She must have seen that I was resisting.

‘Hey, you schedule your time so you don’t waste it, right?’

‘Correct.’

‘So, you’ve committed to two days with me. If you shut yourself down, you’re wasting two days of your life that someone is trying to make exciting and productive and fun for you. I’m going to –’ She stopped. ‘I left the guidebook in my room. When I come down, we’re going to breakfast.’ She turned and walked to the elevators.

I was disturbed by Rosie’s logic. I had always justified my schedule in terms of efficiency. But was my allegiance to efficiency or was it to the schedule itself? Was I really like my father, who had insisted on sitting in the same chair every night? I had never mentioned this to Rosie. I had my own special chair too.

There was another argument that she had not presented, because she could not have known it. In the last eight weeks I had experienced two of the three best times of my adult life, assuming all visits to the Museum of Natural History were treated as one event. They had both been with Rosie. Was there a correlation? It was critical to find out.

By the time Rosie came back I had performed a brain reboot, an exercise requiring a considerable effort of will. But I was now configured for adaptability.

‘So?’ she said.

‘So, how do we find the world’s best breakfast?’

We found the World’s Best Breakfast round the corner. It may have been the unhealthiest breakfast I had ever eaten, but I would not put on significant weight, nor lose fitness, brain acuity or martial-arts skills if I neglected them for two days. This was the mode in which my brain was now operating.

‘I can’t believe you ate all that,’ said Rosie.

‘It tasted so good.’

‘No lunch. Late dinner,’ she said.

‘We can eat any time.’

Our server approached the table. Rosie indicated the empty coffee cups. ‘They were great. I think we could both manage another.’

‘Huh?’ said the server. It was obvious that she hadn’t understood Rosie. It was also obvious that Rosie had very poor taste in coffee – or she had done as I had and ignored the label ‘coffee’ and was enjoying it as an entirely new beverage. The technique was working brilliantly.

‘One regular coffee with cream and one regular coffee without cream … please,’ I said.

‘Sure.’

This was a town where people talked straight. My kind of town. I was enjoying speaking American: cream instead of milk, elevator instead of lift, check instead of bill. I had memorised a list of differences between American and Australian usage prior to my first trip to the US, and had been surprised at how quickly my brain was able to switch into using them automatically.

We walked uptown. Rosie was looking at a guidebook called Not for Tourists, which seemed a very poor choice.

‘Where are we going?’ I asked.

‘We’re not going anywhere. We’re there.’

We were outside a clothing store. Rosie asked if it was okay to go inside.

‘You don’t have to ask,’ I said. ‘You’re in control.’

‘I do about shops. It’s a girl thing. I was going to say, “I suppose you’ve been on Fifth Avenue before”, but I don’t suppose anything with you.’

The situation was symmetrical. I knew not to suppose anything about Rosie, or I would have been surprised by her describing herself as a ‘girl’, a term that I understood to be unacceptable to feminists when referring to adult women.

Rosie was becoming remarkably perceptive about me. I had never been beyond the conference centres and the museum, but with my new mind configuration, I was finding everything fascinating. A whole shop for cigars. The prices of jewellery. The Flatiron Building. The sex museum. Rosie looked at the last of these, and chose not to go in. This was probably a good decision – it might be fascinating, but the risk of a faux pas would be very high.

‘Do you want to buy anything?’ said Rosie.

‘No.’

A few minutes later, a thought occurred to me. ‘Is there somewhere that sells men’s shirts?’

Rosie laughed. ‘On Fifth Avenue, New York City. Maybe we’ll get lucky.’ I detected sarcasm, but in a friendly way. We found a new shirt of the same genre as the Claudia shirt at a huge store called Bloomingdale’s, which was not, in fact, on Fifth Avenue. We could not choose between two candidate shirts and bought both. My wardrobe would be overflowing!

We arrived at Central Park.

‘We’re skipping lunch, but I could handle an ice-cream,’ said Rosie. There was a vendor in the park, and he was serving both cones and prefabricated confections.

I was filled with an irrational sense of dread. I identified it immediately. But I had to know. ‘Is the flavour important?’

‘Something with peanuts. We’re in the States.’

‘All ice-creams taste the same.’

‘Bullshit.’

I explained about tastebuds.

‘Wanna bet?’ said Rosie. ‘If I can tell the difference between peanut and vanilla, two tickets to Spiderman. On Broadway. Tonight.’

‘The textures will be different. Because of the peanuts.’

‘Any two. Your choice.’

I ordered an apricot and a mango. ‘Close your eyes,’ I said. It wasn’t really necessary: the colours were almost identical, but I didn’t want her to see me tossing a coin to decide which one to show her. I was concerned that with her psychological skills she might guess my sequence.