arguments tend to rely on the innocuous-seeming claim that a system of human mathematicians (or some idealization of human mathematicians) is both consistent (completely free of error) and believes fully in its own consistency (and can make all logical inferences that follow from its own consistency, including belief in its Gödel statement) . This is provably impossible for a Turing machine to do (see Halting problem); therefore, the Gödelian concludes that human reasoning is too powerful to be captured by a Turing machine, and by extension, any digital mechanical device. However, the modern consensus in the scientific and mathematical community is that actual human reasoning is inconsistent; that any consistent "idealized version" H of human reasoning would logically be forced to adopt a healthy but counter-intuitive open-minded skepticism about the consistency of H (otherwise H is provably inconsistent); and that Gödel's theorems do not lead to any valid argument that humans have mathematical reasoning capabilities beyond what a machine could ever duplicate. This consensus that Gödelian anti-mechanist arguments are doomed to failure is laid out strongly in Artificial Intelligence: "any attempt to utilize (Gödel's incompleteness results) to attack the computationalist thesis is bound to be illegitimate, since these results are quite consistent with the computationalist thesis." Stuart Russell and Peter Norvig agree that Gödel's argument does not consider the nature of real-world human reasoning. It applies to what can theoretically be proved, given an infinite amount of memory and time. In practice, real machines (including humans) have finite resources and will have difficulty proving many theorems. It is not necessary to be able to prove everything in order to be an intelligent person. Less formally, Douglas Hofstadter, in his Pulitzer prize winning book Gödel, Escher, Bach: An Eternal Golden Braid, states that these "Gödel-statements" always refer to the system itself, drawing an analogy to the way the Epimenides paradox uses statements that refer to themselves, such as "this statement is false" or "I am lying". But, of course, the Epimenides paradox applies to anything that makes statements, whether they are machines or humans, even Lucas himself. Consider: Lucas can't assert the truth of this statement. This statement is true but cannot be asserted by Lucas. This shows that Lucas himself is subject to the same limits that he describes for machines, as are all people, and so Lucas's argument is pointless. After concluding that human reasoning is non-computable, Penrose went