In the 1820s, the books people used to do their sums — tables of numbers for sailors, bankers and astronomers — were riddled with errors. They were worked out by hand and copied by hand, and a single mistaken digit could wreck a calculation, or sink a ship. A London mathematician named Charles Babbage looked at those error-strewn pages and had a thought that would echo for two centuries: a machine would not make these mistakes.
Babbage designed a machine to do the job — the Difference Engine, a vast clockwork calculator of brass cogs that would work out the tables flawlessly and even print them, with no tired human hand to slip. It was clever. But it could do only one thing: that single kind of sum, over and over.
Then he had the larger idea — the one that makes him the start of our story. What if a machine were not locked to one task? What if you could tell it, each time, what to do — feed it instructions, and have it follow them, whatever they were? He called this second machine the Analytical Engine, and although it was never built in his lifetime, its design holds every big idea a computer still uses today.
For over a century people wondered whether Babbage's designs were no more than a dreamer's drawings. So the Science Museum in London built his Difference Engine No. 2 — from his own plans, using only materials he could have had — finishing it in 1991. Eight thousand parts, five tonnes, and it calculated perfectly. He had been right all along.
Babbage's mind never switched off. Besides his engines, he is credited with dreaming up the cowcatcher — the wedge on the front of a train that sweeps the line clear — and he studied lighthouse signals and codes too. He could not stop solving problems.
This is the difference that matters, and it is worth slowing down for. A pocket calculator is fixed — it adds, it multiplies, and that is all it will ever do. Babbage's Analytical Engine was designed to be general-purpose: change the instructions, and the same machine would do an entirely different job. That one idea — a machine you program — is the seed that everything else in this whole subject grows from.
To pull it off, Babbage gave his engine three parts that your phone, hidden under the glass, still has versions of today:
Where numbers are kept while the machine works — columns of geared wheels, each holding a digit. It is exactly what we now call memory.
Where the actual arithmetic happens — numbers are fetched from the Store, worked on, and sent back. It is what we now call the processor.
And the instructions themselves? They were fed in on stiff cards with holes punched in them — punched cards. Babbage borrowed the idea from the Jacquard loom, a weaving machine that used punched cards to control which threads lifted, so it could weave any pattern you encoded in the holes — even a portrait in silk. Babbage saw it and realised: if a loom can be told what to weave by a pattern of holes, a calculating engine can be told what to compute the very same way.
The Jacquard loom could weave pictures, not only cloth. One woven-silk portrait of Jacquard himself was so fine it looked like a print — and it took around 24,000 punched cards to make. Each card wove a single line of the image.
Here is the whole engine as a plan. Read it top to bottom: instructions come in, the Mill does the work, the Store holds the numbers it needs, and a printer puts the answer on paper. Notice the shape of it — because it has never really changed.
Tap each card — what is the modern name for that part of the engine?
Why Mill and Store? Babbage took the words from the cloth mills of his day, where a store held the raw material and the mill did the work. Two-hundred-year-old factory words, still quietly running inside every computer.
Babbage needed someone who could see what his engine truly was. He found her in Ada Lovelace — a young mathematician (and, as it happens, the only child of the poet Lord Byron). In 1843 she translated a paper describing the Analytical Engine, then added notes of her own that ran far longer than the paper itself. In one of them, known as Note G, she wrote out a complete step-by-step method for the engine to calculate a tricky sequence of numbers.
That method is widely regarded as the first computer program ever written — composed a hundred years before there was a working machine to run it on. And like almost every program since, it had a loop: a set of steps the engine would repeat. To feel how that works, watch the engine do something small — multiply 3 by 4 — the only way it could, by adding 3 to a running total, again and again. Reveal each step and predict the total before you move on:
Notice there were two kinds of thing in play: the numbers (0, 3, the total) living in the Store, and the instruction ("add 3, four times") on the card. Keeping those two apart — the data, and the program that works on it — is an idea you will meet again and again. It is one of the pillars the whole of computing stands on.
Ada's program is tucked inside a set of notes she labelled A to G — and those notes ran almost three times longer than the article she was supposedly translating. The first program in history was, in effect, a very long footnote.
Babbage thought he had built a magnificent calculator. Ada saw something he had missed entirely. She realised that the numbers in the engine did not have to stay numbers — they could stand for anything you could capture in symbols and rules. Pitches in a piece of music. Letters in a word. If the relationships could be written down, the machine could work on them.
