Scientists exhausted by the relentless demand to “demonstrate impact” and churn out peer-reviewed papers find ways of cheering themselves up. A popular consolation is to imagine reviewers’ reports on Einstein’s “grant application” for his work on special relativity, condemning his revolutionary thoughts as sheer speculation, devoid of any practical application, and worthy of no funding at all.
Lost golden ages are rarely as golden as we remember: back in 1905 Einstein wasn’t funded either, but still working in the Swiss patent office. The rueful jokes do, however, make a valid point about the way conservatism and bandwagon-riding often dictate progress in scientific careers today. Now you need polish, pizzazz, and state-of-the-art facilities. Gone are the days when it was possible to conduct cutting-edge experiments, as Ernest Rutherford did, with little more than sealing wax and string. But something has been lost in the face of the incessant need to score CV points, create spin-off companies, and descend into ever-narrower specialisms. The greatest of scientists, like physicist Erwin Schrödinger, have often thought profoundly outside their own particular specialisms; others, like Francis Crick, one half of the pair who unravelled the mysteries of DNA and partly inspired by Schrödinger, had the versatility to switch fields entirely.
Many virtues of that vanished age, before the intellectually narrowing pressures on today’s careers, are preserved in the person of the veteran British mathematical physicist, Roger Penrose—a theorist of black holes and quantum particles, sometime collaborator of Stephen Hawking, and an unlikely best-selling author. I met the 85-year-old don in the new Mathematical Institute at Oxford, where he is still cooking up challenging new ideas. You have to enter the building across a tiling scheme Penrose invented in the 1970s, which covers the courtyard in a pattern that seems to be orderly but can never quite repeat itself.
Although his insights are often fiendishly technical and expressed in eye-watering mathematics, Penrose is irrepressibly eclectic in his learning. He is given to mixing the insightful with the wildly speculative in a way that is almost unknown today, floating ideas that younger colleagues would never dare to—such as the notion that quantum mechanics might explain consciousness. Penrose shrugs off labels such as “maverick,” pleading that he is “much more accepting of conventional wisdom than most of the others I know.” It is hard to tell how much of this bemusement is real and how much a wry performance, but whatever it is that he seeks, it’s neither approval nor modish notoriety.
His career has traced the remarkable arc of physics over the second half of the 20th century, a period during which the baffling intricacies of general relativity have moved from the mathematical fringe of his discipline to its heart, culminating in the discovery of gravitational waves last year (in which he played no small part). He is a representative of the now near-extinct generation—which included John Wheeler, Murray Gell-Mann, Philip Anderson and Richard Feynman—who launched themselves into an unfamiliar universe armed only with their wits and imagination. They thought about whatever they fancied, and found threads that hinted at a unified concept of reality. They all seemed to have something insightful to say about pretty much any problem in physics.
On meeting Penrose one wonders how on earth such a fruitful mind is formed, and whether it could ever develop in and among the intellectual silos of today. The most important thing is not exactly what he writes about string theory, cosmology and quantum mechanics in his latest book—Fashion, Faith and Fantasy—but that a book so wide and deep in its erudition could be written at all. If his successors cannot do the same, science will be all the poorer.
The eye’s mind
Penrose hails from one of the great intellectual dynasties of the 20th century. His father Lionel was a distinguished psychiatrist and geneticist, his uncle was the surrealist artist Roland Penrose. Roger was one of four children; older brother Oliver became a theoretical physicist, younger brother Jonathan was British chess champion a record-breaking 10 times, and sister Shirley Hodgson is a professor of cancer genetics.
In this house there was no escaping mathematics. “I used to make polyhedra with my father,” Penrose told me. “There were no clear lines between games and toys for children and his professional work.” That, needless to say, may have been a mixed blessing: “He wasn’t very good at relating to us in an emotional way—it was all about science and mathematics.”
But if number games substituted for play in the Penrose home, one happy result may have been an almost playful quality of his approach to mathematics. His thinking is animated by a phenomenal visual sense of geometry. The sheer power of his mind’s eye is, his peer Martin Rees, the current Astronomer Royal, suggested to me, his defining characteristic.
