Computability: theoretical or practical?
Alan Turing defined in 1936 the now well known "Turing Machine" to define computation. A Turing Machine is actually an abstract mathematical construction, which cannot be fully materialized, since it requires an infinite tape (memory). Nevertheless, people have been discussing their brains out on whether the human mind (whatever that may be) is computable or not. This is because people believe that if whatever our brains or minds do is computable, then (in principle) it could be modelled in a computer, thus reaching the ultimate goal of artificial intelligence: a machine with the same intellectual abilities as a human (whatever that may be). Still, computability as we understand it, i.e. Turing computability, i.e. a function that a Turing machine can perform, is only computability in theory . In practice , there are Turing-computable numbers that are not computable in practice by our computers, since there would not be enough time in the universe to calculate them, or memor...