Editing Roger Penrose (section)

== Research and career ==
Penrose spent the academic year 1956–57 as an assistant lecturer at Bedford College (now [[Royal Holloway, University of London]]) and was then a research fellow at [[St John's College, Cambridge]]. During that three-year post, he married Joan Isabel Wedge, in 1959. Before the fellowship ended Penrose won a [[NATO]] Research Fellowship for 1959–61, first at [[Princeton]] and then at [[Syracuse University]]. Returning to the [[University of London]], Penrose spent 1961–1963 as a researcher at [[King's College, London]], before returning to the United States to spend 1963–64 as a visiting associate professor at the [[University of Texas at Austin]].<ref>{{Cite web|title=Professor Sir Roger Penrose awarded the 2020 Nobel Prize in Physics|url=https://www.kcl.ac.uk/news/professor-sir-roger-penrose-awarded-the-2020-nobel-prize-in-physics|access-date=7 October 2020|website=King's College London|language=en-EN|archive-date=22 October 2020|archive-url=https://web.archive.org/web/20201022121930/https://www.kcl.ac.uk/news/professor-sir-roger-penrose-awarded-the-2020-nobel-prize-in-physics|url-status=live}}</ref> He later held visiting positions at [[Yeshiva University]], Princeton and [[Cornell]] during 1966–67 and 1969.

In 1964, while a [[Reader (academic rank)|reader]] at [[Birkbeck College]], London, (and having had his attention drawn from pure mathematics to astrophysics by the cosmologist [[Dennis Sciama]], then at Cambridge)<ref name="Roger Penrose - Biography"/> in the words of [[Kip Thorne]] of Caltech, "Roger Penrose revolutionised the mathematical tools that we use to analyse the properties of spacetime".<ref>{{Cite web|date=12 March 2019|title=The second Cambridge Cutting Edge Lecture: Professor Sir Roger Penrose|url=https://cambridgesocietyofparis.com/event/cambridge-cutting-edge-lecture-professor-sir-roger-penrose/|access-date=7 October 2020|website=Cambridge Society of Paris|language=en-GB|archive-date=8 October 2020|archive-url=https://web.archive.org/web/20201008185043/https://cambridgesocietyofparis.com/event/cambridge-cutting-edge-lecture-professor-sir-roger-penrose/|url-status=live}}</ref><ref>{{Cite book|last1=Thorne|first1=Kip|url=https://books.google.com/books?id=GzlrW6kytdoC&q=roger+penrose+kip+thorne+mathematical+tools+spacetime&pg=PA465|title=Black Holes and Time Warps: Einstein's Outrageous Legacy|last2=Thorne|first2=Kip S.|last3=Hawking|first3=Stephen|date=1994|publisher=W. W. Norton & Company|isbn=978-0-393-31276-8|language=en|access-date=12 October 2020|archive-date=3 February 2021|archive-url=https://web.archive.org/web/20210203044944/https://books.google.com/books?id=GzlrW6kytdoC&q=roger+penrose+kip+thorne+mathematical+tools+spacetime&pg=PA465|url-status=live}}</ref> Until then, work on the curved geometry of general relativity had been confined to configurations with sufficiently high symmetry for Einstein's equations to be solvable explicitly, and there was doubt about whether such cases were typical. One approach to this issue was by the use of [[perturbation theory]], as developed under the leadership of [[John Archibald Wheeler]] at Princeton.<ref>{{Cite journal|last1=Ellis|first1=George F. R.|last2=Penrose|first2=Sir Roger|date=1 January 2010|title=Dennis William Sciama. 18 November 1926 – 19 December 1999|journal=Biographical Memoirs of Fellows of the Royal Society|language=en|volume=56|pages=401–422|doi=10.1098/rsbm.2009.0023|s2cid=73035217|issn=0080-4606|doi-access=free}}</ref> The other, and more radically innovative, approach initiated by Penrose was to overlook the detailed geometrical structure of spacetime and instead concentrate attention just on the topology of the space, or at most its [[conformal structure]], since it is the latter – as determined by the lay of the lightcones – that determines the trajectories of lightlike geodesics, and hence their causal relationships. The importance of Penrose's paper "Gravitational Collapse and Space-Time Singularities"<ref name=Penrose1965>{{cite journal|last1=Penrose|first1=Roger|title=Gravitational Collapse and Space-Time Singularities|journal=Physical Review Letters|date=January 1965|volume=14|issue=3|pages=57–59|doi=10.1103/PhysRevLett.14.57|bibcode = 1965PhRvL..14...57P }}</ref> (summarised roughly as that if an object such as a dying star implodes beyond a certain point, then nothing can prevent the gravitational field getting so strong as to form some kind of singularity) was not its only result. It also showed a way to obtain similarly general conclusions in other contexts, notably that of the cosmological [[Big Bang]], which he dealt with in collaboration with Sciama's student [[Stephen Hawking]].<ref>{{Cite web|last=Clark|first=Stuart|title=A brief history of Stephen Hawking: A legacy of paradox|url=https://www.newscientist.com/article/2053929-a-brief-history-of-stephen-hawking-a-legacy-of-paradox/|access-date=7 October 2020|website=New Scientist|language=en-US|archive-date=5 October 2020|archive-url=https://web.archive.org/web/20201005145715/https://www.newscientist.com/article/2053929-a-brief-history-of-stephen-hawking-a-legacy-of-paradox/|url-status=live}}</ref><ref>{{Cite web|title=Roger Penrose|url=https://www.newscientist.com/people/roger-penrose/|access-date=7 October 2020|website=[[New Scientist]]|language=en-US|archive-date=11 October 2020|archive-url=https://web.archive.org/web/20201011180710/https://www.newscientist.com/people/roger-penrose/|url-status=live}}</ref><ref>{{Cite web|last=Wolchover|first=Natalie|title=Physicists Debate Hawking's Idea That the Universe Had No Beginning|url=https://www.quantamagazine.org/physicists-debate-hawkings-idea-that-the-universe-had-no-beginning-20190606/|access-date=7 October 2020|website=Quanta Magazine|date=6 June 2019|language=en|archive-date=5 October 2020|archive-url=https://web.archive.org/web/20201005235915/https://www.quantamagazine.org/physicists-debate-hawkings-idea-that-the-universe-had-no-beginning-20190606/|url-status=live}}</ref>

