Ada — the note that dreamed of a thinking machine

Transcript

Bram: There is a tray on my hands and the tray has eleven full glasses on it, and I arrive already walking. That is the worst of them. Not the falling, not the fire — the ones where the body is already committed. My feet are going and I do not know the room and there is a wall of backs in front of me with no gap in it, and the wine is doing the little circular thing wine does a half-second before it stops being in the glass. The hands save me. They always do. They come round without asking, drop the tray to hip height, turn it flat with the fingers spread underneath like a man holding up a small ceiling, and go through the wall of backs sideways at a speed I would not have attempted. Nobody spills. Nobody looks. One elderly gentleman says ah at the exact moment a glass arrives at his elbow, without turning round, the way you say ah to a dog you did not know was under the table. So. Evening dress, gas-light, and a room with a temperature you could stand a spoon up in. Two drawing rooms opened into one and the crowd going all the way up the staircase behind me. Wax and hot gas and wine and a great deal of warm wool. Hair oil. Somebody's violets. And underneath all of it a thin metal smell, oiled and cold, that has no business in a drawing room at all. I count the room the way this body counts it, which is by hands. Three hundred pairs, and my entire professional interest is in where they are. And in the middle of the room, on a stand, is the reason all these hands are here. It is about the size of a small chest of drawers, and it is made of bronze and steel, and it is beautiful. Not beautiful the way a horse is. Beautiful the way a good knife is. Columns of wheels, one above another, each wheel with the numbers nought to nine cut into its edge, the whole of it standing in a frame with the parts you are meant to see polished and the parts you are not left grey. Two thousand pieces. I know that because I have heard the number said in this room more often than I have heard my own name. On the side of it, at about the height of my hip, there is a handle. And here is the master of the house coming through the crush like weather, big and broad and pleased, with two Members of Parliament and a woman in grey silk in tow, and he has already started talking before he is anywhere near.

Babbage: — no, no, madam, you have it precisely backwards, and I am delighted, because the mistake is the interesting one. It does not know the answers. Nothing in it knows anything. It is not a cabinet of answers, it is a method, made out of brass.

A_lady: Then what is it doing, Mr Babbage?

Babbage: Adding. That is all. Adding, over and over, at a speed and a regularity no human clerk can hold — and out of nothing but adding, correctly arranged, it will lay down a table of squares, or of logarithms, and every figure in it right. Which no book of tables in Europe can honestly claim.

A_gentleman: And it will not tire.

Babbage: It will not tire, it will not be bored, it will not be in love, and it will not have been at a funeral in the morning. Those are the four commonest causes of an error in a printed table, and I did not invent one of them.

Bram: The room laughs. It always laughs there. I have heard him say that on eleven Saturdays and the room has laughed on all eleven, and I have got very good at getting a tray past the laugh, because for about two seconds afterwards everybody's elbows go outward.

Babbage: Now. Since you ask, madam — and everyone always asks.

Bram: He looks round for me without looking round for me. It is a particular movement of the shoulder that means the man with the tray will now come and turn the handle, and I put the tray down on the pier table where the tray always goes, and I go and stand at the machine's right side, where I have stood, at a guess, a hundred times. I set the wheels back to nought. There is a way of doing it, with the flat of the thumb, that does not put a mark on the engraved figures, and this body does it without me.

Babbage: Whenever you are ready.

Bram: And I turn the handle. It is heavier than anybody expects. That is the first thing everyone gets wrong about it and it is the thing I like best. You put your hand on it thinking clock and you get press. There is a real weight in there, the weight of two thousand parts all deciding at once, and it comes up through the palm before there is any sound at all — and then the sound arrives, which is not a whirr and not a hum, but a long soft stepping noise, a hundred small certainties going over one after another. And every figure on the front face of the thing has changed to the next number in the table. All of them. Together. Once. The room does what the room does. There is a gasp, and then there is applause, and a man near the window says good God with real feeling, and the woman in grey silk has both hands over her mouth like she has watched a bird come back to life. And I stand there with my hand on the handle and I think what I think every single Saturday, which is: it is a very expensive way of doing sums a clerk would do for eightpence. I am not being clever. I have done the sum. There is a boy at a counting house in Cornhill who would give you that column by Tuesday for a shilling and his dinner, and this thing has swallowed more public money than I will earn if I live to be four hundred — and it is a piece of the machine. That is the part nobody in this room seems to hear when he says it. A piece. He got as far as this and stopped, and it stands in his drawing room being astonishing on Saturdays. Then somebody wants the Silver Lady, and somebody always wants the Silver Lady, so I go and wind her. She is a clockwork dancer, silver-plated, life-size to about the waist of a small woman, and she has been in this house since the master was a boy. Twenty-three turns of the key. She raises one arm, and there is a bird on her finger that opens its beak, and she inclines her head, and — this is the part that has never once failed — she looks at whoever is directly in front of her, with an eyeglass raised, as if she has just noticed them and is not entirely impressed. I like the Lady. The Lady I understand. She cost a great deal of money and she is worth exactly what she cost, which is an evening's astonishment, and she has never once pretended to be the future. And it is while I am winding her that I notice the girl. She has been at the machine a quarter of an hour. Not in front of it — beside it, on the far side, where there is nothing to see except the frame and the underneath. Seventeen, at a guess. Dark, long face, in white, with an older woman beside her doing all the talking to the company so that the girl does not have to. And while three hundred people have been looking at the front of the engine and going oh, she has spent fifteen minutes bent slightly at the waist, looking at the part where the wheels come off their columns. She catches me watching and she is not embarrassed at all.

