Roger Penrose Explained

Sir Roger Penrose
Birth Date:	8 August 1931
Birth Place:	Colchester, Essex, England
Fields:	Mathematical physics, tessellations
Education:	University College London (BSc) St John's College, Cambridge (PhD)
Thesis Title:	Tensor Methods in Algebraic Geometry
Thesis Url:	https://idiscover.lib.cam.ac.uk/permalink/f/t9gok8/44CAM_ALMA21428192330003606
Thesis Year:	1958
Doctoral Advisor:	John A. Todd
Academic Advisors:	W. V. D. Hodge
Spouse:
Children:	4
Relatives:	Lionel Penrose (father), Roland Penrose (uncle), Jonathan Penrose (brother), Oliver Penrose (brother), Shirley Hodgson (sister), Antony Penrose (cousin)

Sir Roger Penrose, (born 8 August 1931) is a British mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics.^[1] He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge, and University College London.^{[2] [3] [4]}

Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems,^[5] and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity".^{[6] [7]}

Early life and education

Born in Colchester, Essex, Roger Penrose is a son of physician Margaret (née Leathes) and psychiatrist and geneticist Lionel Penrose. His paternal grandparents were J. Doyle Penrose, an Irish-born artist, and The Hon. Elizabeth Josephine Peckover, daughter of Alexander Peckover, 1st Baron Peckover; his maternal grandparents were physiologist John Beresford Leathes and Sonia Marie Natanson, a Russian Jew.^{[8] [9] [10]} His uncle was artist Sir Roland Penrose, whose son with American photographer Lee Miller is Antony Penrose.^{[11] [12]} Penrose is the brother of physicist Oliver Penrose, of geneticist Shirley Hodgson and of chess Grandmaster Jonathan Penrose.^{[13] [14]} Their stepfather was the mathematician and computer scientist Max Newman.

Penrose spent World War II as a child in Canada where his father worked in London, Ontario.^[15] Penrose studied at University College School. He then attended University College London, where he obtained a BSc degree with First Class Honours in mathematics in 1952.^[16]

In 1955, while a doctoral student, Penrose reintroduced the E. H. Moore generalised matrix inverse, also known as the Moore–Penrose inverse,^[17] after it had been reinvented by Arne Bjerhammar in 1951.^[18] Having started research under the professor of geometry and astronomy, Sir W. V. D. Hodge, Penrose received his PhD in algebraic geometry at St John's College, Cambridge in 1958, with his thesis titled "Tensor Methods in Algebraic Geometry"^[19] supervised by algebraist and geometer John A. Todd.^[20] He devised and popularised the Penrose triangle in the 1950s in collaboration with his father, 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.^{[21] [22]} Escher's Waterfall and Ascending and Descending were in turn inspired by Penrose.^[23]

thumb|right|The Penrose triangleAs reviewer Manjit Kumar puts it:

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 1961–63 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.^[24] He later held visiting positions at Yeshiva University, Princeton and Cornell during 1966–67 and 1969.

In 1964, while a reader at Birkbeck College, London, (and having had his attention drawn from pure mathematics to astrophysics by the cosmologist Dennis Sciama, then at Cambridge)^[13] in the words of Kip Thorne of Caltech, "Roger Penrose revolutionised the mathematical tools that we use to analyse the properties of spacetime".^{[25] [26]} 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.^[27] 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 epoch-making paper "Gravitational Collapse and Space-Time Singularities"^[28] (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 most famous student, Stephen Hawking.^{[29] [30] [31]}

thumb|300px|right|Predicted view from outside the event horizon of a black hole lit by a thin accretion discIt was in the local context of gravitational collapse that the contribution of Penrose was most decisive, starting with his 1969 cosmic censorship conjecture,^[32] 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.^{[33] [34]}

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 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.^[35] 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.^{[36] [37]}

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).^{[38] [39]}

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. In 1984, such patterns were observed in the arrangement of atoms in quasicrystals.^[40] Another noteworthy contribution is his 1971 invention of spin networks, which later came to form the geometry of spacetime in loop quantum gravity.^[41] He was influential in popularizing what are commonly known as Penrose diagrams (causal diagrams).^[42]

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.^[43] His doctoral students have included, among others, Andrew Hodges,^[44] Lane Hughston, Richard Jozsa, Claude LeBrun, John McNamara, Tristan Needham, Tim Poston, Asghar Qadir, and Richard S. Ward.

In 2004, Penrose released , a 1,099-page comprehensive guide to the Laws of Physics that includes an explanation of his own theory. The Penrose Interpretation predicts the relationship between quantum mechanics and general relativity, and proposes that a quantum state remains in superposition until the difference of space-time curvature attains a significant level.^{[45] [46]}

Penrose is the Francis and Helen Pentz Distinguished Visiting Professor of Physics and Mathematics at Pennsylvania State University.^[47]

An earlier universe

In 2010, Penrose reported possible evidence, based on concentric circles found in Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background sky, of an earlier universe existing before the Big Bang of our own present universe.^[48] He mentions this evidence in the epilogue of his 2010 book Cycles of Time,^[49] 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.^{[50] [51]} 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.^[52] 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.^[53]

