Dorset Street, London
June 1833

And so we are going to visit Mr Babbage, and his mythical-sounding machine.

The evening is warm; there’s a feeling in the air of possibility, movement. The carriage rattles through Manchester Square; people are strolling along the pavements, beautifully dressed, full of leisurely intent. My mother’s doll-like profile is perfectly still. One shoe taps a subtle tattoo on the carriage floor: a sign that she is looking forward to whatever the evening has in store.

It is not the first time that Mamma has taken me to look at machinery: I remember (dimly) our visit to the North of England where we examined the workings of the glass factory; and there were, I’m sure, other trips besides that I don’t recall. Mamma derives a kind of sincere satisfaction from these excursions; she wants to understand how the machines work, and she wants me to understand how they work, and then, somehow, all will be right with the world for a while if both of these things take place.

‘Now, Ada,’ she says, interrupting my thoughts. ‘You must be sure to ask pertinent questions.’

To this, I don’t respond, giving her instead a look that says that I have never asked a question of anyone that was not pertinent. The carriage slows to a halt. We climb out, Mamma first, me following; then, taking my elbow, Mamma steers me along the pavement, as though I am a circus creature. Gently, but firmly, I shake my sleeve from her grip. I do not require steering. She settles for a hand between my shoulder blades instead. ‘Come, Ada. Don’t dawdle.’

As we approach Mr Babbage’s house, I think about what it might mean to lose a beloved spouse, as I’ve learned he did a little over five years ago. I found my mother’s reaction to the death of my father curious, and have continued to find it so, all these years – and it is almost ten years now, a fact which I decide is rather astonishing. I think of those bittersweet tears in the Hampstead library, as bright and sharp as a clatter of jewels; and the way she looked at the Villa Diodati, and the fact that our continental trip bore so many signs of a pilgrimage. But she cannot talk freely of him – never could – and while she might sometimes bring up some brief memory of him in conversation, she is just as likely to call an immediate halt to any such discussion, as though for fear of what might be said. Did she love him? I don’t know; I still don’t know. She can be so glacially cold sometimes that I find it hard to believe that she could ever have loved anyone. Not the way that I have felt love... I think of James Hopkins once again; my mind drifts into a kind of memorial pleasure garden, a landscape studded with kisses, and whispered sweet-nothings, and a shed at midnight, and a telltale pool of blue-black ink.

‘Yes,’ Mamma is saying now. ‘I think we shall enjoy making Babbage’s acquaintance properly. Many were offended by his criticisms of the Royal Society, but I for one am a firm believer that enterprises such as his should be fully supported. His machine is the talk of London, you know.’

Upon our arrival, a servant leads us up the stairs and into the drawing room on the first floor, and there Babbage receives us – he seems even taller, somehow, in his own setting, and no less exuberant, despite the fact that we are the only guests. He has the look, I think, of one who enjoys the act of creation: of twisting things to his whims, of designing.

He says with great warmth, ‘It is wonderful that you have come.’

Drinks are offered, and then, without further ado, he leads us to a low table in the centre of the room. There it is: the machine that so much of London is discussing. Mamma is as collected as ever, but I find myself suddenly quite breathless with anticipation, and do my best to hide it. The demonstration piece is made of bronze and steel, perhaps two and a half feet high, and highly polished. Three columns of stacked cogwheels are interlaced with arms in a helical arrangement. The numbers from zero to nine appear above each wheel. Clever lighting lends the machine an alluring glow.

‘What is the relation in size between this piece and a fully-operating model?’ my mother enquires, strolling first this way and then that around the table, inspecting the machine from all angles.

‘One seventh, milady,’ Mr Babbage replies.

‘And why is the machine so named?’

‘Ah,’ he says. ‘Yes. The Difference Engine is named thus because of the principle on which it is founded: the method of finite differences. In order to produce more or less any kind of arithmetical table, you see, all that is required is a machine that can add orders of difference – provided, of course, that one enters the initial values. Do you... do you see?’

Mamma nods slowly. ‘I do see,’ she says. ‘If one wishes to count: one, three, five, seven, and so forth, then the difference, each time, is two. It is a fixed order of difference.’

All thoughts of James Hopkins forgotten entirely, I edge a little closer to the machine. How nice that it is named for its ability to judge differences; I, Ada, have always adored those small moments in which a difference can be perceived – the windmills on the Continent, for example, or the taste of chocolate. So much can be measured in terms of differences, after all; it seems somehow fitting, and quite brilliant, that Mr Babbage has designed a machine to do exactly that.