The_girl: How many teeth on the carry?

Bram: Nobody has ever asked me that. In eleven Saturdays and three hundred people a Saturday, nobody has ever asked me anything about the machine except whether it is difficult to turn. Ten, I tell her. Same as the wheel.

The_girl: Then the carry costs the same as the add.

Bram: I couldn't say, miss.

The_girl: No. But you knew the number.

Bram: And she goes back to looking at the underneath. Which is when it lands on me properly — the who and the where and the when of it, the way it always does, about four minutes later than would be useful. I am a footman. I am twenty-six years old, I have a place in a house in Dorset Street in Marylebone, and my place depends entirely on nothing in this room getting broken or spoiled, and it is a Saturday night in June, in the year eighteen thirty-three. And the girl at the wrong side of the machine, the only person here tonight who has looked at the mechanism instead of at the company — nobody has introduced her to anybody. She is somebody's daughter. She is seventeen. She is not going to be asked what she thinks by a single person in this room, tonight or for the next ten years. I am going to tell you her name in about four minutes and you are going to be very cross with me for making you wait. This is Chronicles — history, lived from the inside. Not the dates and the names cut into the monument, but the morning it actually happened, close enough to touch. We drop you into the room where the world turned, and we make you feel why it still matters now. And there's only one honest way in: to actually be there, in a body, on the day. So one traveller goes where the rest of us can't — the same soul, life after life, moving through all of history, waking inside someone who was really there. I'm the Traveller. Episode twelve. Three Initials — nine months, one desk, and a sentence a hundred years early. Nine years before any of the rest of this, that girl at the wrong side of the machine was seventeen and had just been taken to her first grown-up party. Her name was Augusta Ada Byron. Everybody in the room knew exactly who she was, which is a different thing from being introduced. She was born in London on the tenth of December, eighteen fifteen, and she was the only legitimate child of Lord Byron — the most famous, most read, most gossiped-about man in Europe. Her parents separated a month after she was born. Byron left England in the spring and never came back, and never saw her again. He died in Greece when she was eight. She met him exactly once, as an infant, and remembered nothing of it, and was famous for him for every day of her life. Her mother was Anne Isabella Milbanke, Lady Byron, and Lady Byron did an unusual thing with her daughter. She had her taught mathematics. Not accomplishments. Not a little geometry between the harp and the Italian. Real teachers, one after another, over fifteen years: William Frend, a Cambridge mathematician; Dr William King, a physician who set her problems; and Mary Somerville, who was the most distinguished woman of science in Britain and who took her seriously enough to argue with her. And then, from eighteen forty to eighteen forty-one, the thing that actually made the difference — a two-year course in the calculus with Augustus De Morgan, professor of mathematics at University College London. By post. Every letter, every worked exercise, every correction, sent up and down the Surrey road, because there was no university in Britain that would have put her in a room. The historians who have gone through her papers put her, by the end of it, at about the level of a good university student of the day — with a habit of asking questions that stopped De Morgan in his tracks. She met Charles Babbage at a party on the fifth of June, eighteen thirty-three. A fortnight later she was standing beside his machine, and a woman who was there wrote down that she understood how it worked and saw the great beauty of the invention. She was seventeen. It was the single most consequential introduction of her life. Two years later she married William King, who became Earl of Lovelace in eighteen thirty-eight, which made her the Countess of Lovelace. Three children by eighteen thirty-nine: Byron, Annabella, Ralph. Now. Hold all of that, and let me put you in the year, because I think you already own it and do not know you own it. Eighteen forty-three. Victoria is twenty-four and six years on the throne. In March the Thames Tunnel opens to the public — the first tunnel ever driven under a navigable river anywhere on earth, and for a shilling you can walk under the water with a band playing at the bottom. In July, at Bristol, Brunel launches the Great Britain: iron hull, screw propeller, the largest ship afloat. Nelson's Column is finished that year in Trafalgar Square, which was a building site. In September a new weekly paper called The Economist puts out its first number, arguing about the Corn Laws, which is what the country is actually shouting about. And on the nineteenth of December, in the same city, Charles Dickens publishes A Christmas Carol. That is the eighteen forty-three you already have. Gas-light and cobbles and iron and Scrooge. Coal smoke sitting on the roofs like a lid. A country that has just watched the impossible become a ticketed attraction twice in one year, and has decided that this is simply what happens now. In the same twelve months, in the same city, a twenty-seven-year-old countess published a table of instructions for a machine to carry out, and wrote down the idea that such a machine might one day compose music. And here is the thing you have to hold on to for the next hour, because everything in this story is bent around it, and it is the fact that almost everybody gets wrong. The machine did not exist. Not "was a prototype". Not "was in an early form". The thing at the centre of this entire story — the Analytical Engine — had not one working part, ever, in her lifetime or in his. It was never built. Not a piece of it. What existed was paper. Around five hundred large design drawings, some of them the size of a door. About a thousand sheets of a private diagrammatic notation Babbage invented so that he could describe what every part of it did and when. Thousands more sheets of working notes. All of it in a room off Dorset Street, on long tables under north light. And what those drawings describe is not a bigger calculator. It is a general machine, and it has four organs. The Mill, which does the arithmetic — the part that adds and multiplies. The Store, which holds numbers until they are wanted, so the machine can put something down and pick it up again later. A reader, which takes the machine's instructions. And a printer, so the answers come out without a human hand copying them and making a mistake. And the instructions were to be fed in on punched cards — taken, whole and unaltered, from the silk looms of Lyon. The one machine in this story that was ever actually assembled is the one you have just had your hand on: a portion of the Difference Engine, about two thousand parts, finished in eighteen thirty-two, sitting on a stand in a drawing room being astonishing on Saturdays. It works. It is not the machine the story is about. It is a different machine, for a smaller job — it makes tables, and only tables — and the man who built it abandoned it because he had thought of something enormously better.