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. 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.^[54] 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.^{[55] [56]} Alternatively, one can use the Einstein–Maxwell–Dirac equations.^[57]

Consciousness

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.^[58] 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).^[59] Penrose uses a variant of Turing's halting theorem to demonstrate that a system can be deterministic without being algorithmic. (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.)^{[60] [61]}

Penrose believes that such deterministic yet non-algorithmic processes may come into play in the quantum mechanical 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.^[62] This contrasts with supporters of 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. These claims were originally espoused by the philosopher John Lucas of Merton College, Oxford.^[63]

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.^[64] 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."^[65]

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.^[66]

Penrose and Hameroff have argued that consciousness is the result of quantum gravity effects in microtubules, which they dubbed Orch-OR (orchestrated objective reduction). Max Tegmark, in a paper in Physical Review E,^[67] 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 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'".^[68] 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.^[68]

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^[69] supports the hypothesis of 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.^[70]

Publications

His popular publications include:

• The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics (1989)^[71]
• Shadows of the Mind: A Search for the Missing Science of Consciousness (1994)^[72]
• (2004)^[73]
• Cycles of Time: An Extraordinary New View of the Universe (2010)^[74]
• Fashion, Faith, and Fantasy in the New Physics of the Universe (2016)^[75]

His co-authored publications include:

• The Nature of Space and Time (with Stephen Hawking) (1996)^[76]
• The Large, the Small and the Human Mind (with Abner Shimony, Nancy Cartwright, and Stephen Hawking) (1997)^[77]
• White Mars: The Mind Set Free (with Brian Aldiss) (1999)^[78]

His academic books include:

• Techniques of Differential Topology in Relativity (1972,)
• Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (with Wolfgang Rindler, 1987) (paperback)
• Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler, 1988) (reprint), (paperback)

His forewords to other books include:

• Foreword to "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.^[79]
• Foreword to 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.^[80]
• Foreword to "A Computable Universe" by Hector Zenil. Published by World Scientific Publishing Co in December 2012.^[81]
• Foreword to Quantum Aspects of Life by Derek Abbott, Paul C. W. Davies, and Arun K. Pati. Published by Imperial College Press in 2008.^[82]
• Foreword to Fearful Symmetry by Anthony Zee's. Published by Princeton University Press in 2007.^[83]

Awards and honours

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 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 and Prize of the British Institute of Physics. He was also made an Honorary Fellow of the Institute of Physics (HonFInstP).^[84] 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. 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.^[85] In the same year, he was also awarded an honorary degree of Doctor of Science (DSc) by the University of Bath,^[86] and became a member of Polish Academy of Sciences. In 1998, he was elected Foreign Associate of the United States National Academy of Sciences.^[87] In 2000, he was appointed a Member of the Order of Merit (OM).^[88]

In 2004, he was awarded the De Morgan Medal by the London Mathematical Society for his wide and original contributions to mathematical physics.^[89] To quote the citation from the society:

In 2005, Penrose received an Doctorate Honoris Causa (Dr.h.c.) from each the Warsaw University (Poland)^[90] and the Katholieke Universiteit Leuven (Belgium).^[91] In 2006, he was conferred the honorary degree of Doctor of the University (DUniv) by the University of York^[92] and also won the 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.^[93] 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)^[94] as well a Honorary Doctorate degree by the Igor Sikorsky Kyiv Polytechnic Institute (Ukraine).^[95]

In 2015 Penrose was awarded an Doctorate Honoris Causa (Dr.h.c.) by CINVESTAV (Mexico).^[96]

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.^[97]

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 supermassive compact object at the centre of our galaxy.^[6] In the same year, he was also awarded the honorary degree of Doctor of Science (DSc) by the University of Cambridge.^{[98] [99]}

Personal life

Penrose's first marriage was to American Joan Isabel Penrose (née Wedge), whom he married in 1959. They had three sons.^{[100] [101]} Penrose is now married to Vanessa Thomas, director of Academic Development at Cokethorpe School and former head of mathematics at Abingdon School.^{[102] [103]} They have one son.^{[104] [102]}

Religious views

During an interview with BBC Radio 4 on 25 September 2010, Penrose stated, "I'm not a believer myself. I don't believe in established religions of any kind."^[105] He regards himself as an agnostic.^[106] In the 1991 film A Brief History of Time, he also said, "I think I would say that the universe has a purpose, it's not somehow just there by chance … some people, I think, take the view that the universe is just there and it runs along—it's a bit like it just sort of computes, and we happen somehow by accident to find ourselves in this thing. But 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."^[107]

Penrose is a patron of Humanists UK.^[108]

