The Info List - Roger Penrose

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Roger Penrose
Roger Penrose
OM FRS (born 8 August 1931) is an English mathematical physicist, mathematician and philosopher of science. He is Emeritus Rouse Ball Professor of Mathematics
in the University of Oxford and Emeritus Fellow of Wadham College, Oxford. Penrose is known for his work in mathematical physics, in particular for his contributions to general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize for physics, which he shared with Stephen Hawking
Stephen Hawking
for the Penrose–Hawking singularity theorems.[1]


1 Early life and academia 2 Later activity 3 An earlier universe 4 Physics and consciousness 5 Personal life

5.1 Family life 5.2 Religious views

6 Awards and honours 7 Depictions in popular culture 8 Works

8.1 Popular publications

8.1.1 Co-authored

8.2 Academic books 8.3 Foreword to other books

9 See also 10 Notes 11 References 12 Further reading 13 External links

Early life and academia[edit] Born in Colchester, Essex, Roger Penrose
Roger Penrose
is a son of psychiatrist and mathematician Lionel Penrose
Lionel Penrose
and Margaret Leathes,[a] and the grandson of the physiologist John Beresford Leathes
John Beresford Leathes
and his Russian wife, Sonia Marie Natanson.[2] Penrose told a Russian audience that his grandmother had left St. Petersburg
St. Petersburg
in the late 1880s.[3] His uncle was artist Roland Penrose, whose son with photographer Lee Miller
Lee Miller
is Antony Penrose. Penrose is the brother of physicist Oliver Penrose and of chess Grandmaster Jonathan Penrose. Penrose attended University College School and University College, London, where he graduated with a first class degree in mathematics. In 1955, while still a student, Penrose reintroduced the E. H. Moore
E. H. Moore
generalised matrix inverse, also known as the Moore–Penrose inverse,[4] after it had been reinvented by Arne Bjerhammar in 1951. Having started research under the professor of geometry and astronomy, Sir
W. V. D. Hodge, Penrose finished his PhD at Cambridge in 1958, with a thesis on "tensor methods in algebraic geometry" under algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle
Penrose triangle
in the 1950s, 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. Escher's Waterfall, and Ascending and Descending were in turn inspired by Penrose. 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 [see tri-bar for an image] – 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.[5]

Having become 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) it was in 1964 that, in the words of Kip Thorne
Kip Thorne
of Caltech, " Roger Penrose
Roger Penrose
revolutionised the mathematical tools that we use to analyse the properties of spacetime". 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 soluble 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
John Archibald Wheeler
at Princeton. The other, 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"[6] was not only its result (roughly 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). 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 Dennis Sciama's most famous student, Stephen Hawking.

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, 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. Following up his "weak cosmic censorship hypothesis", Penrose went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis". Together with the BKL conjecture
BKL 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.[7] 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
Terrell rotation
or Penrose–Terrell rotation.[8][9]

Oil painting by Urs Schmid (1995) of a Penrose tiling
Penrose tiling
using fat and thin rhombi.

In 1967, Penrose invented the twistor theory which maps geometric objects in Minkowski space
Minkowski space
into the 4-dimensional complex space with the metric signature (2,2).

A Penrose tiling

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. Penrose developed these ideas based on the article Deux types fondamentaux de distribution statistique[10] (1938; an English translation Two Basic Types of Statistical Distribution) by Czech geographer, demographer and statistician Jaromír Korčák. In 1984, such patterns were observed in the arrangement of atoms in quasicrystals.[11] Another noteworthy contribution is his 1971 invention of spin networks, which later came to form the geometry of spacetime in loop quantum gravity. He was influential in popularising what are commonly known as Penrose diagrams (causal diagrams). In 1983, Penrose was invited to teach at Rice University
Rice University
in Houston, by the then provost Bill Gordon. He worked there from 1983 to 1987.[12] Later activity[edit] 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.[13][14] Penrose is the Francis and Helen Pentz Distinguished Visiting Professor of Physics and Mathematics
at Pennsylvania State University, USA.[15] He is also a member of the Editorial Board of The Astronomical Review and of the Advisory Board of Universe. An earlier universe[edit]

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

In 2010, Penrose reported possible evidence, based on concentric circles found in WMAP
data of the CMB
sky, of an earlier universe existing before the Big Bang
Big Bang
of our own present universe.[16] He mentions this evidence in the epilogue of his 2010 book Cycles of Time,[17] 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
Big Bang
could have been smooth enough for a previous universe to survive it. He made several conjectures about C and the WCH, some of which were subsequently proved by others, and the smoothness is real, and where he also popularized his conformal cyclic cosmology (CCC) theory. In simple terms, he believes that the singularity in Einstein's field equation at the Big Bang
Big Bang
is only an apparent singularity, similar to the well-known apparent singularity at the event horizon of a black hole. The latter singularity can be removed by a change of coordinate system, and Penrose proposes a different change of coordinate system that will remove the singularity at the big bang. One implication of this is that the major events at the Big Bang
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. Alternatively, one can use the Einstein–Maxwell–Dirac equations. Physics and consciousness[edit]

Prof. Penrose at a conference.