So: two people spent the year eighteen forty-three arguing, at length and in writing and eventually very bitterly, about the powers and the limits of an object that neither of them, nor anyone then alive, would ever see move.

Bram: One last piece. In September eighteen forty, Babbage went to Turin and gave the only full public account of the Analytical Engine he ever gave in his life, to an assembly of Italian scientists. A young military engineer in the audience, Luigi Federico Menabrea — who would end up a general and then prime minister of Italy — took notes and wrote them up, and in October eighteen forty-two his paper appeared in French, in a journal in Geneva. Notions sur la machine analytique de M. Charles Babbage. A sketch. A careful, competent, entirely descriptive account of a machine that did not exist, in a language most English readers of science could manage but would not bother with. Somebody needed to put it into English. It was, on the face of it, the smallest job in this story. Ockham Park, in Surrey, on an afternoon in October, and the first fact about the place is cold. England indoors in autumn is cold, and the way you tell how rich a house is is how many rooms have a fire going at four in the afternoon. Here the answer is two. I am on my knees at a grate with a scuttle beside me and my hands are black to the second knuckle, and they are doing something I have never in my life known how to do — building a coal fire that will last a whole working night without being touched. You do not do it by piling it on. There is a shape to it: a back wall of the big lumps set close, a hollow in the middle for the draw, the small stuff banked left where the chimney pulls, and then the part that is craft — a layer of dust and slack over the top of the whole thing, which looks like ruining it and is the reason it is still alive at three in the morning. There is a rag in my apron pocket for my hands. This body reaches for it without looking, and I discover I know where it is. The room is a lady's sitting room, not a study — nobody would call it a study, and the difference matters. A sofa with a slope of cushions at one end. A writing slope on a table you could carry with one hand. A stone inkwell. Quills, and beside them one of the new steel-nib pens, which everyone claims to dislike. Heavy curtains half drawn against a grey Surrey window. And paper — on the table, on the sofa, in a slither on the carpet where it has come off the arm. And the smell. Coal, obviously, and lamp oil, and the sulphur of a struck lucifer, and ink. And under all of it, thin and sweetish and bitter at the same time, from a bottle on the mantel with a paper label — the smell I know before this body tells me, and which this body does not remark on, because remarking on it is not her place. Her ladyship is on the sofa. She has been on the sofa since eleven. She works lying down when her back is bad, and her back has been bad since the second week of September, and I have been dressing her, feeding her and lying to her mother about it ever since. The housekeeper puts her head round the door and does not come in.

The_housekeeper: Post's come. And there's a boy at the kitchen door says he's not to go till he's had an answer.

Bram: There is always a boy at the kitchen door who is not to go till he has had an answer, and there is never an answer, and the boy always goes. I take the packet up. It is not heavy. It is a French pamphlet in a paper wrapper, tied with string, and a folded note on top of it, and the whole thing weighs less than a pair of gloves.

Ada: What is it?

Bram: I say what it is. A packet, my lady, and a note with it.

Ada: Well, open the note, I'm on my back and my hands are covered in the last one.

Bram: So I open the note and read it out, which I do badly, because it has a French word in it and I am not going to attempt the French word.

Ada: Bibliothèque Universelle. Geneva. Oh — it's the Menabrea. Wheatstone said it would come.

Bram: She says it exactly the way you say the name of a thing you have been half expecting for a month and have already decided is a small matter.