See also

• List of things named after Roger Penrose

External links

• Awake in the Universe – Penrose debates how creativity, the most elusive of faculties, has helped us unlock the country of the mind and the mysteries of the cosmos with Bonnie Greer.
  • – Penrose was one of the principal interviewees in a BBC documentary about the mathematics of infinity directed by David Malone
• Penrose's new theory "Aeons Before the Big Bang?":
  • Original 2005 lecture: "Before the Big Bang? A new perspective on the Weyl curvature hypothesis" (Isaac Newton Institute for Mathematical Sciences, Cambridge, 11 November 2005).
  • Original publication: "Before the Big Bang: an outrageous new perspective and its implications for particle physics". Proceedings of EPAC 2006. Edinburgh. 2759–2762 (cf. also Hill, C.D. & Nurowski, P. (2007) "On Penrose's 'Before the Big Bang' ideas". Ithaca)
  • Revised 2009 lecture: "Aeons Before the Big Bang?" (Georgia Institute of Technology, Center for Relativistic Astrophysics)
    • Roger Penrose on The Forum
  • Hilary Putnam's review of Penrose's 'Shadows of the Mind' claiming that Penrose's use of Godel's Incompleteness Theorem is fallacious
    • Penrose Tiling found in Islamic Architecture
• Two theories for the formation of quasicrystals resembling Penrose tilings
• Tegmark . Max . Max Tegmark . 2000 . The importance of quantum decoherence in brain processes . Physical Review E . 61 . 4. 4194–4206 . 10.1103/physreve.61.4194. 11088215 . quant-ph/9907009 . 2000PhRvE..61.4194T . 17140058 .
  • "Biological feasibility of quantum states in the brain" – (a disputation of Tegmark's result by Hagan, Hameroff, and Tuszyński)
    • Tegmarks's rejoinder to Hagan et al.
• – D. Trull about Penrose's lawsuit concerning the use of his Penrose tilings on toilet paper
• Roger Penrose: A Knight on the tiles (Plus Magazine)
• Penrose's Gifford Lecture biography
• Quantum-Mind
• Audio: Roger Penrose in conversation on the BBC World Service discussion show
• Roger Penrose speaking about Hawking's new book on Premier Christian Radio
• "The Cyclic Universe – A conversation with Roger Penrose", Ideas Roadshow, 2013
• Forbidden crystal symmetry in mathematics and architecture, filmed event at the Royal Institution, October 2013
• Oxford Mathematics Interviews: "Extra Time: Professor Sir Roger Penrose in conversation with Andrew Hodges." These two films explore the development of Sir Roger Penrose's thought over more than 60 years, ending with his most recent theories and predictions. 51 min and 42 min. (Mathematical Institute)
• BBC Radio 4 – The Life Scientific – Roger Penrose on Black Holes – 22 November 2016 Sir Roger Penrose talks to Jim Al-Khalili about his trailblazing work on how black holes form, the problems with quantum physics and his portrayal in films about Stephen Hawking.
• The Penrose Institute Website
• A chess problem holds the key to human consciousness?, Chessbase