‘Multiplication can be done by the same process,’ says Mr Babbage. ‘Multiplication is a form of addition, after all.’

‘Mr Babbage,’ I say. ‘What inspired you to use cogwheels for this machine?’

He looks at me and seems pleased to be able to answer. (See, Mamma, I think. I am pertinent.)

‘Indeed, it’s a perfectly apt question. The nature of the cogwheel seemed indicated from the first, although in fact each wheel has to be made by hand at great expense. What I – and others – have spent on it all so far! I can hardly begin to tell you... Now: each wheel has a certain quantity of “teeth”, as you can see. Those teeth stand for numbers; there are ten fixed positions for each wheel.’

‘Base ten,’ says Mamma, nodding.

‘Exactly. The wheel at the bottom represents the units. The one above, the tens; the one above that, the hundreds, you see. Though not yet thousands, I fear, not on this model. Allow me to show you.’

For a few moments he busies himself, turning a few of the wheels with gentleness and precision. ‘A simple calculation, to begin with,’ he mutters. Now he takes hold of the handle, and the arms of the demonstration piece begin to oscillate, dancing to their own peculiar choreography.

Click... click... click. It is strange music, this; soothing in its repetitions, but startling in its newness.

‘I envisage, one day, a printer,’ says Mr Babbage. ‘For now, results can be read from this display. Here.’

He shows us, and we watch in silent fascination. He performs a variety of calculations for us, raising numbers to their second and third powers, and even – by some wondrous means that I cannot quite fathom – extracting the root of a quadratic equation. I watch the wheels click and whirr – they are quieter than I might have imagined, and feel a silvery thrill unfold across my palms.

‘I do not understand,’ says Mamma. ‘What is preventing you from building the machine proper?’

Mr Babbage says: ‘Dear lady, it is a rather longer story than I fear I have the patience to tell... I first sought funding for the Engine – well, it must be twelve years ago now. I don’t think the Home Secretary, Mr Peel, saw the point of what I wanted to do: he thought the hand-printed mathematical tables were accurate enough, even though we both knew that they were prone to errors. But he referred the matter to the Royal Society. They discussed it and allowed me an initial grant. I took my plans to Europe. They were far more interested. When I returned, I asked the Duke of Wellington for more money. I built a workshop on land that adjoins this property, in the expectation that my machinist, Mr Clement, would come to reside with his family above the workshop, so that he might devote himself fully to the Difference Engine. That he was loath to do. The fellow submitted a bill for work done last year that was, frankly, extortionate. I refused to pay until he agreed to move; he then fired every man in his employment. My hope is that I shall find another machinist, but until an agreement has been made with Clement, I doubt he’ll hand over the pieces of the machine that have already been crafted.’

We listen to this tale of frustration and complexity in silence. Mamma ventures a sympathetic word or two, as Mr Babbage draws his remarks to a close, and he thanks her for her understanding.

‘This whole business,’ he says, ‘has been a fiasco.’

‘Well,’ says Mamma, as we journey home. ‘I think I have understood the basic principles of his machine. Such uniformity of function. And, apart from the handle, fully automated. I am impressed. I could see, Ada, that you were too.’

I would like to demur, just for the thrill of irritating her, but I cannot in all good conscience do that. Instead, I say: ‘Yes. Yes, I was.’

Mamma chatters on in her precise way, recounting the evening’s events as though to describe them to one who had been absent. I let her talk. The thunderous roll of the cab wheels is quite distinct from the smooth operation of Mr Babbage’s machine. It wasn’t just the beauty of the thing that kept my eyes fastened to it, mapping every rotation, every ripple; its real beauty was its inhuman accuracy. Pictures appear in my head of ships crossing ice-strewn waters without fear, safe in the knowledge that their navigators are in possession of flawless numerical tables with which to steer them...

‘It is a shame that Mr Babbage cannot build the fully-sized machine,’ I say.

I am thinking again of Flyology; of the anguish I suffered when I realised that I would not be able to build my own flying machine. It is a sad thing indeed when a dream is prevented from coming to fruition.

Then I add, ‘He seems the sort of man who will not allow such setbacks to deter him. I wonder... I do think, Mamma, that he will find a way.’

Although I shall not meet Mr Babbage again for some time, I shall not forget this first glimpse of the demonstration piece. Its motions have imprinted themselves on the fabric of my brain; as we journey home, I close my eyes, and realise that I can still see those wheels turning.