Ada: A translation. Somebody has finally written the thing down properly and it is in French, and Mr Wheatstone thinks the English ought to be able to read it, and the English will not learn French, so.

Bram: So it goes to the countess who reads French, and it goes to her because it is the kind of work a woman of her rank is permitted to do — which nobody in this room says out loud, including me, and I am the only one here who is not a countess.

Ada: How long is it? Hold it up. Don't untie it, just hold it.

Bram: I hold it up.

Ada: Thirty pages? Forty?

Bram: About that, my lady.

Ada: A fortnight, then. Three weeks if the children are ill.

Bram: And I will tell you what I thought, standing there with a French pamphlet held up at arm's length like a dead mouse, because I have been in this house four years and I have some standing on this question. I thought: a fortnight is generous. I have watched her ladyship do a great many things very fast and then not finish them. There is a Latin grammar in the box room. There is an unfinished harp piece with her own pencil marks on it. Last winter she was going to build — build, with her own hands, she had the drawings — a machine to fly, and there was a man from Ockham village here twice about the framing, and now there is not. So. A fortnight. I put the packet on the writing slope and I go to see about the fire. Master Byron comes in at half past four, because he always comes in at half past four, and he is seven and he has a wooden horse with two legs.

Byron: Mama, it's come off again.

Ada: Bring it here. No — bring it here, I can't sit up. Right. That's not the leg, that's the peg. Do you see? The leg is perfectly sound, it's the hole that's gone soft. So gluing the leg back will do nothing at all, will it, because the leg isn't the trouble.

Byron: Then what do we do?

Ada: We make the hole smaller. Go and get me a bit of the string off that packet and don't tell Nurse.

Bram: And she wraps the peg in a turn of string and pushes it back in, one-handed, lying down, and the horse stands up on the carpet, and the boy goes off with it entirely satisfied and does not thank her, and she watches him go with an expression I have not got a word for. Then she puts her hand out for the packet. I bring her the lamp at five, because the light goes early in October. I bring her dinner at seven and she does not look up, and I take it away again at half past eight barely touched, and she does not look up. I bank the fire at ten. At eleven she asks me to fetch the other French dictionary, the big one, from the room across the landing, which weighs as much as a child, and I carry it in and she takes it out of my hands and opens it on her chest, lying flat, holding it up in both arms above her face. At midnight she is still there. And she has not untied the string on the wrapper the way you untie string on a parcel. She has undone it and kept it, and wound it round her fingers, and it is still there in her left hand at midnight, going round and round. I have seen her start a great many things. I have never once seen her forget to put a thing down. A fortnight. Hold on to that, because somebody else is going to make an estimate at the end of this hour and they are going to be just as wrong, and it is the only joke this story tells twice. But first — why her? Why is a countess doing the translating at all, and why is a translation the job? Because in eighteen forty-two, in Britain, here is the complete list of things a woman could be, in the sciences. She could not matriculate at a university. Not Oxford, not Cambridge, not the new one in London. No degree, no lectures, no laboratory, no library ticket. She could not be a member of a learned society: the Royal Society, the Astronomical, the Geological, the Statistical — all closed. When the Royal Astronomical Society wanted, in eighteen thirty-five, to recognise Mary Somerville and Caroline Herschel, the two most accomplished women of science in the country, it had to invent a category for them. It made them honorary members. Honorary, because full was not available. There was no salary anywhere. There was no post to hold. There was no job. What there was, was a door. A narrow one, and everybody knew where it was. You could translate. A translation was work a lady could do without anyone being embarrassed, because on the face of it a translator is a servant of somebody else's thought. You are not claiming anything. You are not putting yourself forward. You are doing, for the language, roughly what a good copyist does for a manuscript. And because nobody was watching that door, a very great deal walked through it. Mary Somerville had gone through it eleven years earlier. She was asked to render Laplace's Mécanique Céleste into English — a translation — and what she actually produced was a book that explained the whole subject from the ground up, three times the length of a translation, and that Cambridge then set for its own students. That is the precedent sitting on the shelf. Somerville was Ada's teacher and her friend, and Ada had watched her do it. So when a French paper arrives at Ockham Park and the household reckons a fortnight, the household is reading the job correctly and reading the door wrong. It is not a small job because it is a translation. It is a small job because everyone has agreed to call it one. In January she goes up to London, and the man whose machine it is asks her a question that nobody has ever asked her, and it takes about nine seconds, and it costs him everything. Charles Babbage has the wrong hands. It is always the hands, and never the thing you would expect. Not the face, not the height, not the voice. These are broad and thick across the palm, with ink worked so far into the creases of the right forefinger that it has stopped being a stain and become a colour, and a healed cut across the base of the thumb from something with an edge on it, and they are fifty-one years old and extremely quick. I am in a first-floor room in Dorset Street with the curtains open and a cold January light coming off the street, and there is a table down the middle of the room with about four hundred sheets of paper on it in nine stacks, and I am holding a fair copy in English of a paper I have read in French. And I am pleased. That is the whole weather of this body this morning and it is worth stopping on, because of what happens in August. I am pleased with the morning. I am pleased with the coffee. I am extremely pleased with what is in my hands. It is good. I do not say that lightly, and I have read a great many bad accounts of my own work. Menabrea did well in Turin — he sat there for four days while I explained it and he understood a remarkable amount of it — but this English is better than his French. Whoever did it has not merely turned the words round. In three places she has gone into the thing itself and come out the other side with a cleaner sentence than the one she went in with, and in one place she has quietly repaired a description of the carriage that I would have had to write to Geneva about. She is sitting across the table drinking coffee she does not want and pretending she is not watching me read.