Notes and References

1. Web site: Roger Penrose | Biography, Books, Awards, & Facts. 7 March 2021. 7 March 2021. https://web.archive.org/web/20210307224416/https://www.britannica.com/biography/Roger-Penrose. live.
2. Web site: Oxford Mathematician Roger Penrose jointly wins the Nobel Prize in Physics University of Oxford. 7 October 2020. www.ox.ac.uk. 6 October 2020 . en. 9 October 2020. https://web.archive.org/web/20201009063427/https://www.ox.ac.uk/news/2020-10-06-oxford-mathematician-roger-penrose-jointly-wins-nobel-prize-physics. live.
3. Ferguson, Kitty (1991). Stephen Hawking: Quest for a Theory of Everything. Franklin Watts.
4. Book: Misner, Charles. Thorne, Kip S.. Wheeler, John Archibald. amp . Gravitation . San Francisco . W. H. Freeman . 1973 . 978-0-7167-0344-0. (See Box 34.2.)
5. Siegel. Matthew. 8 January 2008. Wolf Foundation Honors Hawking and Penrose for Work in Relativity. Physics Today. en. 42. 1. 97–98. 10.1063/1.2810893. 0031-9228. 7 October 2020. 7 December 2021. https://web.archive.org/web/20211207185551/https://physicstoday.scitation.org/doi/abs/10.1063/1.2810893. live.
6. Web site: The Nobel Prize in Physics 2020. 6 October 2020. NobelPrize.org. en-US. 6 October 2020. https://web.archive.org/web/20201006101114/https://www.nobelprize.org/prizes/physics/2020/summary/. live.
7. News: Overbye . Dennis . Taylor . Derrick Bryson . Nobel Prize in Physics Awarded to 3 Scientists for Work on Black Holes – The prize was awarded half to Roger Penrose for showing how black holes could form and half to Reinhard Genzel and Andrea Ghez for discovering a supermassive object at the Milky Way's center . 6 October 2020 . . 6 October 2020 . 6 October 2020 . https://web.archive.org/web/20201006102031/https://www.nytimes.com/2020/10/06/science/nobel-prize-physics.html . live .
8. Book: Brookfield, Tarah . Our voices must be heard : women and the vote in Ontario . 2018 . 978-0-7748-6019-2 . Vancouver . 1066070267.
9. Book: Brookfield, Tarah. Our Voices Must Be Heard: Women and the Vote in Ontario. 2018. UBC Press. 978-0-7748-6022-2. en. 6 October 2020. 7 December 2021. https://web.archive.org/web/20211207185547/https://books.google.com/books?id=LVlxDwAAQBAJ&pg=PA126. live.
10. John Beresford Leathes. 1864–1956. Rudolph Peters. Biographical Memoirs of Fellows of the Royal Society. 4. 185–191. 10.1098/rsbm.1958.0016. 1958. free.
11. News: Hall. Chris. 19 March 2016. Lee Miller, the mother I never knew. en-GB. The Guardian. 7 October 2020. 0261-3077. 12 November 2020. https://web.archive.org/web/20201112020323/https://www.theguardian.com/lifeandstyle/2016/mar/19/lee-miller-the-mother-i-never-knew. live.
12. Web site: Illustrated Mathematics. 7 October 2020. Farleys House and Gallery. en-GB. 11 October 2020. https://web.archive.org/web/20201011191035/https://www.farleyshouseandgallery.co.uk/exhibitions/illustrated-mathematics/. dead.
13. Web site: Roger Penrose – Biography. 7 October 2020. Maths History. en. 8 October 2020. https://web.archive.org/web/20201008122312/https://mathshistory.st-andrews.ac.uk/Biographies/Penrose/. live.
14. Web site: AP and TOI staff. Scientist of Jewish heritage among trio to win Nobel prize for black hole finds. 7 October 2020. www.timesofisrael.com. en-US. 6 October 2020. https://web.archive.org/web/20201006214254/https://www.timesofisrael.com/scientist-of-jewish-heritage-among-trio-to-win-nobel-prize-for-black-hole-finds/. live.
15. News: Ogilvie . Megan . Just Visiting: Sir Roger Penrose . 9 October 2020 . . 23 March 2009 . 7 January 2021 . https://web.archive.org/web/20210107212737/https://www.thestar.com/news/gta/2009/03/23/just_visiting_sir_roger_penrose.html . live .
16. https://www.ucl.ac.uk/news/2020/oct/ucl-alumnus-professor-sir-roger-penrose-awarded-nobel-prize UCL alumnus Professor Sir Roger Penrose awarded Nobel Prize
17. Penrose. R.. A generalized inverse for matrices. Mathematical Proceedings of the Cambridge Philosophical Society. 1955. 51. 3. 406–413. 10.1017/S0305004100030401. 1955PCPS...51..406P . free.
18. Web site: Zheng. Wenjie. The 100th anniversary of Moore–Penrose inverse and its role in statistics and machine learning. 7 October 2020. www.zhengwenjie.net. 11 October 2020. https://web.archive.org/web/20201011201508/http://www.zhengwenjie.net/pseudoinverse/. live.
19. PhD. Tensor Methods in Algebraic Geometry. Roger. Penrose. 71366928. cam.ac.uk. University of Cambridge. .
20. Web site: 6 October 2020. Roger Penrose wins 2020 Nobel Prize in Physics for discovery about black holes. 7 October 2020. University of Cambridge. en. 9 October 2020. https://web.archive.org/web/20201009072829/https://www.cam.ac.uk/research/news/roger-penrose-wins-2020-nobel-prize-in-physics-for-discovery-about-black-holes. live.
21. Web site: Welch. Chris. 23 March 2012. 'Frustro' typeface applies the Penrose impossible triangle concept to words. 7 October 2020. The Verge. en. 26 January 2021. https://web.archive.org/web/20210126162258/https://www.theverge.com/2012/3/23/2898025/frustro-typeface-matrzi-hegedus-penrose-triangle. live.
22. Book: Baggini, Julian. Philosophy: All That Matters. 2012. John Murray Press. 978-1-4441-5585-3. en. 12 October 2020. 7 December 2021. https://web.archive.org/web/20211207185548/https://books.google.com/books?id=rws0AgAAQBAJ&q=roger+penrose+%22penrose+triangle%22+%22impossibility+in+its+purest+form%22&pg=PT21. live.
