Roger Penrose

Sir

Roger Penrose

OM FRS

Penrose in 2011

Born|  (1931-08-08) 8 August 1931 (age 94)

Colchester, Essex, England

Education|

* University College London (BSc)
* St John's College, Cambridge (PhD)

Known for|

List of contributions

* Moore–Penrose inverse
* Twistor theory
* Spin network
* Abstract index notation
* Black hole bomb
* Geometry of spacetime
* Cosmic censorship
* Illumination problem
* Weyl curvature hypothesis
* Penrose inequalities
* Penrose interpretation of quantum mechanics
* Diósi–Penrose model
* Newman–Penrose formalism
* GHP formalism
* Penrose diagram
* Penrose inequality
* Penrose process
* Penrose tiling
* Penrose triangle
* Penrose stairs
* Penrose–Hawking singularity theorems
* Penrose graphical notation
* Penrose transform
* Penrose–Terrell effect
* pp-wave spacetime
* Schrödinger–Newton equations
* Orch-OR/Penrose–Lucas argument
* FELIX experiment
* Trapped surface
* Andromeda paradox
* Conformal cyclic cosmology

Spouse(s)|

* Joan Isabel Wedge
(m. 1959, divorced)

* Vanessa Thomas (m. 1988)

[1]

Children| 4
Awards|

List of awards

* Adams Prize (1966)
* Heineman Prize (1971)
* Fellow of the Royal Society (1972)
* Eddington Medal (1975)
* Royal Medal (1985)
* Wolf Prize (1988)
* Dirac Medal (IOP) (1989)
* Albert Einstein Medal (1990)
* Naylor Prize and Lectureship (1991)
* Knight Bachelor (1994)
* James Scott Prize Lectureship (1997–2000)
* Karl Schwarzschild Medal (2000)
* De Morgan Medal (2004)
* Dalton Medal (2005)
* Copley Medal (2008)
* Fonseca Prize (2011)
* Nobel Prize in Physics (2020)

Scientific career
Fields| Mathematical physics, tessellations
Institutions|

* Cornell University
* Bedford College, London
* Princeton University
* Rice University
* Syracuse University
* King's College, London
* Birkbeck, University of London
* Wadham College, Oxford
* Polish Academy of Sciences

Thesis| Tensor Methods in Algebraic Geometry (1957)
Doctoral advisor| John A. Todd
Other academic advisors| W. V. D. Hodge
Doctoral students|

* Andrew Hodges
* Lane Hughston
* Richard Jozsa
* Claude LeBrun
* John McNamara
* Tristan Needham
* Tim Poston
* Asghar Qadir
* Richard S. Ward

Sir Roger Penrose (born 8 August 1931)[1] is an English mathematician, mathematical physicist, and philosopher of science.[2] He is Emeritus Rouse Ball Professor of Mathematics at 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.[3][4][5] He shared the 1988 Wolf Prize in Physics with Stephen Hawking for the Penrose–Hawking singularity theorems,[6] and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity".[7][8][9][lower-alpha 1] He proposed the Penrose triangle and corresponded with M. C. Escher, influencing his Waterfall and Ascending and Descending. Penrose's eponymous aperiodic tiling presaged the discovery of quasicrystals by Dan Shechtman.

Penrose won the Royal Society Science Books Prize for The Emperor's New Mind (1989), which outlines his views on physics and consciousness. He followed it with The Road to Reality (2004), billed as "A Complete Guide to the Laws of the Universe".

## Contents

* 1 Early life and education
* 2 Research and career
* 2.1 An earlier universe
* 2.2 Consciousness
* 2.3 Publications
* 2.4 Awards and honours
* 3 Personal life
* 3.1 Religious views
* 4 See also
* 5 Notes
* 6 References
* 7 Further reading
* 8 External links

## Early life and education

Born in Colchester, Essex, Roger Penrose is a son of Margaret (née Leathes), a physician, and Lionel Penrose, a psychiatrist and geneticist.[lower-alpha 2][10] His paternal grandparents were J. Doyle Penrose, an Irish-born painter, and the Hon. Elizabeth Josephine Peckover, daughter of Alexander Peckover, 1st Baron Peckover; his maternal grandparents were John Beresford Leathes, a physiologist, and Sonia Marie Natanson, a concert pianist.[11][12][13][14] His uncle was the artist Sir Roland Penrose, whose son with the American photographer Lee Miller is Antony Penrose.[15][16] Penrose is the brother of the physicist Oliver Penrose, of the geneticist Shirley Hodgson and of the chess grandmaster Jonathan Penrose.[17][18] Their stepfather was the mathematician and computer scientist Max Newman. He found inspiration in George Gamow's Mr. Tompkins books: "I remember reading (or being read) the Tompkins stories as a quite young child, and I'm sure that their magic was responsible, to a very considerable extent, for the great excitement that fundamental physics has held for me for the rest of my life."[19]

Penrose spent the Second World War as a child in Canada where his father worked in London, Ontario, at the Ontario Hospital[20] and Western University.[21] Penrose studied at University College School.[1] He then attended University College London, where he obtained a BSc degree with First Class Honours in mathematics in 1952.[17][22]

In 1955, while a doctoral student, Penrose reintroduced the E. H. Moore generalised matrix inverse, also known as the Moore–Penrose inverse,[23] after it had been reinvented by Arne Bjerhammar in 1951.[24] Having started research under the professor of geometry and astronomy W. V. D. Hodge, Penrose received his PhD in algebraic geometry at St John's College, Cambridge, in 1957, with his thesis titled "Tensor Methods in Algebraic Geometry"[25] supervised by the algebraist and geometer John A. Todd.[26] 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.[27][28] Escher's Waterfall and Ascending and Descending were in turn inspired by Penrose.[29]

The Penrose triangle

As the reviewer Manjit Kumar puts it:

> As a student in 1954, Penrose was attending a conference in Amsterdam when by chance he came across an exhibition of Escher's work. Soon he was trying to conjure up impossible figures of his own and discovered the tribar – a triangle that looks like a real, solid three-dimensional object, but isn't. Together with his father, a physicist and mathematician, Penrose went on to design a staircase that simultaneously loops up and down. An article followed and a copy was sent to Escher. Completing a cyclical flow of creativity, the Dutch master of geometrical illusions was inspired to produce his two masterpieces.[30]

## 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 University 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.[31] He later held visiting positions at Yeshiva University, Princeton and Cornell University during 1966–67 and 1969.

