For all that people talk a lot about artificial intelligence, “there is no consensus as yet on the definition of the “intelligence” part of the phrase.”
One key feature of the automata hierarchy is that everything above can copy everything below but the reverse is not the case. So, oracle machines can copy everything else on the hierarchy, including Turing machines, but nothing below the oracle machines can copy them. Another important feature of the oracle machine is that the oracular part cannot be a machine. All physical machines can be copied by a Turing machine. But because oracle machines are above Turing machines, they cannot be copied by Turing machines. Because all physical machines can be copied by Turing machines, then oracle-machines cannot be physical machines. And the only significant addition that an oracle machine features is the oracle. Therefore, the oracle is something that lies beyond physical mechanism, i.e., it is non-physical.
So what have we established? We’ve identified that human language is, with very high confidence, unrecognizable for Turing machines. And we’ve established that to recognize more complex languages, we must go higher up on the automata hierarchy. Thus, we must conclude that to recognize human language, we must go higher up the automata hierarchy than Turing machines. Therefore, we need something that is at least as powerful as an oracle machine to recognize human language. Oracle machines are necessarily non-physical, so whatever can recognize human language is also beyond the physical universe.Eric Holloway, “We need a better test for true AI intelligence.” at Mind Matters News
Holloway: Intelligence, like randomness, is mathematically undefinable.
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See also: Also by Eric Holloway: Will artificial intelligence design artificial superintelligence?
Human intelligence as a Halting Oracle