# Roger Penrose

Infobox Scientist

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name = Sir Roger Penrose

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caption = Roger Penrose at Brookhaven Lab, February 6, 2007

birth_date = birth date and age|1931|08|08

birth_place =Colchester ,Essex ,England

death_date =

death_place =

residence =United Kingdom Canada (DuringWorld War II )

citizenship =

nationality = British

ethnicity =

fields =Mathematical physicist

workplaces =Bedford College, London St John's College, Cambridge Princeton University Syracuse University King’s College, London Birkbeck, University of London University of Oxford

alma_mater =University of Cambridge University College London

University College School

doctoral_advisor =John A. Todd

academic_advisors =William Hodge

doctoral_students =Tristan Needham Richard Jozsa

notable_students =

known_for =Penrose tiling Twistor Theory

Geometry of spacetime

nowrap|Moore-Penrose pseudoinverse Newman-Penrose formalism Penrose stairs

Penrose inequalitiesOrch-OR

author_abbrev_bot =

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influences =

influenced =

awards =Wolf Prize (1988)

Dirac Medal (1989)

religion =Materialist [*[*]*http://www.leaderu.com/ftissues/ft9511/articles/revessay.html The Aethism of the Gaps*]Platonist [*[*] with no doctrinal stance [*http://www.infidels.org/library/modern/vic_stenger/polkrev.html Belief in God in an Age of Science by John Polkinghorne*]*[*]*http://www.guardian.co.uk/uk/2006/oct/29/books.religion Atheists top book charts by deconstructing God | UK news | The Observer*]

footnotes = He is the brother ofJonathan Penrose andOliver Penrose , and son ofLionel Penrose . He is the nephew ofRoland Penrose .**Sir Roger Penrose**,Ph.D. , OM, FRS (born8 August 1931 ) is an Englishmathematical physicist andEmeritus Rouse Ball Professor of Mathematics at theMathematical Institute ,University of Oxford and Emeritus Fellow ofWadham College . He is renowned for his work in mathematical physics, in particular his contributions togeneral relativity and cosmology. He is also a recreational mathematician andphilosopher and has anErdős number of three.**Career**Born in

Colchester ,Essex ,England , Lionel S. Penrose and Margaret Leathes, [*Penrose and his father shared mathematical concepts with Dutch graphic artist*] Roger is the brother of mathematicianM. C. Escher which were incorporated into a number of pieces, including Waterfall, which is based on the "Penrose triangle ", and Up and Down.Oliver Penrose and correspondence chess grandmasterJonathan Penrose . Penrose was precocious as a child. [*J. C. Raven's 1936 MSc thesis features introspections from Penrose, aged four and two thirds, as he solved what are now known as*] Penrose graduated with a first class degree inRaven's Progressive Matrices , c.f. note 52 of Watt, D. C. (1998). [*http://links.jstor.org/sici?sici=0035-9149%28199801%2952%3A1%3C137%3ALPF%28AE%3E2.0.CO%3B2-%23 Lionel Penrose, F.R.S. (1898-1972) and Eugenics: Part One*] . "Notes and Records of the Royal Society of London", 52, 137-151mathematics fromUniversity College London . In 1955, while still a student, Penrose reinvented the generalized matrix inverse (also known asMoore-Penrose inverse , see Penrose, R. "A Generalized Inverse for Matrices." Proc. Cambridge Phil. Soc. 51, 406-413, 1955.) Penrose earned his Ph.D. atCambridge (St John's College) in 1958, writing a thesis on "tensor methods in algebraic geometry" under the well known algebraist and geometerJohn A. Todd . In 1965 at Cambridge, Penrose proved that singularities (such asblack hole s) could be formed from the gravitational collapse of immense, dyingstar s. (Ferguson, 1991: 66).In 1967, Penrose invented thetwistor theory which maps geometric objects inMinkowski space into the 4-dimensional complex space with the metric signature (2,2). In 1969 he conjectured thecosmic 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 anevent 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 theBKL conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems ingeneral relativity . Also from 1979 dates Penrose's influentialWeyl curvature hypothesis on the initial conditions of the observable part of the Universe and the origin of thesecond law of thermodynamics . [*cite conference | author = R. Penrose | title = Singularities and Time-Asymmetry | booktitle = General Relativity: An Einstein Centenary Survey | editor = S. W. Hawking and W. Israel | publisher = Cambridge University Press | year = 1979 | pages = 581–638*] . Penrose wrote an interesting paper on theTerrell rotation .Roger Penrose is well known for his 1974 discovery of

