achievements, despite his repellent politics. Perhaps he was afraid of being outshone.

Carla said: ‘All my grades are better than yours: biology, chemistry, maths—’

‘All right, all right.’

‘And the scholarship is available to female students, in principle – I checked.’

Their mother came in at the end of this exchange, dressed in a grey watered-silk bathrobe with the cord doubled around her narrow waist. ‘They should follow their own rules,’ she said. ‘This is Germany, after all.’ Mother said she loved her adopted country, and perhaps she did, but since the coming of the Nazis she had taken to making wearily ironic remarks.

Carla dipped bread into milky coffee. ‘How will you feel, Mother, if England attacks Germany?’

‘Miserably unhappy, as I felt last time,’ she replied. ‘I was married to your father throughout the Great War, and every day for more than four years I was terrified that he would be killed.’

Erik said in a challenging tone: ‘But whose side will you take?’

‘I’m German,’ she said. ‘I married for better or worse. Of course, we never foresaw anything as wicked and oppressive as this Nazi regime. No one did.’ Erik grunted in protest and she ignored him. ‘But a vow is a vow, and, anyway, I love your father.’

Carla said: ‘We’re not at war yet.’

‘Not quite,’ said Mother. ‘If the Poles have any sense, they will back down and give Hitler what he asks for.’

‘They should,’ said Erik. ‘Germany is strong now. We can take what we want, whether they like it or not.’

Mother rolled her eyes. ‘God spare us.’

A car horn sounded outside. Carla smiled. A minute later her friend Frieda Franck entered the kitchen. She was going to accompany Carla to the interview, just to give moral support. She, too, was dressed in sober-schoolgirl fashion, though she, unlike Carla, had a wardrobe full of stylish clothes.

She was followed in by her older brother. Carla thought Werner Franck was wonderful. Unlike so many handsome boys he was kind and thoughtful and funny. He had once been very left wing, but all that seemed to have faded away, and he was non-political now. He had had a string of beautiful and stylish girlfriends. If Carla had known how to flirt she would have started with him.

Mother said: ‘I’d offer you coffee, Werner, but ours is ersatz, and I know you have the real thing at home.’

‘Shall I steal some from our kitchen for you, Frau von Ulrich?’ he said. ‘I think you deserve it.’

Mother blushed slightly, and Carla realized, with a twinge of disapproval, that even at forty-eight Mother was susceptible to Werner’s charm.

Werner glanced at a gold wristwatch. ‘I have to go,’ he said. ‘Life is completely frantic at the Air Ministry these days.’

Frieda said: ‘Thank you for the lift.’

Carla said to Frieda: ‘Wait a minute – if you came in Werner’s car, where’s your bike?’

‘Outside. We strapped it to the back of the car.’

The two girls belonged to the Mercury Cycling Club and went everywhere by bike.

Werner said: ‘Best wishes for the interview, Carla. Bye, everyone.’

Carla swallowed the last of her bread. As she was about to leave, her father came down. He had not shaved or put on a tie. He had been quite plump, when Carla was a girl, but now he was thin. He kissed Carla affectionately.

Mother said: ‘We haven’t listened to the news!’ She turned on the radio that stood on the shelf.

While the set was warming up, Carla and Frieda left the house, so they did not hear the news.

The University Hospital was in Mitte, the central area of Berlin where the von Ulrichs lived, so Carla and Frieda had a short bicycle ride. Carla began to feel nervous. The fumes from car exhausts nauseated her, and she wished she had not eaten breakfast. They reached the hospital, a new building put up in the twenties, and found their way to the room of Professor Bayer, who had the job of recommending a student for the scholarship. A haughty secretary said they were early and told them to wait.

Carla wished she had worn a hat and gloves. That would have made her look older and more authoritative, like someone sick people would trust. The secretary might have been polite to a girl in a hat.

The wait was long, but Carla was sorry when it came to an end and the secretary said the professor was ready to see her.

Frieda whispered: ‘Good luck!’

Carla went in.

Bayer was a thin man in his forties with a small grey moustache. He sat behind a desk, wearing a tan linen jacket over the waistcoat of a grey business suit. On the wall was a photograph of him shaking hands with Hitler.

He did not greet Carla, but barked: ‘What is an imaginary number?’

She was taken aback by his abruptness, but at least it was an easy question. ‘The square root of a negative real number; for example, the square root of minus one,’ she said in a shaky voice. ‘It cannot be assigned a real numerical value but can, nevertheless, be used in calculations.’

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