Last time you left Ada Lovelace's line in your pocket — that a machine "can do whatever we know how to order it to perform," and nothing more. Hold onto it; we will come back to it. But first, meet the person who decided to argue with it. In 1936 a young English mathematician named Alan Turing — he was only twenty-three — sat down to answer a dry question about the limits of mathematics, and on the way invented the idea that the whole modern world runs on.
Babbage's Analytical Engine, you'll remember, was general-purpose: change the instructions and the same brass machine would do a different job. Turing took that idea and pushed it as far as it could go. He imagined one single machine — an imaginary one, on paper — that, given the right set of instructions, could imitate any other machine at all. A machine to add numbers? Feed it the instructions for adding. A machine to sort words? Feed it those instead. One device, endlessly many jobs, decided entirely by what you tell it. He called it the universal machine.
It sounds almost too simple to matter. It is, in fact, the reason the slab of glass in your hand can be a camera one second, a piano the next, and a library the second after that. It does not become a new machine each time. It is one universal machine, reading different instructions — and we have a everyday word for "a set of instructions that turns the universal machine into a particular one." We call it an app. Or, more honestly, a program.
Turing dreamed up the universal machine to settle a problem in pure logic — he was not trying to build anything at all. The most important machine of the century arrived first as a thought experiment, sketched to win an argument about mathematics. The hardware came later. The idea came first — exactly as Ada had said it would, a lifetime before.
To think clearly about what a machine could and could not do, Turing imagined the simplest possible one. No screen, no keyboard, almost nothing. Three parts only — and astonishingly, those three parts are enough to compute anything a computer can compute today. We now call it a Turing machine. Here it is:
Read the rule table like this: "When I am in state A and I read a 1, I write a 0, move one cell right, and stay in state A." That is all the machine knows. No cleverness, no understanding — only a lookup: what I'm in, plus what I see, tells me what to do next. Let us run it. The rules flip every cell — turning each 1 into a 0 and each 0 into a 1 — until the head reaches a blank. Reveal each move and predict the tape before you go on:
That toy is not a toy. A machine this simple, given enough tape and the right table of rules, can do anything your laptop can do — run a game, sort a million names, send a message. Slower, yes. But there is nothing a modern computer can compute that a Turing machine cannot. Every device you own is, at heart, one of these wearing a very fast disguise.
You have studied the First World War. A generation on came the Second — and this time, a great deal of it was fought in messages. The German military sent its orders by radio, which anyone could hear, so every message was scrambled first by a machine called Enigma. To anyone listening, an Enigma message was meaningless: a stream of jumbled letters that changed its scrambling pattern with every single keystroke, and reset to a brand-new pattern every day. The number of possible settings ran into the millions of millions. It was widely believed to be unbreakable.
In a country house north of London called Bletchley Park, Britain gathered its sharpest minds — mathematicians, chess champions, crossword setters — to break it anyway. Turing was among them, and central to it. Building on earlier breakthroughs by Polish codebreakers, he helped design an electro-mechanical machine called the Bombe: not a computer, but a tireless device that could whirr through Enigma's possible settings far faster than any room of people, throwing out the millions that could not be right so the codebreakers could test what remained.
Here is the heart of why Enigma could be broken — a flaw hidden inside its own cleverness:
Because of that flaw, a codebreaker could rule out any guess that asked a letter to stand for itself — and the Bombe could exploit that to chop the millions of settings down to a handful to test by hand. The intelligence this unlocked, kept utterly secret, is widely credited with shortening the war by perhaps two years, and saving a great many lives.
Tap each card for one true thing about Bletchley.
The whole of Bletchley Park stayed secret until the 1970s — thirty years. People who had quietly changed the course of history went home, raised families, and told no one, not even their husbands or wives. Some took the secret to their graves. The codebreakers won partly because they could keep a secret as well as they could break one.
Real Enigma is far too tangled to crack by hand — that is exactly why they needed the Bombe. But the idea underneath all codebreaking is one you can feel in a minute, with the oldest trick there is: a substitution cipher. Here, each letter has been shifted three places along the alphabet: the writer turned every A into D, every B into E, and so on. To read it, you slide each letter three places back. Here is the secret message:
Take it one letter at a time. Reveal each step and try to guess the word before the next one opens:
Notice what cracked the code: not testing every letter, but spotting the one rule behind all of them. Find the pattern, and the work collapses from thousands of steps to one. That move — hunt for the rule, not the answer — is the heart of codebreaking, of mathematics, and, you will see, of how we teach machines to learn.
After the war, Turing returned to the question that had been waiting for him since 1936 — and in 1950 he published a paper that opened with five of the most consequential words in the subject: "Can machines think?" He saw at once that the question was a trap. Before you could answer it, you would argue forever about what "think" even means. So he did something clever: he put the question to one side and replaced it with a game he could actually run.
