Roger Penrose was born on August 8th, 1931 in Colchester, Essex, England. His father Lionel Sharples Penrose FRS was a distinguished medically trained scientist, who worked primarily on human genetics, studying mainly the genetic origins of numerous mental conditions, particularly the issue of Downs Syndrome. He had earlier, in around 1920, studied psychoanalysis, travelling to Vienna to attend lectures by Sigmund Freud, then returning to England to obtain a medical degree in Cambridge. Lionel had considerable talents also as an artist and as a chess problemist. He enjoyed playing the piano and a spinet (small harpsichord). He frequently occupied himself making things out of wood such as puzzles of various kinds and, in later life, gadgets that would reproduce themselves if shaken together appropriately. Lionel’s father, James Doyle Penrose was a Quaker and very distinguished painter of portraits and religious topics, and Lionel’s mother, Elizabeth Josephine Peckover, came from a very well-to-do religious Quaker pacifist banking family. Lionel eventually donated his entire inheritance to various good causes.

Lionel was one of four brothers, one of whom, Sir Roland Algernon Penrose CBE, became one of Britain’s leading surrealists, and was a good friend of Pablo Picasso and many others of the surrealist community. Roland’s second marriage was to an American, Lee Miller, a well-known 2nd World War photographer. Both Lionel and Roland served in the 1st World War in the Friends’ Ambulance Unit.

Roger’s mother, Margaret (Leathes) had studied medicine at Newnham College Cambridge. Her father, John Beresford Leathes FRS, was a professor of physiology at the University of Sheffield. Margaret’s mother, Sonia Marie Natanson (though named “Sara Mara Natansohn” on her birth certificate) was Jewish – although completely secretive about her heritage, even keeping her maiden name a secret. She had lived with her strict Jewish family in in St Petersburg, Russia, though born in Latvia. She was a concert-level pianist, having known various Russian composers and classical music performers. She had apparently left her family to study in Switzerland when she met John Leathes, and returned to England with him, whom she subsequently married.

Margaret first met Lionel on a Swiss mountain trip (the Grossglockner). She was a highly intelligent, talented, and attractive young woman with a medical degree and a talent for amusing writing. She had been Head Girl at her school, Bedales, in southern England. However, after her marriage to Lionel, Margaret found that her circumstances with him made it particularly difficult for her to develop these talents, except in relation to her children.

After Lionel died in 1972, Margaret gained some freedom to express herself. She married Maxwell Herman Alexander Newman FRS, a prominent mathematician, who had been a close friend of both Lionel and Margaret in earlier days (Max having accompanied Lionel on his early trip to Vienna, Max’s purpose there to meet the Viennese mathematical logicians). Max Newman was born in 1897 and died in 1984. Margaret was born in 1901 and died in 1989.

Max Newman had done particularly important work at Bletchley Park, during World War 2, being in charge of the “Newmanry” which was responsible for decoding Hitler’s especially secret Lorenz code that he used for communication with his generals. It should be mentioned also, that there was a crucial component to their being able to crack the Lorenz code, coming from a brilliant contribution from the mathematician W.T. Tutte. This decoding is not so well known publicly as that, associated with the name of Alan Turing, who cracked the Nazi Enigma code using electronic devices referred to as “Bombes”. Newman concluded that cracking the Lorenz code required the construction of a more flexible computer assembly, termed “Colossus”. This was designed and constructed by the research telephone engineer Thomas H. Flowers, under Newman’s guidance. It first worked on 1 June 1944, just in time for the Normandy landings on D-Day, 6 June 1944. The existence of the Colossus was kept secret until the mid-1970s, Colossus is now being commonly regarded as being the world’s first programmable electronic digital computer.

Margaret and Lionel had four children, Roger being the second-born of their three sons, the fourth being a girl, Shirley, born in Canada much later. The eldest, Oliver, was born on June 6th, 1929 and the youngest of the sons, Jonathan, was born on October 7th, 1933, and in early 1939 the five of them sailed to the USA on the Aquitania, in view of the impending danger of the 2nd World War, Lionel taking up a job in Philadelphia, Pennsylvania. There, the three boys attended a Quaker school, the main thing that Roger could remember about it being the forced nap that pupils had to have in the afternoon during which he never once succeeded in sleeping. In the summer of 1939, the family travelled to London, Ontario, Canada, where Lionel had obtained a job at the Ontario Hospital, and the family lived at 1000 Wellington Street, where they stayed until the end of the war with Germany, in 1945, when the family had also been able to celebrate, with their 4th child – a lovely baby daughter, Shirley Victoria, born on February 22nd 1945.