Ada: You've gone back three pages.

Bram: I say that I have.

Ada: Twice.

Bram: I say that a man may go back three pages in his own subject without being cross-examined about it in his own house.

Ada: You may. You've done it twice, though.

Bram: Wheatstone is at the window with his back to us, doing the thing Wheatstone does, which is to be entirely present in a room and take no part in it whatever until the exact moment he is useful.

Wheatstone: He's going back because it's right and he wants to catch it being wrong.

Ada: Yes. That is exactly what he's doing.

Bram: It is exactly what I am doing. I put the sheets down. And then I ask her the question, and I want to be honest about how little thought went into it, because everything after this turns on it and I would rather not be given credit I have not earned. I did not plan it. I did not weigh it. It came out of me the way a remark about the weather comes out of a man, and here it is. I ask her why she has never written anything of her own. And the room goes different. Not silent — Wheatstone shifts his feet at the window, and there is a cart going over the setts outside, and somewhere below us a door. But she has stopped, and she has stopped in a particular way. She has put her cup down without looking at where she is putting it.

Ada: On the engine?

Bram: On the engine, I say. Or on anything. You have understood this machine better than any living person except me for nine years. You have read every serious thing published on the calculus in English and a good deal in French. And you are twenty-seven, and you have never in your life put your own name at the top of a page.

Ada: No.

Bram: And then she says a thing I have never forgotten and did not understand at the time.

Ada: It hadn't occurred to me.

Bram: I said something back. I said — and I am reaching for it now across a great many years — I said something like why on earth not, and she looked at me for what felt like a considerable time.

Ada: Because nobody has ever suggested it.

Bram: There is a version of me that hears that properly. That version puts down the sheets and thinks about what it means that a woman of that ability has arrived at twenty-seven with no one having suggested it, and about who exactly was supposed to have done the suggesting.

This_version_says: well. Append some notes, then. To the translation. A few of your own remarks at the end — you have plenty, you have been making them at me since you were seventeen.

Ada: Notes.

Bram: Notes. As long as you like. Taylor will print them; he prints what the translator sends him, more or less, and Francis is reasonable about length.

Ada: How long is "as long as I like"?

Bram: And I laughed at her, and I said: as long as you like, madam. Nobody has ever finished a set of notes because they ran out of room. She did not laugh. She sat there for a moment with her hands flat on the table on either side of the coffee she had not drunk, and she said one more thing before Wheatstone turned round and the morning went on to other business.

Ada: Then I shall want the Bernoulli numbers off you at some point. Not today.

Bram: The Bernoulli numbers being a sequence out of the calculus that every serious analyst in Europe knows and nobody enjoys — and being, therefore, not the sort of thing a person mentions unless they have already decided to do something with it. I said, God help us both, and I meant it as a joke, and it was the last entirely easy sentence that ever passed between us. Here is what I want to be exact about, standing in this body, on this morning, with the light coming off the street and my own machine in nine stacks on the table beside me. I did that. Nobody made me. It is the best thing I ever did for another person and I did it in about four seconds without attending to it, the way you hold a door. And in seven months I am going to ask her to burn it. He is not being modest and he is not being careless. He genuinely does not know what he has just handed her, and to see why, you need to know the size of the thing she has just agreed to write about. Walk down one floor and along the passage at the back of the Dorset Street house and there is a long room under north light with tables in it, and this is where the Analytical Engine lives. On paper. The Store — the part that holds numbers until they are wanted — was designed to hold one thousand numbers, of fifty decimal digits each. Sit with that a moment, because the number is only impressive if you put it next to the right thing. Do not put it next to the machine in your pocket. Put it next to a clerk. A good counting-house clerk in eighteen forty-three works to six figures and checks his work by doing it twice. A first-rate table of logarithms, the kind ships navigate by, runs to seven places. Fifty is not an improvement on that. Fifty is a different order of thing entirely — it is a number of digits nobody in commerce or navigation or astronomy had any use for, chosen because Babbage wanted a machine that could never be embarrassed by the arithmetic, whatever you fed it. A thousand of them. Held. Simultaneously. Waiting. And every one of those thousand numbers would have been a column of brass figure-wheels, standing about the height of a man, in a hall of columns, all of them geared together, all of them turning off one engine. It was drawn on paper. In an age of brass and steam and water and horses. By a man of fifty-one who had already spent nineteen years and a very great deal of other people's money failing to finish a far simpler machine that only made tables. That is what she has agreed to write a few remarks about. And she has just told him she will be wanting the Bernoulli numbers, which means she has already decided — in the room, on the morning, before she has written a word — that the notes are going to have a worked example in them. But the winter comes first. And the winter is bad. The same room at Ockham in February, same grate, four months on — and notice what the room has become, because nobody in the house has, and I am in it twice a day. The paper has taken over. Not spread — taken over, the way ivy takes a wall. Menabrea's printed French sheets are pinned open on the table with the margins written into so heavily that the print is the minority. Her own foolscap is in two stacks, fair and rough, and the rough one is four times the other. There are letters with broken seals in a drift down the side of the sofa, every single one of them in the same hand, and it is his. And there is a run of sheets on the floor by the window that I am forbidden to touch, in an order I am forbidden to alter, which I have twice now had to save from a child and once from the dog. Her ladyship is on the sofa and has not been off it since Tuesday. Now. The bottle. It lives on the mantel and it holds laudanum, which is opium dissolved in alcohol, and it is not a secret and not a vice. Her physician prescribed it. Every second household in England has one. It is what there is — for a cough, for a colic, for a child that will not settle, and for the thing that has been happening in her back and her legs and her stomach on and off since she was thirteen, which nobody in this house or out of it can put a name to. The dose goes on a spoon. Stand next to me for this, because this is the arithmetic of the year and it is not a metaphor.

