[geysersam]

> we are "computationally" equivalent to a turing machine:

Why do you think that?

We know of modes of computation different from Turing machines, quantum computers. There's nothing saying there might not be yet other kinds of computers currently undiscovered.

[edanm]

> We know of modes of computation different from Turing machines, quantum computers.

That's wrong. Quantum computers are Turing complete just like any other form of computation we've found / invented. You can't do something on a quantum computer that you can't do on any computer, albeit in some cases you can get a speed-up by using a quantum computer.

[zzzzzzzza]

actually i think we are more limited than a turing machine since even the default turing machine has a (single) infinite tape/running time. But there is a quantum turing machine/quantum lambda calculus as well. just has (probably?) a faster running time on a subset of algorithms.

but essentially turing machine/quantum turing machine have the same kinds of inpus/outputs or domain/range, whereas a hyper turing machine has a bigger domain/range.

[geysersam]

I don't understand what makes you think humans operate anything like Turing machines to begin with.

The only way I see to reach this conclusion is to assume Turing machines are all that exist, and the conclusion follows.

[kbelder]

Physics (as far as we know) is calculable and can be simulated with a Turing machine. Humans reside within the domain of physics.

Basically, either humans operate like Turing machines, or we're magic.