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I think, If you compare LLMs with biological consciousness you need to consider the whole system, the OS and hardware too.

If the binary is executed, running a loop, governed by the OS, the system has state. I think the question you are raising is about determinism and volatile, emergent states "typical" for human consciousness.

The thing is, we don't understand biological consciousness at all, can't even define it properly. So any argument here about what is or is not is kinda moot IMO.

That said, I also predict, if anything goes conscious in an artificial system, it's gonna be the scheduler :D