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v t e

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. 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). 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
Turing machine
halts and OFF when the Turing machine
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
Turing machine
stops.) 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 the present computer is unable to have intelligence because it is an algorithmically deterministic system. 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. 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 things such as the insolubility of the halting problem and Gödel's incompleteness theorem prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight. These claims were originally espoused by the philosopher John Lucas of Merton College, Oxford. The Penrose–Lucas argument
Penrose–Lucas argument
about the implications of Gödel's incompleteness theorem for computational theories of human intelligence has been widely criticised by mathematicians, computer scientists and philosophers, and the consensus among experts in these fields seems to be that the argument fails, though different authors may choose different aspects of the argument to attack.[18] 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."[19] 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 that of anesthesiologist Stuart Hameroff. 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,[20] 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'".[21] Tegmark's paper has been widely cited by critics of the Penrose–Hameroff position. In their reply to Tegmark's paper, also published in Physical Review E, the physicists Scott Hagan, Jack Tuszyński and Hameroff[22][23] claimed that Tegmark did not address the Orch-OR
model, but instead a model of his own construction. This involved superpositions of quanta separated by 24 nm rather than the much smaller separations stipulated for Orch-OR. As a result, Hameroff's group claimed a decoherence time seven orders of magnitude greater than Tegmark's, but still well short of the 25 ms required if the quantum processing in the theory was to be linked to the 40 Hz gamma synchrony, as Orch-OR
suggested. To bridge this gap, the group made a series of proposals. He supposed that the interiors of neurons could alternate between liquid and gel states. In the gel state, it was further hypothesized that the water electrical dipoles are oriented in the same direction, along the outer edge of the microtubule tubulin subunits. Hameroff et al. proposed that this ordered water could screen any quantum coherence within the tubulin of the microtubules from the environment of the rest of the brain. Each tubulin also has a tail extending out from the microtubules, which is negatively charged, and therefore attracts positively charged ions. It is suggested that this could provide further screening. Further to this, there was a suggestion that the microtubules could be pumped into a coherent state by biochemical energy.

Roger Penrose
Roger Penrose
in the University of Santiago de Compostela
University of Santiago de Compostela
to receive the Fonseca Prize.

Finally, he suggested that the configuration of the microtubule lattice might be suitable for quantum error correction, a means of holding together quantum coherence in the face of environmental interaction. Hameroff, in a lecture in part of a Google Tech talks series exploring quantum biology, gave an overview of current research in the area, and responded to subsequent criticisms of the Orch-OR
model.[24] In addition to this, a recent 2011 paper by Roger Penrose
Roger Penrose
and Stuart Hameroff gives an updated model of their Orch-OR
theory, in light of criticisms, and discusses the place of consciousness within the universe.[25] 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.[21] In January 2014 Hameroff and Penrose claimed that a discovery of quantum vibrations in microtubules by Anirban Bandyopadhyay of the National Institute for Materials Science in Japan[26] confirms the hypothesis of Orch-OR
theory.[27] 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.[28] Personal life[edit] Family life[edit] Penrose is married to Vanessa Thomas, director of Academic Development at Cokethorpe School
Cokethorpe School
and former head of mathematics at Abingdon School,[29][30] with whom he has one son.[29] He has three sons from a previous marriage to American Joan Isabel Wedge, whom he married in 1959. Religious views[edit] Penrose is an atheist.[31] In the film A Brief History of Time, he 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."[32] Penrose is a Distinguished Supporter of Humanists UK. Awards and honours[edit]