[[file: CNRSblackhole.jpg|thumb|300px|right|Predicted view from outside the [[event horizon]] of a [[black hole]] lit by a thin accretion disc]]
It was in the local context of gravitational collapse that the contribution of Penrose was most decisive, starting with his 1969 cosmic censorship conjecture,<ref>{{cite arXiv|last=Fernandez|first=Rodrigo L.|date=21 July 2020|title=Cosmic Censorship Conjecture violation: A semiclassical approach|class=gr-qc|eprint=2007.10601}}</ref> to the effect that any ensuing singularities would be confined within a well-behaved [[event horizon]] surrounding a hidden space-time region for which Wheeler coined the term [[black hole]], leaving a visible exterior region with strong but finite curvature, from which some of the gravitational energy may be extractable by what is known as the [[Penrose process]], while accretion of surrounding matter may release further energy that can account for astrophysical phenomena such as [[quasars]].<ref name="Curiel 2020">{{Citation|last=Curiel|first=Erik|title=Singularities and Black Holes|date=2020|url=https://plato.stanford.edu/archives/sum2020/entries/spacetime-singularities/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Summer 2020|publisher=Metaphysics Research Lab, Stanford University|access-date=7 October 2020}}</ref><ref>{{Cite journal|title=1979ApJ...229...46K Page 46|url=http://adsabs.harvard.edu/full/1979ApJ...229...46K|access-date=7 October 2020|journal=The Astrophysical Journal|bibcode=1979ApJ...229...46K|last1=Kafatos|first1=M.|last2=Leiter|first2=D.|year=1979|volume=229|page=46|doi=10.1086/156928|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185549/https://adsabs.harvard.edu/full/1979ApJ...229...46K|url-status=live}}</ref><ref>{{Cite web|title=Penrose process|url=https://www.oxfordreference.com/view/10.1093/oi/authority.20110810105604640|access-date=7 October 2020|website=Oxford Reference|language=en|archive-date=2 February 2021|archive-url=https://web.archive.org/web/20210202201151/https://www.oxfordreference.com/view/10.1093/oi/authority.20110810105604640|url-status=live}}</ref>

Following up his "weak [[cosmic censorship hypothesis]]", Penrose went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis". Together with the [[BKL conjecture|Belinski–Khalatnikov–Lifshitz 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]].<ref>{{cite conference |author=Penrose |first=Roger |date=1979 |editor-last=Hawking |editor-first=Stephen W. |editor2=Israel |editor2-first=W. |title=Singularities and Time-Asymmetry |conference= |publisher=Cambridge University Press |pages=581–638 |book-title=General Relativity: An Einstein Centenary Survey |editor=}}</ref> Penrose and James Terrell independently realised that objects travelling near the speed of light will appear to undergo a peculiar skewing or rotation. This effect has come to be called the [[Terrell rotation]] or Penrose–Terrell rotation.<ref>{{Cite journal |first=James |last=Terrell |date=1959 |title=Invisibility of the Lorentz Contraction |journal=[[Physical Review]] |issue= 4|pages=1041–1045 |doi=10.1103/PhysRev.116.1041 |volume=116 |bibcode = 1959PhRv..116.1041T }}</ref><ref>{{Cite journal |doi=10.1017/S0305004100033776 |first=Roger |last=Penrose |date=1959 |title=The Apparent Shape of a Relativistically Moving Sphere |journal=Proceedings of the Cambridge Philosophical Society |volume=55 |issue= 1|pages=137–139 |bibcode = 1959PCPS...55..137P |s2cid=123023118 }}</ref>

[[File:Penrose Tiling (Rhombi).svg|thumb|A [[Penrose tiling]]|alt=]]
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).<ref>{{Cite web|title=New Horizons in Twistor Theory {{!}} Mathematical Institute|url=http://www.maths.ox.ac.uk/groups/mathematical-physics/events/twistors50|access-date=7 October 2020|website=www.maths.ox.ac.uk|archive-date=8 October 2020|archive-url=https://web.archive.org/web/20201008153713/http://www.maths.ox.ac.uk/groups/mathematical-physics/events/twistors50|url-status=live}}</ref><ref>{{Cite book |last1=Huggett |first1=S. A. |url=http://dx.doi.org/10.1017/cbo9780511624018 |title=An Introduction to Twistor Theory |last2=Tod |first2=K. P. |date=1994-07-21 |publisher=Cambridge University Press |isbn=978-0-521-45157-4 |edition=2nd |pages=1|doi=10.1017/cbo9780511624018 }}</ref>

Penrose is well known for his 1974 discovery of [[Penrose tiling]]s, which are formed from two tiles that can only [[tessellation|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 in [[quasicrystal]]s.<ref>{{Cite journal |doi=10.1073/pnas.93.25.14267 |first=Paul |last=Steinhardt |title=New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings |journal=[[Proceedings of the National Academy of Sciences|PNAS]] |volume=93 |issue= 25|pages=14267–14270 |date=1996 |pmid=8962037 |pmc=34472 |bibcode = 1996PNAS...9314267S |doi-access=free }}</ref> Another noteworthy contribution is his 1971 invention of [[spin network]]s, which later came to form the geometry of [[spacetime]] in [[loop quantum gravity]].<ref>{{Cite web|title=Penrose on Spin Networks|url=https://math.ucr.edu/home/baez/penrose/|access-date=7 October 2020|website=math.ucr.edu|archive-date=12 October 2020|archive-url=https://web.archive.org/web/20201012031549/https://math.ucr.edu/home/baez/penrose/|url-status=live}}</ref> He was influential in popularizing what are commonly known as [[Penrose diagram]]s (causal diagrams).<ref>{{Cite web|title=Penrose diagrams|url=https://jila.colorado.edu/~ajsh/insidebh/penrose.html|access-date=7 October 2020|website=jila.colorado.edu|language=en|archive-date=11 November 2020|archive-url=https://web.archive.org/web/20201111203436/https://jila.colorado.edu/~ajsh/insidebh/penrose.html|url-status=live}}</ref>

In 1983, Penrose was invited to teach at [[Rice University]] in Houston, by the then provost Bill Gordon. He worked there from 1983 to 1987.<ref>{{cite web|url=http://ricehistorycorner.com/2013/05/22/roger-penrose-at-rice-1983-87/|title=Roger Penrose at Rice, 1983–87|work=Rice History Corner|date=22 May 2013|access-date=29 January 2014|archive-date=17 June 2016|archive-url=https://web.archive.org/web/20160617233239/https://ricehistorycorner.com/2013/05/22/roger-penrose-at-rice-1983-87/|url-status=live}}</ref> His doctoral students have included, among others, [[Andrew Hodges]],<ref name=aphd>{{cite thesis|degree=PhD|publisher=Birkbeck, University of London|url=http://catalogue.libraries.london.ac.uk/record=b3004898|doi=|title=The Description of Mass within the Theory of Twistors|first= Andrew Philip|last=Hodges|date=1975|id={{EThOS|uk.bl.ethos.459296}}|website=london.ac.uk|oclc=500473477}}</ref> [[Lane P. Hughston|Lane Hughston]], [[Richard Jozsa]], [[Claude LeBrun]], [[John McNamara (mathematical biologist)|John McNamara]], [[Tristan Needham]], [[Tim Poston]],<ref name=mathgene>{{MathGenealogy}}</ref> [[Asghar Qadir]], and [[Richard S. Ward]].