Dennis Sciama drew his attention from pure mathematics to astrophysics.[17] In 1964, while a reader at Birkbeck College, Penrose, per Kip Thorne of the California Institute of Technology, "revolutionised the mathematical tools that we use to analyse the properties of spacetime".[32][33] 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.[34] 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"[35] (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.[36][37][38]

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,[39] 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.[40][41][42]

Following up his "weak cosmic censorship hypothesis", Penrose went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis".

Penrose in 1978

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.[43] 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.[44][45]

A Penrose tiling

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).[46][47]

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.[48] Another noteworthy contribution is his 1971 invention of spin networks, which later came to form the geometry of spacetime in loop quantum gravity.[49] He was influential in popularising what are commonly known as Penrose diagrams (causal diagrams).[50]

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.[51] His doctoral students have included, among others, Andrew Hodges,[52] Lane Hughston, Richard Jozsa, Claude LeBrun, John McNamara, Tristan Needham, Tim Poston,[53] 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 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.[54][55]

Penrose is the Francis and Helen Pentz Distinguished Visiting professor of Physics and Mathematics at Pennsylvania State University.[56]

### An earlier universe

WMAP image of the (extremely tiny) anisotropies in the cosmic background radiation

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 the present universe.[57] He mentions this evidence in the epilogue of his 2010 book Cycles of Time,[58] 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.[59][60] 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.[61] 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.[62]

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.[40] 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.[63] 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.[64][65] Alternatively, one can use the Einstein–Maxwell–Dirac equations.[66]

### Consciousness

Penrose at a conference c. 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.[67] 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).[68] 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.)[69][70]

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.[71] 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.[71] These claims were originally espoused by the philosopher John Lucas of Merton College, Oxford.[72]

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 choose different aspects of the argument to attack.[73] Marvin Minsky, a leading proponent of artificial intelligence, was particularly critical, writing 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."[74]

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.[75]

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,[76] 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 billion. The paper's reception 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'".[77] 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 a minority view in scientific circles, citing Minsky's criticisms and quoting the 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.[77]

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[78] 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.[79]

He appeared on In Our Time discussing consciousness with Ted Honderich.[80]

### Publications

A copy of The Emperor's New Mind Italian edition signed by Penrose, 2005

His popular publications include:

* The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics (1989)[81]
* Shadows of the Mind: A Search for the Missing Science of Consciousness (1994)[82]
* The Road to Reality: A Complete Guide to the Laws of the Universe (2004)[83]
* Cycles of Time: An Extraordinary New View of the Universe (2010)[84]
* Fashion, Faith, and Fantasy in the New Physics of the Universe (2016)[85]

His co-authored publications include:

* The Nature of Space and Time (with Stephen Hawking) (1996)[86]
* The Large, the Small and the Human Mind (with Abner Shimony, Nancy Cartwright, and Stephen Hawking) (1997)[87]
* White Mars: The Mind Set Free (with Brian Aldiss) (1999)[88]

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 "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.[89]
* 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.[90]
* Foreword to "A Computable Universe" by Hector Zenil. Published by World Scientific Publishing Co in December 2012.[91]
* Foreword to Quantum Aspects of Life by Derek Abbott, Paul C. W. Davies, and Arun K. Pati. Published by Imperial College Press in 2008.[92]
* Foreword to Fearful Symmetry by Anthony Zee. Published by Princeton University Press in 2007.[93]

### Awards and honours

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 Fellow of the Royal Society (FRS) in 1972. In 1975 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 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).[94] 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,[95] and an honorary degree from the University of Surrey in 1993.[96] 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.[97] In the same year, he was also awarded an honorary degree of Doctor of Science (DSc) by the University of Bath,[98] and became a member of Polish Academy of Sciences. Penrose was awarded honorary degrees from the University of London in 1995,[99] the University of Glasgow (Doctor of Science, DSc)[100] and University of Essex, both in 1996,[101] from the University of St Andrews in 1997,[99] and the Visva-Bharati University of Santiniketan (India)[99] and Open University (Doctor of the University, DUniv),[102] both in 1998. In 1998 he was elected Foreign Associate of the United States National Academy of Sciences.[103] In 2000 he was appointed a Member of the Order of Merit (OM).[104] He was awarded an honorary doctorate from the University of Southampton in 2002.[105]

In 2004 Penrose was awarded an honorary Doctor of Science (DSc) degree from the University of Waterloo (Ontario, Canada)[106][107] and was awarded the De Morgan Medal by the London Mathematical Society for his wide and original contributions to mathematical physics.[108] To quote the citation from the society:

> His deep work on General Relativity has been a major factor in our understanding of black holes. His development of Twistor Theory has produced a beautiful and productive approach to the classical equations of mathematical physics. His tilings of the plane underlie the newly discovered quasi-crystals.[109]

In 2005 Penrose received a Doctorate Honoris Causa (Dr.h.c.) from each the Warsaw University (Poland)[110] and the Katholieke Universiteit Leuven (Belgium),[111] and an honorary Doctor of Philosophy (PhD) degree from the Athens University of Economics and Business (Greece).[112] In 2005 he was also awarded the Manchester Literary and Philosophical Society Dalton Medal.[113] In 2006 he was conferred the honorary degree of Doctor of the University (DUniv) by the University of York[114] 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.[115] 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)[116] as well an honorary doctorate degree by the Igor Sikorsky Kyiv Polytechnic Institute (Ukraine).[117]

In 2015 Penrose was awarded a Doctorate Honoris Causa (Dr.h.c.) by CINVESTAV (Mexico).[118] 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.[119] In 2018 Penrose received an honorary degree from King's College London.[120]

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.[8] In the same year, he was also awarded the honorary degree of Doctor of Science (DSc) by the University of Cambridge.[121][122]

In 2025 Penrose received the Golden Plate Award of the American Academy of Achievement.[123]

## Personal life

Penrose's first marriage was to Joan Isabel Penrose (born Wedge), an American he married in 1959. They had three sons.[124][125] Penrose is now married to Vanessa Thomas, director of Academic Development at Cokethorpe School in Witney, Oxfordshire, and former head of mathematics at Abingdon School.[126][127] They have one son.[128][126]

### 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."[129] He regards himself as an agnostic.[130] 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."[131]

Penrose is a patron of Humanists UK.[132]

## See also

* List of things named after Roger Penrose

## Notes

1. ↑ The 2020 Nobel Prize was also awarded jointly to Reinhard Genzel and Andrea Ghez "for the discovery of a supermassive compact object at the centre of our galaxy".
2. ↑ Penrose and his father shared mathematical concepts with Dutch graphic artist M. C. Escher, which were incorporated into a lot of pieces, including Waterfall, which is based on the 'Penrose triangle', and Ascending and Descending.

