I felt I had made my point effectively, and Julie did not think we needed to continue with the genetics. The parents appeared to be reflecting on what their children had learned and left without interacting with me further. It was only 7.43 p.m. An excellent outcome.

As I packed up my laptop, Julie burst out laughing.

‘Oh my God,’ she said. ‘I need a drink.’

I was not sure why she was sharing this information with someone she had known for only forty-six minutes. I planned to consume some alcohol myself when I arrived home but saw no reason to inform Julie.

She continued, ‘You know, we never use that word. Aspies. We don’t want them thinking it’s some sort of club.’ More negative implications from someone who was presumably paid to assist and encourage.

‘Like homosexuality?’ I said.

‘Touché,’ said Julie. ‘But it’s different. If they don’t change, they’re not going to have real relationships – they’ll never have partners.’ This was a reasonable argument, and one that I could understand, given my own difficulties in that sphere. But Julie changed the subject. ‘But you’re saying there are things – useful things – they can do better than … non-aspies? Besides killing babies.’

‘Of course.’ I wondered why someone involved in the education of people with uncommon attributes was not aware of the value of and market for such attributes. ‘There’s a company in Denmark that recruits aspies for computer applications testing.’

‘I didn’t know that,’ said Julie. ‘You’re really giving me a different perspective.’ She looked at me for a few moments. ‘Do you have time for a drink?’ And then she put her hand on my shoulder.

I flinched automatically. Definitely inappropriate contact. If I had done that to a woman there would almost certainly have been a problem, possibly a sexual harassment complaint to the Dean, which could have consequences for my career. Of course, no one was going to criticise her for it.

‘Unfortunately, I have other activities scheduled.’

‘No flexibility?’

‘Definitely not.’ Having succeeded in recovering lost time, I was not about to throw my life into chaos again.

Before I met Gene and Claudia I had two other friends. The first was my older sister. Although she was a mathematics teacher, she had little interest in advances in the field. However, she lived nearby and would visit twice weekly and sometimes randomly. We would eat together and discuss trivia, such as events in the lives of our relatives and social interactions with our colleagues. Once a month, we drove to Shepparton for Sunday dinner with our parents and brother. She was single, probably as a result of being shy and not conventionally attractive. Due to gross and inexcusable medical incompetence, she is now dead.

The second friend was Daphne, whose friendship period also overlapped with Gene and Claudia’s. She moved into the apartment above mine after her husband entered a nursing home, as a result of dementia. Due to knee failure, exacerbated by obesity, she was unable to walk more than a few steps, but she was highly intelligent and I began to visit her regularly. She had no formal qualifications, having performed a traditional female homemaker role. I considered this to be an extreme waste of talent – particularly as her descendants did not return the care. She was curious about my work, and we initiated the Teach Daphne Genetics Project, which was fascinating for both of us.

She began eating her dinner in my apartment on a regular basis, as there are massive economies of scale in cooking one meal for two people, rather than two separate meals. Each Sunday at 3.00 p.m. we would visit her husband at the nursing home, which was 7.3 kilometres away. I was able to combine a 14.6-kilometre walk pushing a wheelchair with interesting conversation about genetics. I would read while she spoke to her husband, whose level of comprehension was difficult to determine but definitely low.

Daphne had been named after the plant that was flowering at the time of her birth, on the twenty-eighth of August. On each birthday, her husband would give her daphne flowers, and she considered this a highly romantic action. She complained that her approaching birthday would be the first occasion in fifty-six years on which this symbolic act would not be performed. The solution was obvious, and when I wheeled her to my apartment for dinner on her seventy-eighth birthday, I had purchased a quantity of the flowers to give her.

She recognised the smell immediately and began crying. I thought I had made a terrible error, but she explained that her tears were a symptom of happiness. She was also impressed by the chocolate cake that I had made, but not to the same extent.

During the meal, she made an incredible statement: ‘Don, you would make someone a wonderful husband.’

This was so contrary to my experiences of being rejected by women that I was temporarily stunned. Then I presented her with the facts – the history of my attempts to find a partner, beginning with my assumption as a child that I would grow up and get married and finishing with my abandonment of the idea as the evidence grew that I was unsuitable.

Her argument was simple: there’s someone for everyone. Statistically, she was almost certainly correct. Unfortunately, the probability that I would find such a person was vanishingly small. But it created a disturbance in my brain, like a mathematical problem that we know must have a solution.

For her next two birthdays, we repeated the flower ritual. The results were not as dramatic as the first time, but I also purchased gifts for her – books on genetics – and she seemed very happy. She told me that her birthday had always been her favourite day of the year. I understood that this view was common in children, due to the gifts, but had not expected it in an adult.