# Roger Penrose: Twistor Theory in a Cosmological Setting

## About The Professor

Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. He is renowned for his work in mathematical physics, in particular his contributions to general relativity and cosmology. He is also a recreational mathematician and amateur philosopher.

**Career**

Born in Colchester, Essex, England, Roger Penrose is a son of Lionel S. Penrose and Margaret Leathes.[1] Penrose is the brother of mathematician Oliver Penrose and correspondence chess grandmaster Jonathan Penrose. Penrose was precocious as a child.[2] He attended University College School. Penrose graduated with a first class degree in mathematics from University College London. In 1955, while still a student, Penrose reinvented the generalized matrix 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 (St John's College) in 1958, writing a thesis on 'tensor methods in algebraic geometry' under algebraist and geometer John A. Todd. He devised and popularized the Penrose triangle in the 1950s, describing it as "impossibility in its purest form" and exchanged material with the artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it. In 1965 at Cambridge, Penrose proved that singularities (such as black holes) could be formed from the gravitational collapse of immense, dying stars (Ferguson, 1991: 66).

Oil painting by Urs Schmid (1995) of a Penrose tiling using fat and thin rhombus.

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 the one in the centre of a black hole) by hiding them from our view behind an event horizon. 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. Also from 1979 dates Penrose's influential Weyl curvature hypothesis on the initial conditions of the observable part of the Universe and the origin of the second law of thermodynamics.[3] Penrose wrote a paper on the Terrell rotation.

Roger Penrose is well known for his 1974 discovery of Penrose tilings, which are formed from two tiles that can only tile the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry. Penrose developed here ideas from the article Deux types fondamentaux de distribution statistique[4] (1938; an English translation Two Basic Types of Statistical Distribution) of Czech geographer, demographer and statistician Jaromir Korcák. In 1984, such patterns were observed in the arrangement of atoms in quasicrystals. Another noteworthy contribution is 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. He has proposed a novel interpretation of quantum mechanics.[5] Penrose is the Francis and Helen Pentz Distinguished (visiting) Professor of Physics and Mathematics at Pennsylvania State University.[6]

Penrose is married to Vanessa Thomas, with whom he has one child. He has three sons from a previous marriage to American Joan Isabel Wedge (1959).

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 are inadequate to explain the phenomenon of human consciousness. Penrose hints at the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he terms correct quantum gravity, CQG). He claims that the present computer is unable to have intelligence because it is a deterministic system that for the most part simply executes algorithms, as a billiard table where billiard balls act as message carriers and their interactions act as logical decisions. He argues against the viewpoint that the rational processes of the human mind are completely algorithmic and can thus be duplicated by a sufficiently complex computer—this is in contrast to views, e.g., biological naturalism, that human thought can be simulated. This is based on claims that human consciousness transcends formal logic systems because things such as the insolubility 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 expanding 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. Furthermore, he says that artificial intelligence (AI) programs can also conclude that false statements are true, so error is not unique to humans.

Penrose and Stuart Hameroff have speculated that human consciousness is the result of quantum gravity effects in microtubules, which they dubbed Orch-OR (orchestrated objective reduction). 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). In particular, Hameroff points out the peculiarity that Tegmark's formula for the decoherence time includes a factor of T2 in the numerator, meaning that higher temperatures would lead to longer decoherence times. Tegmark's rejoinder keeps the factor of T2 for the decoherence time.