23. Web site: 21 May 2013. Ascending and Descending by M.C. Escher – Facts about the Painting. 7 October 2020. Totally History. en-US. 29 June 2020. https://web.archive.org/web/20200629065147/http://totallyhistory.com/ascending-and-descending/. live.
24. Web site: Professor Sir Roger Penrose awarded the 2020 Nobel Prize in Physics. 7 October 2020. King's College London. en-EN. 22 October 2020. https://web.archive.org/web/20201022121930/https://www.kcl.ac.uk/news/professor-sir-roger-penrose-awarded-the-2020-nobel-prize-in-physics. live.
25. Web site: 12 March 2019. The second Cambridge Cutting Edge Lecture: Professor Sir Roger Penrose. 7 October 2020. Cambridge Society of Paris. en-GB. 8 October 2020. https://web.archive.org/web/20201008185043/https://cambridgesocietyofparis.com/event/cambridge-cutting-edge-lecture-professor-sir-roger-penrose/. live.
26. Book: Thorne. Kip. Black Holes and Time Warps: Einstein's Outrageous Legacy. Thorne. Kip S.. Hawking. Stephen. 1994. W. W. Norton & Company. 978-0-393-31276-8. en. 12 October 2020. 3 February 2021. https://web.archive.org/web/20210203044944/https://books.google.com/books?id=GzlrW6kytdoC&q=roger+penrose+kip+thorne+mathematical+tools+spacetime&pg=PA465. live.
27. Ellis. George F. R.. Penrose. Sir Roger. 1 January 2010. Dennis William Sciama. 18 November 1926 – 19 December 1999. Biographical Memoirs of Fellows of the Royal Society. en. 56. 401–422. 10.1098/rsbm.2009.0023. 73035217. 0080-4606. free.
28. Penrose. Roger. Gravitational Collapse and Space-Time Singularities. Physical Review Letters. January 1965. 14. 3. 57–59. 10.1103/PhysRevLett.14.57. 1965PhRvL..14...57P .
29. Web site: Clark. Stuart. A brief history of Stephen Hawking: A legacy of paradox. 7 October 2020. New Scientist. en-US. 5 October 2020. https://web.archive.org/web/20201005145715/https://www.newscientist.com/article/2053929-a-brief-history-of-stephen-hawking-a-legacy-of-paradox/. live.
30. Web site: Roger Penrose. 7 October 2020. New Scientist. en-US. 11 October 2020. https://web.archive.org/web/20201011180710/https://www.newscientist.com/people/roger-penrose/. live.
31. Web site: Wolchover. Natalie. Physicists Debate Hawking's Idea That the Universe Had No Beginning. 7 October 2020. Quanta Magazine. 6 June 2019. en. 5 October 2020. https://web.archive.org/web/20201005235915/https://www.quantamagazine.org/physicists-debate-hawkings-idea-that-the-universe-had-no-beginning-20190606/. live.
32. Fernandez. Rodrigo L.. 21 July 2020. Cosmic Censorship Conjecture violation: A semiclassical approach. gr-qc. 2007.10601.
33. 1979ApJ...229...46K Page 46. 7 October 2020. The Astrophysical Journal. 1979ApJ...229...46K. Kafatos. M.. Leiter. D.. 1979. 229. 46. 10.1086/156928. 7 December 2021. https://web.archive.org/web/20211207185549/https://adsabs.harvard.edu/full/1979ApJ...229...46K. live.
34. Web site: Penrose process. 7 October 2020. Oxford Reference. en. 2 February 2021. https://web.archive.org/web/20210202201151/https://www.oxfordreference.com/view/10.1093/oi/authority.20110810105604640. live.
35. R. Penrose . Singularities and Time-Asymmetry . General Relativity: An Einstein Centenary Survey . S. W. Hawking . W. Israel . Cambridge University Press . 1979 . 581–638.
36. James . Terrell . 1959 . Invisibility of the Lorentz Contraction . . 4. 1041–1045 . 10.1103/PhysRev.116.1041 . 116 . 1959PhRv..116.1041T .
37. 10.1017/S0305004100033776 . Roger . Penrose . 1959 . The Apparent Shape of a Relativistically Moving Sphere . Proceedings of the Cambridge Philosophical Society . 55 . 1. 137–139 . 1959PCPS...55..137P . 123023118 .
38. Web site: New Horizons in Twistor Theory Mathematical Institute. 7 October 2020. www.maths.ox.ac.uk. 8 October 2020. https://web.archive.org/web/20201008153713/http://www.maths.ox.ac.uk/groups/mathematical-physics/events/twistors50. live.
39. Book: Huggett . S. A. . An Introduction to Twistor Theory . Tod . K. P. . 1994-07-21 . Cambridge University Press . 978-0-521-45157-4 . 2nd . 1. 10.1017/cbo9780511624018 .
40. 10.1073/pnas.93.25.14267 . Paul . Steinhardt . New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings . . 93 . 25. 14267–14270 . 1996 . 8962037 . 34472 . 1996PNAS...9314267S . free .
41. Web site: Penrose on Spin Networks. 7 October 2020. math.ucr.edu. 12 October 2020. https://web.archive.org/web/20201012031549/https://math.ucr.edu/home/baez/penrose/. live.
42. Web site: Penrose diagrams. 7 October 2020. jila.colorado.edu. en. 11 November 2020. https://web.archive.org/web/20201111203436/https://jila.colorado.edu/~ajsh/insidebh/penrose.html. live.
43. Web site: Roger Penrose at Rice, 1983–87. Rice History Corner. 22 May 2013. 29 January 2014. 17 June 2016. https://web.archive.org/web/20160617233239/https://ricehistorycorner.com/2013/05/22/roger-penrose-at-rice-1983-87/. live.
44. PhD. Birkbeck, University of London. The Description of Mass within the Theory of Twistors. Andrew Philip. Hodges. 1975. . london.ac.uk. 500473477.
45. Web site: 'The Road to Reality': A Really Long History of Time . George . Johnson . 27 February 2005 . The New York Times . 3 April 2017 . 3 January 2021 . 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 . live .