Ada: Level. Not rounded. You round it and I lose the afternoon.

Bram: I hold the spoon level. It is a reddish brown and it moves slowly, thicker than wine, and it beads a little at the edge of the spoon before it decides.

Ada: More than that and I write like a person under water. Everything I put down is true and none of it is sharp, and I read it back the next morning and it is somebody else's, and I have to do it all again. And less than that and I cannot sit up long enough to reach the inkwell. So it is a very narrow window and it is about the width of that spoon, and I would be obliged if the household would stop treating it as a moral question.

Bram: Nobody in the household has said a word to her about it. Her mother has said several. She takes it and she makes the face she always makes, because it is genuinely foul — bitter and then sweet and then bitter again, and it stays at the back of the throat for an hour. Then she takes a mouthful of water and then she lies still for eleven minutes, and I know it is eleven because I have counted it enough times to have stopped counting. And then, for about four hours, she is the cleverest person in Surrey. What it costs, in the parts nobody writes down: she has not been to the necessary in three days, and that is what the opium does, and it makes her wretched in a way she will not discuss. She sweats at night through the linen so that I change it in the dark. Her skin has gone a colour. Her eyes have got smaller and the black in the middle has got smaller with them, so that she looks at you very hard and slightly past you at the same time. She has stopped eating anything that requires an opinion. And there is the fog. Not stupidity. She is never stupid. It is worse than that — it is a delay. She says something, and it is right, and then she stops, and her mouth stays half open, and you can watch her go back along the sentence looking for the next word in a place where the next word is not, and she finds it about two seconds late. Two seconds. Every time. And she knows. That is the thing about her that I would not tell anyone in this house. She knows. The surgeon comes on the Thursday, up from Guildford. He is perfectly good at his trade and I do not like him, and the only reason I can give is that he talks the whole time.

The_surgeon: Filthy road up from Guildford. Filthy. Two hours, and a wheel off a brewer's dray at the turnpike holding up the entire county. — Arm out, my lady, the left, we did the right in November.

Bram: He ties the fillet round her upper arm, above the elbow. It is a strip of linen tape and he ties it tight, tight enough that her hand goes a dull colour almost at once, and he taps the inside of her elbow twice with two fingers to bring the vein up.

The_surgeon: Make a fist for me. And again. Good.

Bram: I hold the basin. That is my part. It is a white bowl with a notch in the rim for the arm and it is chipped on the inside where nobody sees, and I hold it under her elbow with both hands and I do not look at her face, because she does not want me to.

The_surgeon: Now. Little scratch.

Bram: The lancet is small — smaller than you would want it to be, about the length of a thumbnail, with a spring in it — and it goes in and comes out in the same movement, and there is a sound, which is not much of a sound. A tap. And then a wet noise beginning. It comes fast. That is the thing nobody tells you. It is not a seep. It arrives in a thin dark line straight out of the crook of her arm and it hits the bottom of the bowl hard enough to splash, and the sound of it is high and quick and hollow, like water into an empty jug. And then, as the bowl fills, the note comes down. It goes lower and lower and flatter as it goes, and by the end it is a soft heavy plopping into itself, and the whole time you can hear exactly how much is in there without looking. Twelve ounces. That is the figure. Twelve ounces, or until she goes pale about the mouth, whichever is first.

