Detective Chief Inspector Parkes was an older man, surely too buoyant and relaxed for a homicide detective. He had a way of aiming his wire-frame glasses, so his eyes were lost in the glare. He started out by appreciating my house, scanning the rows of books in my downstairs lounge as if sifting for clues.

Parkes dealt his questions apologetically, as if he knew this was a futile exercise. In fact, his questions were so oblique that I wound up narrating my story: my routine, my walks, the encounters with Grace Cricklewood. In short, the truth.

“It’s a matter of discipline and persistence,” I explained, answering his question about routine. “Perhaps you recognize that in your job?”

He smiled.

“Are you any closer to solving it?”

“A murder case is like a kidnapping one. With kidnapping it’s the first twenty-four hours that are crucial. For murder it’s longer, some say forty-eight hours. The point is the odds grow longer with each tick of the clock. After a time, the process becomes rather passive. We must wait for the right person to be arrested for other reasons, or somebody remembers something. Now, tell me why you entered Shaftsbury Mansions, climbed four flights of stairs, and stood in front of the victim’s door?”

“I was in shock, I hardly knew what I was doing.”

“You heard the news, late, so it came all at once, and in shock you sleep-walked to the crime scene?”

“That sounds like a reasonable summary. ‘Sleepwalking’ is overdoing it a bit.”

“Then perhaps you can explain why you infiltrated the Mansions twice?”

“I did?” I had forgotten my first incursion, the one that stopped at the lobby, the one that could be explained by my shock story. “I didn’t do it. It’s hard to explain.”

He waited me out.

“You’re not going to understand this,” I started. “It’s all about a writer’s imagination. As I told you, I never met Grace—met to talk to anyway. She was more alive in my imagination. I guess that meant her murder was alive there too. The biggest mystery was that door, how the killer got through it. I’ve obsessed over that entry. If I could just see that door, all the details of it, it might calm me down. Nothing limits imagination like facts. Even a few details such as what her apartment building and her door looked like, the stairs she climbed, the area she lived in, help to hem in my stories about her. Each fact is something that can’t explode into a welter of permutations. This exact door and not wild speculation of a hundred types of doors. I don’t expect you to understand.”

He accepted my offer of tea, no doubt to snoop around while I was in the kitchen. He was talking on his phone when I returned. Requesting the paddy wagon, no doubt.

“You say you have an active imagination. What is your best story that explains this murder?”

“I don’t understand,” I said. “It will simply be a story.”

“I presume you bother to fit the facts of the case into your story?”

“The few that I know.” Was it a trap to go into my imaginings? Or was it a way out of a trap: by showing my detective skills I would be moving toward rationality and away from an unbalanced obsession that had me lurking around the murder flat. I blurted out the first thing that came to mind. “She didn’t know him well so I’m thinking an early romance.”

He was quiet, so I added. “You see, having seen that her door, the fisheye lens—”

“I’m rather confused here. What you appear to be doing is exactly what I do in my job. In other words, you appear to be acting as a detective. We’ve also been working on that as a main line of attack.”

“Line of attack,” I muttered to myself, then to him, “Really?”

He nodded, the light off his lenses hitting me.

“But you have so much more. You know all her phone calls and online searches, and who knows what else? I’m simply playing around with crumbs.”

He took a slow sip of tea. “I can’t give you privileged information, your facts, but I suppose I can go as far as saying her internet activity is a jumble of contradictions.”

I thought about my internet searches, few of which related to me. I might trawl for a girl’s school in Somerset, not because I’m a perv but because I’m building the biography of one of my characters. Types of knives because another character is a chef and I need telling detail. Real searches on behalf of fictional characters in made-up worlds. I explained that to Parkes.

“You identify with the victim rather closely.”

“I identify with her profession, which is my profession. As I told you. I didn’t know her.”

“Have you read any of her books?”

“Not all the way through. They’re rather long and my free time is short.”

He cleared his throat. “You’re saying that if we find something that feels out of character, way out of character, it might be down to fictional characters, that it may not be about her… proclivities?”

“You must have the book she was working on. If it doesn’t correlate to a character in it then you could be zeroing in on her character.”

I agreed to give a DNA swab to eliminate me from their “enquiries.”

At the door I was expecting the Colombo prod, the one incisive question he’d been saving for the end. Instead, he said, “What are your books about?”

About to make me a few thousand pounds. About 300 pages. It’s one of those lazy questions that writers bristle at. “Near dystopian satire,” I said, borrowing from one of my blurbs, which in turn was quoting a review in the Times Literary Supplement.

I shut the door with one word ringing in my head. Proclivities. It felt as if Parkes had popped up like a jack-in-the-box, said that one word, and then went back into his box.