It was obviously not possible to discuss this issue rationally. I moved to her other statement.

‘Is there a problem with being Jewish?’

‘Jewish is fine. Freyberg is not fine. But if it’s Freyberg it would explain why my mother kept mum. No pun intended. You’ve never heard of him?’

‘Only as a result of this project.’

‘If you followed football you would have.’

‘He was a footballer?’

‘A club president. And well-known jerk. What about the third person?’

‘Geoffrey Case.’

‘Oh my God.’ Rosie went white. ‘He died.’

‘Correct.’

‘Mum talked about him a lot. He had an accident. Or some illness – maybe cancer. Something bad, obviously. But I didn’t think he was in her year.’

It struck me now that we had been extremely careless in the way we had addressed the project, primarily because of the misunderstandings that had led to temporary abandonments followed by restarts. If we had worked through the names at the outset, such obvious possibilities would not have been overlooked.

‘Do you know any more about him?’

‘No. Mum was really sad about what happened to him. Shit. It makes total sense, doesn’t it? Why she wouldn’t tell me.’

It made no sense to me.

‘He was from the country,’ Rosie said. ‘I think his father had a practice out in the sticks.’

The website had provided the information that Geoffrey Case was from Moree in northern New South Wales, but this hardly explained why Rosie’s mother would have hidden his identity if he was the father. His only other distinguishing feature was that he was dead, so perhaps it was this to which Rosie was referring – her mother not wanting to tell her that her father had died. But surely Phil could have been given this information to pass on when Rosie was old enough to deal with it.

While we were talking, Gene entered. With Bianca! They waved to us then went upstairs to the private dining section. Incredible.

‘Gross,’ said Rosie.

‘He’s researching attraction to different nationalities.’

‘Right. I just pity his wife.’

I told Rosie that Gene and Claudia had an open marriage.

‘Lucky her,’ said Rosie. ‘Are you planning to offer the same deal to the winner of the Wife Project?’

‘Of course,’ I said.

‘Of course,’ said Rosie.

‘If that was what she wanted,’ I added in case Rosie had misinterpreted.

‘You think that’s likely?’

‘If I find a partner, which seems increasingly unlikely, I wouldn’t want a sexual relationship with anyone else. But I’m not good at understanding what other people want.’

‘Tell me something I don’t know,’ said Rosie for no obvious reason.

I quickly searched my mind for an interesting fact. ‘Ahhh … The testicles of drone bees and wasp spiders explode during sex.’

It was annoying that the first thing that occurred to me was related to sex. As a psychology graduate, Rosie may have made some sort of Freudian interpretation. But she looked at me and shook her head. Then she laughed. ‘I can’t afford to go to New York. But you’re not safe by yourself.’

There was a phone number listed for an M. Case in Moree. The woman who answered told me that Dr Case, Sr, whose name was confusingly also Geoffrey, had passed away some years ago and that his widow Margaret had been in the local nursing home with Alzheimer’s disease for the past two years. This was good news. Better that the mother was alive than the father – there is seldom any doubt about the identity of the biological mother.

I could have asked Rosie to come with me, but she had already agreed to the New York visit and I did not want to create an opportunity for a social error that might jeopardise the trip. I knew from my experience with Daphne that it would be easy to collect a DNA sample from a person with Alzheimer’s disease. I hired a car and packed swabs, cheek-scraper, zip-lock bags and tweezers. I also took a university business card from before I was promoted to associate professor. Doctor Don Tillman receives superior service in medical facilities.

Moree is one thousand two hundred and thirty kilometres from Melbourne. I collected the hire car at 3.43 p.m. after my last lecture on the Friday. The internet route-planner estimated fourteen hours and thirty-four minutes of driving each way.

When I was a university student, I had regularly driven to and from my parents’ home in Shepparton, and found that the long journeys had a similar effect to my market jogs. Research has shown that creativity is enhanced when performing straightforward mechanical tasks such as jogging, cooking and driving. Unobstructed thinking time is always useful.

I took the Hume Highway north, and used the precise speed indication on the GPS to set the cruise control to the exact speed limit, rather than relying on the artificially inflated figure provided by the speedometer. This would save me some minutes without the risk of law-breaking. Alone in the car, I had the feeling that my whole life had been transformed into an adventure, which would culminate in the trip to New York.

I had decided not to play podcasts on the journey in order to reduce cognitive load and encourage my subconscious to process its recent inputs. But after three hours I found myself becoming bored. I take little notice of my surroundings beyond the need to avoid accidents, and in any case the freeway was largely devoid of interest. The radio would be as distracting as podcasts, so I decided to purchase my first CD since the Bach experiment. The service station just short of the New South Wales border had a limited selection but I recognised a few albums from my father’s collection. I settled on Jackson Browne’s Running on Empty. With the repeat button on, it became the soundtrack to my driving and reflections over three days. Unlike many people, I am very comfortable with repetition. It was probably fortunate that I was driving alone.