The_surgeon: You'll want to keep her quiet a day or two after. Rest. And I would say a good deal less of the mathematics. It is the tension of it, you see — the mind draws on the same fund as the body, and the fund is not large in a lady. That is not my notion, that is the general opinion of the profession.

Ada: Is it.

The_surgeon: You have three children and an uncertain constitution and you are up till two in the morning with a French pamphlet. It does not want a physician to see where that ends.

Bram: And her ladyship, who is white to the lips, with her arm over a chipped bowl and a strip of linen cutting into it, and who cannot at this moment lift her own head off the cushion, says:

Ada: Then you may set your mind entirely at rest, doctor, because it is not French any more. The French part took a fortnight. This part is mine.

Bram: He laughs. He thinks she is being charming. He unties the fillet and puts a pad on and folds her arm up over it and tells her to hold it there, and he talks about the road back to Guildford, and he goes. And then it is me and her and a bowl I have to carry out through the house without meeting anybody on the stairs. She wants to get up. Of course she wants to get up. She wants the writing slope, and the slope is eight feet away on the small table, and she has just lost three-quarters of a pint of blood and taken forty drops, and she gets her legs off the sofa on the second attempt and sits there with both hands flat on the cushion, breathing.

Ada: Don't.

Bram: I don't. I stand there and I do not put my hands out and I let her try, because that is what she has asked for and because I have got it wrong the other way before. She gets about six inches up and her arms fold and she goes back down, hard, and the sofa takes it. And then she says it. Not loudly.

Ada: All right. Both hands. Under the arms. And don't — don't be kind about it, just do it fast.

Bram: So I put both hands under her arms and I take a countess's whole weight, which is nothing, which is frighteningly nothing, and I walk her the eight feet to the chair at the small table like a piece of furniture that has to be got round a corner, and she is looking at the ceiling the entire way. I put the slope in front of her. I put the ink where her right hand can reach it without leaning. I put the lamp on the left so the shadow of her own hand does not fall on the line. And she starts writing, and her hand is shaking, and she keeps going. His lordship looks in at eleven. He is a kind man who does not know what to do, which is the whole truth about him and is not a criticism.

Lord_lovelace: How long has she been up?

Bram: Since three, my lord.

Lord_lovelace: And she has been bled today.

Bram: Yes, my lord.

Lord_lovelace: Don't tell her mother.

