Shadows of the Mind
Hardcover edition
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| Author | Roger Penrose |
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| Cover artist | Joel Nakamura |
| Country | United States |
| Language | English |
| Subject | Artificial intelligence, mathematics, & quantum mechanics |
| Publisher | Oxford University Press, 1st edition |
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Publication date
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1994 (1st ed.) |
| Media type | Print, e-book |
| Pages | 457 pages |
| ISBN | (1st ed.) |
| OCLC | 30593111 |
| 006.3 20 | |
| LC Class | Q335 .P416 1994 |
| Preceded by | The Emperor's New Mind |
| Followed by | The Road to Reality |
Shadows of the Mind: A Search for the Missing Science of Consciousness is a 1994 book by mathematical physicist Roger Penrose, and serves as a followup to his 1989 book The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics.
Penrose hypothesizes that:
In 1931, the mathematician and logician Kurt Gödel proved his incompleteness theorems, showing that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. Further to that, for any consistent formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory. The essence of Penrose's argument is that while a formal proof system cannot, because of the theorem, prove its own incompleteness, Gödel-type results are provable by human mathematicians. He takes this disparity to mean that human mathematicians are not describable as formal proof systems and are not running an algorithm, so that the computational theory of mind is false, and computational approaches to artificial general intelligence are unfounded. (The argument was first given by Penrose in The Emperor's New Mind (1989) and is developed further in Shadows of The Mind. An earlier version of the argument was given by J. R. Lucas in 1959. For this reason, the argument is sometimes called the Penrose-Lucas argument).
Penrose's theory of Objective Reduction is a prediction of Sir Roger Penrose about the relationship between quantum mechanics and general relativity. Penrose proposes that a quantum state remains in superposition until the difference in space-time curvature reaches a significant level. This idea is inspired by quantum gravity, because it uses both the physical constants and . It is an alternative to the Copenhagen interpretation, which posits that superposition fails under observation, and the many-worlds hypothesis, which states that each alternative outcome of a superposition becomes real in a separate world.
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