As for the boys’ schooling, while at London, Ontario, Oliver demonstrated his considerable precocity by moving rapidly up, owing to his extremely high rating on an IQ test and consequent attendance at what was called an “advancement class”, thereby skipping elementary school altogether and transferring to Central Collegiate, where he was two years younger than anyone else in the same class, and nevertheless being first or second in each subject. Jonathan was precocious in a different way, showing natural skills in most games, but particularly in chess. Roger did not excel at school while in Canada, having a “bumpy ride” at best, though the main problem was spotted by one of his teachers, Mr Stenett, who, with considerable insight, realized that Roger was basically just slow, and when subsequently given as long as needed in mathematics tests, could consistently get marks in the 90s where without the extra time would obtain perhaps 40% to 50%. This helped Roger’s confidence in later years! At home, Roger liked making things with moving parts that he had designed, like a perpetual calendar and a moon clock, and also some “pop-up” books that described simple stories that he wrote. He also found a close relation with Lionel constructing various regular polyhedra. Roger also gained much from his older brother Oliver, who read science-related books to him and, on one occasion, showing him what could be achieved with the manipulations of simple algebra. The family returned to England by boat in the summer of 1949, after the war with Germany had ended.

On returning to England, Lionel took up a professorship at University College, London, named the Galton Chair of Eugenics. However, Lionel, being strongly against the notion of “eugenics”, regarding this as a distinctly unsavoury political movement, rather than a scientifically motivated pursuit, was determined to change the name of his chair, which he finally succeeded in doing, changing it to its current title “Galton Chair of Human Genetics”, though this change took many more years than Lionel had anticipated. As far as the schooling of the three of their boys was concerned, Oliver was already at the stage of going to University, so he embarked on a 3-year degree course in Physics at University College. However, it was perhaps the jolt of moving directly to University in a different country, at the young age of 16, had been a bit more than had been anticipated, and he ended up getting what he referred to as “a miserable 2nd”. However, it was good enough for him to get a place to do research in statistical mechanics at Cambridge in 1948, at the age of 19.

In contrast, Roger started at University College School (UCS), in Hampstead, north London at the age of 14 in Grade 3, in which he was one year older than the normal age of 13 for that grade, apparently due to his grossly insufficient knowledge of Latin, for which he had obtained a little private tuition in Canada.

Fortunately, he was able to be top of the class that year and was promoted up to Grade 5 for the next year. After that, he was able to impress his teachers with his natural grasp of mathematics – geometry in particular – once finding a nice geometrical result unknown to his teacher.

At one point, Roger told Lionel that his maths teacher had informed his class that on the following day he would explain about the ideas of calculus. Lionel, with an element of desperation, immediately took Roger to a table in the corner of the room and gave him a rapid account of the ideas and the beauty of calculus! This made a big impression on Roger, not necessarily that he understood everything that Lionel told him, but more that Lionel regarded calculus as being such a beautiful and powerful set of ideas that he couldn’t bear to have someone else have the privilege of being the first to reveal this magic to Roger! Later, Roger learnt from Oliver that Lionel had done the same thing with him, several years earlier!

One day in Roger’s second year at UCS, there was an event when each pupil in the class, in turn, had to go up to a table in the room where the headmaster (Mr Walton) would discuss which specialist subjects would be appropriate for that pupil, for his final two years of study. When Roger’s time came, as he walked up to the table, he was of the clear opinion that he would be the one to carry on the family tradition to study medicine. Both Lionel and Margaret were keen on this. For many years, they had regarded Roger as being the obvious one to carry on the family tradition. Clearly Oliver would not do, as he was dedicated to the study of physics. Moreover, Jonathan’s primary interest was chess, having never expressed any interest in science at all. As Roger walked up to the headmaster’s table, he also believed that he would become a doctor – or perhaps a brain surgeon as even at that time he had hopes that he might find something out about how that strange and wonderful organ actually worked! Accordingly, Roger sat down, facing the headmaster, firmly believing that he would be a doctor. When the headmaster asked Roger what subjects did he want to study in his final two years, Roger asserted: “biology, chemistry, and mathematics”. However, the headmaster immediately responded: “No, that combination is not possible. If you want to do mathematics you can’t do biology; if you want to do biology, you can’t do mathematics. Make your choice.” Without hesitation, Roger said “Mathematics, chemistry and physics”. At that moment his medical career evaporated! His love for mathematics had become too strong for him to leave that subject behind.

