The argument from the gap between chimpanzees and humans is interesting but can not be used to extrapolate onwards from human general intelligence. It is pure speculation that humans are not Turing complete and that there are levels above our own.
Surely humans are Turing complete. I don’t think anybody disputes that.
We know that capabilities extend above our own in all the realms where machines already outstrip our capabilities—and we have a pretty good idea what greater speed, better memory and more memory would do.
Agree with your basic point, but a nit-pick: limited memory and speed (heat death of the universe, etc) put many neat Turing machine computations out of reach of humans (or other systems in our world) barring new physics.
Sure: I meant in the sense of the “colloquial usage” here:
In colloquial usage, the terms “Turing complete” or “Turing equivalent” are used to mean that any real-world general-purpose computer or computer language can approximately simulate any other real-world general-purpose computer or computer language, within the bounds of finite memory—they are linear bounded automaton complete. A universal computer is defined as a device with a Turing complete instruction set, infinite memory, and an infinite lifespan; all general purpose programming languages and modern machine instruction sets are Turing complete, apart from having finite memory.
Surely humans are Turing complete. I don’t think anybody disputes that.
We know that capabilities extend above our own in all the realms where machines already outstrip our capabilities—and we have a pretty good idea what greater speed, better memory and more memory would do.
Agree with your basic point, but a nit-pick: limited memory and speed (heat death of the universe, etc) put many neat Turing machine computations out of reach of humans (or other systems in our world) barring new physics.
Sure: I meant in the sense of the “colloquial usage” here: