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]} He is regarded as one of the greatest living physicists, mathematicians and scientists, and is particularly noted for the breadth and depth of his work in both natural and formal sciences.^{
[11]}^{
[12]}^{
[13]}^{
[14]}^{
[15]}^{
[16]}^{
[17]}^{
[18]}^{
[19]}
In 1955, while a student, Penrose reintroduced the
E. H. Moore generalised matrix inverse, also known as the
Moore–Penrose inverse,^{
[29]} after it had been reinvented by
Arne Bjerhammar in 1951.^{
[30]} Having started research under the professor of geometry and astronomy, Sir
W. V. D. Hodge, Penrose finished his PhD at
St John's College, Cambridge, in 1958, with a thesis on tensor methods in algebraic geometry^{
[31]} supervised by algebraist and geometer
John A. Todd.^{
[32]} 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.^{
[33]}^{
[34]} Escher's
Waterfall, and
Ascending and Descending were in turn inspired by Penrose.^{
[35]}
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.^{
[36]}
Research and career
Penrose spent the academic year 1956–57 as an assistant lecturer at
Bedford College, 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 two years, 1961–63, as a researcher at
King's College, London, before returning to the United States to spend the year 1963–64 as a visiting associate professor at the
University of Texas at Austin.^{
[37]} He later held visiting positions at Yeshiva, 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)^{
[26]} in the words of
Kip Thorne of Caltech, "Roger Penrose revolutionised the mathematical tools that we use to analyse the properties of spacetime".^{
[38]}^{
[39]} 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.^{
[40]} 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"^{
[41]} was not its only result, 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. 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.^{
[42]}^{
[43]}^{
[44]} The
Penrose–Hawking singularity theorems were inspired by
Amal Kumar Raychaudhuri's
Raychaudhuri equation.
It was in the local context of gravitational collapse that the contribution of Penrose was most decisive, starting with his 1969 cosmic censorship conjecture,^{
[45]} 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.^{
[46]}^{
[47]}^{
[48]}
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.^{
[49]} 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.^{
[50]}^{
[51]}
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).^{
[52]}^{
[53]}
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.^{
[54]} Another noteworthy contribution is his 1971 invention of
spin networks, which later came to form the geometry of
spacetime in
loop quantum gravity.^{
[55]} He was influential in popularizing what are commonly known as
Penrose diagrams (causal diagrams).^{
[56]}
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.^{
[63]} He mentions this evidence in the epilogue of his 2010 book Cycles of Time,^{
[64]} 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.^{
[65]}^{
[66]} 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.^{
[67]} 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. ^{
[68]}
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.^{
[46]} 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.^{
[69]} 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.^{
[70]}^{
[71]} Alternatively, one can use the Einstein–Maxwell–Dirac equations.^{
[72]}
Consciousness
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.^{
[73]} 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).^{
[74]} 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.)^{
[75]}^{
[76]}
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.^{
[77]} 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.^{
[77]}^{
[78]} These claims were originally espoused by the philosopher
John Lucas of
Merton College,
Oxford.^{
[79]} G. Hirase has paraphrased Penrose' argument and reinforced it.^{
[80]}
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.^{
[81]}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."^{
[82]}
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,^{
[84]} 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'".^{
[85]} 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^{
[86]}^{
[87]} 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.^{
[86]} They 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.^{
[86]} 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.^{
[88]}
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.^{
[88]}
Hameroff, in a lecture in part of a Google Tech^{[
clarification needed]} talks series exploring
quantum biology, gave an overview of current research in the area, and responded to subsequent criticisms of the Orch-OR model.^{
[89]} In addition to this, a 2011 paper by Roger Penrose and Stuart Hameroff published in the Journal of Cosmology gives an updated model of their Orch-OR theory, in light of criticisms, and discusses the place of consciousness within the universe.^{
[90]}
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.^{
[85]}
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^{
[91]} supports the hypothesis of
Orch-OR theory.^{
[92]} 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.^{
[93]}
White Mars: The Mind Set Free (with
Brian Aldiss) (1999)^{
[101]}
His academic books include:
Techniques of Differential Topology in Relativity (1972,
ISBN0-89871-005-7)
Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (with
Wolfgang Rindler, 1987)
ISBN0-521-33707-0 (paperback)
Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler, 1988) (reprint),
ISBN0-521-34786-6 (paperback)
In 2004, he was awarded the
De Morgan Medal for his wide and original contributions to mathematical physics.^{
[112]} 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 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.^{
[113]}
In 2012, Penrose was awarded the Richard R. Ernst Medal by
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).^{
[115]}
In 2017, he was awarded the Commandino Medal at the
Urbino University for his contributions to the history of science.
Penrose married Vanessa Thomas, director of Academic Development at
Cokethorpe School and former head of mathematics at
Abingdon School,^{
[116]}^{
[117]} with whom he has one son.^{
[116]} He has three sons from a previous marriage to American Joan Isabel Penrose (née Wedge), whom he married in 1959.^{
[118]}^{
[119]}
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."^{
[120]} He regards himself as an agnostic.^{
[121]} 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."^{
[122]}
^Fernandez, Rodrigo L. (21 July 2020). "Cosmic Censorship Conjecture violation: A semiclassical approach".
arXiv:2007.10601 [
gr-qc].
^
^{a}^{b}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
^"Penrose process". Oxford Reference.
Archived from the original on 2 February 2021. Retrieved 7 October 2020.
^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.
^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)
^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.
In an article at
"King's College London – Department of Mathematics". 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 ConservativenessArchived 19 October 2012 at the
Wayback Machine (published in Kurt Gödel: Essays for his Centennial, with the following comments found on
pp. 131–132Archived 27 December 2016 at the
Wayback Machine) 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."
^Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings,
National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991.
^Hameroff, S. (2006). "Consciousness, Neurobiology and Quantum Mechanics". In Tuszynski, Jack (ed.). The Emerging Physics of Consciousness. Springer. pp. 193–253.
Bibcode:
2006epc..book.....T.
^
^{a}^{b}Hameroff, Stuart; Marcer, P. (1998). "Quantum Computation in Brain Microtubules? The Penrose—Hameroff 'Orch OR' Model of Consciousness [and Discussion]". Philosophical Transactions: Mathematical, Physical and Engineering Sciences. 356 (1743): 1869–1896.
ISSN1364-503X.
JSTOR55017.
^Abbott, Derek; Davies, Paul C. W.; Pati, Arun Kumar (12 September 2008).
Quantum Aspects Of Life. World Scientific.
ISBN978-1-908978-73-8.
Archived from the original on 26 January 2021. Retrieved 12 October 2020.
^"Patrons". Humanists UK.
Archived from the original on 5 October 2020. Retrieved 6 October 2020.
Notes
^The 2020 Nobel Prize was also awarded jointly to
Reinhard Genzel and
Andrea Ghez for their work on black holes.
^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
Up and Down.
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?":
"Toilet Paper Plagiarism" at the
Wayback Machine (archived 12 March 2005) – D. Trull about Penrose's lawsuit concerning the use of his Penrose tilings on toilet paper