"Penrose's career has traced the remarkable arc of physics over the second half of the 20th century"In all of Penrose’s books, abstruse theories are illuminated by pictorial representations. He puts this visual sensibility down to his father, but his grandfather James Doyle Penrose was, like his uncle Ronald, a professional artist. In Roger, this ability manifests itself in an intuition of complex spatial relationships, which gave him an affinity for the Dutch artist MC Escher. While a graduate student, Penrose saw “an exhibition in the Van Gogh Museum by this artist I’d never heard of. I was quite blown over. I came away and drew pictures of bridges and roads, which gradually simplified into the tribar.” This is the optical illusion of an “impossible triangle,” the corners of which make sense spatially on their own but not together.
Penrose worked on these illusory structures with his father, who devised a staircase that seemed to ascend forever around the perimeter of a square. They published their inventions in the British Journal of Psychology, and sent a copy of the paper to Escher, who wrote back enthusiastically and was inspired to make his famous lithograph of the endless stair.
Later, while in the Netherlands, “I telephoned him, and he said come along and have some tea,” Penrose told me. “I expected him to be in a house with all these impossible staircases and so on, but it was very neat and tidy.” He was deeply impressed with Escher’s untutored intuition. “He said he was no good mathematically at school, but I suspect his teachers didn’t appreciate his skill. His understanding of the geometry was remarkable.” Escher’s intricate designs, of interlocking lizards and birds morphing into fish, were evidently in Penrose’s mind when, in the 1970s, he dreamed up those ingenious rhomboid tiles—without gaps, and yet also without repetition—which are on display outside his office today, and which also turned out to explain the baffling atomic structures of metal alloys called quasicrystals.
Penrose sets Escher’s images to work in his new book to show how shapes and lines in space can be distorted by changing the underlying geometry of the coordinate system. (Think of how different the continents of the world can look when projected in different ways onto a flat map.) Get your head around this morphing, and you’re one step on the way towards understanding Einstein’s theory of general relativity, which explains gravity by considering how a distortion of spacetime—a four-dimensional “coordinate grid,” if you like—produced by the presence of mass, bends the trajectories of objects and light waves moving through it.
This is difficult stuff, but things become clearer if you can—in Penrose fashion—find the right imagery. Imagine drawing parallel lines on a deflated balloon, then blowing it up and finding that they no longer seem parallel on the inflated surface. By deforming the underlying fabric, Euclid’s rules of geometry (“parallel lines never cross”) are rewritten. Such non-Euclidean thinking is vital to Einstein’s theory, which rightly predicted that light rays are bent by gravity. The theory also predicted the expansion of the universe: an expansion of space itself, not unlike that inflating balloon. But Einstein, like most of his contemporaries believing that the universe was fixed and eternal (in a “steady state”), introduced a cosmological fudge to get around this apparent inconvenience.
Handling the geometric complexities of general relativity involves some fearsome maths, known as algebraic geometry. At Cambridge, Penrose studied that subject under the Scottish mathematician William Hodge. At that time, general relativity itself was far more likely to be studied in a maths than a physics department. Although Arthur Eddington had observed starlight being bent by the sun’s gravity during a solar eclipse in 1919, in line with general relativity’s predictions, even in the 1950s the theory really wasn’t knitted into the mainstream of physics. Nobody knew quite what to do with it. Only for absurdly large masses did its account of gravity differ significantly from that of Isaac Newton, which had worked well enough for hundreds of years.
While an undergraduate, Penrose went to hear the great astrophysicist Fred Hoyle lecture on cosmology. Hoyle did pioneering work on stars and the formation of elements within them. But he remained an advocate of a “steady-state” universe, despite the growing evidence that the universe was expanding: he is said to have coined the term Big Bang as a derisory epithet. “He was describing the steady-state model and things about the universe accelerating,” says Penrose of that lecture, “and I drew little pictures and convinced myself that what he said couldn’t be true.”
