Geneva
September 1826

One day, a week or so before we are due to depart from Geneva, Mamma summons me to her sitting room. ‘I think that it is now time for you to engage formally with the principles of geometry,’ she says.

I don’t know what has prompted this; perhaps she has been thinking further about my mind, and how best to trammel it, or else perhaps she has always meant to give me the book, which she is holding out to me now, at around this point in our journey.

The book is called The Elements of Euclid. I open it to its first section, entitled ‘Definitions’.

I. A point is that which hath no parts, or which hath no magnitude.

II. A line is length without breadth.

I look up. Mamma is watching me, almost hungrily; she wants a reaction from me, a declaration of sorts. It feels like a test. Either I will be drawn to Euclid and his writing, or I won’t be; if I am, it will be a victory for her, and if I am not, a failure – on my part as well as hers. But I am thinking so much about what she is thinking that I am forgetting to read on.

III. The extremities of a line are points.

IV. A straight line is that which lies evenly between its extreme points.

The definitions continue, develop, running into pages and pages, deepening in complexity. I turn to another section, mouthing words to myself, absorbing it. This is nothing like fellowship and alligation and the Rule of Three – these are not problems of money and quantity; men mowing acres and boys eating apples. This is... pure, somehow. Unassailable. The fundamental truth of shapes.

‘When was this written?’ I say.

‘Oh, hundreds of years ago. Thousands,’ says Mamma.

The thought of this fills me with an inexplicable feeling – a sense of time passing and triangles and squares and pentagons remaining fixed, immutable, dependable. Inventions change the world and how it works, but the mathematical truths that underlie those changes stay the same.

‘What do you think, Ada?’ says Mamma.

‘It’s... like poetry,’ I say quietly.

Mamma sniffs. ‘It is not in the least like poetry. These are rules,’ she says.

‘What I mean is... I mean that reading this gives me the same sense of something beautiful and constant, such as I would get from reading a passage of Milton,’ I explain.

At this, Mamma nods very slightly. I think she does understand. She herself writes a good deal of poetry, not that I have read much of it. It’s not poetry that she dislikes; it’s more behaviour that she might describe as ‘poetical’ – having a disorganised mind, for example, or behaving in an unpredictable way. In Mamma’s mind, there exists, I think, a certain separation between the notions of poetry and poetical behaviour; this is certainly true in her own case. It may be less true as far as my father is concerned, for I have not yet been allowed to read anything that he wrote.

‘But do you like it?’ she persists, gesturing to the page.

‘Oh yes,’ I say. ‘I like it very much.’

‘That’s good,’ she says.

I have long been an observer of my mother’s desire to ‘do good’; she is by nature a reformer, one who wishes people and projects to adhere to rigid guidelines. She is unsettled by change, or rather, by change that she has not herself anticipated. On the ferry crossing, for example, she thought that the weather would be fine, and the waves unthreatening; when the opposite turned out to be true, she was very ill indeed, from seasickness of course, but also from the fact that things had not happened quite as she had imagined they would. When a roadside inn that had been recommended to her was full, and we had to find lodgings at another, she found it impossible to be happy there, even for a short time, although our accommodation was perfectly agreeable. If Mamma thinks that my mind is disorganised, I believe that the reverse holds true for her: her mind is too organised.

But Euclid provides something on which we can both agree. And now she and I spend our afternoons puzzling over the nature of circles and spheres, circumferences and intersections, and I come to realise that mathematics is a language that we share.

When Mamma organises a sailing trip on Lake Geneva on the last day of our stay there, I imagine that she means it as a reward for my hard work. It’s a windy afternoon; the surface of the lake is not as mirror-smooth as it was when we first glimpsed it from the Jura mountainside. Miss Stamp has gone sight-seeing alone, and so it’s just the two of us, Mamma and I, and our guide, a tall young man named Franz, who speaks English in a slow, careful, heavily-accented voice.

‘How big is the lake?’ I ask, as we climb aboard the little boat.

‘Nineteen leagues in length, and perhaps three and a half in breadth at the widest part, miss,’ he replies.

The lake feels as big as an ocean, hemmed by prim houses on one side and statuesque mountains on the other – and our boat as small as a dust-speck in a soup tureen. I enjoy how strangely unstable it is; the feeling of seesawing.

For a while, Mamma and I don’t say much, and I wonder what she is thinking about. The boat circumnavigates the lake, slowly. Then Mamma says: ‘As you know, we are to leave Geneva shortly and travel to Hofwyl. Perhaps it would be useful for you to hear some of its history.’

Overhead, the cornflower sky is scuffed with clouds; I tilt my head upwards, counting them, and half close my eyes to listen as she talks. Mamma isn’t a natural storyteller, but this is a story that she knows exceptionally well; her voice, often a little stiff and halting, flows smoothly as she tells it.

