I must stress that the idea of "Science predicting facts" is a consolidated formula in Philosophy of Science.
And there has never been a doubt that prediction is probabilistic. But, see the example in in the parallel additional post about "dreaming and wake", the predicting activities of a junkie under psychedelics and that of a lucid thinker are substantially different.
> You've never memorized
You have the framework very very wrong: the point is not that we memorize, the point is that those LLMs don't check. When you state an idea, you are supposed to have checked it in other occasions before memorization.
Procedural operations, of which counting is just an example, can fail in those LLMs, which means they are simulating it instead of doing it, which suggests that they «seem to be guessing an output instead of actually checking to build the output», which makes them structurally untrustworthy, unreliable - broken by design.
Being black boxes (bad), they must be stress tested to see whether proper functioning is present or just simulated: the chief problem is not that they can't count, it is that they must be missing the roots of counting: procedural lucid thinking.
Check the parallel submission about the detective game ("Temporal Clue")*: an algorithm that cannot fully reason with a lucid world model, solving logic puzzles, is unreliable. The probabilistic nature of the architecture in this case is below the intelligent, as opposed to the sophistication of considering less probable unexpected branches of possibilities.