Roger Penrose
Roger Penrose
during a lecture

Penrose has been awarded many prizes for his contributions to science. He was elected a Fellow of the Royal Society
Fellow of the Royal Society
(FRS) in 1972. In 1975, Stephen Hawking
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 Foundation Prize for Physics in 1988. In 1989 he was awarded the Dirac Medal and Prize of the British Institute of Physics. In 1990 Penrose was awarded the Albert Einstein
Albert Einstein
Medal for outstanding work related to the work of Albert Einstein
Albert Einstein
by the Albert Einstein Society. 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.[33] In the same year he was also awarded an Honorary Degree (Doctor of Science) by the University of Bath.[34] In 1998, he was elected Foreign Associate of the United States National Academy of Sciences. In 2000 he was appointed to the Order of Merit. In 2004 he was awarded the De Morgan Medal for his wide and original contributions to mathematical physics. To quote the citation from the London Mathematical Society:

His deep work on General Relativity has been a major factor in our understanding of black holes. His development of Twistor Theory
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.[35]

In 2005 Penrose was awarded an honorary doctorate by Warsaw University and Katholieke Universiteit Leuven
Katholieke Universiteit Leuven
(Belgium), and in 2006 by the University of York. In 2008 Penrose was awarded the Copley Medal. He is also a Distinguished Supporter of Humanists UK
Humanists UK
and one of the patrons of the Oxford University Scientific Society. In 2011, Penrose was awarded the Fonseca Prize by the University of Santiago de Compostela. In 2012, Penrose was awarded the Richard R. Ernst Medal by ETH Zürich
ETH Zürich
for his contributions to science and strengthening the connection between science and society. In 2015 Penrose was awarded an honorary doctorate by CINVESTAV-IPN (Mexico). Depictions in popular culture[edit]

In the 2004 BBC TV movie Hawking, Penrose is played by Tom Ward In the 2014 movie The Theory of Everything, Penrose is played by Christian McKay

Works[edit] Popular publications[edit]

The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics (1989) Shadows of the Mind: A Search for the Missing Science of Consciousness (1994) The Road to Reality: A Complete Guide to the Laws of the Universe (2004)(New Edition from Vintage Digital; 31 Mar. 2016) Cycles of Time: An Extraordinary New View of the Universe
(2010) Fashion, Faith, and Fantasy in the New Physics of the Universe


The Nature of Space and Time
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 - The Mind Set Free (with Brian Aldiss) (1999)

Academic books[edit]

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)

Foreword to other books[edit]

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

See also[edit]

Conformal cyclic cosmology Illumination problem Orchestrated objective reduction Penrose graphical notation Quantum Aspects of Life Quantum mind


^ Penrose and his father shared mathematical concepts with Dutch graphic artist M. C. Escher
M. C. Escher
which were incorporated into a lot of pieces, including Waterfall, which is based on the 'Penrose triangle', and Up and Down.


^ Penrose, R (2005). The Road to Reality: A Complete guide to the Laws of the Universe. Vintage Books. ISBN 0-09-944068-7.  ^ Rudolph Peters. "John Beresford Leathes. 1864-1956". Royal Society Publishing.  ^ Elementy.ru (May 2016). "Roger Penrose. Cycles of Time: Is It Possible to Discern the Previous Universe
Through the Big Bang?". YouTube.  ^ Penrose, R. (1955). "A generalized inverse for matrices". Mathematical Proceedings of the Cambridge Philosophical Society. 51 (03): 406. Bibcode:1955PCPS...51..406P. doi:10.1017/S0305004100030401.  ^ "Cycles of Time: An Extraordinary New View of the Universe
by Roger Penrose – review". The Guardian.  ^ 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.  ^ R. Penrose (1979). "Singularities and Time-Asymmetry". In S. W. Hawking; W. Israel. General Relativity: An Einstein Centenary Survey. Cambridge University Press. pp. 581–638.  ^ Terrell, James (1959). "Invisibility of the Lorentz Contraction". Physical Review. 116 (4): 1041–1045. Bibcode:1959PhRv..116.1041T. doi:10.1103/PhysRev.116.1041.  ^ Penrose, Roger (1959). "The Apparent Shape of a Relativistically Moving Sphere". Proceedings of the Cambridge Philosophical Society. 55: 137–139. Bibcode:1959PCPS...55..137P. doi:10.1017/S0305004100033776.  ^ Jaromír Korčák (1938): Deux types fondamentaux de distribution statistique. Prague, Comité d'organisation, Bull. de l'Institute Int'l de Statistique, vol. 3, pp. 295–299. ^ 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.  ^ " Roger Penrose
Roger Penrose
at Rice, 1983-87". Rice History Corner.  ^ Johnson, George (27 February 2005). "'The Road to Reality': A Really Long History of Time". The New York Times, USA. Retrieved 3 April 2017.  ^ "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.  ^ "Dr. Roger Penrose
Roger Penrose
at Penn State University". Archived from the original on 16 April 2008. Retrieved 9 July 2007.  ^ 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].  ^ Roger Penrose, Cycles of Time, Vintage; Reprint edition (1 May 2012) ^ Criticism of the Lucas/Penrose argument that intelligence can not be entirely algorithmic:

