Roger Penrose

Last updated

Sir Roger Penrose
OM FRS HonFInstP
Roger Penrose at Festival della Scienza Oct 29 2011.jpg
Penrose in 2011
Born (1931-08-08) 8 August 1931 (age 93)
Colchester, Essex, England
Education
Known for
List of contributions 
Spouses
Joan Isabel Wedge
​
​
(m. 1959,divorced)​
Vanessa Thomas
​
(m. 1988)​
[1]
Children4
Relatives Lionel Penrose (father), Roland Penrose (uncle), Jonathan Penrose (brother), Oliver Penrose (brother), Shirley Hodgson (sister), Antony Penrose (cousin)
Awards
List of awards 
Scientific career
Fields Mathematical physics, tessellations
Institutions
Thesis Tensor Methods in Algebraic Geometry  (1957)
Doctoral advisor John A. Todd
Other academic advisors W. V. D. Hodge
Doctoral students

Sir Roger Penrose (born 8 August 1931) [1] is a British mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. [2] 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. [3] [4] [5]

Contents

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, [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] [10] [a]

Early life and education

Born in Colchester, Essex, Roger Penrose is a son of physician Margaret (née Leathes) and psychiatrist and geneticist Lionel Penrose. [b] 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. [11] [12] [13] [14] His uncle was artist Sir Roland Penrose, whose son with American photographer Lee Miller is Antony Penrose. [15] [16] Penrose is the brother of physicist Oliver Penrose, of geneticist Shirley Hodgson and of chess Grandmaster Jonathan Penrose. [17] [18] 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 at the Ontario Hospital and Western University. [19] [20] 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] [21]

In 1955, while a doctoral student, Penrose reintroduced the E. H. Moore generalised matrix inverse, also known as the Moore–Penrose inverse, [22] after it had been reinvented by Arne Bjerhammar in 1951. [23] 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 1957, with his thesis titled "Tensor Methods in Algebraic Geometry" [24] supervised by algebraist and geometer John A. Todd. [25] 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. [26] [27] Escher's Waterfall and Ascending and Descending were in turn inspired by Penrose. [28]

The Penrose triangle Penrose-dreieck.svg
The Penrose triangle

As 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. [29]

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. [30] 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) [17] in the words of Kip Thorne of Caltech, "Roger Penrose revolutionised the mathematical tools that we use to analyse the properties of spacetime". [31] [32] 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. [33] 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" [34] (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. [35] [36] [37]

Predicted view from outside the event horizon of a black hole lit by a thin accretion disc CNRSblackhole.jpg
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, [38] 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. [39] [40] [41]

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. [42] 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. [43] [44]

A Penrose tiling Penrose Tiling (Rhombi).svg
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). [45] [46]

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

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

Penrose is the Francis and Helen Pentz Distinguished Visiting Professor of Physics and Mathematics at Pennsylvania State University. [55]

An earlier universe

WMAP image of the (extremely tiny) anisotropies in the cosmic background radiation WMAP 2010.png
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 our own present universe. [56] He mentions this evidence in the epilogue of his 2010 book Cycles of Time , [57] 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. [58] [59] 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. [60] 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. [61]

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. [39] 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. [62] 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. [63] [64] Alternatively, one can use the Einstein–Maxwell–Dirac equations. [65]

Consciousness

Penrose at a conference Roger Penrose 9671.JPG
Penrose at a conference

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. [66] 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). [67] 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.) [68] [69]

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. [70] 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. [70] These claims were originally espoused by the philosopher John Lucas of Merton College, Oxford. [71]

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. [72] 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." [73]

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. [74]

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, [75] 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'". [76] 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. [76]

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 [77] 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 . [78]

Publications

His popular publications include:

His co-authored publications include:

His academic books include:

His forewords to other books include:

Awards and honours

Penrose during a lecture RogerPenrose CapturingInfinity cropped.jpg
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, 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). [92] 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. [93] In the same year, he was also awarded an honorary degree of Doctor of Science (DSc) by the University of Bath, [94] and became a member of Polish Academy of Sciences. In 1998, he was elected Foreign Associate of the United States National Academy of Sciences. [95] In 2000, he was appointed a Member of the Order of Merit (OM). [96]