In 2004, Penrose released ''[[The Road to Reality: A Complete Guide to the Laws of the Universe]]'', a 1,099-page comprehensive guide to the [[physical law|Laws of Physics]] that includes an explanation of his own theory. The [[Penrose interpretation|Penrose Interpretation]] predicts the relationship between [[quantum mechanics]] and [[general relativity]], and proposes that a [[quantum state]] remains in [[Quantum superposition|superposition]] until the difference of [[space-time curvature]] attains a significant level.<ref>{{cite web |url=https://www.nytimes.com/2005/02/27/books/review/the-road-to-reality-a-really-long-history-of-time.html?_r=0 |title='The Road to Reality': A Really Long History of Time |first1=George |last1=Johnson |author-link=George Johnson (writer)| date=27 February 2005 |work=[[The New York Times]] |access-date=3 April 2017 |archive-date=3 January 2021 |archive-url=https://web.archive.org/web/20210103115129/https://www.nytimes.com/2005/02/27/books/review/the-road-to-reality-a-really-long-history-of-time.html?_r=0 |url-status=live }}</ref><ref>{{cite web  | title=If an Electron Can Be in Two Places at Once, Why Can't You? | last=Folger| first=Tim| author-link=Tim Folger| work=[[Discover (magazine)| Discover]]| url=http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=0&-C= | access-date = 27 October 2008 | archive-url=https://web.archive.org/web/20121101130211/http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=0&-C= | archive-date=1 November 2012}}</ref>

Penrose is the Francis and Helen Pentz Distinguished Visiting Professor of Physics and Mathematics at [[Pennsylvania State University]].<ref>{{cite web| title =Dr. Roger Penrose at Penn State University| url =http://www.phys.psu.edu/people/display/index.html?person_id=233&mode=contact.| access-date =9 July 2007| url-status =dead| archive-url =https://web.archive.org/web/20080416131322/http://www.phys.psu.edu/people/display/index.html?person_id=233&mode=contact.| archive-date =16 April 2008| df =dmy-all}}</ref>

=== An earlier universe ===
[[File:WMAP 2010.png|thumb|300px|[[Wilkinson Microwave Anisotropy Probe|WMAP]] image of the (extremely tiny) anisotropies in the [[cosmic background radiation]]]]

In 2010, Penrose reported possible evidence, based on concentric circles found in [[WMAP|Wilkinson Microwave Anisotropy Probe]] data of the [[CMB|cosmic microwave background]] sky, of an earlier universe existing before the [[Big Bang]] of our own present universe.<ref name="Gurzadyan">{{cite arXiv |eprint=1011.3706 |class=astro-ph.CO |first1=V. G. |last1=Gurzadyan |first2=R. |last2=Penrose |title=Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity". volume "v1 |date=2010}}</ref> He mentions this evidence in the epilogue of his 2010 book ''[[Cycles of Time]]'',<ref>Roger Penrose, ''Cycles of Time'', Vintage; Reprint edition (1 May 2012)</ref> a book in which he presents his reasons, to do with [[Einstein's field equations]], the [[Weyl curvature]] C, and the [[Weyl curvature hypothesis]] (WCH), that the transition at the Big Bang could have been smooth enough for a previous universe to survive it.<ref>{{Cite journal|last=Stoica|first=Ovidiu-Cristinel|date=November 2013|title=On the Weyl Curvature Hypothesis|journal=Annals of Physics|volume=338|pages=186–194|doi=10.1016/j.aop.2013.08.002|arxiv=1203.3382|bibcode=2013AnPhy.338..186S|s2cid=119329306}}</ref><ref>{{cite conference |author=Penrose |first=Roger |date=1979 |editor-last=Hawking |editor-first=S. W. |editor2=Israel |editor2-first=W. |title=Singularities and Time-Asymmetry |conference= |publisher=[[Cambridge University Press]] |pages=581–638 |book-title=General Relativity: An Einstein Centenary Survey}}</ref> He made several conjectures about C and the WCH, some of which were subsequently proved by others, and he also popularized his [[conformal cyclic cosmology]] (CCC) theory.<ref>{{Cite web|date=21 August 2018|title=New evidence for cyclic universe claimed by Roger Penrose and colleagues|url=https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/|access-date=7 October 2020|website=Physics World|language=en-GB|archive-date=1 November 2020|archive-url=https://web.archive.org/web/20201101015848/https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/|url-status=live}}</ref> In this theory, Penrose postulates that at the end of the universe all matter is eventually contained within black holes, which subsequently evaporate via [[Hawking radiation]]. At this point, everything contained within the universe consists of [[photons]], which "experience" neither time nor space. There is essentially no difference between an infinitely large universe consisting only of photons and an infinitely small universe consisting only of photons. Therefore, a singularity for a [[Big Bang]] and an infinitely expanded universe are equivalent.<ref>{{Cite web|url = https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/|title = New evidence for cyclic universe claimed by Roger Penrose and colleagues|date = 21 August 2018|access-date = 7 October 2020|archive-date = 1 November 2020|archive-url = https://web.archive.org/web/20201101015848/https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/|url-status = live}}</ref>

In simple terms, Penrose believes that the singularity in [[Einstein's field equation]] at the Big Bang is only an apparent singularity, similar to the well-known apparent singularity at the [[event horizon]] of a [[black hole]].<ref name="Curiel 2020"/> The latter singularity can be removed by a change of [[coordinate system]], and Penrose proposes a different change of coordinate system that will remove the singularity at the big bang.<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=9XKYDwAAQBAJ&q=roger+penrose+%22change+of+coordinate%22&pg=PA55|title=Fashion, Faith, and Fantasy in the New Physics of the Universe|date=5 September 2017|publisher=Princeton University Press|isbn=978-0-691-17853-0|language=en|access-date=12 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185551/https://books.google.com/books?id=9XKYDwAAQBAJ&q=roger+penrose+%22change+of+coordinate%22&pg=PA55|url-status=live}}</ref> One implication of this is that the major events at the Big Bang can be understood without unifying general relativity and quantum mechanics, and therefore we are not necessarily constrained by the [[Wheeler–DeWitt equation]], which disrupts time.<ref>{{Cite journal|last=Kiefer|first=Claus|date=13 August 2013|title=Conceptual Problems in Quantum Gravity and Quantum Cosmology|journal=ISRN Mathematical Physics|volume=2013|pages=1–17|doi=10.1155/2013/509316|language=en|doi-access=free|arxiv=1401.3578}}</ref><ref>{{Cite arXiv |last=Vaas |first=Rüdiger |title=The Inverted Big-Bang <!-- unsupported parameter |url=https://arxiv.org/pdf/physics/0407071.pdf --> |year=2004 |eprint=physics/0407071}}</ref> Alternatively, one can use the Einstein–Maxwell–Dirac equations.<ref>{{Cite web |last1=Finster |first1=F. |last2=Smoller |first2=J. A. |last3=Yau |first3=S. -T. |title=The Einstein–Dirac–Maxwell Equations – Black Hole Solutions |url=https://cds.cern.ch/record/403056/files/9910030.pdf |url-status=live |archive-url=https://web.archive.org/web/20201007132312/https://cds.cern.ch/record/403056/files/9910030.pdf |archive-date=7 October 2020 |access-date=7 October 2020}}</ref>