MindPapers: 6.1b. Godelian arguments References for Criticisms of the Gödelian Argument* Boolos, George, et al. 1990. An Open Peer Commentary on The Emperor's New Mind. Behavioral and Brain Sciences 13 (4) 655. Davis, Martin 1993. How subtle is Gödel's theorem? More on Roger Penrose. Behavioral and Brain Sciences, 16, 611–612. Online version at Davis' faculty page at http://cs.nyu.edu/cs/faculty/davism/ Feferman, Solomon (1996). "Penrose's Gödelian argument". Psyche: An Interdisciplinary Journal of Research on Consciousness. 2: 21–32. CiteSeerX .  Krajewski, Stanislaw 2007. On Gödel's Theorem and Mechanism: Inconsistency or Unsoundness is Unavoidable in any Attempt to 'Out-Gödel' the Mechanist. Fundamenta Informaticae 81, 173–181. Reprinted in Topics in Logic, Philosophy and Foundations of Mathematics
and Computer Science:In Recognition of Professor Andrzej Grzegorczyk (2008), p. 173 LaForte, Geoffrey; Hayes, Patrick J.; Ford, Kenneth M. (1998). "Why Gödel's Theorem Cannot Refute Computationalism". Artificial Intelligence. 104: 265–286. doi:10.1016/s0004-3702(98)00052-6. [permanent dead link] Lewis, David K. 1969. Lucas against mechanism. Philosophy 44 231–233. Putnam, Hilary 1995. Review of Shadows of the Mind. In Bulletin of the American Mathematical Society 32, 370–373 (also see Putnam's less technical criticisms in his 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 "Archived copy". Archived from the original on 25 January 2001. Retrieved 22 October 2010.  L.J. Landau at the Mathematics
Department of King's College London writes that "Penrose's argument, its basis and implications, is rejected by experts in the fields which it touches."

Sources that also note that different sources attack different points of the argument:

Princeton Philosophy professor John Burgess writes in On the Outside Looking In: A Caution about Conservativeness (published in Kurt Gödel: Essays for his Centennial, with the following comments found on pp. 131–132) that "the consensus view of logicians today seems to be that the Lucas–Penrose argument is fallacious, though as I have said elsewhere, there is at least this much to be said for Lucas and Penrose, that logicians are not unanimously agreed as to where precisely the fallacy in their argument lies. There are at least three points at which the argument may be attacked." Nachum Dershowitz 2005. The Four Sons of Penrose, in Proceedings of the Eleventh Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR; Jamaica), G. Sutcliffe and Andrei Voronkov, eds., Lecture Notes in Computer Science, vol. 3835, Springer-Verlag, Berlin, pp. 125–138.

^ Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991. ^ Tegmark, Max (2000). "The importance of quantum decoherence in brain processes". Physical Review E. 61: 4194–4206. arXiv:quant-ph/9907009 . Bibcode:2000PhRvE..61.4194T. doi:10.1103/physreve.61.4194.  ^ a b 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.  ^ Hagan, S.; Hameroff, S. & Tuszyński, J. (2002). "Quantum Computation in Brain Microtubules? Decoherence and Biological Feasibility". Physical Review E. 65: 061901. arXiv:quant-ph/0005025 . Bibcode:2002PhRvE..65f1901H. doi:10.1103/PhysRevE.65.061901.  ^ Hameroff, S. (2006). "Consciousness, Neurobiology and Quantum Mechanics". In Tuszynski, Jack. The Emerging Physics of Consciousness. Springer. pp. 193–253  ^ "Clarifying the Tubulin bit/qubit – Defending the Penrose-Hameroff Orch OR Model (Quantum Biology)". YouTube. 22 October 2010. Retrieved 13 August 2012.  ^ Roger Penrose
Roger Penrose
& Stuart Hameroff
Stuart Hameroff
(4 July 1992). " Consciousness
in the Universe: Neuroscience, Quantum Space-Time Geometry and Orch OR Theory". Journal of Cosmology. Quantumconsciousness.org. Archived from the original on 16 June 2012. Retrieved 13 August 2012.  ^ "Anirban Bandyopadhyay". ResearchGate. Retrieved 2014-02-22.  ^ "Discovery of quantum vibrations in 'microtubules' inside brain neurons supports controversial theory of consciousness". ScienceDaily. Retrieved 2014-02-22.  ^ 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. Retrieved 29 March 2014.  ^ a b "The Peter & Patricia Gruber Foundation, St. Thomas US Virgin Islands – Grants and International Awards". Gruberprizes.org. 8 August 1931. Retrieved 13 August 2012.  ^ "Vanessa Penrose". Abingdon School. 6 July 2012. Retrieved 13 August 2012.  ^ " Big Bang
Big Bang
follows Big Bang
Big Bang
follows Big Bang". BBC News. 25 September 2010. Retrieved 1 December 2010.  ^ See A Brief History of Time (1991) film script - springfieldspringfield.co.uk ^ "Supplement 53696,10 June 1994, London Gazette". The Gazette. Retrieved 16 August 2015.  ^ "Honorary Graduates 1989 to present". University of Bath. Retrieved 18 February 2012.  ^ London Mathematical Society
London Mathematical Society
Archived 31 December 2004 at the Wayback Machine.