## References

1. ↑ 1.0 1.1 1.2 Anon (2017). ",". Who's Who (online Oxford University Press ed.). A & C Black, an imprint of Bloomsbury Publishing plc. doi:10.1093/ww/9780199540884.013.U30531. https://www.ukwhoswho.com/view/article/oupww/whoswho/U30531. (subscription or UK public library membership required)
2. ↑ "Roger Penrose | Biography, Books, Awards, & Facts". https://www.britannica.com/biography/Roger-Penrose.
3. ↑ "Oxford Mathematician Roger Penrose jointly wins the Nobel Prize in Physics | University of Oxford" (in en). 6 October 2020. https://www.ox.ac.uk/news/2020-10-06-oxford-mathematician-roger-penrose-jointly-wins-nobel-prize-physics.
4. ↑ Ferguson, Kitty (1991). Stephen Hawking: Quest for a Theory of Everything. Franklin Watts. ISBN 0-553-29895-X.
5. ↑ Misner, Charles; Thorne, Kip S.; Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 978-0-7167-0344-0. (See Box 34.2.)
6. ↑ Siegel, Matthew (8 January 2008). "Wolf Foundation Honors Hawking and Penrose for Work in Relativity" (in en). Physics Today 42 (1): 97–98. doi:10.1063/1.2810893. ISSN 0031-9228. https://physicstoday.scitation.org/doi/abs/10.1063/1.2810893. Retrieved 7 October 2020.
7. ↑ O'Connor, John J.; Robertson, Edmund F., "Roger Penrose", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Penrose.html .
8. ↑ 8.0 8.1 "The Nobel Prize in Physics 2020" (in en-US). https://www.nobelprize.org/prizes/physics/2020/summary/.
9. ↑ Overbye, Dennis; Taylor, Derrick Bryson (6 October 2020). "Nobel Prize in Physics Awarded to 3 Scientists for Work on Black Holes". The New York Times. https://www.nytimes.com/2020/10/06/science/nobel-prize-physics.html.
10. ↑ "Roger Penrose - Biographical". The Nobel Foundation. https://www.nobelprize.org/prizes/physics/2020/penrose/biographical/.
11. ↑ Brookfield, Tarah (2018). Our voices must be heard : women and the vote in Ontario. Vancouver: UBC Press. ISBN 978-0-7748-6019-2. OCLC 1066070267.
12. ↑ Brookfield, Tarah (2018) (in en). Our Voices Must Be Heard: Women and the Vote in Ontario. UBC Press. ISBN 978-0-7748-6022-2. https://books.google.com/books?id=LVlxDwAAQBAJ&pg=PA126. Retrieved 6 October 2020.
13. ↑ Peters, Rudolph (1958). "John Beresford Leathes. 1864–1956". Biographical Memoirs of Fellows of the Royal Society 4 (4): 185–191. doi:10.1098/rsbm.1958.0016.
14. ↑ Roger Penrose. Cycles of Time: Is It Possible to Discern the Previous Universe Through the Big Bang? on YouTube
15. ↑ Hall, Chris (19 March 2016). "Lee Miller, the mother I never knew" (in en-GB). The Guardian. ISSN 0261-3077. https://www.theguardian.com/lifeandstyle/2016/mar/19/lee-miller-the-mother-i-never-knew.
16. ↑ "Illustrated Mathematics" (in en-GB). https://www.farleyshouseandgallery.co.uk/exhibitions/illustrated-mathematics/.
17. ↑ 17.0 17.1 17.2 "Roger Penrose – Biography" (in en). https://mathshistory.st-andrews.ac.uk/Biographies/Penrose/.
18. ↑ AP and TOI staff (6 October 2020). "Scientist of Jewish heritage among trio to win Nobel prize for black hole finds" (in en-US). ISSN 0040-7909. https://www.timesofisrael.com/scientist-of-jewish-heritage-among-trio-to-win-nobel-prize-for-black-hole-finds/.
19. ↑ Introduction by Roger Penrose Gamow, George. Mr Tompkins in Paperback.
20. ↑ Ogilvie, Megan (23 March 2009). "Just Visiting: Sir Roger Penrose". Toronto Star. https://www.thestar.com/news/gta/2009/03/23/just_visiting_sir_roger_penrose.html.
21. ↑ "Lionel Sharples Penrose". https://history.rcp.ac.uk/inspiring-physicians/lionel-sharples-penrose.
22. ↑ UCL alumnus Professor Sir Roger Penrose awarded Nobel Prize, website of the University College London.
23. ↑ Penrose, R. (1955). "A generalized inverse for matrices". Mathematical Proceedings of the Cambridge Philosophical Society 51 (3): 406–413. doi:10.1017/S0305004100030401. Bibcode: 1955PCPS...51..406P.
24. ↑ Zheng, Wenjie. "The 100th anniversary of Moore–Penrose inverse and its role in statistics and machine learning". http://www.zhengwenjie.net/pseudoinverse/.
25. ↑ Penrose, Roger. Tensor Methods in Algebraic Geometry. cam.ac.uk (PhD thesis). University of Cambridge. OCLC 71366928. ProQuest 301242962.
26. ↑ "Roger Penrose wins 2020 Nobel Prize in Physics for discovery about black holes" (in en). 6 October 2020. https://www.cam.ac.uk/research/news/roger-penrose-wins-2020-nobel-prize-in-physics-for-discovery-about-black-holes.
27. ↑ Welch, Chris (23 March 2012). "'Frustro' typeface applies the Penrose impossible triangle concept to words" (in en). https://www.theverge.com/2012/3/23/2898025/frustro-typeface-matrzi-hegedus-penrose-triangle.
28. ↑ Baggini, Julian (2012) (in en). Philosophy: All That Matters. John Murray Press. ISBN 978-1-4441-5585-3. https://books.google.com/books?id=rws0AgAAQBAJ&q=roger+penrose+"penrose+triangle"+"impossibility+in+its+purest+form"&pg=PT21. Retrieved 12 October 2020.
29. ↑ "Ascending and Descending by M.C. Escher – Facts about the Painting" (in en-US). 21 May 2013. http://totallyhistory.com/ascending-and-descending/.
30. ↑ Kumar, Manjit (15 October 2010). "Cycles of Time: An Extraordinary New View of the Universe by Roger Penrose – review". The Guardian. https://www.theguardian.com/books/2010/oct/16/cycles-time-roger-penrose-review.
31. ↑ "Professor Sir Roger Penrose awarded the 2020 Nobel Prize in Physics" (in en-EN). https://www.kcl.ac.uk/news/professor-sir-roger-penrose-awarded-the-2020-nobel-prize-in-physics.
32. ↑ "The second Cambridge Cutting Edge Lecture: Professor Sir Roger Penrose" (in en-GB). 12 March 2019. https://cambridgesocietyofparis.com/event/cambridge-cutting-edge-lecture-professor-sir-roger-penrose/.