=== Consciousness ===
[[File:Roger Penrose 9671.JPG|thumb|Penrose at a conference circa 2011]]
Penrose has written books on the connection between fundamental physics and human (or animal) consciousness. In ''[[The Emperor's New Mind]]'' (1989), he argues that known laws of physics are inadequate to explain the phenomenon of consciousness.<ref>{{Cite news|last=Ferris|first=Timothy|date=19 November 1989|title=HOW THE BRAIN WORKS, MAYBE (Published 1989)|language=en-US|work=[[The New York Times]]| author-link=Timothy Ferris| url=https://www.nytimes.com/1989/11/19/books/how-the-brain-works-maybe.html|access-date=7 October 2020|issn=0362-4331|archive-date=19 November 2021|archive-url=https://web.archive.org/web/20211119091901/https://www.nytimes.com/1989/11/19/books/how-the-brain-works-maybe.html|url-status=live}}</ref> Penrose proposes the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he calls ''correct quantum gravity'').<ref>{{Cite web|last=Stork|first=David G.|date=29 October 1989|title=The Physicist Against the Hackers : THE EMPEROR'S NEW MIND: On Computers, Minds, and the Laws of Physics by Roger Penrose (Oxford University Press: $24.95; 428 pp.)|url=https://www.latimes.com/archives/la-xpm-1989-10-29-bk-90-story.html|access-date=7 October 2020|website=Los Angeles Times|language=en-US|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185551/https://www.latimes.com/archives/la-xpm-1989-10-29-bk-90-story.html|url-status=live}}</ref> Penrose uses a variant of [[Turing's halting theorem]] to demonstrate that a system can be [[deterministic]] without being [[algorithm]]ic. (For example, imagine a system with only two states, ON and OFF. If the system's state is ON when a given [[Turing machine]] halts and OFF when the Turing machine does not halt, then the system's state is completely determined by the machine; nevertheless, there is no algorithmic way to determine whether the Turing machine stops.)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=JF4vDwAAQBAJ&q=turing+halting|title=The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics|date=28 April 2016|publisher=Oxford University Press|isbn=978-0-19-255007-1|language=en|access-date=12 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185551/https://books.google.com/books?id=JF4vDwAAQBAJ&q=turing+halting|url-status=live}}</ref><ref>{{Cite web|title=20th WCP: Computational Complexity and Philosophical Dualism|url=https://www.bu.edu/wcp/Papers/Cogn/CognTeix.htm|access-date=7 October 2020|website=www.bu.edu|archive-date=13 October 2020|archive-url=https://web.archive.org/web/20201013092220/https://www.bu.edu/wcp/Papers/Cogn/CognTeix.htm|url-status=live}}</ref>

Penrose believes that such deterministic yet non-algorithmic processes may come into play in the quantum mechanical [[Wave function collapse|wave function reduction]], and may be harnessed by the brain. He argues that computers today are unable to have intelligence because they are algorithmically deterministic systems. He argues against the viewpoint that the rational processes of the mind are completely algorithmic and can thus be duplicated by a sufficiently complex computer.<ref name="Penrose-2016">{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=X28sDwAAQBAJ&q=G%C3%B6del's+incompleteness+theorem|title=The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics|date=2016|publisher=Oxford University Press|isbn=978-0-19-878492-0|language=en|access-date=7 December 2021|archive-date=19 November 2021|archive-url=https://web.archive.org/web/20211119091917/https://books.google.com/books?id=X28sDwAAQBAJ&q=G%C3%B6del%27s+incompleteness+theorem|url-status=live}}</ref> This contrasts with supporters of [[computational theory of mind|strong artificial intelligence]], who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends [[formal logic]] because factors such as the insolubility of the [[halting problem]] and [[Gödel's incompleteness theorem]] prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight.<ref name="Penrose-2016" /> These claims were originally espoused by the philosopher [[John Lucas (philosopher)|John Lucas]] of [[Merton College, Oxford|Merton College]], [[University of Oxford|Oxford]].<ref>{{Cite web|title=In Memoriam: John Lucas|url=https://www.philosophy.ox.ac.uk/article/in-memoriam-john-lucas|access-date=7 October 2020|website=www.philosophy.ox.ac.uk|language=en|archive-date=9 October 2020|archive-url=https://web.archive.org/web/20201009111739/https://www.philosophy.ox.ac.uk/article/in-memoriam-john-lucas|url-status=live}}</ref>

The [[Penrose–Lucas argument]] about the implications of Gödel's incompleteness theorem for computational theories of human intelligence has been criticised by mathematicians, computer scientists and philosophers. Many experts in these fields assert that Penrose's argument fails, though different authors may choose different aspects of the argument to attack.<ref>Criticism of the Lucas/Penrose argument that intelligence can not be entirely algorithmic:

* [http://consc.net/mindpapers/6.1b MindPapers: 6.1b. Godelian arguments]. {{Webarchive|url=https://web.archive.org/web/20110611213335/http://consc.net/mindpapers/6.1b|date=11 June 2011}}.
* [http://users.ox.ac.uk/~jrlucas/Godel/referenc.html References for Criticisms of the Gödelian Argument]. {{Webarchive|url=https://web.archive.org/web/20200703180031/http://users.ox.ac.uk/~jrlucas/Godel/referenc.html|date=3 July 2020}}.
* [[George Boolos|Boolos, George]], et al. 1990. ''An Open Peer Commentary on The Emperor's New Mind.'' Behavioral and Brain Sciences 13 (4), p. 655.
* [[Martin Davis (mathematician)|Davis, Martin]] 1993. ''How subtle is Gödel's theorem? More on Roger Penrose.'' Behavioral and Brain Sciences, 16, pp. 611–612. Online version at Davis' faculty page at http://cs.nyu.edu/cs/faculty/davism/. {{Webarchive|url=https://web.archive.org/web/19981203160909/http://www.cs.nyu.edu/cs/faculty/davism/|date=3 December 1998}}.
* {{cite journal |last=Feferman |first=Solomon |author-link=Solomon Feferman |date=1996 |title=Penrose's Gödelian argument |journal=[[Psyche (consciousness journal)|Psyche]] |volume=2 |pages=21–32 |citeseerx=10.1.1.130.7027}}
* Krajewski, Stanislaw 2007. ''On Gödel's Theorem and Mechanism: Inconsistency or Unsoundness is Unavoidable in any Attempt to 'Out-Gödel' the Mechanist.'' Fundamenta Informaticae 81, pp. 173–181. Reprinted in [https://books.google.com/books?id=0jSS-3Bl06cC&pg=PA173 Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science:In Recognition of Professor Andrzej Grzegorczyk (2008), p. 173]. {{Webarchive|url=https://web.archive.org/web/20161226205008/https://books.google.com/books?id=0jSS-3Bl06cC&lpg=PP1&pg=PA173|date=26 December 2016}}.
* {{cite journal |last1=LaForte |first1=Geoffrey |last2=Hayes |first2=Patrick J. |last3=Ford |first3=Kenneth M. |year=1998 |title=Why Gödel's Theorem Cannot Refute Computationalism |journal=Artificial Intelligence |volume=104 |issue=1–2 |pages=265–286 |doi=10.1016/s0004-3702(98)00052-6 |doi-access=free}}
* [[David Kellogg Lewis|Lewis, David K.]] 1969. ''[http://www2.units.it/etica/2003_1/7_monographica.doc Lucas against mechanism]. {{Webarchive|url=https://web.archive.org/web/20210225215326/http://www2.units.it/etica/2003_1/7_monographica.doc|date=25 February 2021}}''. Philosophy 44, pp. 231–233.
* [[Hilary Putnam|Putnam, Hilary]] 1995. ''Review of Shadows of the Mind.'' In Bulletin of the American Mathematical Society 32, pp. 370–373 (also see Putnam's less technical criticisms in his [https://www.nytimes.com/books/97/04/27/nnp/17540.html ''The New York Times'' review]. {{Webarchive|url=https://web.archive.org/web/20210309045619/https://archive.nytimes.com/www.nytimes.com/books/97/04/27/nnp/17540.html|date=9 March 2021}}).
Sources that indicate Penrose's argument is generally rejected:

