Machines

The name is exact. It is trained on language, so the signal is syntactic: which symbol follows which. Meaning is never handed to it.

Context in, a probability for every next token out, one sampled, appended, and round again. The answer becomes the next question.

It cost megawatts for weeks; you run on twenty watts. Either way it is arithmetic on bits, which mipster could run.

A model with a few hundred billion parameters is a point in a state space of the kind week 2 measured. Its behaviour — its output on every context — is one of week 7's infinite answer sheets.

So when a laboratory says a model was tested extensively, you know what that means. What the tests exercised, the machine did. What they did not, nobody knows.

Testing shows presence, not absence. Dijkstra, 1969, about programs. It was always about this.

Fluency is syntax. Correctness is semantics. We built a machine of extraordinary fluency, so the gap between the two — week 7's gap — is something you now meet before breakfast.

Not a defect to be patched away: it is the proof/truth distinction at consumer scale. Harnad, 1990: symbols defined only by other symbols never touch the world.

So the durable response is not "trust it more" or "trust it less" but check it against something with a semantics — a compiler, a test, an experiment, a source, a colleague.

Not more text but a model of the world: state, dynamics, consequence. Predict what happens, not what is said: real semantics, and efficiency. On a fixed budget efficiency is capability, so world models may well outperform language models.

And still a finite notation inside the world it models. Counting: models are countable, behaviours are not. Rice: "is this model right?" is semantic. Gödel: no self-certificate. Cost: the state space did not shrink. Only the map did.

Models are trained on text that models wrote, and degrade measurably when the loop tightens (model collapse, 2024). Models grade models, write the code that trains models, and invoke themselves as agents.

"Is this system safe?" is a semantic property of a program. Rice: no general decision procedure. Not hard — impossible. And by Gödel's second theorem no system this expressive certifies itself: an explanation of its own output is more output.

Not despair: it says where to spend effort — on external, independent, bounded checks.

A prompt returns plausible notation. Unchecked, there is no semantics in the loop. Checked, it meets a compiler, a test, a proof, and is kept or sent back.

Fourth appearance: Cantor's list needed an outside object, Gödel's system a stronger one, Thompson's compiler a second. The generator needs a check it cannot be.