In 1965 an engineer named Gordon Moore sat down to write a short magazine article about the tiny electronic chips his industry was learning to make. He had only a handful of years of data — chips were brand new — so what he did next was bold. He looked at how many of the tiny switches called transistors engineers had managed to pack onto a single chip each year, noticed the number was roughly doubling about every year, and predicted it would carry on.
That prediction — later settled to a doubling roughly every two years — became known as Moore's Law. And here is the strange thing: it broadly held for about fifty years. Not because nature forces it to — it is not a law of physics like gravity — but because it became a target the whole industry quietly agreed to chase, year after year.
The result is hard to take in. The transistors got smaller, and smaller, and smaller. The first chips held a few thousand. A chip in a phone today holds billions — and each switch is now far tinier than a single human cell, smaller even than most viruses. You are carrying, in your pocket, something a 1965 engineer could only sketch as a dream on the back of his article.
It is worth being straight about this, because grown-ups often aren't. Moore's Law is not a law at all — it is an observation, a trend people chose to keep up. And in the last few years it has clearly slowed: transistors are now so small that the makers are bumping into the size of atoms themselves, and you cannot build a switch out of half an atom. The doubling hasn't stopped dead, but the effortless years are over. A trend is not a promise.
If cars had improved at the pace chips did under Moore's Law, a family car would now cost a few pence, do millions of miles to the gallon, and go faster than sound. The comparison gets wheeled out so often that engineers half-joke about it — but it does capture something true: no other technology in history has ever sped up like this.
The word for repeated doubling is exponential growth — and the single most important thing to know about it is that your gut feeling about it is almost always going to be off. Human intuition is built for things that grow by adding a steady amount — a plant a few centimetres a week, a savings jar a pound a day. We are not, by nature, wired for things that grow by multiplying.
Look at the difference. Start at 1, and add 2 each step: 1, 3, 5, 7, 9, 11… After ten steps you reach 21. Calm, predictable, a straight gentle slope. Now start at 1 and double each step instead: 1, 2, 4, 8, 16, 32… After those same ten steps you are past a thousand. After twenty, past a million. The two start side by side, almost touching — and then one of them quietly leaves the planet.
Tap each card. One side grows by adding; the other by doubling. Watch where they end up.
This is a habit worth carrying out of this lesson and into the rest of your life. When you hear that something is doubling — users, cases, prices, computer power — your instinct will quietly whisper "that's fine, it's small." Don't trust that whisper. Ask instead: doubling how often, and for how long? A thing that doubles is not adding up. It is winding up. Naming it as exponential is half the battle.
Fold a sheet of paper in half, then in half again, and again — each fold doubles the thickness. If you somehow managed 42 folds, the stack would be thick enough to reach the Moon. You can't actually fold paper more than about seven or eight times, which is rather the point: doubling outruns the real world astonishingly fast.
There is a story told for hundreds of years, in many lands, that teaches doubling better than any sum. An inventor shows a ruler a wonderful new game — chess — and the ruler, delighted, offers any reward he likes. The inventor asks for something that sounds almost insultingly modest: one grain of rice on the first square of the board, two on the second, four on the third — only doubling, square by square, to the sixty-fourth.
The ruler laughs and agrees, thinking he has got off lightly. He has not. Reveal the squares one at a time, and try to feel the moment it runs away from you:
There's a neat shortcut hidden in the board. The grains on any one square are one more than every square before it added together — so the last square alone holds slightly more than the other sixty-three combined. The grand total works out to a number mathematicians write as 2 to the power of 64, minus 1: 18,446,744,073,709,551,615. Worth seeing written out at least once in your life.
Here is the move that makes the whole lesson click. Moore's Law is the chessboard. Each "square" is roughly two years, and the thing being doubled is the number of transistors on a chip. So the count of switches climbed exactly the way the rice did: a few thousand in the early squares, then millions, then — by the squares we live in now — billions.
This curve shows it, roughly. Notice the steepness: nearly flat for years, then rising faster and faster, almost standing on end. That upward sweep is the signature of doubling. Read the numbers up the side carefully, though — each line is ten times the one below it, so the curve is far steeper than it even looks.
One honest note on the picture. Drawn on an ordinary scale, this line would shoot straight off the top of the page within a few decades — so, as scientists often do, the side has been squashed so that each step up means ten times as much. On a squashed scale like that, steady doubling shows up as a straight climbing line. That's the tidy trick: a near-straight line here is the fingerprint of something exploding.
The transistors on a recent chip are spaced only a few nanometres apart — a nanometre being a millionth of a millimetre. To picture it: if one transistor were blown up to the size of a full stop on this page, that same magnification would make you taller than the entire planet. We are now building switches only a few dozen atoms wide.
You might be wondering what rice and transistors have to do with the AI Florence can talk to today. Everything, as it turns out. The ideas behind modern AI are surprisingly old — some are from the 1950s, as you'll see next lesson. For decades they mostly didn't work, and it wasn't because the ideas were poor. It was because two ingredients hadn't piled up high enough yet.
Raw thinking-power — the ability to do staggering numbers of tiny sums very fast. This is the gift of Moore's Law: the doubling chessboard made compute so plentiful and so cheap that calculations once unthinkable became ordinary.
Vast piles of examples to learn from — text, photos, sound. The internet quietly produced these by the billion, as the whole world wrote, posted and uploaded. Suddenly there were oceans of examples to study.
