**Sir Roger Penrose**, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the University of Oxford. He is highly regarded for his work in mathematical physics, in particular his contributions to general relativity and cosmology. He is also a recreational mathematician and controversial philosopher. Roger Penrose is the son of scientist Lionel S. Penrose and Margaret Leathes, and the brother of mathematician Oliver Penrose and chess grandmaster Jonathan Penrose.

## Contents

## Career

In 1955, while still a student, Penrose reinvented the generalized inverse (also known as Moore-Penrose inverse, see Penrose, R. "A Generalized Inverse for Matrices." Proc. Cambridge Phil. Soc. 51, 406-413, 1955.)

Penrose earned his Ph.D. at Cambridge in 1958, writing a thesis on *tensor methods in algebraic geometry* under the well known algebraist and geometer John A. Todd. In 1965 at Cambridge, Penrose proved that singularities (such as black holes) could be formed from the gravitational collapse of dying immense stars. (Ferguson, 1991: 66).

In 1967, Penrose invented the 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. This form is now known as the **weak censorship hypothesis**; in 1979, Penrose formulated a stronger version called the **strong censorship hypothesis**. Together with the BKL conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems in general relativity.

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. He was influential in popularizing what are commonly known as Penrose diagrams (causal diagrams).

In 2004 Penrose released *The Road to Reality: A Complete Guide to the Laws of the Universe*, a 1,099-page book aimed at giving a comprehensive guide to the laws of physics.

In the June 2005 Discover, Penrose outlined his interpretation of quantum mechanics.

## Physics and consciousness

Penrose has written controversial books on the connection between fundamental physics and human consciousness. In *The Emperor's New Mind* (1989), he argues that known laws of physics do not constitute a complete system and that human consciousness cannot be explained until a new physical theory (what he terms correct quantum gravity, CQG) has been devised. He argues against the strong AI viewpoint that the rational processes of the human mind are completely algorithmic and can thus be duplicated by a sufficiently complex computer. This is based on claims that human consciousness transcends formal logic systems because things such as the insolvability of the halting problem and Gödel's incompleteness theorem restrict an algorithmically based logic from traits such as mathematical insight. These claims were originally made by the philosopher John Lucas of Merton College, Oxford.

In 1994, Penrose followed up *The Emperor's New Mind* with *Shadows of the Mind* and in 1997 with *The Large, the Small and the Human Mind*, further updating and explaining his theories.

Penrose's views on the human thought process are not widely accepted in scientific circles. According to Marvin Minsky, because people can construe false ideas to be factual, the process of thinking is not limited to formal logic. Further, AI programs can also conclude that false statements are true, so error is not unique to humans. Another dissenter, Charles Seife, has said, "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."

Penrose and Stuart Hameroff have constructed a theory in which human consciousness is the result of quantum gravity effects in microtubules. But 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. The reception of the paper is summed up by this statement in his support: "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." The Tegmark paper has been widely cited by critics of the Penrose-Hameroff proposal. It has been claimed by Hameroff to be based on a number of incorrect assumptions (see linked paper below from Hameroff, Hagan and Tuszynski), but Tegmark in turn has argued that the critique is invalid (see rejoinder link below).

## Awards

Roger Penrose has been awarded many prizes for his contributions to science. He was elected a Fellow of the Royal Society of London in 1972. In 1975, Stephen Hawking and Roger Penrose were jointly awarded the Eddington Medal of the Royal Astronomical Society. In 1985, he was awarded the Royal Society Royal Medal. In 1989 he was awarded the Dirac Medal and Prize of the British Institute of Physics. Along with Stephen Hawking, he was awarded the prestigious Wolf Foundation Prize for Physics in 1988. In 1990 Roger Penrose was awarded the Albert Einstein Medal for outstanding work related to the work of Albert Einstein by the Albert Einstein Society. In 1991, he was awarded the Naylor Prize of the London Mathematical Society. In 1994 he was knighted for services to science. In 1998, he was elected Foreign Associate of the United States National Academy of Sciences. In 2000 he was appointed to the Order of Merit. In 2004 he was awarded the De Morgan Medal for his wide and original contributions to mathematical physics. To quote the citation from the London Mathematical Society:

*His deep work on General Relativity has been a major factor in our understanding of black holes. His development of Twistor Theory has produced a beautiful and productive approach to the classical equations of mathematical physics. His tilings of the plane underlie the newly discovered quasi-crystals.*

In 2005 Sir Roger Penrose was awarded an honorary doctorate (Honoris Causa) by Warsaw University and Katholieke Universiteit Leuven (Belgium).

## Books

- Roger Penrose,
*Techniques of Differential Topology in Relativity*, Society for Industrial & Applied Mathematics, 1972, ISBN 0898710057 (rare) - Roger Penrose and Wolfgang Rindler,
*Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields*, Cambridge University Press, 1987 (reprint), ISBN 0521337070 (paperback) - Roger Penrose and Wolfgang Rindler,
*Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry*, Cambridge University Press, 1988 (reprint), ISBN 0521347866 (paperback) - Roger Penrose,
*The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics*, Oxford University Press, 1989, ISBN 0-14-014534-6 (paperback) - Roger Penrose,
*Shadows of the Mind: A Search for the Missing Science of Consciousness*, Oxford University Press, 1994, ISBN 0-19-853978-9 (hardback) - Stephen Hawking and Roger Penrose,
*The Nature of Space and Time*, Princeton University Press, 1996, ISBN 0691037914 (hardback), ISBN 0691050848 (paperback) - Roger Penrose,
*The Large, the Small, and the Human Mind*, (with Abner Shimony, Nancy Cartwright, and Stephen Hawking), Cambridge University Press, 1997, ISBN 0-521-56330-5 (hardback), ISBN 0-521-65538-2 (paperback), Canto edition: ISBN 0-521-78572-3 - Roger Penrose,
*The Road to Reality: A Complete Guide to the Laws of the Universe*, Jonathan Cape, London, 2004, ISBN 0224044478 (hardcover), ISBN 0099440687 (paperback)

## See also

## References

- Ferguson, Kitty (1991).
*Stephen Hawking: Quest For A Theory of Everything*. Franklin Watts. ISBN 0553-29895-X. - Misner, Charles; Thorne, Kip S. & Wheeler, John Archibald (1973).
*Gravitation*, San Francisco: W. H. Freeman. ISBN 0-7167-0344-0.; see*Box 34.2*.

## External links

- Two theories for the formation of quasicrystals resembling Penrose tilings
- Tegmark, Max. 2000. "The importance of quantum decoherence in brain processes".
*Physical Review E*. vol 61. pp. 4194-4206.- "Biological feasibility of quantum states in the brain" -(a disputation of Tegmark's result by Hagan, Hameroff, and Tuszynski)

- Toilet Paper Plagiarism
- Links to lectures and interviews with Roger Penrose

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