33. ↑ Thorne, Kip S.; Hawking, Stephen W. (1994) (in en). Black Holes and Time Warps: Einstein's Outrageous Legacy. W. W. Norton & Company. ISBN 978-0-393-31276-8. https://books.google.com/books?id=GzlrW6kytdoC&q=roger+penrose+kip+thorne+mathematical+tools+spacetime&pg=PA465. Retrieved 12 October 2020.
34. ↑ Ellis, George F. R.; Penrose, Sir Roger (1 January 2010). "Dennis William Sciama. 18 November 1926 – 19 December 1999" (in en). Biographical Memoirs of Fellows of the Royal Society 56: 401–422. doi:10.1098/rsbm.2009.0023. ISSN 0080-4606.
35. ↑ Penrose, Roger (January 1965). "Gravitational Collapse and Space-Time Singularities". Physical Review Letters 14 (3): 57–59. doi:10.1103/PhysRevLett.14.57. Bibcode: 1965PhRvL..14...57P. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.14.57.
36. ↑ Clark, Stuart. "A brief history of Stephen Hawking: A legacy of paradox" (in en-US). https://www.newscientist.com/article/2053929-a-brief-history-of-stephen-hawking-a-legacy-of-paradox/.
37. ↑ "Roger Penrose" (in en-US). https://www.newscientist.com/people/roger-penrose/.
38. ↑ Wolchover, Natalie (6 June 2019). "Physicists Debate Hawking's Idea That the Universe Had No Beginning" (in en). https://www.quantamagazine.org/physicists-debate-hawkings-idea-that-the-universe-had-no-beginning-20190606/.
39. ↑ Fernandez, Rodrigo L. (21 July 2020). "Cosmic Censorship Conjecture violation: A semiclassical approach". arXiv:2007.10601 [gr-qc].
40. ↑ 40.0 40.1 Curiel, Erik (2020), Zalta, Edward N., ed., Singularities and Black Holes (Summer 2020 ed.), Metaphysics Research Lab, Stanford University, https://plato.stanford.edu/archives/sum2020/entries/spacetime-singularities/, retrieved 7 October 2020
41. ↑ Kafatos, M.; Leiter, D. (1979). "1979ApJ...229...46K Page 46". The Astrophysical Journal 229: 46. doi:10.1086/156928. Bibcode: 1979ApJ...229...46K. http://adsabs.harvard.edu/full/1979ApJ...229...46K. Retrieved 7 October 2020.
42. ↑ "Penrose process" (in en). https://www.oxfordreference.com/view/10.1093/oi/authority.20110810105604640.
43. ↑ Penrose, Roger (1979). "Singularities and Time-Asymmetry". in Hawking, Stephen W.. Cambridge University Press. pp. 581–638.
44. ↑ Terrell, James (1959). "Invisibility of the Lorentz Contraction". Physical Review 116 (4): 1041–1045. doi:10.1103/PhysRev.116.1041. Bibcode: 1959PhRv..116.1041T.
45. ↑ Penrose, Roger (1959). "The Apparent Shape of a Relativistically Moving Sphere". Proceedings of the Cambridge Philosophical Society 55 (1): 137–139. doi:10.1017/S0305004100033776. Bibcode: 1959PCPS...55..137P.
46. ↑ "New Horizons in Twistor Theory | Mathematical Institute". http://www.maths.ox.ac.uk/groups/mathematical-physics/events/twistors50.
47. ↑ Huggett, S. A.; Tod, K. P. (21 July 1994). An Introduction to Twistor Theory (2nd ed.). Cambridge University Press. pp. 1. doi:10.1017/cbo9780511624018. ISBN 978-0-521-45157-4. http://dx.doi.org/10.1017/cbo9780511624018.
48. ↑ Steinhardt, Paul (1996). "New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings". PNAS 93 (25): 14267–14270. doi:10.1073/pnas.93.25.14267. PMID 8962037. Bibcode: 1996PNAS...9314267S.
49. ↑ "Penrose on Spin Networks". https://math.ucr.edu/home/baez/penrose/.
50. ↑ "Penrose diagrams" (in en). https://jila.colorado.edu/~ajsh/insidebh/penrose.html.
51. ↑ "Roger Penrose at Rice, 1983–87". Rice History Corner. 22 May 2013. http://ricehistorycorner.com/2013/05/22/roger-penrose-at-rice-1983-87/.
52. ↑ Hodges, Andrew Philip (1975). The Description of Mass within the Theory of Twistors. london.ac.uk (PhD thesis). Birkbeck, University of London. OCLC 500473477. EThOS uk.bl.ethos.459296.
53. ↑ Roger Penrose at the Mathematics Genealogy Project
54. ↑ Johnson, George (27 February 2005). "'The Road to Reality': A Really Long History of Time". The New York Times. https://www.nytimes.com/2005/02/27/books/review/the-road-to-reality-a-really-long-history-of-time.html?_r=0.
55. ↑ Folger, Tim. "If an Electron Can Be in Two Places at Once, Why Can't You?". Discover. http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=0&-C=.
56. ↑ "Dr. Roger Penrose at Penn State University". http://www.phys.psu.edu/people/display/index.html?person_id=233&mode=contact..
57. ↑ Gurzadyan, V. G.; Penrose, R. (2010). "Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity". volume "v1". arXiv:1011.3706 [astro-ph.CO].
58. ↑ Roger Penrose, Cycles of Time, Vintage; Reprint edition (1 May 2012)
59. ↑ Stoica, Ovidiu-Cristinel (November 2013). "On the Weyl Curvature Hypothesis". Annals of Physics 338: 186–194. doi:10.1016/j.aop.2013.08.002. Bibcode: 2013AnPhy.338..186S.
60. ↑ Penrose, Roger (1979). "Singularities and Time-Asymmetry". in Hawking, S. W.. Cambridge University Press. pp. 581–638.
61. ↑ "New evidence for cyclic universe claimed by Roger Penrose and colleagues" (in en-GB). 21 August 2018. https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/.
62. ↑ "New evidence for cyclic universe claimed by Roger Penrose and colleagues". 21 August 2018. https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/.
63. ↑ Penrose, Roger (5 September 2017) (in en). Fashion, Faith, and Fantasy in the New Physics of the Universe. Princeton University Press. ISBN 978-0-691-17853-0. https://books.google.com/books?id=9XKYDwAAQBAJ&q=roger+penrose+"change+of+coordinate"&pg=PA55. Retrieved 12 October 2020.
64. ↑ Kiefer, Claus (13 August 2013). "Conceptual Problems in Quantum Gravity and Quantum Cosmology" (in en). ISRN Mathematical Physics 2013: 1–17. doi:10.1155/2013/509316.