* Bringsford, S. and Xiao, H. 2000. ''[http://kryten.mm.rpi.edu/refute.penrose.pdf A Refutation of Penrose's Gödelian Case Against Artificial Intelligence]. {{Webarchive|url=https://web.archive.org/web/20210224130103/http://kryten.mm.rpi.edu/refute.penrose.pdf|date=24 February 2021}}.'' [[Journal of Experimental and Theoretical Artificial Intelligence]] 12: 307–329. The authors write that it is "generally agreed" that Penrose "failed to destroy the computational conception of mind."
* In an article at {{cite web |title=King's College London – Department of Mathematics |url=http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html |url-status=dead |archive-url=https://web.archive.org/web/20010125011300/http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html |archive-date=25 January 2001 |access-date=22 October 2010}} L. J. Landau at the Mathematics Department of King's College London writes that "Penrose's argument, its basis and implications, is rejected by experts in the fields which it touches."
Sources that also note that different sources attack different points of the argument:

* Princeton Philosophy professor John Burgess writes in ''[http://www.princeton.edu/~jburgess/Montreal.doc On the Outside Looking In: A Caution about Conservativeness]. {{Webarchive|url=https://web.archive.org/web/20121019093317/http://www.princeton.edu/~jburgess/Montreal.doc|date=19 October 2012}}'', (published in Kurt Gödel: Essays for his Centennial, with the following comments found on [https://books.google.com/books?id=83Attf6BsJ4C&pg=PA131 pp. 131–132]. {{Webarchive|url=https://web.archive.org/web/20161227005431/https://books.google.com/books?id=83Attf6BsJ4C&lpg=PP1&pg=PA131|date=27 December 2016}}) that "the consensus view of logicians today seems to be that the Lucas–Penrose argument is fallacious, though as I have said elsewhere, there is at least this much to be said for Lucas and Penrose, that logicians are not unanimously agreed as to where precisely the fallacy in their argument lies. There are at least three points at which the argument may be attacked."
* [[Nachum Dershowitz]] 2005. ''[http://www.cs.tau.ac.il/~nachumd/papers/FourSonsOfPenrose.pdf The Four Sons of Penrose]. {{Webarchive|url=https://web.archive.org/web/20170809142617/http://www.cs.tau.ac.il/%7Enachumd/papers/FourSonsOfPenrose.pdf|date=9 August 2017}}'', in ''Proceedings of the Eleventh Conference on [[Logic for Programming, Artificial Intelligence and Reasoning]] (LPAR; Jamaica)'', G. Sutcliffe and [[Andrei Voronkov]], eds., Lecture Notes in Computer Science, vol. 3835, Springer-Verlag, Berlin, Germany, pp. 125–138.</ref> [[Marvin Minsky]], a leading proponent of artificial intelligence, was particularly critical, stating that Penrose "tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle." Minsky's position is exactly the opposite – he believed that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintained that "one can carry that quest [for scientific explanation] too far by only seeking new basic principles instead of attacking the real detail. This is what I see in Penrose's quest for a new basic principle of physics that will account for consciousness."<ref>Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, [[National Research Council of Canada]], 75th Anniversary Symposium on Science in Society, June 1991.</ref>

Penrose responded to criticism of ''The Emperor's New Mind'' with his follow-up 1994 book ''[[Shadows of the Mind]]'', and in 1997 with ''[[The Large, the Small and the Human Mind]]''. In those works, he also combined his observations with those of anesthesiologist [[Stuart Hameroff]].<ref>{{Cite web|title=Can Quantum Physics Explain Consciousness? One Scientist Thinks It Might|url=https://www.discovermagazine.com/the-sciences/can-quantum-physics-explain-consciousness-one-scientist-thinks-it-might|access-date=7 October 2020|website=Discover Magazine|language=en|archive-date=3 October 2020|archive-url=https://web.archive.org/web/20201003024544/https://www.discovermagazine.com/the-sciences/can-quantum-physics-explain-consciousness-one-scientist-thinks-it-might|url-status=live}}</ref>

Penrose and Hameroff have argued that [[consciousness]] is the result of quantum gravity effects in [[microtubule]]s, which they dubbed [[Orch-OR]] (orchestrated objective reduction). [[Max Tegmark]], in a paper in ''Physical Review E'',<ref>{{cite journal | last1 = Tegmark | first1 = Max | date = 2000 | title = The importance of quantum decoherence in brain processes | journal = [[Physical Review E]] | volume = 61 | issue = 4| pages = 4194–4206 | doi=10.1103/physreve.61.4194| pmid = 11088215 |arxiv = quant-ph/9907009 |bibcode = 2000PhRvE..61.4194T | s2cid = 17140058 }}</ref> calculated that the time scale of neuron firing and excitations in microtubules is slower than the [[quantum decoherence|decoherence]] time by a factor of at least 10,000,000,000. The reception of the paper is summed up by this statement in Tegmark's support: "Physicists outside the fray, such as IBM's [[John A. 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'".<ref name="Tetlow 2007 166">
{{cite book
|url=https://books.google.com/books?id=3mPI9rUuhJ8C&q=penrose%20
|last=Tetlow
|first=Philip
|title=The Web's Awake: An Introduction to the Field of Web Science and the Concept of Web Life
|publisher=John Wiley & Sons
|location=Hoboken, New Jersey
|date=2007
|isbn=978-0-470-13794-9
|page=166
|access-date=5 October 2020
|archive-date=7 December 2021
|archive-url=https://web.archive.org/web/20211207185552/https://books.google.com/books?id=3mPI9rUuhJ8C&q=penrose+
|url-status=live
}}</ref> Tegmark's paper has been widely cited by critics of the Penrose–Hameroff position.