He called it the imitation game — we now know it as the Turing Test. Imagine you are passing written notes to two hidden players: one is a person, one is a machine. You can ask anything you like. If, after a long conversation, you genuinely cannot tell which is which — then on what grounds, Turing asked, would you insist the machine is not thinking? He was not claiming the machine truly understands. He was making a sharper point: if the behaviour is indistinguishable, "thinking" may be the unhelpful thing to measure. Judge what it does, not what it secretly is.
A taste of the game. Tap each — could you tell who wrote it?
Turing made a quiet prediction: that by about the year 2000, machines would chat well enough to fool an ordinary person for five minutes, perhaps a third of the time. He was close. The machines you can talk to today would astonish him — and they would not surprise him in the least, because he saw them coming, on paper, in 1950.
Now we keep our promise. Remember Ada's objection from last time: the machine "has no pretensions to originate anything; it can do whatever we know how to order it to perform." A machine only follows. Turing read that exact sentence — he named it in his paper, calling it Lady Lovelace's Objection — and instead of agreeing, he asked a quieter, harder question back.
"Who can be certain that 'original work' that he has done was not simply the growth of the seed planted in him by teaching, or the effect of following well-known general principles?" Alan Turing, on Lady Lovelace's Objection, 1950
Look closely at what he is doing. Ada said a machine only follows rules, so it cannot truly think. Turing replies: are you sure you do anything more? Much of what a person calls original — a sentence, a tune, an idea — comes from rules they were taught and patterns they absorbed. If "merely following instructions" disqualifies a machine from thinking, he asks, does it not put humans in an awkward position too? He did not prove Ada was mistaken. He did something better: he showed the question was far from settled — and handed it forward, to us.
Twice now this story has turned on the same move. Ada asked, what is this machine, really, underneath? Turing asked, what is thinking, really — and how would we even know? When an argument feels stuck, the way out is often to question the word everyone has been taking for granted. "Can machines think?" depends entirely on what you decide "think" means — and choosing that definition is the whole game. Hold that in your pocket now. The rest of this subject is us deciding, together.
Fresh one. Same flipping machine. If the tape starts as 1 1 0, what does it read once all three cells are flipped?
Fresh one. Same shift-by-three trick, sliding each letter back three places. Decode this word: G R J. What word is it?
Fresh one. In which year did Turing first describe the universal machine, in his paper "On Computable Numbers"?
Here is Turing's game, put to you. Imagine you are passing written notes back and forth with someone hidden — and after a long, real conversation, you cannot tell at all whether it is a person or a machine. Would that be enough to say it can think? Or is there something that would still be missing, even then — and if so, what, exactly? There is no right answer here. Take the side you actually believe, and give a reason or an example to stand it on.
Say what you think in your first line, then back it. One sharp example does more work than a long list — and naming what would be missing is often stronger than saying nothing is.
strong You set out your position in the first line and stood by it — that clarity is the spine of any good argument, and yours is clear to follow from the very first sentence.
try this The place to press is the word "think" itself. You lean on it a fair amount — what would you need to see before you'd grant it? Pinning down what the word has to mean, before you judge the machine against it, makes the whole case harder to argue with.
to add A question worth carrying: is there a difference between seeming to think and actually thinking — and could you ever tell, from the outside, which one you were looking at? That is the exact crack Turing was pointing at.
He was born in London in 1912 — a quiet, original boy who ran long distances to think, and who could be impatient with anyone slower than the ideas in his head. By twenty-three he had written the paper that imagined the universal machine. By his early thirties he was at the centre of the most important secret of the war. He is, by a wide margin, one of the people who built the century you live in.
His later life was harder than any life ought to be. In 1952 Turing was prosecuted under the law of the time for being a gay man — a cruelty that cut his career short and, two years later, his life. For decades his name was barely spoken. Then, slowly, the world caught up with what it owed him. In 2009 the British government issued a formal apology; in 2013 he received a royal pardon; and his face is now on the Bank of England's £50 note. The man who asked whether a machine could think turned out to be one of the most human figures in the whole story.
The highest honour in computing — its equivalent of a Nobel Prize — is called the Turing Award. Every year it goes to someone who has pushed the field forward, and it carries his name precisely because so much of the field traces back to a single paper he wrote at twenty-three. The argument you joined today is fought, quite literally, in his name.
A short film from Computerphile. Watch for the three parts you met a moment ago — the tape, the head, and the table of rules — and how something so simple can compute anything at all.
For the Bletchley story as a film, The Imitation Game (2014) follows Turing and the breaking of Enigma. It is rated UK 12A, so fine for you and Isabel together — though a quick word: it touches on Turing's prosecution and his death, so it is one to watch with Dad nearby rather than alone.
You met Turing's universal machine — the idea that one device, given different instructions, can become any machine at all. You ran a Turing machine by hand and saw how three plain parts can compute the world. You broke a code, the way Bletchley broke Enigma, by hunting for the rule instead of the answer. And you watched Turing take Ada's line — that a machine can only follow — and turn it into a question we are still living inside: can it think, and how would we ever know? We have met the idea of a machine that can be anything. Next time, Florence, we open the box and ask the plainer question underneath it all: what is that machine actually made of?
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