In 2004, he was awarded the De Morgan Medal by the London Mathematical Society for his wide and original contributions to mathematical physics. [97] 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. [98]

In 2005, Penrose received a Doctorate Honoris Causa (Dr.h.c.) from each the Warsaw University (Poland) [99] and the Katholieke Universiteit Leuven (Belgium). [100] In 2006, he was conferred the honorary degree of Doctor of the University (DUniv) by the University of York [101] 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. [102] 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) [103] as well a Honorary Doctorate degree by the Igor Sikorsky Kyiv Polytechnic Institute (Ukraine). [104]

In 2015, Penrose was awarded a Doctorate Honoris Causa (Dr.h.c.) by CINVESTAV (Mexico). [105]

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. [106]

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. [9] In the same year, he was also awarded the honorary degree of Doctor of Science (DSc) by the University of Cambridge. [107] [108]

Personal life

Penrose's first marriage was to American Joan Isabel Penrose (née Wedge), whom he married in 1959. They had three sons. [109] [110] Penrose is now married to Vanessa Thomas, director of Academic Development at Cokethorpe School and former head of mathematics at Abingdon School. [111] [112] They have one son. [113] [111]

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." [114] He regards himself as an agnostic. [115] 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." [116]

Penrose is a patron of Humanists UK. [117]

See also

Notes

  1. ↑ The 2020 Nobel Prize was also awarded jointly to Reinhard Genzel and Andrea Ghez for their work on black holes.
  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 .

Related Research Articles

<span class="mw-page-title-main">Big Bang</span> Physical theory

The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. The notion of an expanding universe was first scientifically originated by physicist Alexander Friedmann in 1922 with the mathematical derivation of the Friedmann equations. The earliest empirical observation of the notion of an expanding universe is known as Hubble's law, published in work by physicist Edwin Hubble in 1929, which discerned that galaxies are moving away from Earth at a rate that accelerates proportionally with distance. Independent of Friedmann's work, and independent of Hubble's observations, physicist Georges Lemaître proposed that the universe emerged from a "primeval atom" in 1931, introducing the modern notion of the Big Bang.

The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities arising in general relativity.

<span class="mw-page-title-main">General relativity</span> Theory of gravitation as curved spacetime

General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever present matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations.

<span class="mw-page-title-main">Gravitational singularity</span> Condition in which spacetime itself breaks down

A gravitational singularity, spacetime singularity or simply singularity is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete.

<i>A Brief History of Time</i> 1988 book by Stephen Hawking

A Brief History of Time: From the Big Bang to Black Holes is a book on theoretical cosmology by the physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for readers who had no prior knowledge of physics.

<i>The Large Scale Structure of Space–Time</i> 1973 book by S. W. Hawking and G. F. R. Ellis

The Large Scale Structure of Space–Time is a 1973 treatise on the theoretical physics of spacetime by the physicist Stephen Hawking and the mathematician George Ellis. It is intended for specialists in general relativity rather than newcomers.

<span class="mw-page-title-main">Big Crunch</span> Hypothetical scenario for the ultimate fate of the universe

The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach absolute zero, an event potentially followed by a reformation of the universe starting with another Big Bang. The vast majority of evidence, however, indicates that this hypothesis is not correct. Instead, astronomical observations show that the expansion of the universe is accelerating rather than being slowed by gravity, suggesting that a Big Freeze is much more likely to occur. Nonetheless, some physicists have proposed that a "Big Crunch-style" event could result from a dark energy fluctuation.

In general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy-matter, light and information can escape from it. In this sense, it is the reverse of a black hole, from which energy-matter, light and information cannot escape. White holes appear in the theory of eternal black holes. In addition to a black hole region in the future, such a solution of the Einstein field equations has a white hole region in its past. This region does not exist for black holes that have formed through gravitational collapse, however, nor are there any observed physical processes through which a white hole could be formed.