Phillip Tetlow, although himself supportive of Penrose's views, acknowledges that Penrose's ideas about the human thought process are at present a minority view in scientific circles, citing Minsky's criticisms and quoting science journalist [[Charles Seife]]'s description of Penrose as "one of a handful of scientists" who believe that the nature of consciousness suggests a quantum process.<ref name="Tetlow 2007 166"/>

In January 2014, Hameroff and Penrose ventured that a discovery of quantum vibrations in microtubules by Anirban Bandyopadhyay of the National Institute for Materials Science in Japan<ref>{{cite web |url=https://www.researchgate.net/profile/Anirban_Bandyopadhyay |title=Anirban Bandyopadhyay |access-date=22 February 2014 |archive-date=10 March 2014 |archive-url=https://web.archive.org/web/20140310053951/http://www.researchgate.net/profile/Anirban_Bandyopadhyay/ |url-status=live }}</ref> supports the hypothesis of [[Orchestrated objective reduction|Orch-OR theory]]. A reviewed and updated version of the theory was published along with critical commentary and debate in the March 2014 issue of ''[[Physics of Life Reviews]]''.<ref name="Hameroff2014">{{cite journal |author1=Hameroff |first=S. |author2=Penrose |first2=R. |date=2014 |title=Consciousness in the universe: A review of the 'Orch OR' theory |journal=Physics of Life Reviews |volume=11 |issue=1 |pages=39–78 |bibcode=2014PhLRv..11...39H |doi=10.1016/j.plrev.2013.08.002 |pmid=24070914 |doi-access=free}}</ref>

=== Publications ===
His popular publications include:
* ''[[The Emperor's New Mind|The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics]]'' (1989)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=_ibtvQEACAAJ|title=The Emperor's New Mind|date=1989|language=en|access-date=7 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185554/https://books.google.com/books?id=_ibtvQEACAAJ|url-status=live}}</ref>
* ''[[Shadows of the Mind|Shadows of the Mind: A Search for the Missing Science of Consciousness]]'' (1994)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=gDbOAK89tmcC&q=Shadows+of+the+Mind:+A+Search+for+the+Missing+Science+of+Consciousness|title=Shadows of the Mind: A Search for the Missing Science of Consciousness|date=1994|publisher=Oxford University Press|isbn=978-0-19-510646-6|language=en|access-date=12 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185555/https://books.google.com/books?id=gDbOAK89tmcC&q=Shadows+of+the+Mind%3A+A+Search+for+the+Missing+Science+of+Consciousness|url-status=live}}</ref>
* ''[[The Road to Reality: A Complete Guide to the Laws of the Universe]]'' (2004)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=VWTNCwAAQBAJ|title=The Road to Reality: A Complete Guide to the Laws of the Universe|date=31 March 2016|publisher=Random House|isbn=978-1-4464-1820-8|language=en|access-date=7 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185554/https://books.google.com/books?id=VWTNCwAAQBAJ|url-status=live}}</ref>
* ''[[Cycles of Time|Cycles of Time: An Extraordinary New View of the Universe]]'' (2010)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=gv8o1XydoCQC&q=Cycles+of+Time:+An+Extraordinary+New+View+of+the+Universe|title=Cycles of Time: An Extraordinary New View of the Universe|date=6 September 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-59674-1|language=en}}</ref>
* ''[[Fashion, Faith, and Fantasy in the New Physics of the Universe]]'' (2016)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=9XKYDwAAQBAJ&q=Fashion,+Faith,+and+Fantasy+in+the+New+Physics+of+the+Universe|title=Fashion, Faith, and Fantasy in the New Physics of the Universe|date=5 September 2017|publisher=Princeton University Press|isbn=978-0-691-17853-0|language=en}}</ref>

His co-authored publications include:
* ''[[The Nature of Space and Time]]'' (with [[Stephen Hawking]]) (1996)<ref>{{Cite book|last1=Hawking|first1=Stephen W.|url=https://books.google.com/books?id=8RatQgAACAAJ|title=The Nature of Space and Time|last2=Penrose|first2=Roger|date=1996|publisher=Princeton University Press|isbn=978-0-691-03791-2|language=en|access-date=7 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185837/https://books.google.com/books?id=8RatQgAACAAJ|url-status=live}}</ref>
* ''[[The Large, the Small and the Human Mind]]'' (with [[Abner Shimony]], [[Nancy Cartwright (philosopher)|Nancy Cartwright]], and Stephen Hawking) (1997)<ref>{{Cite book|last1=Penrose|first1=Roger|url=https://books.google.com/books?id=jWHqlijAjyMC&q=The+Large,+the+Small+and+the+Human+Mind|title=The Large, the Small and the Human Mind|last2=Shimony|first2=Abner|last3=Cartwright|first3=Nancy|last4=Hawking|first4=Stephen|date=28 April 2000|publisher=Cambridge University Press|isbn=978-0-521-78572-3|language=en}}</ref>
* ''White Mars: The Mind Set Free'' (with [[Brian Aldiss]]) (1999)<ref>{{Cite book|last1=Aldiss|first1=Brian W.|url=https://books.google.com/books?id=K_-jBwAAQBAJ&q=White+Mars:+The+Mind+Set+Free(1999)|title=White Mars; or, The Mind Set Free: A 21st-Century Utopia|last2=Penrose|first2=Roger|date=19 May 2015|publisher=Open Road Media|isbn=978-1-5040-1028-3|language=en}}</ref>

His academic books include:
* ''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)

His forewords to other books include:
* Foreword to [https://www.springer.com/book/9783319724775 "The Map and the Territory: Exploring the foundations of science, thought and reality"] by Shyam Wuppuluri and Francisco Antonio Doria. Published by Springer in "The Frontiers Collection", 2018.<ref>{{Cite book|last1=Wuppuluri|first1=Shyam|url=https://books.google.com/books?id=mRBMDwAAQBAJ&q=%E2%80%9CThe+Map+and+the+Territory:+Exploring+the+foundations+of+science,+thought+and+reality+roger+penrose|title=The Map and the Territory: Exploring the Foundations of Science, Thought and Reality|last2=Doria|first2=Francisco Antonio|date=13 February 2018|publisher=Springer|isbn=978-3-319-72478-2|language=en}}</ref>
* Foreword to [http://www.worldscientific.com/worldscibooks/10.1142/p856 ''Beating the Odds: The Life and Times of E. A. Milne''], written by Meg Weston Smith. Published by World Scientific Publishing Co in June 2013.<ref>{{Cite book|last=Weston-smith|first=Meg|url=https://books.google.com/books?id=P826CgAAQBAJ&q=Beating+the+Odds:+The+Life+and+Times+of+E.+A.+Milne+roger+penrose&pg=PR3|title=Beating The Odds: The Life And Times Of E A Milne|date=16 April 2013|publisher=World Scientific|isbn=978-1-84816-943-2|language=en|access-date=12 October 2020|archive-date=26 January 2021|archive-url=https://web.archive.org/web/20210126000706/https://books.google.com/books?id=P826CgAAQBAJ&q=Beating+the+Odds:+The+Life+and+Times+of+E.+A.+Milne+roger+penrose&pg=PR3|url-status=live}}</ref>
* Foreword to [http://www.worldscientific.com/worldscibooks/10.1142/8306 "A Computable Universe"] by Hector Zenil. Published by World Scientific Publishing Co in December 2012.<ref>{{Cite book|last=Zenil|first=Hector|url=https://books.google.com/books?id=SGG6CgAAQBAJ&q=%22A+Computable+Universe%22+roger+penrose|title=A Computable Universe: Understanding and Exploring Nature as Computation|date=2013|publisher=World Scientific|isbn=978-981-4374-30-9|language=en}}</ref>
* Foreword to ''[[Quantum Aspects of Life]]'' by Derek Abbott, Paul C. W. Davies, and Arun K. Pati. Published by Imperial College Press in 2008.<ref>{{Cite book|last1=Abbott|first1=Derek|url=https://books.google.com/books?id=C1y7CgAAQBAJ&q=Quantum+Aspects+of+Life+roger+penrose|title=Quantum Aspects Of Life|last2=Davies|first2=Paul C. W.|last3=Pati|first3=Arun Kumar|date=12 September 2008|publisher=World Scientific|isbn=978-1-908978-73-8|language=en|access-date=12 October 2020|archive-date=26 January 2021|archive-url=https://web.archive.org/web/20210126162257/https://books.google.com/books?id=C1y7CgAAQBAJ&q=Quantum+Aspects+of+Life+roger+penrose|url-status=live}}</ref>
* Foreword to [http://press.princeton.edu/chapters/p8509.pdf ''Fearful Symmetry''] by [[Anthony Zee]]'s. Published by Princeton University Press in 2007.<ref>{{Cite book|last=Zee|first=A.|url=https://books.google.com/books?id=Xq1mCgAAQBAJ&q=fearful+symmetry+roger+penrose|title=Fearful Symmetry: The Search for Beauty in Modern Physics|date=1 October 2015|publisher=Princeton University Press|isbn=978-1-4008-7450-7|language=en|access-date=12 October 2020|archive-date=26 January 2021|archive-url=https://web.archive.org/web/20210126162300/https://books.google.com/books?id=Xq1mCgAAQBAJ&q=fearful+symmetry+roger+penrose|url-status=live}}</ref>