Further reading[edit]

Ferguson, Kitty (1991). Stephen Hawking: Quest For A Theory of Everything. Franklin Watts. ISBN 0-553-29895-X. Misner, Charles; Thorne, Kip S. & Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0.  (See Box 34.2.)

External links[edit]

Wikiquote has quotations related to: Roger Penrose

Wikimedia Commons has media related to Roger Penrose.

Roger Penrose
Roger Penrose
on IMDb 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. 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
Isaac Newton
Institute for Mathematical Sciences, Cambridge, 11 Nov 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
Roger Penrose
on The Forum Penrose on sidestepping reason on YouTube O'Connor, John J.; Robertson, Edmund F., "Roger Penrose", MacTutor History of Mathematics
archive, University of St Andrews . Hilary Putnam's review of Penrose's 'Shadows of the Mind' claiming that Penrose's use of Godel's Incompleteness Theorem is fallacious

Beyond the Doubting of a Shadow: A Reply to Commentaries on Shadows of the Mind at the Wayback Machine
Wayback Machine
(archived 18 June 2008)

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: 4194–4206. arXiv:quant-ph/9907009 . Bibcode:2000PhRvE..61.4194T. doi:10.1103/physreve.61.4194. 

"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.

"Toilet Paper Plagiarism" at the Wayback Machine
Wayback Machine
(archived 12 March 2005) – 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
Roger Penrose
in conversation on the BBC World Service discussion show Roger Penrose
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
Roger Penrose
on Black Holes - 22 November 2016 Sir
Roger Penrose
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

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Works by Roger Penrose


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

Coauthored books

The Nature of Space and Time
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)

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Copley Medallists (2001–present)

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

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Laureates of the Wolf Prize in Physics


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


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


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


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


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

Agriculture Arts Chemistry Mathematics Medicine Physics

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Special relativity


Principle of relativity Special
relativity Doubly special relativity


Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations


Galilean relativity Galilean transformation Lorentz transformation


Time dilation Relativistic mass Mass–energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Relativistic disks


Light cone World line Spacetime
diagram Biquaternions Minkowski space

General relativity


Introduction Mathematical formulation

Fundamental concepts

relativity Equivalence principle World line Riemannian geometry Minkowski diagram Penrose diagram


Black hole Event horizon Frame-dragging Geodetic effect Lenses Singularity Waves Ladder paradox Twin paradox Two-body problem BKL singularity


ADM formalism BSSN formalism Einstein field equations Geodesic equation Friedmann equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein equation Ernst equation Tolman–Oppenheimer–Volkoff equation

Advanced theories

Brans–Dicke theory Kaluza–Klein Mach's principle Quantum gravity


Schwarzschild (interior) Reissner–Nordström Gödel Kerr Kerr–Newman Kasner Friedmann–Lemaître–Robertson–Walker Taub–NUT Milne pp-wave van Stockum dust Weyl−Lewis−Papapetrou


Einstein Lorentz Hilbert Poincaré Schwarzschild de Sitter Reissner Nordström Weyl Eddington Friedmann Milne Zwicky Lemaître Gödel Wheeler Robertson Bardeen Walker Kerr Chandrasekhar Ehlers Penrose Hawking Taylor Hulse Stockum Taub Newman Yau Thorne Weiss Bondi Misner others

Authority control

WorldCat Identities VIAF: 108188624 LCCN: n82139094 ISNI: 0000 0000 8405 6757 GND: 120520567 SUDOC: 029955475 BNF: cb12147090x (data) BIBSYS: 90192018 MGP: 36928 NDL: 00515