The Penrose–Hawking singularity theorems are a set of results in general relativity that attempt to answer the question of when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation predicts a gravitational singularity in black hole formation. The Hawking singularity theorem is based on the Penrose theorem and it is interpreted as a gravitational singularity in the Big Bang situation. Penrose shared half of the Nobel Prize in Physics in 2020 "for the discovery that black hole formation is a robust prediction of the general theory of relativity".

<span class="mw-page-title-main">Dennis W. Sciama</span> British physicist (1926–1999)

Dennis William Siahou Sciama, was an English physicist who, through his own work and that of his students, played a major role in developing British physics after the Second World War. He was the PhD supervisor to many famous physicists and astrophysicists, including John D. Barrow, David Deutsch, George F. R. Ellis, Stephen Hawking, Adrian Melott and Martin Rees, among others; he is considered one of the fathers of modern cosmology.

<span class="mw-page-title-main">Amal Kumar Raychaudhuri</span> Indian physicist (1923–2005)

Amal Kumar Raychaudhuri was an Indian physicist, known for his research in general relativity and cosmology. His most significant contribution is the eponymous Raychaudhuri equation, which demonstrates that singularities arise inevitably in general relativity and is a key ingredient in the proofs of the Penrose–Hawking singularity theorems. Raychaudhuri was also revered as a teacher during his tenure at Presidency College, Kolkata.

Imaginary time is a mathematical representation of time that appears in some approaches to special relativity and quantum mechanics. It finds uses in certain cosmological theories.

The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Roger Penrose in an article in 1979 in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand, one would like to account for a universe which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties ; on the other hand, there is the deep question on the origin of the second law of thermodynamics.

<span class="mw-page-title-main">Robert Wald</span> American gravitational physicist (born 1947)

Robert M. Wald is an American theoretical physicist and professor at the University of Chicago. He studies general relativity, black holes, and quantum gravity and has written textbooks on these subjects.

The following outline is provided as an overview of and topical guide to black holes:

<span class="mw-page-title-main">Stephen Hawking</span> English theoretical physicist (1942–2018)

Stephen William Hawking was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between 1979 and 2009, he was the Lucasian Professor of Mathematics at Cambridge, widely viewed as one of the most prestigious academic posts in the world.

<span class="mw-page-title-main">Asghar Qadir</span> Pakistani academic

Asghar QadirHI, SI, FPAS, is a Pakistani mathematician and a prominent cosmologist, specialised in mathematical physics and physical cosmology. Nowadays, he is widely considered one of the top mathematicians in Pakistan. Asghar has played a prominent role in promoting Relativity in Pakistan. To this day, Qadir has made important and significant contributions to the fields of differential equations, theoretical cosmology and mathematical physics. He is noted for his work in mathematics and mathematical physics, in particular his contributions to general relativity and cosmology.

Conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity and proposed by theoretical physicist Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big Bang singularity of the next. Penrose popularized this theory in his 2010 book Cycles of Time: An Extraordinary New View of the Universe.

<span class="mw-page-title-main">Alexei Starobinsky</span> Russian theoretical physicist and cosmologist (1948–2023)

Alexei Alexandrovich Starobinsky was a Soviet and Russian theoretical physicist and cosmologist. He was a pioneer of the theory of cosmic inflation, for which he received the 2014 Kavli Prize in Astrophysics together with Alan Guth and Andrei Linde.

<span class="mw-page-title-main">Pankaj Joshi (physicist)</span> Indian physicist and cosmologist

Pankaj S. Joshi is an Indian astrophysicist and cosmologist whose research is mainly focused on areas of gravitational collapse and spacetime singularity. He has published more than 225 research papers in national and international journals, and books and monographs on the subject. Currently, he is a Distinguished Professor of Physics, and founding director of the International Center for Space and Cosmology at Ahmedabad University.

