Part IV · Interlude · Chapter 13
How Big Is It? The Machine in Numbers You Can Picture
The machine can now answer, reason and act, and every ingredient this book set out to add is in place. Before asking what those abilities mean, let us count what they cost: how much text it learned from, how much calculation training required, and how much energy an answer uses.
Nothing in the machine is magic, but everything in it is big. The size is the part that is hardest to picture, so this chapter translates it into books, calculators, kettles and cities.
The bill, rung by rung
Every rung of the climb consumed something: steps, people’s time, data, computing or energy.
| Rung | What it consumes |
|---|---|
| Rule-following (Chapter 1) | Steps and squares of tape: adding one takes at most one step per digit, plus one when the number grows. |
| One machine for every rulebook (Chapter 2) | Extra steps and energy: reading a rulebook from memory is slower than wiring it in. |
| Rules written by hand (Chapter 4) | Experts’ time, the slowest and costliest part; running the rules was nearly free. |
| Learning from examples (Chapter 5) | People’s time to label examples, and computing for every adjustment, many times over. |
| Generalizing (Chapter 6) | More data and computing; each further gain costs many times more of both. |
| Seeing and hearing (Chapter 7) | Labels at scale: over a million labeled photos, 680,000 hours of transcribed audio. |
| Predicting the next word (Chapter 8) | The biggest bill, counted in the rest of this chapter. |
| Imitation (Chapter 9) | Careful human writing: about 13,000 example answers by about forty people (InstructGPT). |
| Feedback (Chapter 10) | Many thousands of human comparisons, and about 2% of the original training computing. |
| Reasoning (Chapter 11) | A cost on every answer: 10,000 tokens of reasoning take about 16 times the computing of a plain 500-word answer. |
| Agents (Chapter 12) | Many model calls per task; an hour-long task can cost tens or hundreds of times an ordinary question. |
The early rungs cost mostly human time. From Chapter 8 on, the bill is mostly computing and energy, paid once to train the model and again, on every question, to run it.
What happened at 2 a.m.
The parent pressed send. A few seconds later the answer appeared: calm, clear, call an ambulance now. What happened in between?
The message traveled to a data center, perhaps hundreds of kilometers away, where a model with hundreds of billions of adjustable numbers produced the reply one word-piece at a time. For each word-piece, every one of those numbers took part in a multiplication and an addition. The whole reply took several hundred trillion operations, done in well under a second of computing time.
None of this is mysterious. It is the multiply, add and bend of Chapter 5, executed by the universal machine of Chapter 2. What is hard is not what happens but how much of it. So let us count.
To keep the numbers honest, the chapter uses one model whose builders published the details: Llama 3.1 405B, released by Meta in 2024, with 405 billion adjustable numbers. Today’s largest models are bigger. Their builders mostly do not publish the figures, and published estimates put the largest training runs roughly ten to thirty times above this one. Only a handful of companies and governments can pay for runs on that scale.
The reading bill
Llama 3.1 was trained on about 15 trillion tokens, the word-pieces of Chapter 8. A token is on average about three-quarters of an English word, so that is roughly 11 trillion words.
How much is that?
- A typical book is around 100,000 words. So the model read the equivalent of about 110 million books.
- In 2010, Google estimated that about 130 million distinct books had ever been published. The model’s reading is of the same order as every book ever printed.
Two cautions. The “books” are a way of measuring volume, not what the model read. Most of its text came from the web, along with code, articles and many languages, filtered to remove duplicates and junk. And reading more is not the same as understanding more: a child learns language from a tiny fraction of this. How people learn so much from so little is still an open question.