When Roger returned home, and explained to his parents what had happened, they were furious, thinking that Roger had been too influenced by a schoolfriend who wanted to study nuclear physics, which they regarded as a taboo subject because of the nuclear bomb. How could he give up his medical career so easily? In the end, however, they won their case. Not only did Roger’s sister Shirley become a doctor, but she married one: Humphrey Hodgson – two for the price of one!

The next such conflict came when Roger wanted to study for a BSc Mathematics degree at University College London. Again, Lionel was unhappy about this, arguing that just studying mathematics alone was too limiting, and a broader perspective on scientific life would be much preferable. After having some difficulties in persuading Roger, Lionel consulted one of his mathematical colleagues at UCL, Hyman Kestelman, who very generously constructed a collection of around 12 different somewhat unusual mathematical problems, giving Roger the rest of the day to see whether he could answer perhaps two or three of them. By the end of the day, Roger had answered all of them, apparently almost all correctly. This impressed Kestelman enough to persuade Lionel to allow Roger to study for his mathematics degree, which he completed, in 1952, after three years, obtaining 1st Class honours. It may be mentioned that he did not just concentrate on his degree work during this period, but also spent time developing other ideas with colleagues, particularly Ian Percival (subsequently FRS) and Peter Ungar. During his 2nd year, Roger gave a seminar at UCL (which Lionel attended), on a geometrical theorem that Roger had found, concerning 8 conics, with numerous remarkable specializations – currently still unpublished!

It is undoubtedly true that from his particular family background – especially from Lionel, but definitely also, on occasion, from Oliver – Roger had grown up with a deep appreciation for science, mathematics, games, puzzles, and geometrical patterns. His siblings all became distinguished intellectuals. His older brother Oliver became a highly respected professor of statistical mechanics and FRS, having done important work on liquid helium and Bose-Einstein condensates, partly collaborating with Lars Onsager (1968 Nobel Prize in Chemistry). Roger’s younger brother Jonathan was a chess prodigy, winning the British Chess Championship a record 10 times (7 consecutively), and once beating the reigning world champion Mikhail Tal in a chess game, becoming a grandmaster and world leader at correspondence chess. Moreover, Roger’s sister Shirley became a distinguished geneticist.

In such an intellectual environment Roger’s entry into a research career was hardly unexpected, and officially started when he was accepted for research at Cambridge, in pure mathematics, specifically in algebraic geometry under the distinguished Cambridge mathematician William V.D. Hodge. Roger had perhaps felt a little uneasy about his choice of specific topic to do research on, having been given a list of possible topics to choose from, only one of which he could really understand. This concerned what are called “Cayley forms” (or “Chow forms”), a Cayley form being an intriguing but unusual way of representing an “algebraic variety” of any particular dimension, where an algebraic variety is, in essence, a curved space defined by algebraic equations. The problem that Hodge had suggested was to find a formula for the Cayley form of the intersection of two algebraic varieties, in terms of the Cayley form of each of them individually. Although this seemed like a complicated problem, its nature was clear, not require an understanding of the more sophisticated abstract conceptual ideas that Roger had not yet come to terms with.

Perhaps he had suffered somewhat from the fact that practically all of the graduate students starting mathematical research at Cambridge would have done an extra year, following their undergraduate degrees, probably doing Cambridge “Part 3”, or possibly, for a student coming from outside Cambridge, some other qualification judged as effectively equivalent. But Roger had had no such prior preparation. After a few weeks, Hodge, perhaps sensing an unease in Roger’s particular choice of research topic, suggested that he might sit in on a supervision session of one of his other beginning graduate students, working on a different topic, to see whether that might be more to Roger’s liking.