46. Web site: If an Electron Can Be in Two Places at Once, Why Can't You? . 27 October 2008 . https://web.archive.org/web/20121101130211/http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=0&-C= . 1 November 2012.
47. Web site: Dr. Roger Penrose at Penn State University. 9 July 2007. dead. https://web.archive.org/web/20080416131322/http://www.phys.psu.edu/people/display/index.html?person_id=233&mode=contact.. 16 April 2008. dmy-all.
48. Gurzadyan . V.G. . Penrose . R. . Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity". volume "v1 . 2010 . 1011.3706 . astro-ph.CO.
49. Roger Penrose, Cycles of Time, Vintage; Reprint edition (1 May 2012)
50. Stoica. Ovidiu-Cristinel. November 2013. On the Weyl Curvature Hypothesis. Annals of Physics. 338. 186–194. 10.1016/j.aop.2013.08.002. 1203.3382. 2013AnPhy.338..186S. 119329306.
51. R. Penrose. 1979. W. Israel. Singularities and Time-Asymmetry. Cambridge University Press. 581–638. General Relativity: An Einstein Centenary Survey. S. W. Hawking.
52. Web site: 21 August 2018. New evidence for cyclic universe claimed by Roger Penrose and colleagues. 7 October 2020. Physics World. en-GB. 1 November 2020. https://web.archive.org/web/20201101015848/https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/. live.
53. Web site: New evidence for cyclic universe claimed by Roger Penrose and colleagues. 21 August 2018. 7 October 2020. 1 November 2020. https://web.archive.org/web/20201101015848/https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/. live.
54. Book: Penrose, Roger. Fashion, Faith, and Fantasy in the New Physics of the Universe. 5 September 2017. Princeton University Press. 978-0-691-17853-0. en. 12 October 2020. 7 December 2021. https://web.archive.org/web/20211207185551/https://books.google.com/books?id=9XKYDwAAQBAJ&q=roger+penrose+%22change+of+coordinate%22&pg=PA55. live.
55. Kiefer. Claus. 13 August 2013. Conceptual Problems in Quantum Gravity and Quantum Cosmology. ISRN Mathematical Physics. 2013. 1–17. 10.1155/2013/509316. en. free. 1401.3578.
56. Vaas . Rüdiger . --> The Inverted Big-Bang . 2004 . physics/0407071.
57. Web site: Finster . F. . Smoller . J.A. . Yau . S.-T. . The Einstein–Dirac–Maxwell Equations – Black Hole Solutions . 7 October 2020 . 7 October 2020 . https://web.archive.org/web/20201007132312/https://cds.cern.ch/record/403056/files/9910030.pdf . live .
58. News: Ferris. Timothy. 19 November 1989. HOW THE BRAIN WORKS, MAYBE (Published 1989). en-US. The New York Times. 7 October 2020. 0362-4331. 19 November 2021. https://web.archive.org/web/20211119091901/https://www.nytimes.com/1989/11/19/books/how-the-brain-works-maybe.html. live.
59. Web site: Stork. David G.. 29 October 1989. 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.). 7 October 2020. Los Angeles Times. en-US. 7 December 2021. https://web.archive.org/web/20211207185551/https://www.latimes.com/archives/la-xpm-1989-10-29-bk-90-story.html. live.
60. Book: Penrose, Roger. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. 28 April 2016. Oxford University Press. 978-0-19-255007-1. en. 12 October 2020. 7 December 2021. https://web.archive.org/web/20211207185551/https://books.google.com/books?id=JF4vDwAAQBAJ&q=turing+halting. live.
61. Web site: 20th WCP: Computational Complexity and Philosophical Dualism. 7 October 2020. www.bu.edu. 13 October 2020. https://web.archive.org/web/20201013092220/https://www.bu.edu/wcp/Papers/Cogn/CognTeix.htm. live.
62. Book: Penrose, Roger. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. 2016. Oxford University Press. 978-0-19-878492-0. en. 7 December 2021. 19 November 2021. https://web.archive.org/web/20211119091917/https://books.google.com/books?id=X28sDwAAQBAJ&q=G%C3%B6del%27s+incompleteness+theorem. live.
63. Web site: In Memoriam: John Lucas. 7 October 2020. www.philosophy.ox.ac.uk. en. 9 October 2020. https://web.archive.org/web/20201009111739/https://www.philosophy.ox.ac.uk/article/in-memoriam-john-lucas. live.
64. Criticism of the Lucas/Penrose argument that intelligence can not be entirely algorithmic:
    • MindPapers: 6.1b. Godelian arguments
    • References for Criticisms of the Gödelian Argument
    • Boolos, George, et al. 1990. An Open Peer Commentary on The Emperor's New Mind. Behavioral and Brain Sciences 13 (4) 655.
    • Davis, Martin 1993. How subtle is Gödel's theorem? More on Roger Penrose. Behavioral and Brain Sciences, 16, 611–612. Online version at Davis' faculty page at http://cs.nyu.edu/cs/faculty/davism/
    • Solomon Feferman . Feferman . Solomon . 1996 . 10.1.1.130.7027 . Penrose's Gödelian argument . . 2 . 21–32 .
    • 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, 173–181. Reprinted in Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science:In Recognition of Professor Andrzej Grzegorczyk (2008), p. 173
    • LaForte . Geoffrey . Hayes . Patrick J. . Ford . Kenneth M. . 1998 . Why Gödel's Theorem Cannot Refute Computationalism . Artificial Intelligence . 104 . 1–2. 265–286 . 10.1016/s0004-3702(98)00052-6 . free .
    • Lewis, David K. 1969. Lucas against mechanism . Philosophy 44 231–233.
    • Putnam, Hilary 1995. Review of Shadows of the Mind. In Bulletin of the American Mathematical Society 32, 370–373 (also see Putnam's less technical criticisms in his The New York Times review)