‘It began at the end of the last century,’ she says, ‘when Switzerland was invaded by the French army. Men and women fought bravely and died, and a good many orphan children were left behind, utterly destitute. In Canton Unterwalden, a philanthropist called Henry Pestalozzi provided shelter for the orphans, and there he set up a little school. His methods were quite unusual: he gave the most intelligent children jobs as his assistants, and enlisted their help in running the school – preparing food, mending garments, and cultivating the plot of land that surrounded them. His endeavours attracted the notice and praise of other philanthropists, and eventually the government offered him the Castle of Burgdorff, in Canton Berne, in which to set up his Educational Institution.

‘Now, Pestalozzi had an acquaintance by the name of Philipp Emanuel de Fellenberg, and this young man, who had long paid heed to the phrase: “The rich have always helpers enough, help thou the poor”, was an ardent follower of Pestalozzi’s ideas. Deeply affected by the principles of the French Revolution, and full of ideas for ways in which the world could change, Dr Fellenberg became Pestalozzi’s neighbour when his father purchased the estate of Hofwyl, just a few miles from Burgdorff. Although there were matters on which the pair did not agree, Pestalozzi arranged to hand over the institute to Dr Fellenberg. And so, twenty years ago, a little cottage was built at Hofwyl. The teachers slept on the upper floor, while the ground floor was used as the school room. Lessons took place all morning; the afternoon was spent working in the garden, while in the evening the teachers would prepare the vegetables for the following day.’

‘Is it a little cottage still?’ I say.

‘I believe it has grown somewhat,’ says Mamma.

‘I like the idea of... of changing the way that the world works,’ I say.

‘So do I,’ says Mamma. ‘The phrase he clung to – the rich have always helpers enough, help thou the poor – is close to my own heart too. When you think, Ada, of the squalor, the cramped living spaces, the lack of opportunity that is the reality for so many in England – why, our lives are charmed by comparison. It’s not enough simply to muddle through the daily haze of one’s own existence, is it? When there is so much to be done.’

She looks at me, eyes bright, and I see someone different, suddenly, on the wooden seat next to me, to the person I used to know. Then, abruptly, she flinches, as though stung by a hidden bee. She looks across the water, scanning the shoreline, frowning as she does so. I follow her gaze. From the edge of the lake, the hills slope up sharply; there, above a plantation of vineyards, upon a ridge, sits a large, square, white villa with a reddish roof.

‘There lies the suburb of Cologny,’ says Franz. ‘And that is the Villa Diodati.’

At this, Mamma catches her breath sharply; watching her hand on the rail, I see how white her knuckles have become. But her voice, when she speaks, is quite level. ‘That is the house.’

‘What house, Mamma?’

‘It’s where... it’s where your father lived, Ada. Ten years ago, now – oh, can it really be ten?’

Hearing our conversation, Franz tactfully steers the boat so that our view of the Villa Diodati is unimpaired. I stare at the villa, examining its proportions, trying to imagine my father inside it, ten years ago. A strange transformation is taking place in my head: those early visions that I have cherished of my father – at the edge of the sea, writing at his desk, surrounded by servants – seem to shift somehow and merge with the real-life villa, with its lake view and bed of vines. He feels more real to me, now, than perhaps he has ever felt before.

‘Your father rented the house in 1816,’ says Mamma. ‘Another poet, a man named Percy Bysshe Shelley, who tragically drowned some years later, lived nearby. They were very good friends. The night that Mary Shelley thought of Frankenstein, there was a storm over the lake. The three writers decided to write stories – ghost stories – to mimic the dramatic weather. Or so it is said. What your father and Percy Bysshe Shelley concocted I do not know, but Frankenstein is deservedly a work of some repute.’

She is talking rather glibly, I notice, just as she did a few moments ago, when she recounted her history of Pestalozzi. It strikes me that these speeches have a purpose other than my elucidation: she is trying to fill some kind of empty space – in our conversation, or else in her own head – perhaps for fear of what else might appear unbidden. Miss Stamp has told me, quite recently, about Mary Shelley and her novel, Frankenstein, about a man who seeks to traverse the bounds of scientific possibility by bringing another man back to life by means of electricity. Clearly, Mary Shelley is a Woman of Ideas. I never knew that my father lived here, so near to the Shelleys.

But there’s something else that I never knew, somehow, until this moment.

‘Then I was only an infant,’ I say slowly, ‘when he left. I was not even one year old.’

Silence at this. Then: ‘That is quite correct, Ada.’

‘Why did he leave so soon, Mamma?’ I say.

The wind picks up and the boat surges wildly for a few minutes as Franz adjusts the sail.

‘Come,’ says Mamma, ‘I think we must go back.’

She does not answer my question; I never really thought that she would, but important questions are always worth asking. As we sail back across the lake – it is beginning to rain – Mamma looks back at the house, just once, as though to imprint it upon her memory. She frowns a little, as though such an imprinting causes her a peculiar kind of pain – a pain that is unpleasant, but also, somehow, necessary.