References

  1. 1 2 3 Anon (2017). "Penrose, Sir Roger" . Who's Who (online Oxford University Press  ed.). Oxford: A & C Black. doi:10.1093/ww/9780199540884.013.U30531.(Subscription or UK public library membership required.)
  2. ↑ "Roger Penrose | Biography, Books, Awards, & Facts". Archived from the original on 7 March 2021. Retrieved 7 March 2021.
  3. ↑ "Oxford Mathematician Roger Penrose jointly wins the Nobel Prize in Physics | University of Oxford". www.ox.ac.uk. 6 October 2020. Archived from the original on 9 October 2020. Retrieved 7 October 2020.
  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". Physics Today. 42 (1): 97–98. doi:10.1063/1.2810893. ISSN   0031-9228. Archived from the original on 7 December 2021. Retrieved 7 October 2020.
  7. ↑ O'Connor, John J.; Robertson, Edmund F., "Roger Penrose", MacTutor History of Mathematics Archive , University of St Andrews
  8. ↑ Roger Penrose at IMDb
  9. 1 2 "The Nobel Prize in Physics 2020". NobelPrize.org. Archived from the original on 6 October 2020. Retrieved 6 October 2020.
  10. ↑ Overbye, Dennis; Taylor, Derrick Bryson (6 October 2020). "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". The New York Times . Archived from the original on 6 October 2020. Retrieved 6 October 2020.
  11. ↑ Brookfield, Tarah (2018). Our voices must be heard : women and the vote in Ontario. Vancouver. ISBN   978-0-7748-6019-2. OCLC   1066070267.{{cite book}}: CS1 maint: location missing publisher (link)
  12. ↑ Brookfield, Tarah (2018). Our Voices Must Be Heard: Women and the Vote in Ontario. UBC Press. ISBN   978-0-7748-6022-2. Archived from the original on 7 December 2021. Retrieved 6 October 2020.
  13. ↑ Rudolph Peters (1958). "John Beresford Leathes. 1864–1956". Biographical Memoirs of Fellows of the Royal Society. 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". The Guardian. ISSN   0261-3077. Archived from the original on 12 November 2020. Retrieved 7 October 2020.
  16. ↑ "Illustrated Mathematics". Farleys House and Gallery. Archived from the original on 11 October 2020. Retrieved 7 October 2020.
  17. 1 2 3 "Roger Penrose – Biography". Maths History. Archived from the original on 8 October 2020. Retrieved 7 October 2020.
  18. ↑ AP and TOI staff. "Scientist of Jewish heritage among trio to win Nobel prize for black hole finds". www.timesofisrael.com. Archived from the original on 6 October 2020. Retrieved 7 October 2020.
  19. ↑ "Lionel Sharples Penrose". Royal College of Physicians.
  20. ↑ Ogilvie, Megan (23 March 2009). "Just Visiting: Sir Roger Penrose". Toronto Star . Archived from the original on 7 January 2021. Retrieved 9 October 2020.
  21. ↑ UCL alumnus Professor Sir Roger Penrose awarded Nobel Prize - website of the University College London
  22. ↑ Penrose, R. (1955). "A generalized inverse for matrices". Mathematical Proceedings of the Cambridge Philosophical Society . 51 (3): 406–413. Bibcode:1955PCPS...51..406P. doi: 10.1017/S0305004100030401 .
  23. ↑ Zheng, Wenjie. "The 100th anniversary of Moore–Penrose inverse and its role in statistics and machine learning". www.zhengwenjie.net. Archived from the original on 11 October 2020. Retrieved 7 October 2020.
  24. ↑ Penrose, Roger. Tensor Methods in Algebraic Geometry. cam.ac.uk (PhD thesis). University of Cambridge. OCLC   71366928. ProQuest   301242962.
  25. ↑ "Roger Penrose wins 2020 Nobel Prize in Physics for discovery about black holes". University of Cambridge. 6 October 2020. Archived from the original on 9 October 2020. Retrieved 7 October 2020.
  26. ↑ Welch, Chris (23 March 2012). "'Frustro' typeface applies the Penrose impossible triangle concept to words". The Verge. Archived from the original on 26 January 2021. Retrieved 7 October 2020.
