That's a nice metaphor for your mother, i like it. I would just touch on one small part, which is that it has more than our judgement though. It has access to laws of physics, to formulas, to all our current scientific knowledge which we have shown to be correct by interacting with the physical world. It can create an (incomplete) model of the world based on verified theories already. Through deduction and reasoning alone it can get pretty far. After all, there's many scientific theories we created long in advance before we actually proved them to be correct through interaction with the physical world. So even before they were proved to be correct, they were already correct. Same can be applied to what LLM can infer through reasoning alone.

Anyway, just a small point which probably still wouldn't change the nice metaphor your made.