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.
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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.
I assume they mean "we don't yet know all the things a computer can't do, only certain limits".