  27. ↑ Baggini, Julian (2012). Philosophy: All That Matters. John Murray Press. ISBN   978-1-4441-5585-3. Archived from the original on 7 December 2021. Retrieved 12 October 2020.
  28. ↑ "Ascending and Descending by M.C. Escher – Facts about the Painting". Totally History. 21 May 2013. Archived from the original on 29 June 2020. Retrieved 7 October 2020.
  29. ↑ Kumar, Manjit (15 October 2010). "Cycles of Time: An Extraordinary New View of the Universe by Roger Penrose – review". The Guardian. Archived from the original on 10 January 2017. Retrieved 13 December 2016.
  30. ↑ "Professor Sir Roger Penrose awarded the 2020 Nobel Prize in Physics". King's College London. Archived from the original on 22 October 2020. Retrieved 7 October 2020.
  31. ↑ "The second Cambridge Cutting Edge Lecture: Professor Sir Roger Penrose". Cambridge Society of Paris. 12 March 2019. Archived from the original on 8 October 2020. Retrieved 7 October 2020.
  32. ↑ Thorne, Kip; Thorne, Kip S.; Hawking, Stephen (1994). Black Holes and Time Warps: Einstein's Outrageous Legacy. W. W. Norton & Company. ISBN   978-0-393-31276-8. Archived from the original on 3 February 2021. Retrieved 12 October 2020.
  33. ↑ 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. 56: 401–422. doi: 10.1098/rsbm.2009.0023 . ISSN   0080-4606. S2CID   73035217.
  34. ↑ Penrose, Roger (January 1965). "Gravitational Collapse and Space-Time Singularities". Physical Review Letters. 14 (3): 57–59. Bibcode:1965PhRvL..14...57P. doi:10.1103/PhysRevLett.14.57.
  35. ↑ Clark, Stuart. "A brief history of Stephen Hawking: A legacy of paradox". New Scientist. Archived from the original on 5 October 2020. Retrieved 7 October 2020.
  36. ↑ "Roger Penrose". New Scientist. Archived from the original on 11 October 2020. Retrieved 7 October 2020.
  37. ↑ Wolchover, Natalie (6 June 2019). "Physicists Debate Hawking's Idea That the Universe Had No Beginning". Quanta Magazine. Archived from the original on 5 October 2020. Retrieved 7 October 2020.
  38. ↑ Fernandez, Rodrigo L. (21 July 2020). "Cosmic Censorship Conjecture violation: A semiclassical approach". arXiv: 2007.10601 [gr-qc].
  39. 1 2 Curiel, Erik (2020), "Singularities and Black Holes", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Summer 2020 ed.), Metaphysics Research Lab, Stanford University, retrieved 7 October 2020
  40. ↑ Kafatos, M.; Leiter, D. (1979). "1979ApJ...229...46K Page 46". The Astrophysical Journal. 229: 46. Bibcode:1979ApJ...229...46K. doi:10.1086/156928. Archived from the original on 7 December 2021. Retrieved 7 October 2020.
  41. ↑ "Penrose process". Oxford Reference. Archived from the original on 2 February 2021. Retrieved 7 October 2020.
  42. ↑ R. Penrose (1979). "Singularities and Time-Asymmetry". In S. W. Hawking; W. Israel (eds.). General Relativity: An Einstein Centenary Survey. Cambridge University Press. pp. 581–638.
  43. ↑ Terrell, James (1959). "Invisibility of the Lorentz Contraction". Physical Review . 116 (4): 1041–1045. Bibcode:1959PhRv..116.1041T. doi:10.1103/PhysRev.116.1041.
  44. ↑ Penrose, Roger (1959). "The Apparent Shape of a Relativistically Moving Sphere". Proceedings of the Cambridge Philosophical Society. 55 (1): 137–139. Bibcode:1959PCPS...55..137P. doi:10.1017/S0305004100033776. S2CID   123023118.
  45. ↑ "New Horizons in Twistor Theory | Mathematical Institute". www.maths.ox.ac.uk. Archived from the original on 8 October 2020. Retrieved 7 October 2020.
  46. ↑ Huggett, S. A.; Tod, K. P. (21 July 1994). An Introduction to Twistor Theory (2nd ed.). Cambridge University Press. p. 1. doi:10.1017/cbo9780511624018. ISBN   978-0-521-45157-4.