At this point, it should be mentioned that Roger was one of four graduate students taken on by Hodge that year. As it eventually turned out, one of the students gave up, after several weeks, while another (Michael Hoskin) did his three years of research, and wrote a very decent thesis to obtain his PhD, but then gave up mathematics to become a philosopher and historian of science, becoming a pre-eminent historian of astronomy. It was the third student in the group whose research session Hodge suggested that Roger might sit in on. Roger did this, but felt totally bewildered, finding that he could not really understand a word of what was going on! He came away thinking “If they are all like this, what am I doing here?”

What Roger didn’t know was that this student, a “Mr Atiyah” was no ordinary student. He would subsequently become Sir Michael Francis Atiyah OM FRS, President of the Royal Society, First Director of the New Isaac Newton Institute in Cambridge, winner of the highly distinguished 1966 Fields Medal in mathematics and a very early winner of the new Abel Prize for 2004 (considered the effective equivalent of a Nobel Prize, in Mathematics) and, indeed, Britain’s leading mathematician. So, they were not “all like this”! Roger stuck with his choice of topic, and after various twists and turns taking him in strange directions, he did eventually write a thesis which grew out of this “Cayley form” topic, finally obtaining his PhD somewhat belatedly in 1957.

As a way of overcoming his uncertainty and unease, with such highpower mathematical colleagues, Roger brought with him to Cambridge a 6-piece assembly puzzle – which he had designed and constructed from Perspex acrylic (using a hacksaw and a broken file) some 6 months before coming to Cambridge. The pieces would have to be put together by means of a complicated locking mechanism involving confusing-looking angular parts, to make a regular tetrahedron when assembled. It went the rounds among the various mathematics graduate students (including Atiyah) taking each of them about 5 hours or more of puzzling time to find the solution. Roger found this to be a good way to gain respect from his mathematical colleagues, despite his lack of confidence with the high-power mathematical activity going on, which he felt unable to keep up with.

The research problem that Roger chose to work on was not really “mainstream”, and it led him in some unorthodox directions, such as devising an unusual diagrammatic notation for the algebra of complicated systems of tensors, these being regarded by Roger as abstract algebraic entities. Certain such “abstract tensors” would have to be taken to be negative dimensional and these provided a formulation of Roger’s concept of “spin-networks” which much later were picked up by others in attempts to provide a combinatorial basis for a “quantized space”, such as in the theory of loop quantum gravity (developed by Ashtekar, Rovelli and Smolin).

One of the more orthodox concepts arising from this work on Cayley forms was the concept of a “generalized inverse”, which exists uniquely for any matrix with complex elements, and was the topic of one of Roger’s very earliest papers. It turned out that this idea was not actually new, having been initially found by E.H. Moore, who was primarily a philosopher, and Moore’s announcement of this discovery apparently lay deep within one of his philosophical treatises. It seems that this “Moore-Penrose pseudo-inverse” finds application in certain statistical problems, arising from Roger’s follow-up paper on this topic.

Roger’s interest in this “generalized inverse” notion arose from its use in the Cayley form problem, in the special case when both the algebraic varieties involved are simply collections of hyperplanes. The required algebraic expression is then a generalized inverse. However, this expression would need to work also when the algebraic varieties are not just collections of hyperplanes, but then it turns out that the expression does not always work and consequently there cannot be a polynomial solution to this general Cayley form problem.

But why should we expect a polynomial solution in any case? This expectation arose from an observation that Roger made very early on, that if this Cayley form problem were expressed in terms of “dual variables”, rather than the original coordinates, then the problem looked much neater than in its original form, and when Roger explained this to Hodge, he was very encouraged, and it looked as though a polynomial solution to the whole problem was very likely. But when Roger subsequently informed Hodge of his negative conclusion for an overall polynomial solution, it appears that Hodge didn’t believe him, but was too polite to say so directly! Instead, at the end of Roger’s first year Hodge decided that John A. Todd would be better as a supervisor for Roger, apparently because he thought that Todd would be better than himself at dealing with the very complicated expressions that Roger had become involved with.

However, there were two misconceptions involved in this decision. The first was that Roger was happy dealing with complicated algebraic equations! This misconception arose because Roger was able to use his diagrammatic notation, whereby certain equations can look pretty simple, although when written out in conventional notation can appear extremely complicated. The other misconception seems to be that Hodge thought Roger must have made a mistake in his calculations, and that Todd should be able to sort him out. Roger eventually found out that Hodge held this view only when, later in Roger’s third year, Todd had repeated (in conventional notation) a particular critical case of Roger’s calculations, finding that Roger was correct about the failure of polynomial solutions, and suggested to Hodge that he, also, might repeat that calculation. Roger was very struck by the delight in Hodge’s expression when coming up to Roger to tell him he had been correct all along!

