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‘Thanks,’ I said, wondering how they managed to fill two hefty tomes on the subject, and why they’d bother. The back sleeves revealed that, apart from sporting obligatory professorial beards, both men suffered from the condition.

‘In Dr Cheyne’s book, I think I may even have found the answer to your out-of-body experience when you entered Eve’s house that night and saw her … you know …’

‘Being attacked by Meehan,’ I finished helpfully.

‘Professor Cheyne has evidence that if sleep paralysis is prolonged, it can become an out-of-body experience. I’ve been thinking, the absinthe you consumed, that had been spiked with cannabis and tranquilliser, could have slowed down your brain’s reactions. You may have stayed asleep for longer than usual.’

I nodded, trying not to look thick.

‘If the cannabis prolonged your sleep paralysis episode, then it would have developed into an out-of-body experience.’

I scoffed: ‘Oh right, so I floated into Eve’s bedroom, for real?’

Lilian’s eyes flashed steel.

‘You really shouldn’t sneer,’ she snapped, ‘out-of-body experiences are scientifically-proven phenomena, even if we don’t fully understand what causes them. In one experiment, a woman came out of her body and memorised a five-digit number positioned in the corner of the room by the scientist, which she couldn’t possibly have seen from the bed. They’re also more common than you might think. One in ten of us has had one. Some people have them regularly. I could induce one in you right now. Look up the God Helmet in the library. Electrical impulses to certain parts of the brain can induce an out-of-body experience.’

‘So you’re saying I left my body, went through the wall of the house and witnessed what happened, in real time?’

‘Cheyne talks about flying over Toronto at night when he’s out of his body. He can see the streets below him, the traffic and the people. It’s called lucid dreaming. It’s a very exciting new field. Look, Donal, all I’m asking you to do is read the books and then we can start breaking down your experiences based on what’s already out there in the field.’

‘Do either of these men know how to stop it happening?’

‘That’s the fascinating thing about Cheyne. He says that as soon as he comes out of his body, he no longer feels fear. Sometimes he can watch himself having a nightmare from above, while feeling totally calm.’

I couldn’t believe what I was hearing: these academic claims were even wilder than mine.

‘The bottom line is: there is no cure. The best you can do is manage it, and the only way to manage it is to prolong the experience so that you come out of your body. You have to train yourself not to freak out and wake up.’

‘You make that sound so easy, Lilian,’ I smiled, ‘I don’t think you quite appreciate how terrifying it feels when I’m having these encounters. Can you imagine waking up in the middle of the night to an imposter who then attacks you?’

‘I’m just saying you could look at this as an amazing opportunity.’

‘Oh I am, Lilian. Some night I’ll fly past your place, maybe tap on the window.’

It bounced off her. She wasn’t one for playful banter. She took a sip of her drink as I poured out my story about Marion’s twin apparition the previous Friday evening. I didn’t mention that I’d been drinking all afternoon, or that I’d wound up in the foetal position next to a tree that had been pissed on that day by two thousand dogs.

I wrapped up: ‘I’m thinking maybe this isn’t connected to the night-time stuff. It didn’t feel as … real.’

I couldn’t wait to drop the punchline: how these appearances had helped me find a key contradiction in Karen’s alibi. Explain that away, Sigmund Fraud

‘This is almost certainly connected to your other visions of Marion,’ she announced, planting her drink firmly on the table. ‘There’s a phenomenon called daytime para-hypnagogia or DPH,’ she began and I stared at her in disbelief. At least it had a good name this time.

She was off: ‘DPH is when a dream-like image or thought intrudes into your waking consciousness. It’s this threshold consciousness thing, between sleep and wakefulness, like sleep paralysis. DPH happens to people suffering from extreme tiredness, or extreme boredom. For example, it’s been described by prisoners who’ve spent a long spell in solitary confinement. The brain normally doesn’t bother remembering the image, unless it’s been influenced by some form of autosuggestion.’

‘Autosuggestion?’

‘Autosuggestion is like, oh I don’t know, “I must I must increase my bust?”’

I managed, somehow, not to look at her tits. It was a miracle.

‘The man who coined the term autosuggestion, Emile Coué, believed that anyone can change themselves by continually feeding their subconscious an idea. For example, he had a group of patients with all sorts of physical ailments say to themselves several times a day: “Every day, in every way, I am getting better and better.” He proved that the patients who did this recovered better than the ones who didn’t.

‘The same man came up with the placebo effect. He found he could prescribe a tablet that was just powder, but if he told the patient it was the best thing ever, their health would improve.’

What the fuck has this got to do with anything? my expression must have said.

‘Okay, so let’s start with DPH. You were exhausted on Friday, from your usual lack of sleep. You’d been walking in extreme heat. The autosuggestion could be that you’d been thinking about Marion over and over. Your subconscious had been slaving over her case. So when your poor dazed brain slipped into REM, it’s only natural that Marion should appear.’

‘Okay but the thing is, since this happened, I’ve found out that the two places where she appeared to me are connected and could be critical to the case.’

She sat forward.

‘It turns out that one of the suspects in the case said in her first statement that she parked her car near the pub on Sangora Road before discovering Marion’s body with Peter.’

Lilian was nodding lots, blinking little.

‘Then in her second statement, which she gave two days later, she said there were no parking spaces available on Sangora, so instead she parked on the only road off it, Strathblaine Road …’

‘So if she wasn’t lying, she must’ve parked near Marion’s home twice that day,’ Lilian finished for me.

‘Exactly. The thing is, I never would have spotted this contradiction had she not appeared to me on both streets a few days earlier.’

Explain that, doc? I almost cried.

Her eyes drifted to a distant horizon. I imagined her scientific mind rampaging away behind that frown, pulling up trees until logic found a course through this bewildering wood.

‘Science accepts that the hypnagogic state can provide the answers to problems. There’s the famous case of a scientist who was trying to figure out the atomic structure of benzene. He was half-asleep in front of the fire. In the flames he could see molecules forming into snakes. Suddenly, one of the snakes grabbed its tail in its mouth. Bingo, he realised that the structure of benzene is a closed ring.’

Her brain was hurtling like a dead star. Mine ached.

‘Edison, Newton, Tesla all credit hypnagogic states for some of their best discoveries. Beethoven, Wagner, Edgar Allan Poe all used it for inspiration.’

I couldn’t stop my head wobbling with pride. But I thought I’d better bring up one key difference between me and my genius hypnagogic brethren.

‘The only thing is, I didn’t make the connection between the roads while I was in that hypno state you describe. I made the connection much later, when I read Karen’s statements.’

‘Yes, but you were most likely in a hypnagogic state when you saw Marion.’

‘Which means?’

‘Supposing you made the connection, and your subconscious stored it until you needed to call upon it. Let’s run with the theory that your subconscious mind has found a way to use sleep paralysis and the hypnagogic state to identify clues in a live case. What if your sleeping disorder actively helps you find contradictions or mistakes – clues – that have got past everyone else? Now that’s a paper I could get published.’