65. ↑ Vaas, Rüdiger (2004). "The Inverted Big-Bang". arXiv:physics/0407071.
66. ↑ Finster, F.; Smoller, J. A.; Yau, S. -T.. "The Einstein–Dirac–Maxwell Equations – Black Hole Solutions". https://cds.cern.ch/record/403056/files/9910030.pdf.
67. ↑ Ferris, Timothy (19 November 1989). "HOW THE BRAIN WORKS, MAYBE (Published 1989)" (in en-US). The New York Times. ISSN 0362-4331. https://www.nytimes.com/1989/11/19/books/how-the-brain-works-maybe.html.
68. ↑ 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.)" (in en-US). https://www.latimes.com/archives/la-xpm-1989-10-29-bk-90-story.html.
69. ↑ Penrose, Roger (28 April 2016) (in en). The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press. ISBN 978-0-19-255007-1. https://books.google.com/books?id=JF4vDwAAQBAJ&q=turing+halting. Retrieved 12 October 2020.
70. ↑ "20th WCP: Computational Complexity and Philosophical Dualism". https://www.bu.edu/wcp/Papers/Cogn/CognTeix.htm.
71. ↑ 71.0 71.1 Penrose, Roger (2016) (in en). The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press. ISBN 978-0-19-878492-0. https://books.google.com/books?id=X28sDwAAQBAJ&q=Gödel's+incompleteness+theorem. Retrieved 7 December 2021.
72. ↑ "In Memoriam: John Lucas" (in en). https://www.philosophy.ox.ac.uk/article/in-memoriam-john-lucas.
73. ↑ 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), p. 655.
* 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/. .
* Feferman, Solomon (1996). "Penrose's Gödelian argument". Psyche 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, pp. 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. doi:10.1016/s0004-3702(98)00052-6.
* Lewis, David K. 1969. Lucas against mechanism. . Philosophy 44, pp. 231–233.
* 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 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 "King's College London – Department of Mathematics". http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html. 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, Germany, pp. 125–138.
74. ↑ Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991.
75. ↑ "Can Quantum Physics Explain Consciousness? One Scientist Thinks It Might" (in en). https://www.discovermagazine.com/the-sciences/can-quantum-physics-explain-consciousness-one-scientist-thinks-it-might.
76. ↑ Tegmark, Max (2000). "The importance of quantum decoherence in brain processes". Physical Review E 61 (4): 4194–4206. doi:10.1103/physreve.61.4194. PMID 11088215. Bibcode: 2000PhRvE..61.4194T.
77. ↑ 77.0 77.1 Tetlow, Philip (2007). The Web's Awake: An Introduction to the Field of Web Science and the Concept of Web Life. Hoboken, New Jersey: John Wiley & Sons. p. 166. ISBN 978-0-470-13794-9. https://books.google.com/books?id=3mPI9rUuhJ8C&q=penrose . Retrieved 5 October 2020.
78. ↑ "Anirban Bandyopadhyay". https://www.researchgate.net/profile/Anirban_Bandyopadhyay.
79. ↑ Hameroff, S.; Penrose, R. (2014). "Consciousness in the universe: A review of the 'Orch OR' theory". Physics of Life Reviews 11 (1): 39–78. doi:10.1016/j.plrev.2013.08.002. PMID 24070914. Bibcode: 2014PhLRv..11...39H.
80. ↑ Bragg, Melvyn; Honderich, Ted; Penrose, Roger (November 25, 1999). "Consciousness". In Our Time. https://www.bbc.co.uk/programmes/p005464j.
81. ↑ Penrose, Roger (1989) (in en). The Emperor's New Mind. https://books.google.com/books?id=_ibtvQEACAAJ. Retrieved 7 October 2020.
82. ↑ Penrose, Roger (1994) (in en). Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press. ISBN 978-0-19-510646-6. https://books.google.com/books?id=gDbOAK89tmcC&q=Shadows+of+the+Mind:+A+Search+for+the+Missing+Science+of+Consciousness. Retrieved 12 October 2020.
83. ↑ Penrose, Roger (31 March 2016) (in en). The Road to Reality: A Complete Guide to the Laws of the Universe. Random House. ISBN 978-1-4464-1820-8. https://books.google.com/books?id=VWTNCwAAQBAJ. Retrieved 7 October 2020.
84. ↑ Penrose, Roger (6 September 2011) (in en). Cycles of Time: An Extraordinary New View of the Universe. Knopf Doubleday Publishing Group. ISBN 978-0-307-59674-1. https://books.google.com/books?id=gv8o1XydoCQC&q=Cycles+of+Time:+An+Extraordinary+New+View+of+the+Universe.
85. ↑ Penrose, Roger (5 September 2017) (in en). Fashion, Faith, and Fantasy in the New Physics of the Universe. Princeton University Press. ISBN 978-0-691-17853-0. https://books.google.com/books?id=9XKYDwAAQBAJ&q=Fashion,+Faith,+and+Fantasy+in+the+New+Physics+of+the+Universe.
86. ↑ Hawking, Stephen W.; Penrose, Roger (1996) (in en). The Nature of Space and Time. Princeton University Press. ISBN 978-0-691-03791-2. https://books.google.com/books?id=8RatQgAACAAJ. Retrieved 7 October 2020.
87. ↑ Penrose, Roger; Shimony, Abner; Cartwright, Nancy; Hawking, Stephen (28 April 2000) (in en). The Large, the Small and the Human Mind. Cambridge University Press. ISBN 978-0-521-78572-3. https://books.google.com/books?id=jWHqlijAjyMC&q=The+Large,+the+Small+and+the+Human+Mind.
88. ↑ Aldiss, Brian W.; Penrose, Roger (19 May 2015) (in en). White Mars; or, The Mind Set Free: A 21st-Century Utopia. Open Road Media. ISBN 978-1-5040-1028-3. https://books.google.com/books?id=K_-jBwAAQBAJ&q=White+Mars:+The+Mind+Set+Free(1999).
89. ↑ Wuppuluri, Shyam; Doria, Francisco Antonio (13 February 2018) (in en). The Map and the Territory: Exploring the Foundations of Science, Thought and Reality. Springer. ISBN 978-3-319-72478-2. https://books.google.com/books?id=mRBMDwAAQBAJ&q=“The+Map+and+the+Territory:+Exploring+the+foundations+of+science,+thought+and+reality+roger+penrose.