A couple of years later, in 1957, Roger wrote a much more general document for his application for a Research Fellowship at St John’s College Cambridge, in which he provided an argument to show that whereas polynomial solutions do not always exist for algebraic/geometrical problems of this general kind, nevertheless, there is always a solution in terms of quotients of polynomials or as factors of polynomial outer products. There was no indication, however, of what this could look like, in the case of the Cayley form problem.

When he had been a graduate student in Cambridge, still working for his PhD in pure mathematics, Roger developed a strong friendship with Dennis Sciama, who had been a graduate student of the great physicist Paul Dirac. Dennis had been a colleague of Roger’s brother Oliver and had first met Roger in the Kingswood Restaurant in Cambridge, when Roger had come up from London and was visiting Oliver. Roger posed a query concerning Fred Hoyle’s very stimulating radio talks on cosmology at that time, but Oliver referred Roger to Dennis, who was sitting at another table. Dennis had no immediate answer but was impressed by Roger’s genuine interest in cosmology, so that when Roger later came to Cambridge as a graduate student, Dennis felt that it was worth developing Roger’s cosmological interests further, particularly in relation to the “steady state” model of cosmology, of which both Hoyle and Sciama were strong proponents. As it turned out, this friendship proved very valuable to Roger, as he learned a great deal of physics from Dennis. Not only did Dennis have a considerable knowledge of physics over a broad range, but he was an excellent expositor and had friends who were experts in several areas of physics, and often made efforts to bring such people together if he felt that it could be valuable in promoting research. Their friendship continued at a high level until Dennis died in 1999.

Despite Dennis’s important influence on Roger in opening his eyes to the wonders of physics, and how he might divert Roger’s talents in that direction, it should be mentioned that there were also other influences on Roger in that direction. In his early years as a graduate student, he attended three courses of lectures that could be said to have had greater influences on his future research than the pure-mathematical courses that were of direct importance to his official research project. These were an impressive course by Herman Bondi on general relativity (clearly of great relevance to Roger’s later work in that area), a course by Dirac on basic quantum mechanics (clearly also of later relevance), and a course by S.W.P. Steen on mathematical logic.

The importance of Steen’s course to Roger was that he described the notion of computability (Turing machines, etc.) and Gödel’s theorem(s), the latter being a revelation to Roger, providing the case that the quality of human understanding cannot be a computational process. Many years later, this insight led to two of Roger’s semi-popular books “The Emperor’s New Mind” and “Shadows of the Mind” (Oxford University Press 1989 and 1994), where Roger presented his case that the phenomenon of consciousness (specifically “conscious understanding”) could not arise from classical-physics processes, nor even from Schrödinger’s quantum evolution of the wave-function, but had to be an effect of the other part of quantum mechanics, namely the “collapse of the wave-function” (denoted OR = objective reduction) which Roger later provided arguments for it being an objective gravitational effect – a “gravitisation of quantum mechanics,” rather the more usual reverse endeavour of “quantized gravity”. When Stuart Hameroff, (University of Arizona) read “The Emperor’s New Mind”, he contacted Roger to suggest that neuronal microtubules (then unknown to Roger) might be promising locations for preserving quantum coherence long enough for this OR effect to be appropriately “orchestrated” thereby providing the macroscopic effects of consciously controlled actions. Though undoubtedly speculative in various respects, this “Orch-OR” proposal is now regarded, after some 20 years, as a serious contender amongst current theories of consciousness.

There were also other topics that Roger worked on from time to time. He constructed self-contradictory pictures, stimulated by the works of M.C Escher, called “impossible objects”. He also produced quasi-symmetric tiling patterns, which have close relations to the quasicrystals discovered by Dan Shechtman (2011 Chemistry Nobel Prize).

