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You're a fast reader :-D

No quantum bullshittery in there I promise.

Equating "classical" with "deterministic" is however pushing it a bit too far, when no one and nothing can ever do even a very small fraction of said determination...

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Quantum is not bullshit and yes, classical is deterministic.

That's why the brain cannot possibly be anything other than an input → output machine, which is functionally deterministic (with maybe some fully random components), but is easiest to describe as probabilistic.

In the same way that LLMs are functionally deterministic, but easiest to describe as probabilistic.

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