Penrose tiling s, which are formed from two tiles that can only tile the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry. In 1984, such patterns were observed in the arrangement of atoms inquasicrystal s. Another noteworthy contribution is his 1971 invention ofspin network s, which later came to form the geometry ofspacetime inloop quantum gravity . He was influential in popularizing what are commonly known asPenrose diagram s (causal diagrams). In 2004 Penrose released "", a 1,099-page book aimed at giving a comprehensive guide to the laws of physics. In the June 2005 issue ofDiscover magazine [*cite web | title =If an Electron Can Be in Two Places at once, Why Can't You? | url =http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=2&-C= | accessdate = 2007-12-29*] , Penrose outlined his interpretation ofquantum mechanics . Penrose is the Francis and Helen Pentz Distinguished (visiting) Professor of Physics and Mathematics atPennsylvania State University . [*cite web | last = | first = | authorlink = | coauthors = | title =Dr. Roger Penrose at Penn State University | work = | publisher = | date = | url =http://www.phys.psu.edu/people/display/index.html?person_id=233&mode=contact. | format = | doi = | accessdate = 2007-07-09*]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 termscorrect 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 completelyalgorithm ic and can thus be duplicated by a sufficiently complex computer -- this is in contrast to views, e.g.,Biological Naturalism , that human behavior but not consciousness might be simulated. This is based on claims that human consciousness transcendsformal logic systems because things such as the insolubility of thehalting problem andGödel'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, and were also discussed by the mathematician H. J. Pringle.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 toMarvin Minsky , because people can construe false ideas to be factual, the process of thinking is not limited to formal logic. Furthermore, he says thatartificial 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 humanconsciousness is the result of quantum gravity effects inmicrotubule s, which they dubbedOrch-OR (orchestrated objective reduction). ButMax 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 Tuszyński), 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 $T^2$ in the numerator, meaning that higher temperatures would lead to longer decoherence times. Tegmark's rejoinder keeps the factor of $T^2$ for the decoherence time.**Awards and honours**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 theEddington Medal of theRoyal Astronomical Society . In 1985, he was awarded theRoyal Society Royal Medal . Along withStephen 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 BritishInstitute of Physics . In 1990 Penrose was awarded theAlbert Einstein Medal for outstanding work related to the work ofAlbert Einstein by theAlbert Einstein Society . In 1991, he was awarded the Naylor Prize of theLondon Mathematical Society . From 1992 to 1995 he served as President of the [*http://grg.maths.qmul.ac.uk/grgsoc/ International Society on General Relativity and Gravitation*] .In 1994, Penrose was knighted for services to science. [*[*] In 1998, he was elected Foreign Associate of the*http://www.gazettes-online.co.uk/ViewPDF.aspx?pdf=53696&geotype=London&gpn=2&type=ArchivedSupplementPage&exact=Roger%20Penrose Official announcement knighthood.*]The London Gazette .11 June 1994 .United States National Academy of Sciences . In 2000 he was appointed to the Order of Merit. In 2004 he was awarded theDe Morgan Medal for his wide and original contributions to mathematical physics. To quote the citation from the [*http://www.lms.ac.uk/activities/prizes_com/citations04.html 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 ) byWarsaw University andKatholieke Universiteit Leuven (Belgium), and in 2006 by theUniversity of York . He is also a Distinguished Supporter of theBritish Humanist Association .**Books by Penrose***Roger Penrose, "Techniques of Differential Topology in Relativity", Society for Industrial & Applied Mathematics, 1972, ISBN 0-89871-005-7 (rare)

*Roger Penrose and Wolfgang Rindler, "Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields", Cambridge University Press, 1987 (reprint), ISBN 0-521-33707-0 (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 0-521-34786-6 (paperback)

*Roger Penrose, "", Oxford University Press, 1989, ISBN 0-14-014534-6 (paperback). Received the Rhone-Poulenc science book prize in 1990.

*Roger Penrose, "", Oxford University Press, 1994, ISBN 0-19-853978-9 (hardback)

*Stephen Hawking and Roger Penrose, "The Nature of Space and Time", foreword byMichael Atiyah , University Press, 1996, ISBN 0-691-03791-4 (hardback), ISBN 0-691-05084-8 (paperback)

**Hawking's part is freely available at: http://arxiv.org/abs/hep-th/9409195

*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

*Brian Aldiss and Roger Penrose, "White Mars Or, The Mind Set Free", Little, Brown, 1999, ISBN 978-0-316-85243-2 (hardback)

*Roger Penrose, "", Jonathan Cape, London, 2004, ISBN 0-224-04447-8 (hardcover), ISBN 0-09-944068-7 (paperback)Penrose also wrote a forward to "

Quantum Aspects of Life ".**Notes****References***Ferguson, Kitty (1991). "Stephen Hawking: Quest For A Theory of Everything". Franklin Watts. ISBN 0-553-29895-X.

