---
title: AI basics — the words under your AI, in eight lessons
description: Eight short lessons on the words under Claude and instibrain: tokens, the three levers, vectors, embeddings, cosine, chunking, RAG, fine-tuning versus context.
url: https://instibrain.ai/guides/ai-basics
updated: 2026-11-07
site: https://instibrain.ai/llms.txt
---

# The words under your AI, in eight short lessons.

Every company uses the same models. These lessons say how a generic model becomes yours, and define the words under that: token, vector, embedding, cosine, chunk, RAG, context. Every number is computed in front of you or is a list price.

Lesson 1: Tokens and the context window  →  Claude basics comes first

No mathematics beyond adding, multiplying and a square root. Lessons 5 and 7 have a live toy to type into.

the lessons · the words under it

## Eight lessons, from a token to why pages beat training.

The first two say what a model is made of and the three places to change it. Lessons 3 to 7 build retrieval from a list of numbers to a cited answer. The last one puts fine-tuning and context side by side.

- 1Tokens and the context window The unit a model reads and pays for, and the fixed space one call fits in.
- 2The three levers Three places to change a generic model: its weights, what it looks up, and what it is told at the start.
- 3A vector is a list of numbers A list of numbers in a fixed order. Two vectors are close when their numbers are close.
- 4An embedding is a vector made from text A model reads a text and writes a vector; texts that mean the same land near each other.
- 5Similarity is an angle: cosine Two vectors are similar when they point the same way. Cosine measures that, from 0 to 1.
- 6Chunking and the index A document is cut into chunks, each chunk gets one vector, and the table of them is the index.
- 7RAG: one question, end to end Embed the question, find the nearest chunks, paste them into the prompt, answer with a citation.
- 8Fine-tuning versus context Training teaches how a model answers; a page in its context teaches what is true today.
Start lesson 1   →

what you learned

## The numbers to hold.

Claude prices are Anthropic's list prices for its API. The rest are computed in the lessons.

| Number | What it is |
| about 0.75 words | One token. 1,000 tokens is about two pages. |
| 1,000,000 tokens | The context window of current Claude models. |
| 128,000 tokens | The most one answer holds. |
| $4 / $20 | Opus 5.5, per million tokens read / written. |
| $2 / $10 | Sonnet 5.5, per million tokens read / written. |
| $0.10 / $0.50 | Haiku 5.5, per million tokens read / written, for prompts up to 100,000 tokens. 40 times under Opus. |
| $0.20 | A cached read on Opus 5.5, per million: a twentieth of a fresh one. |
| $0.04 → $0.002 | A 10,000-token instruction file per call on Opus 5.5, fresh, then cached. |
| 50% off | The Batch API, for work that can wait a few hours. |
| 768 to 3,072 | The numbers in one embedding, by model. |
| 200 to 800 tokens | One chunk. The setting that matters most in RAG. |
| 5 to 20 | Chunks pasted into the prompt per question. |

the next series  How a model works

Inside the chat model: one pass from your text to the next token, attention, layers and weights, training, running, and the kinds of model.
why it matters  Why instibrain

Everyone uses the same models; the difference is what yours knows.
every series  Guides

The four kinds, what you need, and how a lesson works.

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instibrain is made by WebWork AI, Inc. Everyone uses the same models · the difference is what yours knows.