Actually, because a human can simulate a Turing machine’s execution using pencil and paper, humans are Turing complete. (I realize the original statement was that brains are Turing complete, but since each human brain usually come equipped with an attached human, it seems reasonable to discuss whether humans, rather than human brains, are Turing complete.)
I don’t think I know a human who would have a zero error rate doing 1,000,000,000 Turing operations
Nor do I. However, this is irrelevant. In determining whether a system is Turing complete, physical limitations are usually ignored. From Wikipedia:
To show that something is Turing complete, it is enough to show that it can be used to simulate some Turing complete system. For example, an imperative language is Turing complete if it has conditional branching (e.g., “if” and “goto” statements, or a “branch if zero” instruction. See OISC) and the ability to change an arbitrary amount of memory locations (e.g., the ability to maintain an arbitrary number of variables). Since this is almost always the case, most (if not all) imperative languages are Turing complete if the limitations of finite memory are ignored.
If we did not ignore physical limitations, no actual computing system would be Turing complete.
It’s a model. Models have it’s use. It makes sense to model a computer as an ideal Turing machine. It doesn’t make much sense to model a human that way.
Nobody suggested modeling humans as Turing machines. The question was whether humans are Turing complete and you implied that they are not because they make errors. By the same standard, no physical device is Turing complete.
Actually, because a human can simulate a Turing machine’s execution using pencil and paper, humans are Turing complete. (I realize the original statement was that brains are Turing complete, but since each human brain usually come equipped with an attached human, it seems reasonable to discuss whether humans, rather than human brains, are Turing complete.)
I don’t think I know a human who would have a zero error rate doing 1,000,000,000 Turing operations.
Nor do I. However, this is irrelevant. In determining whether a system is Turing complete, physical limitations are usually ignored. From Wikipedia:
If we did not ignore physical limitations, no actual computing system would be Turing complete.
Making errors means not behaving as a Turing machine. It’s separate from limitations of memory.
Any physical Turing machine will make errors.
To the extend that it does it’s no ideal Turing machine.
Ideal Turing machines, being, y’know, ideal, do not exist in reality.
It’s a model. Models have it’s use. It makes sense to model a computer as an ideal Turing machine. It doesn’t make much sense to model a human that way.
Nobody suggested modeling humans as Turing machines. The question was whether humans are Turing complete and you implied that they are not because they make errors. By the same standard, no physical device is Turing complete.