When Penrose asked his brother Oliver if his criticisms of Hoyle made sense, Oliver directed him to the Cambridge cosmologist Dennis Sciama. Thanks to the 2014 Stephen Hawking biopic The Theory of Everything, one can almost say that the rest is history: Sciama took him under his wing. Penrose is gently amused by the film, which shows Hawking arriving in Cambridge in the early 1960s to work under Sciama too. “There is somebody who doesn’t look like me but is supposed to be me [Christian McKay], and he gives a talk, and in the audience is a starstruck Stephen Hawking,” he says, “but in reality he wasn’t there.” Penrose adds, “The portrayal of Hawking was not so bad, but it wasn’t good on all sorts of things technically.”
Poor Hoyle never stood a chance against Sciama’s brilliant protégés. Famously the young Hawking, already needing a stick for support, stood up during a lecture on cosmology given by Hoyle to the Royal Society in 1964, and pointed out an error. When a bristling Hoyle demanded how he knew, Hawking coolly replied that he had “worked it out.” The contrast with Penrose, who went away to check his result, sums up the two men: Hawking brash and attention-seeking, Penrose uninterested in limelight or conflict. But whatever their differences, it was indeed Penrose’s work that switched on Hawking to general relativity and black holes.
At Sciama’s prompting, Penrose headed to a lecture in London by David Finkelstein, an American physicist who was working on an aspect of general relativity connected to black holes: stars that are predicted to collapse under their own gravity until they shrink to nothing, leaving only an infinitely dense point and a gravitational field so strong that not even light can escape. Such a point is called a singularity. General relativity seemed to predict that it could occur, but many physicists in the 1950s considered it a mere mathematical quirk. Finkelstein showed in his talk how such a singularity might really exist. Penrose had his doubts but was nonetheless hooked. In 1959 he travelled to Princeton to work with legendary physicist John Wheeler, who is credited with inventing the term “black hole.”
"His thinking is animated by a phenomenal visual sense. The power of his mind's eye is his defining characteristic"At around this time, black holes suddenly began to seem more than just a weird, even absurd, prediction of general relativity. Astronomers were discovering very distant objects which, while no bigger than a solar system, seemed to be emitting more energy than an entire galaxy. It was hard to explain that without some phenomenally dense thing such as a black hole. “Up to that point, general relativity had been the province of people fiddling around with mathematics,” says Penrose, but now he and his colleagues were confronting actual “objects in which the theory seems to be playing a role.”
Penrose was able to show that the conditions for the formation of a black hole were much less unlikely than previously thought—they could be real. When Hawking saw this work in the early 1960s, they began collaborating on gravitational singularities. The pair realised that you could think of the Big Bang as a collapse to a singularity in reverse: you start with a point of infinite density and then let it expand. In this way, they married ideas about black holes with the cosmological theory of the universe. The ramifications are tremendous: for one thing, it becomes possible to imagine entire new universes forming from black holes—so that our own universe could be just one among many.
The concept of a singularity—mass compressed into an infinitely small space—conflicts with the other foundational theory of physics, quantum mechanics, which insists that the fundamental fabric of nature is granular, and can’t be condensed without limit into an infinitely small space. Black holes thus become more than astrophysical oddities: they force the issue of how to reconcile the 20th century’s two great accounts of the way the physical universe works—general relativity and quantum mechanics. Penrose, whose first passion had been quantum physics, naturally had his own thoughts on the way to proceed.
Speaking to him about his career, you get no sense that there ever was any plan or direction—only interests and curiosity. When he published, it was not out of any professional obligation, only because he had something worth saying. Although his mentors obviously recognised his genius, there is a striking lack of urgency in how he progressed. His turn towards general relativity, once considered something of a backwater in physics, was professionally risky, and perhaps speculative, but that didn’t trouble Penrose. “I just had various interests which weren’t really directed at what I was supposed to be doing,” he says. In science today, you need to know exactly what you are supposed to be doing—it has become something of a treadmill in which you must establish your niche and publish your findings often, ideally in top journals.