90. ↑ Weston-smith, Meg (16 April 2013) (in en). Beating The Odds: The Life And Times Of E A Milne. World Scientific. ISBN 978-1-84816-943-2. https://books.google.com/books?id=P826CgAAQBAJ&q=Beating+the+Odds:+The+Life+and+Times+of+E.+A.+Milne+roger+penrose&pg=PR3. Retrieved 12 October 2020.
91. ↑ Zenil, Hector (2013) (in en). A Computable Universe: Understanding and Exploring Nature as Computation. World Scientific. ISBN 978-981-4374-30-9. https://books.google.com/books?id=SGG6CgAAQBAJ&q="A+Computable+Universe"+roger+penrose.
92. ↑ Abbott, Derek; Davies, Paul C. W.; Pati, Arun Kumar (12 September 2008) (in en). Quantum Aspects Of Life. World Scientific. ISBN 978-1-908978-73-8. https://books.google.com/books?id=C1y7CgAAQBAJ&q=Quantum+Aspects+of+Life+roger+penrose. Retrieved 12 October 2020.
93. ↑ Zee, A. (1 October 2015) (in en). Fearful Symmetry: The Search for Beauty in Modern Physics. Princeton University Press. ISBN 978-1-4008-7450-7. https://books.google.com/books?id=Xq1mCgAAQBAJ&q=fearful+symmetry+roger+penrose. Retrieved 12 October 2020.
94. ↑ "Our Honorary Fellows". Institute of Physics. https://www.iop.org/about/awards/honorary-fellowship/our-honorary-fellows.
95. ↑ 1992 Fredericton Convocation: Penrose, Roger, website of the University of New Brunswick.
96. ↑ Honorary graduates, website of the University of Surrey.
97. ↑ "Supplement 53696,10 June 1994, London Gazette". https://www.thegazette.co.uk/London/issue/53696/supplement/2.
98. ↑ "Honorary Graduates 1989 to present". University of Bath. http://www.bath.ac.uk/ceremonies/hongrads/.
99. ↑ 99.0 99.1 99.2 Professor Sir Roger Penrose OM FRS, website of the Academia Europaea.
100. ↑ Who, Where and When: The History & Constitution of the University of Glasgow, website of The University of Glasgow.
101. ↑ Honorary graduates over the years, website of the University of Essex.
102. ↑ Honorary graduate cumulative website of Open University
103. ↑ "Sir Roger Penrose | Person" (in de-DE). https://www.fetzer-franklin-fund.org/media/sir-roger-penrose/.
104. ↑ Fisher, Connie (January 2012). "Appointments to the Order of Merit" (in en). The Royal Family. https://www.royal.uk/appointments-order-merit.
105. ↑ Nobel Prize winner Sir Roger Penrose congratulated by Southampton academics, website of the University of Southampton.
106. ↑ DAily bulletin September 21, 2004, website of the University of Waterloo.
107. ↑ Honorary degrees granted, website of the University of Waterloo.
108. ↑ "Roger Penrose" (in EN). Physics Today (8). 8 August 2018. doi:10.1063/PT.6.6.20180808a. Bibcode: 2018PhT..2018h4433..
109. ↑ "London Mathematical Society". http://www.lms.ac.uk/activities/prizes_com/citations04.html.
110. ↑ Laudatio by Andrzej Trautman to Roger_Penrose, website of the Faculty of Physics of Warsaw University.
111. ↑ Eredoctor Sir Roger Penrose, website of KU Leuven.
112. ↑ Honorary Doctors of Philosophy at AUEB, website from Athens University of Economics and Business.
113. ↑ Memoirs And Proceedings Of The Manchester Literary And Philosophical Society Volume 152 2013–14
114. ↑ Presentation address by Dr Bernard Kay to Professor Sir Roger Penrose
115. ↑ "APS Member History". https://search.amphilsoc.org/memhist/search?creator=Roger+Penrose&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced.
116. ↑ Registrar: Honorary Degrees 2011–2012, website by the Trinity College Dublin.
117. ↑ Sir Roger Penrose, one of the greatest scientists of our times, visited NTUU "KPI", website of Kyiv Polytechnic Institute.
118. ↑ "Roger Penrose Doctor Honoris Causa por el Cinvestav" (in es-MX). http://micrositios.cinvestav.mx/avance/Publicaciones/ArtMID/4126/ArticleID/36/Roger-Penrose-Doctor-Honoris-Causa-por-el-Cinvestav.
119. ↑ Sir Roger Penrose : Honorary Degree, Whittaker Colloquium and seminar, website of the University of Edinburgh.
120. ↑ Professor Sir Roger Penrose recognised at King's Honorary Degree Ceremony, website of King's College London.
121. ↑ Nominations for honorary degrees 2020, website of the University of Cambridge.
122. ↑ Cambridge confers honorary degrees, website of the University of Cambridge.
123. ↑ "Golden Plate Awardees of the American Academy of Achievement". American Academy of Achievement. https://achievement.org/our-history/golden-plate-awards/#science-exploration.
124. ↑ "7+ Out of This World Facts About Physicist Sir Roger Penrose" (in en-US). 27 October 2019. https://interestingengineering.com/who-is-sir-roger-penrose-and-why-is-he-famous.
125. ↑ "Roger Penrose" (in en). 18 August 2014. https://www.giffordlectures.org/lecturers/roger-penrose.
126. ↑ 126.0 126.1 "The Peter & Patricia Gruber Foundation, St. Thomas US Virgin Islands – Grants and International Awards". Gruberprizes.org. 8 August 1931. http://www.gruberprizes.org/SelectingRecipients/SelectionAdvisoryBoard_Bio.php?id=4.
127. ↑ "Vanessa Penrose". Abingdon School. 6 July 2012. http://www.abingdon.org.uk/vanessa_penrose/.
128. ↑ "Interview with Sir Roger Penrose". European Mathematical Society Newsletter March 2001. https://www.emis.de/newsletter/newsletter39.pdf#page=17.
129. ↑ "Big Bang follows Big Bang follows Big Bang". BBC News. 25 September 2010. https://news.bbc.co.uk/today/hi/today/newsid_9032000/9032626.stm.
130. ↑ "A singular mind: Roger Penrose on his Nobel Prize". 19 December 2020. https://www.spectator.co.uk/article/a-singular-mind-roger-penrose-on-his-nobel-prize.
131. ↑ See A Brief History of Time (1991) film script – springfieldspringfield.co.uk
132. ↑ "Patrons". https://humanism.org.uk/about/our-people/patrons/.