Yet, Roger had a particular respect for Dennis Sciama, not only for his broad understanding and promotion of physical science, but also for his scientific integrity. For over a decade, Dennis had been a strong promoter of steady-state cosmology, according to which the universe had no beginning, its eternal expansion being sustained by the continual creation of hydrogen to compensate for the depletion of material due to the expansion. However, when in 1964 Penzias and Wilson (1978 Physics Nobel Prize) provided a convincing refutation of the steady-state model, with their discovery of the microwave background (CMB), Dennis made gave numerous powerful lectures refuting his earlier viewpoint, and now firmly supporting the idea of a “Big-Bang” origin for our universe and strongly encouraged research into the physical nature of this initial state.

This momentous shift in viewpoint strongly influenced Roger’s own thinking. How is one to deal with the physics of this initial state, where space-time curvatures appear to have to diverge to infinity, resulting in what is referred to as a “singularity” in the classical space-time structure. Large curvatures mean small radii of curvature, so one appears to be forced into considering the nature of physics at the ridiculously tiny “Planck-scale” lengths and times (~10^–33 cm and ~10^–43 s) which are enormously smaller than those encountered in ordinary particle physics. This is indeed taken to be the realm of quantum gravity, where it is supposed that the very nature of space-time must itself be treated in some kind of quantum-theory terms, whether or not the above-mentioned “gravitization” of quantum mechanics also plays a role in unifying these two great theories of 20th century physics.

Roger’s own concern with such “singular” space-time states occurred several years earlier, being basically initiated by a lecture given by David Finkelstein, in early 1959, in the second year of Roger’s Research Fellowship at St Johns College Cambridge. This talk was given at Kings College London, and Dennis drove he two of them there, having persuaded Roger that the talk would be of interest to him – as indeed it turned out to be! Finkelstein’s talk was to show how, using an appropriate choice of coordinates, one can eliminate what had been commonly referred to as the “Schwarzschild singularity” in Karl Schwarzschild’s famous solution of Einstein’s equations for the curved vacuum space-time for the gravitational field of a static spherically symmetrically symmetrical body. This “singularity” occurs at the radius r = 2m, in units where Newton’s gravitational constant G and the speed of light c are both taken to be unity: G = 1, c = 1.

At this radius, a term in Schwarzschild’s expression for the space-time metric becomes infinite, and this is why this radius was referred to as a “singularity”. However, this feature arises from a demand that the solution is time-symmetrical, and Finkelstein, in his talk, showed how an elegant time-asymmetrical change of coordinates can remove this singularity, providing a picture that we currently refer to as a “black hole”. This was the first time that Roger had seen this extension to within the r = 2m radius (though he later learned of other such ways of extending the Schwarzschild solution to within this radius, though not done with the insight or elegance that Finkelstein had demonstrated in his lecture.

After the talk, Roger told Finkelstein about spin-networks, which intrigued him. He later told Roger that on that day they had “swapped topics” since Roger subsequently worked on general relativity and he on combinatorial space-time, this being his approach to the issue of quantum gravity.

Roger began to wonder about the singularity at r = 0, that persists despite the coordinate change. It had seemed to him that this central singularity was much more robust than that at r = 2m, especially since the space-time curvature becomes infinite at r = 0. He began to wonder whether there might be some theorem which showed that even if we perturb the solution away from the spherical symmetry assumed by Schwarzschild, a space-time singularity would persist. He had not heard of such a theorem and began to wonder whether some different slant on the equations of general relativity might be helpful for this. His thoughts turned to the theory of 2-spinors that provides a distinctive way of analysing space-time. This had been greatly clarified for him by Dirac’s 2nd-term lectures in early 1958. In Roger’s diagrammatic notation, the tensor lines in the diagram become double stranded 2-spinor lines, the formalism allowing manipulation of strands independently, thereby providing a way of examining general relativity in ways that are not so immediately addressed in the standard tensor formalism. Many years later, Roger collaborated with Wolfgang Rindler to provide a 2-volume account explaining these procedures in detail (including the “spin-coefficient techniques introduced by Roer and his close colleague Ezra T. Newman): “Spinors and Space-Tine” (Cambridge University Press, 1984 and 1986). Volume 2 also gave an extended account of the theory of twistors, that Roger had introduced in 1967, and which became a major part of Roger’s later research, involving many of his students.