  47. ↑ Steinhardt, Paul (1996). "New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings". PNAS . 93 (25): 14267–14270. Bibcode:1996PNAS...9314267S. doi: 10.1073/pnas.93.25.14267 . PMC   34472 . PMID   8962037.
  48. ↑ "Penrose on Spin Networks". math.ucr.edu. Archived from the original on 12 October 2020. Retrieved 7 October 2020.
  49. ↑ "Penrose diagrams". jila.colorado.edu. Archived from the original on 11 November 2020. Retrieved 7 October 2020.
  50. ↑ "Roger Penrose at Rice, 1983–87". Rice History Corner. 22 May 2013. Archived from the original on 17 June 2016. Retrieved 29 January 2014.
  51. ↑ 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.
  52. ↑ Roger Penrose at the Mathematics Genealogy Project OOjs UI icon edit-ltr-progressive.svg
  53. ↑ Johnson, George (27 February 2005). "'The Road to Reality': A Really Long History of Time". The New York Times. Archived from the original on 3 January 2021. Retrieved 3 April 2017.
  54. ↑ "If an Electron Can Be in Two Places at Once, Why Can't You?". Archived from the original on 1 November 2012. Retrieved 27 October 2008.
  55. ↑ "Dr. Roger Penrose at Penn State University". Archived from the original on 16 April 2008. Retrieved 9 July 2007.
  56. ↑ 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].
  57. ↑ Roger Penrose, Cycles of Time, Vintage; Reprint edition (1 May 2012)
  58. ↑ Stoica, Ovidiu-Cristinel (November 2013). "On the Weyl Curvature Hypothesis". Annals of Physics. 338: 186–194. arXiv: 1203.3382 . Bibcode:2013AnPhy.338..186S. doi:10.1016/j.aop.2013.08.002. S2CID   119329306.
  59. ↑ R. Penrose (1979). "Singularities and Time-Asymmetry". In S. W. Hawking; W. Israel (eds.). General Relativity: An Einstein Centenary Survey. Cambridge University Press. pp. 581–638.
  60. ↑ "New evidence for cyclic universe claimed by Roger Penrose and colleagues". Physics World. 21 August 2018. Archived from the original on 1 November 2020. Retrieved 7 October 2020.
  61. ↑ "New evidence for cyclic universe claimed by Roger Penrose and colleagues". 21 August 2018. Archived from the original on 1 November 2020. Retrieved 7 October 2020.
  62. ↑ Penrose, Roger (5 September 2017). Fashion, Faith, and Fantasy in the New Physics of the Universe. Princeton University Press. ISBN   978-0-691-17853-0. Archived from the original on 7 December 2021. Retrieved 12 October 2020.
  63. ↑ Kiefer, Claus (13 August 2013). "Conceptual Problems in Quantum Gravity and Quantum Cosmology". ISRN Mathematical Physics. 2013: 1–17. arXiv: 1401.3578 . doi: 10.1155/2013/509316 .
  64. ↑ Vaas, Rüdiger (2004). "The Inverted Big-Bang". arXiv: physics/0407071 .
  65. ↑ Finster, F.; Smoller, J.A.; Yau, S.-T. "The Einstein–Dirac–Maxwell Equations – Black Hole Solutions" (PDF). Archived (PDF) from the original on 7 October 2020. Retrieved 7 October 2020.
  66. ↑ Ferris, Timothy (19 November 1989). "HOW THE BRAIN WORKS, MAYBE (Published 1989)". The New York Times. ISSN   0362-4331. Archived from the original on 19 November 2021. Retrieved 7 October 2020.
  67. ↑ 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.)". Los Angeles Times. Archived from the original on 7 December 2021. Retrieved 7 October 2020.
  68. ↑ Penrose, Roger (28 April 2016). The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press. ISBN   978-0-19-255007-1. Archived from the original on 7 December 2021. Retrieved 12 October 2020.
  69. ↑ "20th WCP: Computational Complexity and Philosophical Dualism". www.bu.edu. Archived from the original on 13 October 2020. Retrieved 7 October 2020.
