Penrose is highly regarded for his work in mathematical physics, in particular his contributions to cosmology. He is also a recreational mathematician and controversial philosopher.
Roger Penrose is wellknown for his 1974 invention of Penrose tilings, which are formed from two tiles that can only tile the plane aperiodically. In 1984, similar patterns were found in the arrangement of atoms in quasicrystals.
His most important contribution may be his 1971 invention of spin networks, which later came to form the geometry of spacetime in loop quantum gravity.
He has written books such as The Emperor's New Mind ISBN 0140145346 where he argues there must be errors in the known laws of physics, and that true artificial intelligence is impossible. In this controversial book, he argues this based on claims that humans can do things outside the power of formal logic systems, such as knowing the truth of unprovable statements, or solving the halting problem. These claims were originally made by the philosopher John Lucas[?] of Merton College, Oxford.
Some mathematicians consider these claims to be mathematically incorrect. See the articles on Gödel's incompleteness theorem, the ChurchTuring thesis and the halting problem for more on their reasoning.
This argument is also considered flawed by most in the artificial intelligence community, such as Marvin Minsky, who point out that human beings can understand things to be true facts which are false, and therefore the process of understanding is not limited by mathematical systems of formal logic. They point out that AI programs can also conclude that false statements are true, so this is not unique to humans.
Penrose has also constructed a theory of human consciousness in which human consciousness is the result of quantum gravity effects in microtubules. This theory is not highly regarded in the neuroscience community because there is no neurological reason to believe that consciousness is a quantum phenomenon and because microtubules are found in every cell in the body. Some physicists have also questioned this theory. Max Tegmark, in a paper in Physical Review E, calculated that the time scale of neuron firing and excitations in microtubules is slower than the decoherence time by a factor of at least 10,000,000,000.
See also: Penrose triangle, Penrose stairs[?], Penrose tiling, Stephen Hawking
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