    Sources that indicate Penrose's argument is generally rejected:

    • Bringsford, S. and Xiao, H. 2000. A Refutation of Penrose's Gödelian Case Against Artificial Intelligence . 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 Web site: King's College London – Department of Mathematics . 22 October 2010 . dead . https://web.archive.org/web/20010125011300/http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html . 25 January 2001 . 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 On the Outside Looking In: A Caution about Conservativeness (published in Kurt Gödel: Essays for his Centennial, with the following comments found on pp. 131–132) 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. The Four Sons of Penrose , 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, pp. 125–138.
65. Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991.
66. Web site: Can Quantum Physics Explain Consciousness? One Scientist Thinks It Might. 7 October 2020. Discover Magazine. en. 3 October 2020. https://web.archive.org/web/20201003024544/https://www.discovermagazine.com/the-sciences/can-quantum-physics-explain-consciousness-one-scientist-thinks-it-might. live.
67. Tegmark . Max . 2000 . The importance of quantum decoherence in brain processes . . 61 . 4. 4194–4206 . 10.1103/physreve.61.4194. 11088215 . quant-ph/9907009 . 2000PhRvE..61.4194T . 17140058 .
68. Book: Tetlow , Philip . The Web's Awake: An Introduction to the Field of Web Science and the Concept of Web Life. John Wiley & Sons. Hoboken, New Jersey. 2007. 978-0-470-13794-9. 166. 5 October 2020. 7 December 2021. https://web.archive.org/web/20211207185552/https://books.google.com/books?id=3mPI9rUuhJ8C&q=penrose+. live.
69. Web site: Anirban Bandyopadhyay . 22 February 2014 . 10 March 2014 . https://web.archive.org/web/20140310053951/http://www.researchgate.net/profile/Anirban_Bandyopadhyay/ . live .
70. S. Hameroff. R. Penrose. Consciousness in the universe: A review of the 'Orch OR' theory. Physics of Life Reviews. 2014. 11. 1. 39–78. 24070914. 10.1016/j.plrev.2013.08.002. 2014PhLRv..11...39H . free.
71. Book: Penrose, Roger. The Emperor's New Mind. 1989. en. 7 October 2020. 7 December 2021. https://web.archive.org/web/20211207185554/https://books.google.com/books?id=_ibtvQEACAAJ. live.
72. Book: Penrose, Roger. Shadows of the Mind: A Search for the Missing Science of Consciousness. 1994. Oxford University Press. 978-0-19-510646-6. en. 12 October 2020. 7 December 2021. 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. live.
73. Book: Penrose, Roger. The Road to Reality: A Complete Guide to the Laws of the Universe. 31 March 2016. Random House. 978-1-4464-1820-8. en. 7 October 2020. 7 December 2021. https://web.archive.org/web/20211207185554/https://books.google.com/books?id=VWTNCwAAQBAJ. live.
74. Book: Penrose, Roger. Cycles of Time: An Extraordinary New View of the Universe. 6 September 2011. Knopf Doubleday Publishing Group. 978-0-307-59674-1. en.
75. Book: Penrose, Roger. Fashion, Faith, and Fantasy in the New Physics of the Universe. 5 September 2017. Princeton University Press. 978-0-691-17853-0. en.
76. Book: Hawking. Stephen W.. The Nature of Space and Time. Penrose. Roger. 1996. Princeton University Press. 978-0-691-03791-2. en. 7 October 2020. 7 December 2021. https://web.archive.org/web/20211207185837/https://books.google.com/books?id=8RatQgAACAAJ. live.
77. Book: Penrose. Roger. The Large, the Small and the Human Mind. Shimony. Abner. Cartwright. Nancy. Hawking. Stephen. 28 April 2000. Cambridge University Press. 978-0-521-78572-3. en.
78. Book: Aldiss. Brian W.. White Mars; or, The Mind Set Free: A 21st-Century Utopia. Penrose. Roger. 19 May 2015. Open Road Media. 978-1-5040-1028-3. en.
79. Book: Wuppuluri. Shyam. The Map and the Territory: Exploring the Foundations of Science, Thought and Reality. Doria. Francisco Antonio. 13 February 2018. Springer. 978-3-319-72478-2. en.
80. Book: Weston-smith, Meg. Beating The Odds: The Life And Times Of E A Milne. 16 April 2013. World Scientific. 978-1-84816-943-2. en. 12 October 2020. 26 January 2021. 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. live.
81. Book: Zenil, Hector. A Computable Universe: Understanding and Exploring Nature as Computation. 2013. World Scientific. 978-981-4374-30-9. en.
82. Book: Abbott. Derek. Quantum Aspects Of Life. Davies. Paul C. W.. Pati. Arun Kumar. 12 September 2008. World Scientific. 978-1-908978-73-8. en. 12 October 2020. 26 January 2021. https://web.archive.org/web/20210126162257/https://books.google.com/books?id=C1y7CgAAQBAJ&q=Quantum+Aspects+of+Life+roger+penrose. live.