=== Awards and honours ===
[[File:RogerPenrose CapturingInfinity cropped.jpg|thumb|Penrose during a lecture]]
Penrose has been awarded many prizes for his contributions to science.
In 1971, he was awarded the [[Dannie Heineman Prize for Astrophysics]] by the [[American Astronomical Society]] and [[American Institute of Physics]]. He was elected a [[List of Fellows of the Royal Society elected in 1972|Fellow of the Royal Society (FRS) 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 Prize in Physics]] by the [[Wolf Foundation]] (Israel) in 1988.

In 1989, Penrose was awarded the [[Dirac Medal (IOP)|Dirac Medal and Prize]] of the British [[Institute of Physics]]. He was also made an [[Honorary Fellow of the Institute of Physics]] (HonFInstP).<ref>{{cite web |title=Our Honorary Fellows |url=https://www.iop.org/about/awards/honorary-fellowship/our-honorary-fellows |publisher=[[Institute of Physics]] |access-date=26 December 2022}}</ref> In 1990, Penrose was awarded the [[Albert Einstein Medal]] for outstanding work related to the work of [[Albert Einstein]] by the [[Albert Einstein Society]] (Switzerland). In 1991, he was awarded the [[Naylor Prize]] of the [[London Mathematical Society]]. Penrose was awarded an honorary [[Doctor of Science]] degree (DSc) from the [[University of New Brunswick]] (Canada) in 1992,<ref>[https://graduations.lib.unb.ca/award/17499 1992 Fredericton Convocation: Penrose, Roger], website of the [[University of New Brunswick]].</ref> and an honorary degree from the [[University of Surrey]] in 1993.<ref>[https://www.surrey.ac.uk/about/people/honorary-graduates Honorary graduates], website of the [[University of Surrey]].</ref> From 1992 to 1995, he served as President of the [http://www.isgrg.org/ International Society on General Relativity and Gravitation]. 

In 1994, Penrose was [[Knight Bachelor|knighted]] for services to science.<ref>{{cite web|title=Supplement 53696,10 June 1994, London Gazette|url=https://www.thegazette.co.uk/London/issue/53696/supplement/2|website=The Gazette|access-date=16 August 2015|archive-date=29 April 2016|archive-url=https://web.archive.org/web/20160429222205/https://www.thegazette.co.uk/London/issue/53696/supplement/2|url-status=live}}</ref> In the same year, he was also awarded an honorary degree of [[Doctor of Science]] (DSc) by the [[University of Bath]],<ref>{{cite web |url= http://www.bath.ac.uk/ceremonies/hongrads/ |title= Honorary Graduates 1989 to present |publisher= [[University of Bath]] |access-date= 18 February 2012 |archive-date= 19 December 2015 |archive-url= https://web.archive.org/web/20151219000643/http://www.bath.ac.uk/ceremonies/hongrads/ |url-status= dead }}</ref> and became a member of [[Polish Academy of Sciences]]. Penrose was awarded honorary degrees from the [[University of London]] in 1995,<ref name="ae">[https://www.ae-info.org/ae/Member/Penrose_Roger Professor Sir Roger Penrose OM FRS], website of the [[Academia Europaea]].</ref> the [[University of Glasgow]] ([[Doctor of Science]], DSc)<ref>[https://www.gla.ac.uk/media/Media_61834_smxx.pdf Who, Where and When: The History & Constitution of the University of Glasgow], website of [[The University of Glasgow]].</ref> and [[University of Essex]], both in 1996,<ref>[https://www.essex.ac.uk/alumni/honorary/honorary-graduates Honorary graduates over the years], website of the [[University of Essex]].</ref> from the [[University of St Andrews]] in 1997,<ref name="ae" /> and the [[Visva-Bharati University|Visva-Bharati University of Santiniketan]] (India)<ref name="ae" /> and [[Open University]] ([[Doctor of the University]], DUniv),<ref>[https://www5.open.ac.uk/students/ceremonies/sites/www.open.ac.uk.students.ceremonies/files/Honorary%20graduate%20cumulative%20list(1).pdf Honorary graduate cumulative] website of [[Open University]]</ref> both in 1998. In 1998, he was elected Foreign Associate of the [[United States National Academy of Sciences]].<ref>{{Cite web|title=Sir Roger Penrose {{!}} Person|url=https://www.fetzer-franklin-fund.org/media/sir-roger-penrose/|access-date=7 October 2020|website=Fetzer Franklin Fund|language=de-DE|archive-date=24 September 2020|archive-url=https://web.archive.org/web/20200924081714/https://www.fetzer-franklin-fund.org/media/sir-roger-penrose/|url-status=live}}</ref> In 2000, he was appointed a [[Member of the Order of Merit]] (OM).<ref>{{Cite news|title=Appointments to the Order of Merit|newspaper=The Royal Family |date=January 2012|url=https://www.royal.uk/appointments-order-merit|access-date=25 October 2020|language=en|archive-date=29 September 2020|archive-url=https://web.archive.org/web/20200929015241/https://www.royal.uk/appointments-order-merit|url-status=live|last1=Fisher |first1=Connie }}</ref> He was awarded an [[honorary doctorate]] from the [[University of Southampton]] in 2002.<ref>[https://www.southampton.ac.uk/news/2020/11/roger-penrose-nobel-prize.page Nobel Prize winner Sir Roger Penrose congratulated by Southampton academics], website of the [[University of Southampton]].</ref>

