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rectly convey the phenomenal experience that depends on having an in- dividual brain and body.

Some thinkers feel that explanations are beside the point anyway, believing that our mental functionssuch as using categories to make sense of the worldare innate and cannot be approached by the tools of cognitive science. At least one thinker, however, believes that an explanation is possible, but only by drawing on new phenomena.That tack is taken by the Oxford University mathematical physicist Roger Penrose, as expressed in the subtitle of his 1996 book Shadows of the Mind:A Search for the Missing Science of Consciousness, and in his earlier writings.

Penrose does not deal much with neurons and neurobiology. He begins with a famous mathematical proof called Gödels theorem. This result, derived by the Austrian-born mathematician and logician Kurt Gödel in 1931, is of prime importance in modern mathematics. It proves that any formal systemsuch as the set of axioms that de- fines classical geometry, or a computer programcan logically gener- ate statements that are true, but that cannot be proven within the system. Gödels proof implies that there are true mathematical results that cannot be derived by computers, which operate by strict logical rules, but can be derived by humans.

Thus, concludes Penrose, the human mind supplies something extra, something noncomputablethat lies beyond what computers can do. This quality, Penrose asserts, arises from phenomena at the microscopic quantum level, where everyday laws of cause and effect are replaced by laws of probability. He suggests that a new kind of quantum behavior in the brain, perhaps quantum gravity,provides this essential element of noncomputabilityalthough the details of this novel quantum physics are as yet unknown. But neurons are too big to follow the quantum laws, and so Penrose speculates that con- sciousness arises in smaller structures in the brain called microtubules. Because Penrose hypothesizes that consciousness comes from new natural phenomena without any evidence that these exist, his ideas have been much criticized.

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