The arithmetic of learning
Training is the gradient descent of Chapter 5: show the model text, measure its prediction error, nudge every number, and repeat. Meta’s figure for the whole training run is about 38 trillion trillion operations, written
Picture doing it by hand:
| Who is calculating | How long it would take |
|---|---|
| Every person on Earth (8 billion), one operation per second each, never stopping | about 150 million years, roughly as long ago as the dinosaurs |
| One modern AI chip (an NVIDIA H100) running flat out | about 1,200 years |
| The 16,000 such chips Meta actually used, at realistic efficiency | about two and a half months |
That last line is the real one. The training used about 31 million chip-hours. An estimate using the chips’ rated power, 700 watts, gives about 22 million kilowatt-hours for the chips alone, before counting cooling and the rest of the building. An average American home uses about 10,500 kilowatt-hours of electricity a year. So the chips’ electricity for this one training run was roughly what 2,000 homes use in a year: a small town’s worth. Today’s largest training runs are many times bigger.
The cost of an answer
Training is mostly an upfront cost. Answering adds a cost on every use, billions of times a day.
To produce each token of an answer, a model does about two operations for every adjustable number it uses. For a 405-billion-number model, that is about 800 billion operations per token. A 500-word answer is about 670 tokens:
| What | Operations | By hand, all of humanity |
|---|---|---|
| One token | about |
about 100 seconds |
| A 500-word answer | about |
about 19 hours |
| A “thinking” model that first writes 10,000 tokens of reasoning (Chapter 11) | about |
about 12 days |
One chip does the 500-word answer’s arithmetic in about half a second. Real answers take longer, because the chip spends much of its time waiting for numbers to arrive from memory. Many of today’s largest models also use only part of their numbers for each token, which lowers the cost. These figures are order-of-magnitude guides, not measurements of any particular product.
And the energy? In 2025 Google published careful measurements for its own chatbot, Gemini. They counted the chips, the computers around them, idle spare capacity and cooling. The median text prompt used 0.24 watt-hours. OpenAI’s chief executive gave a similar figure for ChatGPT, 0.34 watt-hours for an average query, without published methods. What is 0.24 watt-hours?
- About nine seconds of television (Google’s comparison).
- About 1/400 of one boil of a one-liter kettle.
A neat comparison lies closer to home. A human brain runs on about 20 watts. In the time it takes you to read a short answer, about forty seconds, your brain uses about as much energy as the machine used to write it.
Figure 13.1. The machine’s scale in human terms, using the figures in this chapter. Reading and training are for Llama 3.1 405B; the energy of one answer is Google’s 2025 median for a Gemini text prompt.
Two cautions again. “Median text prompt” means a short, ordinary question. A long reasoning session, an agent working through a task for an hour (Chapter 12), or generating images or video can cost tens or hundreds of times more. And Google reported that the energy per median prompt fell 33-fold in a single year, so any such figure dates quickly.
The power bill
Add it all up and the scale changes again.
ChatGPT alone was handling about 2.5 billion prompts a day by mid-2025. At about 0.3 watt-hours each, that is around 750,000 kilowatt-hours a day, about 30 megawatts on average. That is the output of a small power station, and only a small part of the story. The very large buildings now going up are built mainly for training ever-bigger models and for the far heavier work of reasoning, agents, images and video.
| Facility or total | Power | Picture it as |
|---|---|---|
| A typical AI-focused data center (IEA) | ~120 megawatts (our conversion) | as much electricity as 100,000 households |
| OpenAI’s Stargate campus, Abilene, Texas (mid-2026) | designed for up to ~1.2 gigawatts | about the size of Central Park. At full capacity it would draw about what a million American homes use on average, roughly eight homes for every person living in Abilene |
| All data centers on Earth, 2024 (IEA) | ~415 billion kWh a year, about 47 GW on average | 1.5% of the world’s electricity |
| All data centers, 2030 (IEA projection) | ~945 billion kWh a year | slightly more than Japan’s entire electricity use today |
Not all of this is AI. Data centers also run search, video streaming, email and banking. But AI is now the main reason the totals are growing, by about 12% a year since 2017, four times faster than electricity use as a whole. And the biggest single AI sites under construction will each draw about twenty times as much as a typical one.
At this step, the machine is Llama 3.1 405B, this chapter’s main example of training scale; the running-energy figures come from other published systems.