AI and LLMs, Without the Hand-Waving

A language model is a function that takes a sequence of text and produces a probability distribution over what comes next. It samples one token from that distribution, appends it, and runs again. That is the whole loop. People deploy this fact in two opposite directions, and both are lazy. "It's just autocomplete" ignores that predicting the next token in a proof, a contract, or a bug report well enough to be useful requires modelling the thing being described. "It understands" ignores that the mechanism has no goals, no memory between calls, and no access to truth — only to the statistical shape of an enormous amount of text. The honest version: it is a very good simulator of the kind of text a knowledgeable person would write. That is genuinely useful and genuinely limited, and almost every surprise you will have with these tools comes from forgetting one half of that sentence.

Models do not see characters or words. They see tokens — subword chunks produced by a tokenizer. In English, one token averages roughly four characters, so 750 words is about 1,000 tokens. Code, JSON, and non-English text tokenize less efficiently, sometimes much less. This matters because tokens are the unit of billing, the unit of the context limit, and the unit of speed. "Make the prompt shorter" and "make it cheaper" are the same instruction. Two consequences people miss. First, the model cannot reliably count letters in a word, because it never saw the letters — this is why the strawberry-has-three-Rs question was ever hard, and why it is a terrible test of intelligence. Second, token counts differ between models: the same paragraph can cost meaningfully more tokens on one model than another, so a cost estimate copied from last year's model is not an estimate.