Bram: And he stands in the doorway a while looking at the back of his wife's head, and then he goes to bed. Here is what changed in me that night, and it is the reason I am telling you this one. Up till February I thought I was managing an illness. I have managed it for four years, I am good at it, and there is a kind of comfort in being good at a thing. And that night, holding a chipped bowl at the top of the back stairs with my thumb over the notch, I understood that I was not managing an illness any more. I was managing a race. There is a thing in that room that wants her, and there is a thing on that table that wants her, and both of them are going to get what they want, and only one of them is in any hurry. Less of the mathematics. Rest. You are going to hear that sentence again at the end of this hour, from somebody far better qualified to say it, and it will be worse. So where did the mathematics come from? It came, in the first place, from her mother — and not the way it is usually put. Anne Isabella Milbanke was mathematically educated in her own right, before she was anybody's wife and long before she was anybody's mother. When Byron was courting her — and mocking her, because mocking was how he courted — he called her, in a letter in October eighteen twelve, the Princess of Parallelograms. Three years before Ada was born. He was not being kind. He was being accurate: the woman he married knew her geometry, liked it, had views about it, and carried the nickname for the rest of her life. So the mathematics is already in that house, on that side, as a thing somebody enjoys. What Lady Byron then did was steer her daughter toward it, deliberately and hard, and away from verse. That is real and it is documented in outline, and you can hear the fear in it if you want to. And the daughter went at it like a terrier, which is the half nobody puts in. She was not handed a curriculum and made to sit still in it. She chased tutors. She wrote to Mary Somerville with questions and kept writing. And in eighteen forty, aged twenty-four, married, with three small children and an unreliable body, she talked a professor of mathematics at University College London into taking her through the calculus by correspondence — and then made him keep it up for two years. De Morgan was not doing it for a fee. He was doing it because the letters were interesting, and because she kept finding the questions underneath the questions — the ones about why a rule was allowed, which are the ones his actual students mostly did not think to ask. That is where the mathematics in this story comes from. Fifteen years of real teachers, two years of hard technical correspondence, and a woman who went and got it. And in the spring, in a cold room, with a shaking hand and forty drops in her, she does something that none of it accounts for. I am inside her, and I want to say at the start that I have not done it lightly and I do not do it again. Everything so far you have watched from a doorway. A footman. A maid. That is on purpose, because that is how almost everybody in her life saw her — from a doorway, at a distance, guessing. There is exactly one place in this whole year where she left a door open, and it is the page, and this is the night she wrote it. So. Spring. The room is cold at the edges and warm in a band four feet wide in front of the grate, and I am in the chair at the small table with a shawl on and my sleeves pushed back off my wrists. The hand is the shock. Small, nails cut short, a hard yellow callus on the inside of the middle finger where the pen sits — the kind you get from years and not from months. Ink on the forefinger. And unsteady: not shaking, tonight, but unreliable, so the downstroke of a long letter has a tremble in it that I can see and cannot stop. There is a stack of finished sheets at my left elbow that is now about three times the height of the printed French it belongs to. I count it most nights. Every so often I stop and look at the two piles side by side and something goes up my back that I would not describe to anybody. Note A is the one I am in, and Note A is where I have to say what this machine actually is, as against the other one — the one on the stand in Dorset Street that makes tables. Everyone who has written about either has said the new one is bigger, or faster, or more general, and every one of those words is wrong. It is not more of the same thing. It is a different kind of thing, and I have spent eleven days trying to say why in a sentence a man who is not a mathematician can carry away in his head. The trouble is that the true statement is about operations — that the old machine computes a class of results, and this one is an instrument for operating on symbols according to rules, and the symbols do not care what they stand for. That is exact. It is also unreadable, and I know it is, because I have read it aloud four times and heard myself. And then I think about the cards. Because that is where he got the control from. Not from a clock, not from an organ barrel — from a loom. From Lyon. From a machine that makes flowered silk, in which the pattern is not in the weaver and is not in the cloth, it is in a chain of punched cards fed over a roller, one card to a row, and the holes decide which threads come up. I have watched one work. I have had a card in my hand. So the loom does not know what a flower is. Nobody in Lyon has ever taught a loom what a flower is. There is no flower anywhere in the machine. There is only which threads, this row — and out the other end comes roses. And I put the pen down, which I do not do, and I sit there. And then I write it, and it takes about forty seconds, and it is the best sentence I will ever write. We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves. There. There it is. Twenty-one words, and a man who has never done an algebraical operation in his life now knows the whole of it — that the machine has no idea what it is doing, and that this is not a limitation, it is the point, because a thing that does not care what the symbols mean will take any symbols you give it. I have a small unbecoming habit of underlining, three strokes, when I am certain. I put three strokes under algebraical patterns and then take a pen-knife and scrape them off again, because Taylor's compositors do not need my opinions. And then the room goes very quiet, because the sentence is not finished with me. If the cards do not care what the symbols mean — then the symbols do not have to be numbers. Number is a special case. Number is only one set of things whose relations can be written down as operations. Anything else whose relations can be expressed that way would go through the machine exactly the same, and the machine would never know the difference, because there is nothing in it to know with. And what else has relations like that? Not weight. Not distance, that is only number again. Not language, not yet, I cannot see how. Harmony. Pitched sounds. The science of harmony is nothing but relations — this interval against that one, this progression permitted, that one forbidden, every rule of it a rule about how one thing stands to another, and not one of them about how loud or how sweet. If you could write the fundamental relations of pitched sounds as operations, and put them on the cards — — the engine would compose music. Not play it. Compose it. Elaborate and scientific pieces of music of any degree of complexity or extent. I sit with my hand over my mouth like a woman at a bad piece of news. Because I know exactly what this is. This is the moment where I write down a thing that no one on earth has written, about a machine that does not exist, at eleven o'clock at night, in a room by myself, with forty drops in me — and there is a version of me, the one my mother has been watching for since I was five, who writes exactly this sort of sentence and is a lunatic. That is the fear and I am not going to pretend it away. My father wrote sentences at night that the world took seriously and my father was, by every measurement anybody had, unwell. If I put this in, and I am wrong, it is not a mistake. It is evidence. It is the thing they have all been waiting to be handed. And then I read it once more, cold, as a proposition — if the relations were so expressible, then the engine might — and it is not madness. It is a conditional. It is correct. It follows from the cards and it follows from Note A and anybody in England who wants to knock it down is welcome to try and will find they cannot, because I have not claimed the antecedent, I have only claimed the inference. So I put it in. And then — and this is the part that undoes me — I want to tell somebody. Now, this minute, out loud, in this room. And there is nobody in England I can tell. Babbage would take it as a remark on his machine and want to talk about the mechanism. De Morgan would be uneasy and say something careful about the difference between mathematics and metaphysics. My mother would write to a physician. So I ring, and the maid comes up, because it is a quarter past eleven and she is still awake because I am.

The_maid: My lady.

Bram: I ask her to sit down. She does not. I ask again and she sits on the edge of the chair by the door the way you sit when you expect to be got up again. And I read her the sentence. Both of them. The loom, and then the other one. She listens the whole way through, properly, with her hands in her lap, and at the end of it she says:

The_maid: That's the weaving in Lyon, my lady? Where the silk comes from?

Bram: Yes. Exactly that.

The_maid: My cousin's at Macclesfield in the silk. She'd like that.

Bram: And that is it. That is the reply. Not a wrong reply — a perfectly good one, a better one than most of the Royal Society would have given me — and it is not the …