**Religious views**

Penrose has stated that he does not hold to any religious doctrine.[7] However, in the film A Brief History of Time he stated: "There is a certain sense in which I would say the universe has a purpose. It's not there just somehow by chance. Some people take the view that the universe is simply there and it runs along–it's a bit as though it just sort of computes, and we happen by accident to find ourselves in this thing. I don't think that's a very fruitful or helpful way of looking at the universe, I think that there is something much deeper about it, about its existence, which we have very little inkling of at the moment."[8]

**Awards and honours**

Roger Penrose during a lecture, explaining the tessellation in the MC Escher lithograph Circle Limit IV

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 Penrose were jointly awarded the Eddington Medal of the Royal Astronomical Society. In 1985, he was awarded the Royal Society Royal Medal. Along with Stephen Hawking, he was awarded the prestigious Wolf Foundation Prize for Physics in 1988. In 1989 he was awarded the Dirac Medal and Prize of the British Institute of Physics. In 1990 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. From 1992 to 1995 he served as President of the International Society on General Relativity and Gravitation. In 1994, Penrose was knighted for services to science.[9] 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 Penrose was awarded an honorary doctorate (Honoris Causa) by Warsaw University and Katholieke Universiteit Leuven (Belgium), and in 2006 by the University of York. In 2008 Penrose was awarded the Copley Medal. He is also a Distinguished Supporter of the British Humanist Association and one of the patrons of the Oxford University Scientific Society.

Works

* Techniques of Differential Topology in Relativity (1972, ISBN 0-89871-005-7)

* Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (with Wolfgang Rindler, 1987) ISBN 0-521-33707-0 (paperback)

* Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler, 1988) (reprint), ISBN 0-521-34786-6 (paperback)

* The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics (1989, ISBN 0-14-014534-6 (paperback); it received the Rhone-Poulenc science book prize in 1990)

* Shadows of the Mind: A Search for the Missing Science of Consciousness (1994, ISBN 0-19-853978-9 (hardback))

* The Nature of Space and Time (with Stephen Hawking, 1996, ISBN 0-691-03791-4 (hardback), ISBN 0-691-05084-8 (paperback))

* The Large, the Small, and the Human Mind (with Abner Shimony, Nancy Cartwright, and Stephen Hawking, 1997, ISBN 0-521-56330-5 (hardback), ISBN 0-521-65538-2 (paperback), Canto edition: ISBN 0-521-78572-3)

* White Mars or, The Mind Set Free (with Brian W. Aldiss, 1999, ISBN 978-0-316-85243-2 (hardback))

* The Road to Reality: A Complete Guide to the Laws of the Universe (2004, ISBN 0-224-04447-8 (hardcover), ISBN 0-09-944068-7 (paperback))

Penrose also wrote forewords to Quantum Aspects of Life and Zee's book Fearful Symmetry.

**Notes**

1. Penrose and his father shared mathematical concepts with Dutch graphic artist M. C. Escher which were incorporated into a number of pieces, including Waterfall, which is based on the 'Penrose triangle', and Up and Down.

2. J. C. Raven's 1936 MSc thesis features introspections from Penrose, aged four and two thirds, as he solved what are now known as Raven's Progressive Matrices, c.f. note 52 of Watt, D. C. (1998). Lionel Penrose, F.R.S. (1898-1972) and Eugenics: Part One. Notes and Records of the Royal Society of London, 52, 137-151

3. R. Penrose (1979). "Singularities and Time-Asymmetry". in S. W. Hawking and W. Israel. General Relativity: An Einstein Centenary Survey. Cambridge University Press. pp. 581–638.

4. Jaromir Korcak (1938): Deux types fondamentaux de distribution statistique. Prague, Comité d’organisation, Bull. de l'Institute Int'l de Statistique, vol. 3, pp. 295–299.

5. "If an Electron Can Be in Two Places at once, Why Can't You?". http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=0&-C=. Retrieved on 2008-10-27.

6. "Dr. Roger Penrose at Penn State University". http://www.phys.psu.edu/people/display/index.html?person_id=233&mode=contact.. Retrieved on 2007-07-09.

7. http://www.samharris.org/site/book_letter_to_christian_nation/

8. http://www.godresources.org/intelligent_design5.shtml

9. Official announcement knighthood. The London Gazette. 11 June 1994.

Name: | Roger Penrose |
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Institution: | Archive Trust Mathematical Sciences & Philosophy |

Website: | Unknown |