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I've come to define a belief as a self-reinforcing opinion. That leaves open how it is reinforced, e.g. by testing against reality in the case of a prediction, or by confirmation bias in the case of a delusion.
Kim Stanley Robinson used this in several books, calling it a "pebble mob". Picture an explosion run in reverse time, with the fragments converging at a point. Or a hundred drones, as in this interview with him.
https://bioneers.org/kim-stanley-robinson-on-his-book-the-ministry-for-the-future/
It's worse than just sometimes being irrational, though. They're incapable of consistently using logic -- see the many demonstrations of billion parameter LLMs failing to add two three-digit numbers, vs the hundred-odd gates that this task conventionally needs.
Humans have limits, like poor memory, but we make up for it with tools and processes. Given their current failings, LLMs need to become tool-users, and to really succeed they need to become tool inventors.
This is another way of saying hybrid-symbolic. But it further points to specific considerations for tools that, for humans, are called User Experience. We need a tool API for use by LLMs that considers standard UX ideas like discoverability, predictably, and compositionality.