*cite book | author=Misner, Charles; Thorne, Kip S. & Wheeler, John Archibald | title=Gravitation | location=San Francisco | publisher=W. H. Freeman | year=1973 | id=ISBN 0-7167-0344-0; see "Box 34.2".**External links*** [

*http://www.youtube.com/watch?v=pEIj9zcLzp0 Penrose interview on the Big Bang*]

* [*http://www.youtube.com/watch?v=xiYDc1LA0I4&feature=user Penrose on sidestepping reason*]

*MacTutor Biography|id=Penrose

* [*http://www.ams.org/bull/pre-1996-data/199507/199507015.pdf Hilary Putnam's review of Penrose's 'Shadows of the Mind' claiming that Penrose's use of Godel's Incompleteness Theorem is fallacious*]

** [*http://psyche.csse.monash.edu.au/v2/psyche-2-23-penrose.html*]**Beyond the Doubting of a Shadow**: A Reply to Commentaries on Shadows of the Mind

* [*http://www.sciencenews.org/articles/20070224/mathtrek.asp Penrose Tiling found in Islamic Architecture*]

* [*http://www.sciencenews.org/sn_arch/10_12_96/bob1.htm Two theories for the formation of quasicrystals resembling Penrose tilings*]

*Tegmark, Max. 2000. " [*http://www.arxiv.org/abs/quant-ph/9907009 The importance of quantum decoherence in brain processes*] ". "Physical Review E". vol 61. pp. 4194-4206.

**" [*http://www.quantumconsciousness.org/pdfs/decoherence.pdf Biological feasibility of quantum states in the brain*] " -(a disputation of Tegmark's result by Hagan, Hameroff, and Tuszyński)

*** [*http://space.mit.edu/home/tegmark/brain.html Tegmarks's rejoinder to Hagan "et al"*]

* [*http://web.archive.org/web/20050312084035/http://www.parascope.com/articles/slips/fs_151.htm "Toilet Paper Plagiarism"*] – D. Trull about Penrose's lawsuit concerning the use of his Penrose tilings on toilet paper

* [*http://plus.maths.org/issue18/features/penrose/index.html Roger Penrose: A Knight on the tiles (Plus magazine)*]

* [*http://www.giffordlectures.org/Author.asp?AuthorID=254 Penrose's Gifford Lecture biography*]Persondata

NAME=Penrose, Roger

ALTERNATIVE NAMES=Penrose, Sir Roger

SHORT DESCRIPTION=British mathematician and writer

DATE OF BIRTH=8 August 1931

PLACE OF BIRTH=Colchester ,Essex ,England

DATE OF DEATH=

PLACE OF DEATH=

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**Roger Penrose**— en Laboratorio Nacional Brookhaven, 6 de febrero de 2007. Nacimiento 8 de agosto de 1931 (80 años) Colchester, Essex … Wikipedia Español**Roger Penrose**— Sir Roger Penrose OM (* 8. August 1931 in Colchester, Essex) ist ein englischer Mathematiker und theoretischer Physiker, dessen Arbeiten auf den Gebieten der mathematischen Physik und der Kosmologie hoch geachtet sind. Er hat sich auch in… … Deutsch Wikipedia**Roger Penrose**— en 2007 Sir Roger Penrose (né à Colchester le 8 août 1931) est un physicien et mathématicien britannique. Il enseigne les mathématiques au Birkbeck College de Londres où il élabore la théorie décrivant l effondrement des étoiles sur elles mêmes,… … Wikipédia en Français**Roger penrose**— Roger Penrose (Colchester, 8 août 1931 ) est un physicien et mathématicien britannique. Il enseigne les mathématiques au Birkbeck College de Londres où il élabore la théorie décrivant l effondrement des étoiles sur elles mêmes, entre … Wikipédia en Français**Roger Penrose**— Sir Roger Penrose (Colchester,8 de agosto de 1931) Matemático y pensador británico. Doctor en ciencias. En 1964 entró en el Birkberck College de Londres como profesor de matemáticas aplicadas y a partir de 1973 ocupó la cátedra de matemáticas… … Enciclopedia Universal**Penrose**— may refer to these places:* Penrose, Arlington, Virginia, a neighborhood in the United States * Penrose, Colorado, a town in the United States * Penrose, Padstow, a small village in north Cornwall, England, with a World War II base near it *… … Wikipedia**Penrose-Dreieck**— Das Penrose Dreieck, auch Tribar genannt, ist eine sogenannte „unmögliche Figur“. Es zeigt drei Balken, die jeweils im rechten Winkel zueinander stehen und dennoch zu einem Dreieck verbunden sind. Damit verstößt es gegen mehrere Gesetze der… … Deutsch Wikipedia**Roger I.**— Roger ist die englische, katalanische und französische Variante des männlichen Vornamens Rüdiger. Inhaltsverzeichnis 1 Namenstag 2 Bekannte Namensträger (Auswahl) 2.1 Roger als Vorname 2.2 Roger als Nachname 3 … Deutsch Wikipedia**Roger II.**— Roger ist die englische, katalanische und französische Variante des männlichen Vornamens Rüdiger. Inhaltsverzeichnis 1 Namenstag 2 Bekannte Namensträger (Auswahl) 2.1 Roger als Vorname 2.2 Roger als Nachname 3 … Deutsch Wikipedia**Roger III.**— Roger ist die englische, katalanische und französische Variante des männlichen Vornamens Rüdiger. Inhaltsverzeichnis 1 Namenstag 2 Bekannte Namensträger (Auswahl) 2.1 Roger als Vorname 2.2 Roger als Nachname 3 … Deutsch Wikipedia