Hold those two side by side, because together they are the answer to the question this lesson is named for. Modern AI didn't arrive because someone had a single brilliant new thought. It arrived because the compute finally got cheap enough — thanks to fifty years of doubling — and the data finally got plentiful enough, thanks to the internet. The old ideas had been waiting, patiently, for the world to grow powerful enough to run them.
That is the deep reason behind the word exploded. For ages, almost nothing seemed to happen — the quiet early squares of the board. Then both ingredients crossed some line at once, and the machines could suddenly do things that looked, for the first time, a little like learning. You're about to meet exactly how, in Lessons 5 and 6.
Training one large modern AI can involve reading a slice of text so big that a person reading day and night, without ever stopping, would need thousands of years to get through it. The machine works through it in weeks — not because it is wiser than you, but because cheap compute lets it read in parallel, at a scale no human life could ever reach.
Cast your mind back over the story so far. In the hardware lesson you met the transistor — the tiny switch that replaced the bulky glass valve, the thing that let computers shrink from room-sized beasts into something pocket-sized. That switch is the very thing this lesson has been counting. Moore's Law is, at heart, the story of how many transistors we learned to crowd onto one chip — and the answer, square by square, was: keep doubling.
And this is real maths, not a trick of the trade. Doubling is powers — 2, 4, 8, 16 is 2 to the power of 1, 2, 3, 4. The difference between adding and multiplying your way along is the difference between a linear graph (a straight slope) and an exponential one (that climbing curve). The intuition you've built today — that exponential things feel slow then pounce — is one of the most useful pieces of mathematics a person can carry. You'll meet it again in graphs, in percentages, in compound interest.
So keep the chessboard in your pocket as we go on. Because the next question is the obvious one: if machines suddenly had all this cheap power and all this data — what did people do with it? The answer is that they returned to a very old dream, one that had failed and been laughed at for decades: building a machine that could learn for itself. With the board finally full of power, that dream got a second life. That's where we're heading.
Notice how the subjects keep talking to each other. The transistor from your hardware lesson is the unit being doubled. The powers and graphs from maths are the shape of the doubling. And the internet you studied in Computing is where the data came from. Three separate things you've learned, tied into a single knot — and that knot is the reason modern AI exists at all.
Gordon Moore co-founded the company Intel, whose chips ran a great many of the world's computers for decades. So the man who merely predicted the doubling also spent his life helping make it come true — which is part of why a loose guess in a 1965 magazine ended up shaping the entire modern world.
Fresh one. Same chessboard, same doubling — 1, 2, 4, 8… How many grains are on the eighth square?
Fresh one. And what word describes the steady kind of growth that adds the same amount each step, drawing a straight slope on a graph?
You now have a kind of radar for doubling. So use it. Think of one thing in the real world — anything at all: something in nature, money, technology, a worry, a hope — that grows by multiplying rather than adding, or that you suspect might. Describe it in your own words, and say what your new radar tells you: does picturing it as exponential change how it looks? There's no single right answer here — pick something that genuinely interests you, and reason it through.
Start by naming your example in one line. Then explain why it multiplies rather than adds — and what that means for where it ends up.
strong The example you reached for is a real one — it genuinely multiplies rather than adds, which is exactly the radar this lesson was trying to switch on. You didn't only name it; you said why it grows the way it does, and that "why" is the part most people skip.
try this One way to push the thinking further: put a rough number on it. Doubling how often? Every day, every year? The same idea feels completely different depending on the speed of the doubling, and pinning that down is where the real insight lives.
to add A question worth sitting with: most things can't double forever — the world runs out of room, like the paper you can't fold past eight times. What is it, do you think, that finally stops your example from doubling? That's a deep question, and a good one.
He was born in California in 1929, the son of a county sheriff, and grew up quiet and curious — a boy who loved chemistry sets and blowing things up gently in the back garden. He trained as a chemist and a physicist, and might have stayed a careful laboratory scientist his whole life, had he not landed, in the late 1950s, in the brand-new business of making electronics out of a material called silicon.
In 1965 a magazine asked him to predict the future of these new chips. He had barely any data to go on, but he drew his line anyway, and guessed the doubling would carry on for a decade. That short article — almost a throwaway — became one of the most famous predictions in the history of technology. Three years later, in 1968, he co-founded a company called Intel, and spent the rest of his working life helping the prediction come true.
He was, by all accounts, a calm and modest man who disliked fuss and gave away most of his fortune to science and conservation before he died in 2023, aged ninety-four. It is a quietly lovely thing: the person whose name is attached to the fastest, loudest change in human history was himself unhurried, careful, and kind. A reminder that you don't have to be loud to change the world.
Moore very nearly didn't get his prediction published as a tidy "doubling." An editor wanted a snappier story, and the famous graph was almost cut for space. The single most quoted line in the computer age survived partly by luck — which is worth remembering the next time someone tells you the future was obvious all along.
We looked hard for a short film to drop in here, but couldn't find one from a source we fully trust that was both on-topic and the right tone — so rather than settle, here are two genuinely good ones to watch with Dad, on a screen bigger than this.
A man named Gordon Moore noticed, in 1965, that chips were doubling — and that doubling held for half a century. You felt how exponential growth hides in a bowl of rice and then buries a city, and you learned the move that matters most: human intuition is poor at doubling, so name it when you see it. And you found the real answer to "why now" — cheap compute from the chessboard, and huge data from the internet, piling up together until the machines could finally do something new. Next time, Florence, with all that power suddenly to hand, people went back to an old, once-laughed-at dream: a machine that could learn for itself. That's where we pick up.