The 2-spinor formalism has an advantage over the standard tensor formalism which makes it much clearer that the free gravitational degrees of freedom are described by the Weyl conformal tensor, closely analogously to the way that the electromagnetic degrees of freedom are described by the Maxwell field tensor. Here “conformal” refers to the structure given by the metric only up to proportionality. The conformal structure of spacetime is effectively its causal structure, i.e., it determines which points can be connected by time-like or null (light-like) curves, this being central to the analysis that Roger eventually used to show that singularities cannot be avoided in gravitational collapse, irrespective of the spherical symmetry of Schwarzschild’s space-time, thereby providing the theorem that Roger had wondered about in 1958, following Finkelstein’s lecture. Roger’s 1965 paper on this, earned his share of the 2020 Physics Nobel Prize. It had been motivated by the discovery of the violently energetic quasars, indicating the presence of very distant enormous gravitational collapse events – black holes!

The 2-spinor formalism had earlier been found useful by Roger in relation to work being carried out mainly in the 196os, concerning gravitationally radiating systems and the mass-energy carried away by the gravitational waves. Following initial contributions by Andrzej Trautman and Bondi, with collaborators, it had indeed become clear that in an asymptotically flat space-time, there was a clear-cut contribution to the mass in the waves, carried away from the sources.

In this work, an intriguing an effect, known as the “peeling-off” property of the Weyl tensor, was pointed out by Rainer Sachs. This was best understood in terms of 2-spinors, and Roger showed, in a 1965 Royal Society paper, that Sachs’s peeling property can be understood as the spin-2 massless field described by the Weyl tensor being finite at a conformally defined boundary J, attached smoothly to the space-time, J being referred to as the space-time’s “conformal infinity”.

Roger also studied cosmological models, using this same conformal technique for “bringing infinity in” to provide a smooth conformal boundary J. He obtained a clear role for Einstein’s cosmological constant Λ, finding that Λ>0 (the observed “dark energy” value) corresponds to J being spacelike, where in the case of asymptotically flat space-times, J is null.

This conformal “squashing down” of the future can be used also in the reverse sense of conformally “stretching out” the big-bang singularity of a cosmological model to obtain a (normally spacelike) initial boundary B. However, this situation is very different from the time-reverse of a realistic collapsing universe, which would involve the congealing of numerous black-hole singularities, very probably involving wildly complicated oscillating and diverging Weyl curvature, as suggested by the BKLM picture (Misner in 1969 and, separately, Beinskii, Khalatnikov and Lifshitz in 1970). One may regard BKLM as presenting an enormous entropy in the gravitational degrees of freedom, hugely exceeding the already enormous Bekenstein-Hawking entropy in the individual congealing black holes, the latter already vastly swamping all other forms of entropy in our observed universe. All this is consistent with the 2nd Law of Thermodynamics and with direct observations, where the earliest direct observations reveal a very uniform CMB, indicating that this enormous reservoir of gravitational degrees of freedom had still hardly been touched, 380,000 years after our Big Bang!

No conventional form of quantum gravity could provide such a vast time-asymmetry in the past/future singularity structure. Nor could the mere introduction of an “inflation field”, the assumed source of an inflationary very early stage of the universe, so we appear to be presented with a fundamental conundrum.

Accordingly, in 2006 – as described in his books Cycles of Time (Knopf 2010), and Fashion, Faith, and Fantasy in the New Physics of the Universe (Princeton University Press 2016) – Roger put forward his exotic “conformal cyclic cosmology” proposal (CCC), proposing that the Big Bang was in fact the conformal continuation of an earlier “aeon” whose conformally squashed remote future joins smoothly to our conformally stretched Big Bang of our own “aeon”, this continuing in both directions with an unending succession of such aeons, joined successively in this way. This incorporates a proposal due to Paul Tod that the conformal smoothness of our B suffices to characterize its extraordinary specialness. Though highly unconventional, this model not only resolves the aforementioned conundrum, but has also obtained some remarkable observational support, the strongest, published in 2020 in the Monthly Notices of the Royal Astronomical Society by Daniel An, Krzysztof Meissner, Pawel Nurowski, and Roger, confirming a predicted effect of CCC at a 99.98 % confidence level.

Roger Penrose had two marriages: in 1958 to Joan Isabel Wedge (divorced 1980; died 2019) and in 1988 to Vanessa Dee Thomas. There were four sons altogether: 1963 Christopher Shaun, 1964 Toby Nicholas, 1966 Eric Alexander; and then in 2000 Maxwell Sebastian.

© The Nobel Foundation 2024