## Further reading

* Barss, Patchen (2024). The Impossible Man: Roger Penrose and the Cost of Genius. New York: Basic Books. ISBN 978-1-5416-0366-0.

## External links

| Scholia has a profile for Roger Penrose ().

|

* 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.
* Error in Template:Internet Archive author: Roger Penrose doesn't exist.
* Dangerous Knowledge on YouTube – 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)
* BBC interview on the new theory on YouTube
* Roger Penrose on The Forum
* Penrose on sidestepping reason on YouTube
* 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 (2000). "The importance of quantum decoherence in brain processes". Physical Review E 61 (4): 4194–4206. doi:10.1103/physreve.61.4194. PMID 11088215. Bibcode: 2000PhRvE..61.4194T.
* "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
* Miss nobel-id as parameter

* v
* t
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Works by Roger Penrose

Books|

* The Emperor's New Mind (1989)
* Shadows of the Mind (1994)
* The Road to Reality (2004)
* Cycles of Time (2010)
* Fashion, Faith, and Fantasy in the New Physics of the Universe (2016)

Coauthored books|

* The Nature of Space and Time (with Stephen Hawking) (1996)
* The Large, the Small and the Human Mind (with Abner Shimony, Nancy Cartwright and Stephen Hawking) (1997)
* White Mars or, The Mind Set Free (with Brian W. Aldiss) (1999)

Academic works|

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

Articles related to Roger Penrose

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Copley Medallists (2001–present)

* Jacques Miller (2001)
* John Pople (2002)
* John Gurdon (2003)
* Harry Kroto (2004)
* Paul Nurse (2005)
* Stephen Hawking (2006)
* Robert May (2007)
* Roger Penrose (2008)
* Martin Evans (2009)
* David Cox / Tomas Lindahl (2010)
* Dan McKenzie (2011)
* John E. Walker (2012)
* Andre Geim (2013)
* Alec Jeffreys (2014)
* Peter Higgs (2015)
* Richard Henderson (2016)
* Andrew Wiles (2017)
* Jeffrey I. Gordon (2018)
* John B. Goodenough (2019)

* v
* t
* e

Laureates of the Wolf Prize in Physics

1970s|

* Chien-Shiung Wu (1978)
* George Uhlenbeck / Giuseppe Occhialini (1979)

1980s|

* Michael Fisher / Leo Kadanoff / Kenneth G. Wilson (1980)
* Freeman Dyson / Gerardus 't Hooft / Victor Weisskopf (1981)
* Leon M. Lederman / Martin Lewis Perl (1982)
* Erwin Hahn / Peter Hirsch / Theodore Maiman (1983–84)
* Conyers Herring / Philippe Nozières (1984–85)
* Mitchell Feigenbaum / Albert J. Libchaber (1986)
* Herbert Friedman / Bruno Rossi / Riccardo Giacconi (1987)
* Roger Penrose / Stephen Hawking (1988)

1990s|

* Pierre-Gilles de Gennes / David J. Thouless (1990)
* Maurice Goldhaber / Valentine Telegdi (1991)
* Joseph H. Taylor Jr. (1992)
* Benoît Mandelbrot (1993)
* Vitaly Ginzburg / Yoichiro Nambu (1994–95)
* John Wheeler (1996–97)
* Yakir Aharonov / Michael Berry (1998)
* Dan Shechtman (1999)

2000s|

* Raymond Davis Jr. / Masatoshi Koshiba (2000)
* Bertrand Halperin / Anthony Leggett (2002–03)
* Robert Brout / François Englert / Peter Higgs (2004)
* Daniel Kleppner (2005)
* Albert Fert / Peter Grünberg (2006–07)

2010s|

* John F. Clauser / Alain Aspect / Anton Zeilinger (2010)
* Maximilian Haider / Harald Rose / Knut Urban (2011)
* Jacob Bekenstein (2012)
* Peter Zoller / Juan Ignacio Cirac (2013)
* James D. Bjorken / Robert P. Kirshner (2015)
* Yoseph Imry (2016)
* Michel Mayor / Didier Queloz (2017)
* Charles H. Bennett / Gilles Brassard (2018)

2020s|

* Rafi Bistritzer / Pablo Jarillo-Herrero / Allan H. MacDonald (2020)

* Agriculture
* Arts
* Chemistry
* Mathematics
* Medicine
* Physics

Template:De Morgan Medallists

* v
* t
* e

Relativity

Special
relativity|

| Background|

* Principle of relativity (Galilean relativity
* Galilean transformation)
* Special relativity
* Doubly special relativity

|

Fundamental
concepts|

* Frame of reference
* Speed of light
* Hyperbolic orthogonality
* Rapidity
* Maxwell's equations
* Proper length
* Proper time
* Relativistic mass

Formulation|

* Lorentz transformation

Phenomena|

* Time dilation
* Mass–energy equivalence
* Length contraction
* Relativity of simultaneity
* Relativistic Doppler effect
* Thomas precession
* Ladder paradox
* Twin paradox

Spacetime|

* Light cone
* World line
* Minkowski diagram
* Biquaternions
* Minkowski space

General
relativity|

| Background|

* Introduction
* Mathematical formulation

|

Fundamental
concepts|

* Equivalence principle
* Riemannian geometry
* Penrose diagram
* Geodesics
* Mach's principle

Formulation|

* ADM formalism
* BSSN formalism
* Einstein field equations
* Linearized gravity
* Post-Newtonian formalism
* Raychaudhuri equation
* Hamilton–Jacobi–Einstein equation
* Ernst equation