  70. 1 2 Penrose, Roger (2016). The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press. ISBN   978-0-19-878492-0. Archived from the original on 19 November 2021. Retrieved 7 December 2021.
  71. ↑ "In Memoriam: John Lucas". www.philosophy.ox.ac.uk. Archived from the original on 9 October 2020. Retrieved 7 October 2020.
  72. ↑ Criticism of the Lucas/Penrose argument that intelligence can not be entirely algorithmic: Sources that indicate Penrose's argument is generally rejected: Sources that also note that different sources attack different points of the argument:
  73. ↑ Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991.
  74. ↑ "Can Quantum Physics Explain Consciousness? One Scientist Thinks It Might". Discover Magazine. Archived from the original on 3 October 2020. Retrieved 7 October 2020.
  75. ↑ Tegmark, Max (2000). "The importance of quantum decoherence in brain processes". Physical Review E . 61 (4): 4194–4206. arXiv: quant-ph/9907009 . Bibcode:2000PhRvE..61.4194T. doi:10.1103/physreve.61.4194. PMID   11088215. S2CID   17140058.
  76. 1 2 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. Archived from the original on 7 December 2021. Retrieved 5 October 2020.
  77. ↑ "Anirban Bandyopadhyay". Archived from the original on 10 March 2014. Retrieved 22 February 2014.
  78. ↑ S. Hameroff; R. Penrose (2014). "Consciousness in the universe: A review of the 'Orch OR' theory". Physics of Life Reviews. 11 (1): 39–78. Bibcode:2014PhLRv..11...39H. doi: 10.1016/j.plrev.2013.08.002 . PMID   24070914.
  79. ↑ Penrose, Roger (1989). The Emperor's New Mind. Archived from the original on 7 December 2021. Retrieved 7 October 2020.
  80. ↑ Penrose, Roger (1994). Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press. ISBN   978-0-19-510646-6. Archived from the original on 7 December 2021. Retrieved 12 October 2020.
  81. ↑ Penrose, Roger (31 March 2016). The Road to Reality: A Complete Guide to the Laws of the Universe. Random House. ISBN   978-1-4464-1820-8. Archived from the original on 7 December 2021. Retrieved 7 October 2020.
  82. ↑ Penrose, Roger (6 September 2011). Cycles of Time: An Extraordinary New View of the Universe. Knopf Doubleday Publishing Group. ISBN   978-0-307-59674-1.
  83. ↑ Penrose, Roger (5 September 2017). Fashion, Faith, and Fantasy in the New Physics of the Universe. Princeton University Press. ISBN   978-0-691-17853-0.
  84. ↑ Hawking, Stephen W.; Penrose, Roger (1996). The Nature of Space and Time. Princeton University Press. ISBN   978-0-691-03791-2. Archived from the original on 7 December 2021. Retrieved 7 October 2020.
  85. ↑ Penrose, Roger; Shimony, Abner; Cartwright, Nancy; Hawking, Stephen (28 April 2000). The Large, the Small and the Human Mind. Cambridge University Press. ISBN   978-0-521-78572-3.
  86. ↑ Aldiss, Brian W.; Penrose, Roger (19 May 2015). White Mars; or, The Mind Set Free: A 21st-Century Utopia. Open Road Media. ISBN   978-1-5040-1028-3.
  87. ↑ Wuppuluri, Shyam; Doria, Francisco Antonio (13 February 2018). The Map and the Territory: Exploring the Foundations of Science, Thought and Reality. Springer. ISBN   978-3-319-72478-2.
  88. ↑ Weston-smith, Meg (16 April 2013). Beating The Odds: The Life And Times Of E A Milne. World Scientific. ISBN   978-1-84816-943-2. Archived from the original on 26 January 2021. Retrieved 12 October 2020.
  89. ↑ Zenil, Hector (2013). A Computable Universe: Understanding and Exploring Nature as Computation. World Scientific. ISBN   978-981-4374-30-9.
  90. ↑ Abbott, Derek; Davies, Paul C. W.; Pati, Arun Kumar (12 September 2008). Quantum Aspects Of Life. World Scientific. ISBN   978-1-908978-73-8. Archived from the original on 26 January 2021. Retrieved 12 October 2020.
