My father looked up as I began to tune the lute, which was sadly awry.

‘Excellent!’ he said. ‘It is weeks since you played your lute.’

‘Months. I hope I have not neglected it so long that the strings will play me false.’

It took a long while, but at last I had it tuned to my satisfaction. As I worked, my father took his treble recorder out of its case and played a few notes so that I could tune my strings to harmonise with it.

‘Morley, I think,’ I said. ‘Oh let my tears fall.’

‘Rather sad.’

‘We can play something more cheerful afterwards.’

I bent my head, gave my father the nod to begin, and soon we were lost in that private world of music-making that only those who know it can understand. I sang the words softly as I played. My voice is true, and fairly sweet, but I have no real power behind it. I could never fill a theatre, as I supposed Simon must sometimes have to do.

We had been playing for perhaps half an hour, everything ranging from jolly Portuguese folk dances to some of Tallis’s pieces with tricky harmony, and were in the middle of Byrd’s My Lord Willoughby’s Welcome Home when we heard a knock on the street door. Joan had been dozing by the fire in the kitchen (and probably not appreciating our music much), but we heard her chair scrape on the floor and then the creak as the door opened. The newcomer’s voice was unmistakable.

‘It’s Master Harriot,’ I said, starting to lay aside my lute as Joan showed him into the parlour.

‘No, no, please don’t stop playing,’ he said, beaming from one to the other of us. ‘I could hear the sweet sounds from the street through the open window, and wondered whether I might join you.’

‘Oh dear!’ said my father. ‘We shall have our neighbours complaining tomorrow.’

‘Not at all. It was the very music of the spheres!’

I gave a snort of laughter. ‘I think not. I am sorely out of practice. You will take some refreshment?’ Laying my lute down beside my stool, I stepped into the kitchen and told Joan to bring in glasses and the cake she had made earlier that day. Behind me, my father was drawing the cork from one of his few precious bottles of wine. It was not often that we had the honour of a visit from Master Harriot.

When I returned, Harriot had picked up my father’s other recorder, a tenor, and was playing a snatch of melody on it. The melody was heart-wrenching, with a dying fall that made me want to weep.

‘What is that?’ I asked.

‘A new piece by John Dowland,’ Harriot said. ‘Not published yet, I believe, but I heard it played at Raleigh’s house last week. Do you think you could extemporise to it?’

Harriot could remember exactly any melody once heard, as I could, and both my father and I could improvise at will, so within minutes the three of us had our instruments winding their melodies about each other like human voices entwined in a madrigal.

At some point Joan must have brought in the tray, but none of us noticed until we had brought our impromptu composition to an end and looked at each other, laughing.

Music and mathematics – surely the most sublime and ethereal of God’s gifts to Man!

Harriot mopped his forehead with a fine silk handkerchief, which he then screwed carelessly into a ball and shoved into his pocket.

‘Ah, I should visit Duck Lane more often. Do the authorities at St Bartholomew’s have any idea what jewels they have buried in their crowded lodgings? Dr Alvarez, you and Kit deserve better than this.’

I saw my father shrug as I moved to pour out the wine and slice the cake.

‘We are given these lodgings free. We could move to one of the better hospital houses, but then we would have to pay rent. I prefer to put the money aside for my old age and Kit’s future. You know that we lost everything when we left Portugal.’

Harriot accepted the wine and cake I passed to him and shook his shaggy head sadly.

‘It is a cruel world we live in. There is so much ignorance and bigotry abroad. I know what they call me – ‘the Conjuror’ – because the ignorant believe that mathematics is some kind of magic. At least we do not have the Inquisition in England.’

‘Yet what could be further from magic,’ I said, ‘when it rests on the most rigorous reasoning of the human brain?’

‘Exactly. But even educated men, who should know better, pretend to subscribe to this view of mathematics as magic.’

‘It comes, perhaps,’ said my father, ‘from their fear of men who may be cleverer than they are. By calling you the Conjuror they demean you, make you less dangerous.’

Harriot shrugged. ‘I’m in no contest with men of power. That is not my world at all.’ He took a large bite of his cake and washed it down with a hearty sip of his wine.

‘And you, Kit? You have not come for your studies with me for weeks now.’

‘My days have not been my own. We have had a difficult time at the hospital, and when I am not there I have been working for Walsingham.’

‘Ah, yes. The code-breaking. I did not realise that it would still be occupying you. When I was approached by that fellow – Robert Polling? – I was able to praise your skills with ciphers, but I thought Sir Francis had just a brief task in mind.’

‘Robert Poley,’ I said. ‘That is his name. Whatever he gave you to understand – and I can well believe he was not honest and straightforward – it seems Sir Francis feels he can call on me whenever there is more work than his own man can do. And that is often.’

‘Well, I suppose it is worthwhile work, for Sir Francis is an upright and honourable gentleman. And I am sure it is bound to be secret in nature.’

‘It is.’

‘I know you can keep your counsel. Yet I have scarce seen you since I returned from the Chesapeake expedition.’ He rubbed his hands together enthusiastically. ‘You remember, Kit, that I told you how I had been compiling a dictionary of the native language from my interviews with the two captives before we left?’

‘I do. And were you able to learn more of the language?’

‘Indeed, indeed. It is most curious. Quite unrelated to any other language I have encountered. Remarkable. And the people are not so savage as we have been led to believe. With a little gentle guidance, I think they will come to accept true faith and civility. They express astonishment at our modern engines such as clocks and compasses, but they do not hate or fear them. When next you come to my rooms, Kit, I will show you the drawings I have made, and my wordlist. Who knows, they might even prove useful in Sir Francis’s codes!’

We all laughed at the idea of Sir Francis using the language of savages from the New World to outwit our country’s enemies. And I could not help smiling to myself that Harriot had not said one word of the Chesapeake expedition when I had seen him last. I had been very curious to hear about his adventures, but had waited for him to open the subject. However, all his enthusiasm on that occasion had been for optics. That was the very essence of him, and it was one of the things that made him so exciting as a teacher, the way he embraced so many branches of knowledge and opened up new countries of the mind where none had travelled before.

‘I have never returned your book on optics, Master Harriot,’ I said, getting up and fetching it from where it stood on our shelf of books.

‘You have read it? And what did you think?’

‘Very interesting. But I thought I noticed a few miscalculations.’

He beamed. ‘I hoped you would. When next you come to me, we will put our heads together and see whether we can do better.’ He put down his glass. ‘Tell Joan her cake is excellent. More? Ah, I think you can persuade me. Afterwards, shall we have more music? Once I am sure that I will not fill your recorder with blown cake crumbs, Dr Alvarez! Was that Byrd you were playing when I arrived?’

We made music far into the night and no more was said of the New World or mathematics or code-breaking or Sir Francis Walsingham.