# Roger Penrose

Sir**Roger Penrose**OM (born August 8 1931) is an English mathematical physicist. He is highly regarded for his work in mathematical physics, in particular his contributions to cosmology. He is also a recreational mathematician and controversial philosopher.

In 1967, Penrose invented twistor theory which maps geometric objects in Minkowski space into the 4-dimensional complex space with the metric signature (2,2). In 1969 he conjectured the cosmic censorship hypothesis. This proposes (rather informally) that the universe protects us from the inherent unpredictability of singularities (such as black holes) by hiding them from our view.

Roger Penrose is well-known for his 1974 discovery 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. Physicists also know Penrose diagrams (causal diagrams).

He has written books such as *The Emperor's New Mind* where he argues that known laws of physics do not constitute a complete system, 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 These claims were originally made by the philosopher John Lucas of Merton College, Oxford.

Later on, Penrose followed up *The Emperor's New Mind* with *Shadows of the Mind* and *The Large, the Small and the Human Mind*, further updating and explaining his theories.

Most mathematicians consider these claims to be mathematically incorrect. See the articles on Gödel's incompleteness theorem;, the Church-Turing thesis and the halting problem for more on their reasoning.

According to Marvin Minsky, 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. Further, AI programs can also conclude that false statements are true, so this is not unique to humans.

Penrose and Hameroff have constructed a theory of human consciousness in which human consciousness is the result of quantum gravity effects in microtubules. This is widely considered a crank view in that it defies Occam's Razor. 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; this paper has been widely cited by critics of the Penrose-Hameroff proposal. However, this paper has since been claimed by Hameroff to be based on a number of incorrect assumptions. See the refutation linked below from Hameroff, Hagan and Tuczynksi. The general gist of the linked page is summed up by this statement in support of Tegmark: *Physicists outside the fray, such as IBM's John Smolin, say the calculations confirm what they had suspected all along. "We're not working with a brain that's near absolute zero. It's reasonably unlikely that the brain evolved quantum behavior," he says.* And another quote, this one from Charles Seife: *Penrose, the Oxford mathematician famous for his work on tiling the plane with various shapes, is one of a handful of scientists who believe that the ephemeral nature of consciousness suggests a quantum process.*

Roger Penrose is the son of scientist Lionel S Penrose and the brother of mathemetician Prof Oliver Penrose and chess Grand Master Jonathan Penrose

See also: Penrose triangle, Penrose stairs, Penrose tiling, Stephen Hawking, Stuart Hameroff

## External links

- Instructions for making the Penrose tiles are here: [1]
- Two theories for the formation of quasicrystals resembling Penrose tilings are here: [1]
- Tegmark, Max. 2000. "The importance of quantum decoherence in brain processes".
*Physical Review E*. vol 61. pp. 4194-4206. - Hagan, Hameroff, Tuczynski: The debate on decoherence - "Biological feasibility of quantum states in the brain"