For instance, we know that a Turing computer cannot calculate whether all such computers will terminate.
It cannot calculate whether two such computers are equivalent (performing an equivalent calculation).
And what exactly "artificial computation", as a class? In contrast to what, and what is the difference?
There is something called the Chuch-Turing Thesis; it is an unproven conjecture which says that any function that can be computed by an 'effective method' can also be computed by a Turing machine. No counterexample has been found.
> We do not yet know what a computer can't do.
What is ths author talking about?
For instance, we know that a Turing computer cannot calculate whether all such computers will terminate.
It cannot calculate whether two such computers are equivalent (performing an equivalent calculation).
And what exactly "artificial computation", as a class? In contrast to what, and what is the difference?
There is something called the Chuch-Turing Thesis; it is an unproven conjecture which says that any function that can be computed by an 'effective method' can also be computed by a Turing machine. No counterexample has been found.