83. Book: Zee, A.. Fearful Symmetry: The Search for Beauty in Modern Physics. 1 October 2015. Princeton University Press. 978-1-4008-7450-7. en. 12 October 2020. 26 January 2021. https://web.archive.org/web/20210126162300/https://books.google.com/books?id=Xq1mCgAAQBAJ&q=fearful+symmetry+roger+penrose. live.
84. Web site: Our Honorary Fellows . . 26 December 2022.
85. Web site: Supplement 53696,10 June 1994, London Gazette. The Gazette. 16 August 2015. 29 April 2016. https://web.archive.org/web/20160429222205/https://www.thegazette.co.uk/London/issue/53696/supplement/2. live.
86. Web site: Honorary Graduates 1989 to present . . 18 February 2012 . 19 December 2015 . https://web.archive.org/web/20151219000643/http://www.bath.ac.uk/ceremonies/hongrads/ . dead .
87. Web site: Sir Roger Penrose Person. 7 October 2020. Fetzer Franklin Fund. de-DE. 24 September 2020. https://web.archive.org/web/20200924081714/https://www.fetzer-franklin-fund.org/media/sir-roger-penrose/. live.
88. News: Appointments to the Order of Merit. The Royal Family . January 2012. 25 October 2020. en. 29 September 2020. https://web.archive.org/web/20200929015241/https://www.royal.uk/appointments-order-merit. live. Fisher . Connie .
89. 8 August 2018. Roger Penrose. EN. 10.1063/PT.6.6.20180808a. Physics Today. 8 . free.
90. https://www.fuw.edu.pl/~amt/laudatioe.pdf Laudatio by Andrzej Trautman to Roger_Penrose
91. https://nieuws.kuleuven.be/nl/2012_en_vroeger/0405/07/eredoctor-sir-roger-penrose Eredoctor Sir Roger Penrose
92. https://www.york.ac.uk/media/mathematics/honorarydrpresentations/Professor%20Sir%20Roger%20Penrose%20Presentation.pdf Presentation address
93. Web site: APS Member History. 2021-04-02. search.amphilsoc.org. 7 December 2021. 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. live.
94. https://www.tcd.ie/registrar/honorary-degrees/2011-12/ Registrar: Honorary Degrees 2011-2012
95. https://kpi.ua/en/penrose-photo Sir Roger Penrose, one of the greatest scientists of our times, visited NTUU "KPI"
96. Web site: Roger Penrose Doctor Honoris Causa por el Cinvestav. 6 October 2020. cinvestav.mx. es-MX. 7 December 2021. https://web.archive.org/web/20211207185555/http://micrositios.cinvestav.mx/avance/Publicaciones/ArtMID/4126/ArticleID/36/Roger-Penrose-Doctor-Honoris-Causa-por-el-Cinvestav. live.
97. https://www.maths.ed.ac.uk/school-of-mathematics/news?nid=712 Sir Roger Penrose : Honorary Degree, Whittaker Colloquium and seminar
98. https://www.staff.admin.cam.ac.uk/features/nominations-for-honorary-degrees-2020 Nominations for honorary degrees 2020
99. https://www.cam.ac.uk/news/cambridge-confers-honorary-degrees Cambridge confers honorary degrees
100. Web site: 27 October 2019. 7+ Out of This World Facts About Physicist Sir Roger Penrose. 7 October 2020. interestingengineering.com. en-US. 8 October 2020. https://web.archive.org/web/20201008211346/https://interestingengineering.com/who-is-sir-roger-penrose-and-why-is-he-famous. live.
101. Web site: 18 August 2014. Roger Penrose. 7 October 2020. The Gifford Lectures. en. 11 October 2020. https://web.archive.org/web/20201011220956/https://www.giffordlectures.org/lecturers/roger-penrose. live.
102. Web site: The Peter & Patricia Gruber Foundation, St. Thomas US Virgin Islands – Grants and International Awards . Gruberprizes.org . 8 August 1931 . 13 August 2012 . 30 October 2012 . https://web.archive.org/web/20121030084628/http://www.gruberprizes.org/SelectingRecipients/SelectionAdvisoryBoard_Bio.php?id=4 . live .
103. Web site: Vanessa Penrose . Abingdon School . 6 July 2012 . 13 August 2012 . https://web.archive.org/web/20120327144417/http://www.abingdon.org.uk/vanessa_penrose/ . 27 March 2012 . dead .
104. Web site: Interview with Sir Roger Penrose. European Mathematical Society Newsletter March 2001. European Mathematical Information Service.
105. News: Big Bang follows Big Bang follows Big Bang. 1 December 2010. BBC News. 25 September 2010. 30 November 2010. https://web.archive.org/web/20101130152519/http://news.bbc.co.uk/today/hi/today/newsid_9032000/9032626.stm. live.
106. Web site: Thomas Fink . A singular mind: Roger Penrose on his Nobel Prize . The Spectator . 18 May 2021 . December 19, 2020 . 18 May 2021 . https://web.archive.org/web/20210518203446/https://www.spectator.co.uk/article/a-singular-mind-roger-penrose-on-his-nobel-prize . live .
107. See A Brief History of Time (1991) film script – springfieldspringfield.co.uk
108. Web site: Patrons . Humanists UK . 6 October 2020 . 5 October 2020 . https://web.archive.org/web/20201005083241/https://humanism.org.uk/about/our-people/patrons/ . live .