In 2004, Penrose was awarded an honorary [[Doctor of Science]] (DSc) degree from the [[University of Waterloo]] ([[Ontario, Canada]])<ref>[https://bulletin.uwaterloo.ca/2004/sep/21tu.html DAily bulletin September 21, 2004], website of the [[University of Waterloo]].</ref><ref>[https://uwaterloo.ca/secretariat/honorary-degrees-granted Honorary degrees granted], website of the [[University of Waterloo]].</ref> and was awarded the [[De Morgan Medal]] by the [[London Mathematical Society]] for his wide and original contributions to mathematical physics.<ref>{{Cite journal|date=8 August 2018|title=Roger Penrose|language=EN|doi=10.1063/PT.6.6.20180808a|journal=Physics Today|issue=8 |page=4433 |doi-access=free|bibcode=2018PhT..2018h4433. }}</ref> To quote the citation from the society:
{{blockquote|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.<ref>{{Cite web|url=http://www.lms.ac.uk/activities/prizes_com/citations04.html|archive-url=https://web.archive.org/web/20041231232542/http://www.lms.ac.uk/activities/prizes_com/citations04.html|title=London Mathematical Society|archive-date=31 December 2004}}</ref>}}

In 2005, Penrose received a [[Doctorate Honoris Causa]] (Dr.h.c.) from each the [[Warsaw University]] (Poland)<ref>[https://www.fuw.edu.pl/~amt/laudatioe.pdf Laudatio by Andrzej Trautman to Roger_Penrose], website of the Faculty of Physics of [[Warsaw University]].</ref> and the [[Katholieke Universiteit Leuven]] (Belgium),<ref>[https://nieuws.kuleuven.be/nl/2012_en_vroeger/0405/07/eredoctor-sir-roger-penrose Eredoctor Sir Roger Penrose], website of [[KU Leuven]].</ref> and an honorary [[Doctor of Philosophy]] (PhD) degree from the [[Athens University of Economics and Business]] (Greece).<ref>[https://www.aueb.gr/en/content/honorary-doctors-philosophy-aueb Honorary Doctors of Philosophy at AUEB], website from [[Athens University of Economics and Business]].</ref> In 2006, he was conferred the honorary degree of [[Doctor of the University]] (DUniv) by the [[University of York]]<ref>[https://www.york.ac.uk/media/mathematics/honorarydrpresentations/Professor%20Sir%20Roger%20Penrose%20Presentation.pdf Presentation address] by Dr Bernard Kay to Professor Sir Roger Penrose</ref> and also won the [[Dirac Medal (UNSW)|Dirac Medal]] given by the [[University of New South Wales]] (Australia). In 2008, Penrose was awarded the [[Copley Medal]] of the Royal Society. He is also a Distinguished Supporter of [[Humanists UK]] and one of the patrons of the [[Oxford University Scientific Society]].

He was elected to the [[American Philosophical Society]] in 2011.<ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?creator=Roger+Penrose&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|access-date=2021-04-02|website=search.amphilsoc.org|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185556/https://search.amphilsoc.org/memhist/search?creator=Roger+Penrose&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|url-status=live}}</ref> The same year, he was also awarded the [[Fonseca Prize]] by the [[University of Santiago de Compostela]] (Spain).

In 2012, Penrose was awarded the Richard R. Ernst Medal by [[ETH Zürich]] (Switzerland) for his contributions to science and strengthening the connection between science and society. In that year, he was also awarded the honorary degree of [[Doctor of Science]] (DSc) by the [[Trinity College Dublin]] (Ireland)<ref>[https://www.tcd.ie/registrar/honorary-degrees/2011-12/ Registrar: Honorary Degrees 2011-2012], website by the [[Trinity College Dublin]].</ref> as well a honorary doctorate degree by the [[Igor Sikorsky Kyiv Polytechnic Institute]] (Ukraine).<ref>[https://kpi.ua/en/penrose-photo Sir Roger Penrose, one of the greatest scientists of our times, visited NTUU "KPI"], website of [[Kyiv Polytechnic Institute]].</ref>

In 2015, Penrose was awarded a [[Doctorate Honoris Causa]] (Dr.h.c.) by [[CINVESTAV]] (Mexico).<ref>{{Cite web|title=Roger Penrose Doctor Honoris Causa por el Cinvestav|url=http://micrositios.cinvestav.mx/avance/Publicaciones/ArtMID/4126/ArticleID/36/Roger-Penrose-Doctor-Honoris-Causa-por-el-Cinvestav|access-date=6 October 2020|website=cinvestav.mx|language=es-MX|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185555/http://micrositios.cinvestav.mx/avance/Publicaciones/ArtMID/4126/ArticleID/36/Roger-Penrose-Doctor-Honoris-Causa-por-el-Cinvestav|url-status=live}}</ref> In 2017, he was awarded the Commandino Medal at the [[Urbino University]] (Italy) for his contributions to the history of science. In that year as well, he was awarded an [[honorary Doctor of Science]] degree (DSc) by the [[University of Edinburgh]].<ref>[https://www.maths.ed.ac.uk/school-of-mathematics/news?nid=712 Sir Roger Penrose : Honorary Degree, Whittaker Colloquium and seminar], website of the [[University of Edinburgh]].</ref> In 2018, Penrose received an honorary degree from [[King's College London]].<ref>[https://www.kcl.ac.uk/news/professor-sir-roger-penrose-recognised-at-kings-honorary-degree-ceremony-1 Professor Sir Roger Penrose recognised at King's Honorary Degree Ceremony], website of [[King's College London]].</ref>

In 2020, Penrose was awarded one half of the [[Nobel Prize in Physics]] by the [[Royal Swedish Academy of Sciences]] for the discovery that black hole formation is a robust prediction of the general theory of relativity, a half-share also going to [[Reinhard Genzel]] and [[Andrea Ghez]] for the discovery of a [[Galactic Center#Supermassive black hole|supermassive compact object]] at the [[centre of our galaxy]].<ref name="Nobel Prize 2020"/> In the same year, he was also awarded the honorary degree of [[Doctor of Science]] (DSc) by the [[University of Cambridge]].<ref>[https://www.staff.admin.cam.ac.uk/features/nominations-for-honorary-degrees-2020 Nominations for honorary degrees 2020], website of the [[University of Cambridge]].</ref><ref>[https://www.cam.ac.uk/news/cambridge-confers-honorary-degrees Cambridge confers honorary degrees], website of the [[University of Cambridge]].</ref>

In 2025, Penrose received the Golden Plate Award of the [[Academy of Achievement|American Academy of Achievement]].<ref>{{cite web|title= Golden Plate Awardees of the American Academy of Achievement |website=www.achievement.org|publisher=American Academy of Achievement|url= https://achievement.org/our-history/golden-plate-awards/#science-exploration}}</ref>