[urgoroger]

In accordance with the Church-Turing thesis, the Turing machine stands to be capable of doing anything that should be called computation. It follows that if the brain is capable of simulating of a Turing machine (this is called a universal Turing machine, by the way), then it too can do any computation. So then the class of things that both can do are the same, and so it is reasonable to call them the same thing, in some sense.

[FakeComments]

This only shows computers are a subset of what brains can do, not that Turing machines can do whatever brains can do.

[mr_toad]

If we conjecture that any physical process can be simulated by a computation then it follows that a Turing machine can simulate it.

While we don’t have any proof of this conjecture (as far as I know) neither have we discovered any exceptions.

This also doesn’t rule out the possibility of non-physical or non-mechanical elements in the brain (dualism/vitalism) but frankly I don’t even entertain that notion.

[FakeComments]

You’re just begging the question: if you assume your conclusion, any claim holds.

Which is exactly my point — everyone is completely okay with those assumptions, without justifying that. I find it suspect.

How about showing physical processes are necessarily Turing computable, that is, justifying your underlying assumptions, before the straw man implication that I’m talking about dualism?

The mathematical equivalent of your argument is that because all finite-length approximations of a number are rational, the number itself must be rational — but this is untrue, in the general case. And in fact, for almost no numbers does a finite set of those rational approximations yield a general rule to predict the full structure of the number.

It’s therefore unclear that our limited scientific models being computable mean the underlying object they’re approximating is computable. But if we don’t know reality is computable, then we don’t know it can be simulated on a Turing machine.

Just assuming an answer doesn’t help us resolve the claim.

[User23]

Amazing how many people miss this. It’s like confusing the implication with the equivalence.

[urgoroger]

What I was trying to communicate was that the Turing machine believed to represent the limits of what is physically possible. So then you have

turing machines >= brain (since a brain is physical) and brain >= turing machine (by simulation argument)

The conclusion is the brain and Turing machine can do the same thing (brain = turing machine).

[User23]

> What I was trying to communicate was that the Turing machine believed to represent the limits of what is physically possible

Another religious tenet with no observable basis.

Where did so many hackers get this misconception that computable and physically possible are proven to be the same? Many claim the Church-Turing thesis shows this. Have they never read it carefully?