  91. ↑ Zee, A. (1 October 2015). Fearful Symmetry: The Search for Beauty in Modern Physics. Princeton University Press. ISBN   978-1-4008-7450-7. Archived from the original on 26 January 2021. Retrieved 12 October 2020.
  92. ↑ "Our Honorary Fellows". Institute of Physics . Retrieved 26 December 2022.
  93. ↑ "Supplement 53696,10 June 1994, London Gazette". The Gazette. Archived from the original on 29 April 2016. Retrieved 16 August 2015.
  94. ↑ "Honorary Graduates 1989 to present". University of Bath. Archived from the original on 19 December 2015. Retrieved 18 February 2012.
  95. ↑ "Sir Roger Penrose | Person". Fetzer Franklin Fund (in German). Archived from the original on 24 September 2020. Retrieved 7 October 2020.
  96. ↑ Fisher, Connie (January 2012). "Appointments to the Order of Merit". The Royal Family. Archived from the original on 29 September 2020. Retrieved 25 October 2020.
  97. ↑ "Roger Penrose". Physics Today (8). 8 August 2018. doi: 10.1063/PT.6.6.20180808a .
  98. ↑ "London Mathematical Society". Archived from the original on 31 December 2004.
  99. ↑ Laudatio by Andrzej Trautman to Roger_Penrose - website of the Faculty of Physics of Warsaw University
  100. ↑ Eredoctor Sir Roger Penrose - website of KU Leuven
  101. ↑ Presentation address by Dr Bernard Kay to Professor Sir Roger Penrose
  102. ↑ "APS Member History". search.amphilsoc.org. Archived from the original on 7 December 2021. Retrieved 2 April 2021.
  103. ↑ Registrar: Honorary Degrees 2011-2012 - website by the Trinity College Dublin
  104. ↑ Sir Roger Penrose, one of the greatest scientists of our times, visited NTUU "KPI" - website of Kyiv Polytechnic Institute
  105. ↑ "Roger Penrose Doctor Honoris Causa por el Cinvestav". cinvestav.mx (in Mexican Spanish). Archived from the original on 7 December 2021. Retrieved 6 October 2020.
  106. ↑ Sir Roger Penrose : Honorary Degree, Whittaker Colloquium and seminar - website of the University of Edinburgh
  107. ↑ Nominations for honorary degrees 2020 - website of the University of Cambridge
  108. ↑ Cambridge confers honorary degrees - website of the University of Cambridge
  109. ↑ "7+ Out of This World Facts About Physicist Sir Roger Penrose". interestingengineering.com. 27 October 2019. Archived from the original on 8 October 2020. Retrieved 7 October 2020.
  110. ↑ "Roger Penrose". The Gifford Lectures. 18 August 2014. Archived from the original on 11 October 2020. Retrieved 7 October 2020.
  111. 1 2 "The Peter & Patricia Gruber Foundation, St. Thomas US Virgin Islands – Grants and International Awards". Gruberprizes.org. 8 August 1931. Archived from the original on 30 October 2012. Retrieved 13 August 2012.
  112. ↑ "Vanessa Penrose". Abingdon School. 6 July 2012. Archived from the original on 27 March 2012. Retrieved 13 August 2012.
  113. ↑ "Interview with Sir Roger Penrose" (PDF). European Mathematical Information Service. European Mathematical Society Newsletter March 2001.
  114. ↑ "Big Bang follows Big Bang follows Big Bang". BBC News. 25 September 2010. Archived from the original on 30 November 2010. Retrieved 1 December 2010.
  115. ↑ Thomas Fink (19 December 2020). "A singular mind: Roger Penrose on his Nobel Prize". The Spectator. Archived from the original on 18 May 2021. Retrieved 18 May 2021.
  116. ↑ See A Brief History of Time (1991) film script – springfieldspringfield.co.uk Archived 24 September 2015 at the Wayback Machine
  117. ↑ "Patrons". Humanists UK. Archived from the original on 5 October 2020. Retrieved 6 October 2020.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.