time in a confined space, maybe the energy has memory, too. There’s one of the colleges at Cambridge where a grey lady was regularly seen moving across the dining hall. About fifty years ago they discovered dry rot and had to put a new floor in, raising the level about a foot. The next time the grey lady was seen, she was cut off at the knees. That’s what I mean by a dumb ghost. It’s some kind of memory within the energy that remains after someone dies – and sometimes it retains the form of that person.’

‘So what’s a smart ghost?’

‘Heh-heh. Hamlet’s father, he’s an example of a smart ghost. He was able to talk. Let not the royal bed of Denmark be a couch for luxury and damned incest. By howsoever thou pursues this act, taint not thy mind nor let thy soul contrive against thy mother aught. Leave her to heaven.’ He grinned at Ollie. ‘Yeah?’

‘So a smart ghost is basically a sentient ghost?’

‘Sentient, yes. Capable of thinking.’

‘Then the next step would be a ghost capable of actually doing something physical? Do you think that’s possible?’

‘Sure.’

Ollie stared hard at him. ‘I thought scientists like you were meant to be rational.’

‘We are.’

‘But you’re not talking about the rational, are you?’

‘You know what I really think?’ Kaplan said. ‘We humans are still at a very early stage in our evolution – and I’m not sure we’re smart enough to get much beyond where we are now before we destroy ourselves. But there’s a whole bunch of stuff waiting for us out there in the distant future if we succeed. All kinds of levels – planes – of existence we don’t even yet know how to access. Take a simple ultrasonic dog whistle as an example. Dogs can hear it but we can’t. What else is going on around us that we’re not aware of?’

‘What do you think is?’

‘I don’t know, but I want to live long enough to find out, heh-heh. Maybe ghosts aren’t ghosts at all, and it’s to do with our understanding of time. We live in linear time, right? We go from A to B to C. We wake up in the morning, get out of bed, have coffee, go to work, and so on. That’s how we perceive every day. But what if our perception is wrong? What if linear time is just a construct of our brains that we use to try to make sense of what’s going on? What if everything that ever was, still is – the past, the present and the future – and we’re trapped in one tiny part of the space–time continuum? That sometimes we get glimpses, through a twitch of the curtain, into the past, and sometimes into the future?’ He shrugged. ‘Who knows?’

Ollie frowned, trying to get his head round his friend’s argument. ‘So are you saying that the ghost in our house isn’t really a ghost at all? That we’re seeing something – or someone – in the past, who’s still there?’

‘Or maybe someone in the future. Heh-heh.’

Ollie grinned, shaking his head. ‘Jesus, you are confusing me.’

‘Go with it – sounds like you are on an amazing ride.’

‘Tell Caro that – she’s scared out of her wits. If you want to know the truth, so am I.’