Phenomena|

* Black hole
* Event horizon
* Singularity
* Two-body problem

* Gravitational waves: astronomy
* detectors (LIGO and collaboration
* Virgo
* LISA Pathfinder
* GEO)
* Hulse–Taylor binary

* Other tests: precession of Mercury
* lensing
* redshift
* Shapiro delay
* frame-dragging / geodetic effect (Lense–Thirring precession)
* pulsar timing arrays

Advanced
theories|

* Brans–Dicke theory
* Kaluza–Klein
* Quantum gravity

Solutions|

* Cosmological: Friedmann–Lemaître–Robertson–Walker (Friedmann equations)
* Kasner
* BKL singularity
* Gödel
* Milne

* Spherical: Schwarzschild (interior
* Tolman–Oppenheimer–Volkoff equation)
* Reissner–Nordström
* Lemaître–Tolman

* Axisymmetric: Kerr (Kerr–Newman)
* Weyl−Lewis−Papapetrou
* Taub–NUT
* van Stockum dust
* discs

* Others: pp-wave
* Ozsváth–Schücking metric

Scientists|

* Poincaré
* Lorentz
* Einstein
* Hilbert
* Schwarzschild
* de Sitter
* Weyl
* Eddington
* Friedmann
* Lemaître
* Milne
* Robertson
* Chandrasekhar
* Zwicky
* Wheeler
* Choquet-Bruhat
* Kerr
* Zel'dovich
* Novikov
* Ehlers
* Geroch
* Penrose
* Hawking
* Taylor
* Hulse
* Bondi
* Misner
* Yau
* Thorne
* Weiss
* others

Categories|

Theory of relativity

* v
* t
* e

Laureates of the Nobel Prize in Physics

1901–1925|

* 1901: Röntgen
* 1902: Lorentz / Zeeman
* 1903: Becquerel / P. Curie / M. Curie
* 1904: Rayleigh
* 1905: Lenard
* 1906: J. J. Thomson
* 1907: Michelson
* 1908: Lippmann
* 1909: Marconi / Braun
* 1910: Van der Waals
* 1911: Wien
* 1912: Dalén
* 1913: Kamerlingh Onnes
* 1914: Laue
* 1915: W. L. Bragg / W. H. Bragg
* 1916
* 1917: Barkla
* 1918: Planck
* 1919: Stark
* 1920: Guillaume
* 1921: Einstein
* 1922: N. Bohr
* 1923: Millikan
* 1924: M. Siegbahn
* 1925: Franck / Hertz

1926–1950|

* 1926: Perrin
* 1927: Compton / C. Wilson
* 1928: O. Richardson
* 1929: De Broglie
* 1930: Raman
* 1931
* 1932: Heisenberg
* 1933: Schrödinger / Dirac
* 1934
* 1935: Chadwick
* 1936: Hess / C. D. Anderson
* 1937: Davisson / G. P. Thomson
* 1938: Fermi
* 1939: Lawrence
* 1940
* 1941
* 1942
* 1943: Stern
* 1944: Rabi
* 1945: Pauli
* 1946: Bridgman
* 1947: Appleton
* 1948: Blackett
* 1949: Yukawa
* 1950: Powell

1951–1975|

* 1951: Cockcroft / Walton
* 1952: Bloch / Purcell
* 1953: Zernike
* 1954: Born / Bothe
* 1955: Lamb / Kusch
* 1956: Shockley / Bardeen / Brattain
* 1957: C. N. Yang / T. D. Lee
* 1958: Cherenkov / Frank / Tamm
* 1959: Segrè / Chamberlain
* 1960: Glaser
* 1961: Hofstadter / Mössbauer
* 1962: Landau
* 1963: Wigner / Goeppert Mayer / Jensen
* 1964: Townes / Basov / Prokhorov
* 1965: Tomonaga / Schwinger / Feynman
* 1966: Kastler
* 1967: Bethe
* 1968: Alvarez
* 1969: Gell-Mann
* 1970: Alfvén / Néel
* 1971: Gabor
* 1972: Bardeen / Cooper / Schrieffer
* 1973: Esaki / Giaever / Josephson
* 1974: Ryle / Hewish
* 1975: A. Bohr / Mottelson / Rainwater

1976–2000|

* 1976: Richter / Ting
* 1977: P. W. Anderson / Mott / Van Vleck
* 1978: Kapitsa / Penzias / R. Wilson
* 1979: Glashow / Salam / Weinberg
* 1980: Cronin / Fitch
* 1981: Bloembergen / Schawlow / K. Siegbahn
* 1982: K. Wilson
* 1983: Chandrasekhar / Fowler
* 1984: Rubbia / Van der Meer
* 1985: von Klitzing
* 1986: Ruska / Binnig / Rohrer
* 1987: Bednorz / Müller
* 1988: Lederman / Schwartz / Steinberger
* 1989: Ramsey / Dehmelt / Paul
* 1990: Friedman / Kendall / R. Taylor
* 1991: de Gennes
* 1992: Charpak
* 1993: Hulse / J. Taylor
* 1994: Brockhouse / Shull
* 1995: Perl / Reines
* 1996: D. Lee / Osheroff / R. Richardson
* 1997: Chu / Cohen-Tannoudji / Phillips
* 1998: Laughlin / Störmer / Tsui
* 1999: 't Hooft / Veltman
* 2000: Alferov / Kroemer / Kilby

2001–
present|

* 2001: Cornell / Ketterle / Wieman
* 2002: Davis / Koshiba / Giacconi
* 2003: Abrikosov / Ginzburg / Leggett
* 2004: Gross / Politzer / Wilczek
* 2005: Glauber / Hall / Hänsch
* 2006: Mather / Smoot
* 2007: Fert / Grünberg
* 2008: Nambu / Kobayashi / Maskawa
* 2009: Kao / Boyle / Smith
* 2010: Geim / Novoselov
* 2011: Perlmutter / Riess / Schmidt
* 2012: Wineland / Haroche
* 2013: Englert / Higgs
* 2014: Akasaki / Amano / Nakamura
* 2015: Kajita / McDonald
* 2016: Thouless / Haldane / Kosterlitz
* 2017: Weiss / Barish / Thorne
* 2018: Ashkin / Mourou / Strickland
* 2019: Peebles / Mayor / Queloz

Template:2020 Nobel Prize winners

Template:Dalton Medallists

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