"The Analytical Engine weaves algebraic patterns just as the Jacquard loom weaves flowers and leaves." Ada Lovelace, 1843
Read that again, because it is one of the most far-sighted sentences ever written about computing. She is saying: this is not a number machine, it is a pattern machine — and patterns can be anything. A century before the first computer hummed to life, she had imagined machines that might one day make music and pictures, not only sums. That imagined leap — from calculation to working on any kind of symbol — is the reason a single device in your hand can be a camera, a piano, a library and a sketchbook all at once.
Watch what Ada actually did: she took a thing everyone saw as a calculator and asked, what is this really, underneath? Stripping a thing back to its true nature and then seeing how far it could stretch — that is one of the most powerful moves in science, and you will see it again every time someone invents the future a little early.
Ada herself drew a firm line. However clever the engine was, she insisted it could not truly create — it could only follow the instructions it was given. In her own words:
"The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform." Ada Lovelace, 1843
It is a careful, honest thought: a machine follows; it does not originate. For Ada, that settled it — a machine could never surprise us with something genuinely new. And for nearly a hundred years, that was the last word on the matter.
Then, a century later, a young mathematician named Alan Turing read that exact sentence — and decided to argue back. Are you sure? he asked. What would it even mean for a machine to think? That question is where our next lesson begins, and in a way, it is the question this whole subject is about. Keep Ada's line in your pocket. We are going to test it.
Turing's question is still everywhere. Each time a website asks you to prove you are human — a CAPTCHA — you are sitting a tiny Turing test. The name even stands for "Completely Automated Public Turing test to tell Computers and Humans Apart".
Fresh one. The part of the engine that actually did the arithmetic — the one we'd now call the processor — was called the ______. What was its name?
Fresh one. The same engine works out 5 × 3 by starting at 0 and adding 5 three times. What total does it print?
Ada said a machine "has no pretensions to originate anything" — it can only do what we tell it. You have grown up with machines she never dreamed of. So have a think, and make your case: is there something a person can do that you believe a machine never truly could? Or do you lean the other way — that there is no such thing, given enough time? There is no right answer here. Argue the side you actually believe, and give a reason or an example.
Start by saying what you think, in one sentence. Then back it up. A single good example is worth more than a long list.
strong You took a clear side in your first line and didn't hedge — that's the hardest part of an argument and you did it cleanly. The example you reached for to back it up is a well-chosen one; it does real work rather than sitting there idle.
try this The one place to push is the other side. You touch on what "someone might say", but only lightly — what is the strongest version of the opposite view? An argument gets stronger, not weaker, when it takes the best counter seriously and answers it.
to add Next time, try ending on the reason you find most convincing, rather than your first one — the last thing a reader reads is the thing they remember. A question worth holding: what would actually change your mind?
She was born in 1815, the only child of the poet Lord Byron — who left when she was a baby, and whom she never knew. Her mother, afraid she might inherit her father's wild streak, had her taught hard in mathematics and logic, an unusual education for a girl of that time. The result was a mind that could do both: rigour and imagination at once.
It was that double gift that let her see, in Babbage's brass engine, something he could not: a machine for working on ideas, not only numbers. She died young, at only thirty-six. For a century her notes were treated as a footnote to Babbage's work — and only later did the world realise that the deepest insight in them was hers.
Today her name is everywhere in computing. There is an Ada Lovelace Day each October, celebrating women in science. And in 1980 the United States named a whole programming language — Ada — after her. Not bad, for someone who wrote her one program with a pen.
A short film from Computerphile. Watch for how the Mill and the Store work together — the same two parts you just met — and how punched cards carried the instructions in.
If you'd like the whole story of Ada and the engine, the BBC documentary Calculating Ada: The Countess of Computing (2015) tells it beautifully — and it's one to watch with Dad, or with Isabel.
Before there were computers, there was the idea of one — a machine you could tell what to do. You saw Babbage's engine and its three parts, the same shape your phone still has. You watched a loop add its way to an answer. And you met Ada Lovelace, who wrote the first program and saw that a machine might one day work on music and pictures, not just numbers — yet drew a line, and said it could never truly originate anything. Hold onto that line, Florence. Next time, a man called Alan Turing is going to push against it — and that push is where artificial intelligence really begins.