Reading between the lines in Fashion, Faith and Fantasy Penrose seems to be worried about such pressures. The particular “fashion” that he attacks is the attempt to unite relativity and quantum mechanics in string theory, in which all the known fundamental particles are considered to be composed of unthinkably small vibrating entities called strings. It’s not string theory per se that Penrose dislikes but the direction it has taken, which requires extra “hidden” dimensions of space. To make it work, it seems that six or seven more spatial dimensions may be needed beyond the usual four of Einstein’s spacetime. We don’t experience these extra dimensions, the story goes, because they are tightly “rolled up,” much as a three-dimensional garden hose looks like a one-dimensional line from a distance. But there is no evidence for extra dimensions, nor any plausible way of obtaining access to them directly: if you were to deploy the sort of particle-smashing experiments carried out at the Large Hadron Collider at CERN, the energies required would be so huge that the accelerator would need to be literally of astronomical dimensions. Many physicists object to string theory for this reason—it isn’t verifiable, they say, and so oughtn’t to qualify as science.
But Penrose, characteristically, has different objections. He has his “public” reason to doubt multidimensional string theory, but also, he confesses, “private” concerns—a way of saying that only one objection is technical, the other intuitive or even emotional. Technically, a universe with so many dimensions is hard to keep under control: it has so many ways to move and shake, that it’s hard to see how things could ever be reduced to the orderly three (or four) dimensional world that we know. But the “private” reason, Penrose cheerfully admits, is that his own ideas about quantum theory would unravel if there really were this many dimensions. Those ideas, he says, fit together so beautifully that he just can’t imagine nature wouldn’t have made use of them. That sentiment echoes Einstein, who was once asked what he would have said if Arthur Eddington’s eclipse observations had contradicted his theory. So much the worse for the experiment, he said: “I would have been sorry for the dear Lord, for the theory is correct.”
"The pressures facing today's young research scientists makes it hard for them to find the time simply to think"String theory has often been presented as the only game in town, so the only way for a young fundamental physicist to get ahead becomes to buy into it. “Students wishing to do research into foundational physics, such as quantum gravity,” Penrose writes, “are still mainly guided into string theory, very often at the expense of other approaches with at least as much promise.” As this intellectual bandwagon rolls on, alternative ideas may be ostracised and become a recipe for career suicide. While science must be discerning and selective, it also needs to keep options open, especially when dealing with matters as speculative as those in string theory.
Was it ever thus? Perhaps: Einstein’s special relativity faced scepticism and, absurdly, was never rewarded with a Nobel Prize. But the institutions and rewards in science today encourage conformism. A recent study of the topics chosen for biomedical chemistry research revealed a growing tendency to play it safe. All of this is exacerbated by the trend towards assessing achievement by tallies of how often your papers are cited. And the peer review process in both publication and funding is notoriously conservative, favouring work that fits solidly within a paradigm over anything disruptive.
One widely-used metric is the so-called h-index, which measures consistency of citation: if you have published 20 papers that each earn at least 20 citations, your h-index is 20. Even though this number is, by construction, bound to rise over the course of a career, Penrose’s h-index is still nothing special today—which shows it is not a measure of everything that matters in a creative and influential scientist.
Worst of all, the career structures and pressures facing young researchers make it increasingly hard to find the time simply to think. According to several early-career scientists interviewed by Nature, the constant need to bring in grant money, to produce papers and administer groups, leaves little time to do any research, still less indulge anything so abstract and risky as an idea.
And if you are struck by the thunderbolt of insight, you’d better be right. The stakes are so high now that a misstep can leave you with a reputation for intellectual incontinence (if not incompetence). Yet no great scientist ever came up with a big idea without sticking their neck out, and most probably without first floating half a dozen other thoughts that proved to be wrong. Forgive the cliché, but failure is indeed the price of creativity. You want an example? Let’s go back to Penrose.
Madness with method
His physics began with quantum mechanics, and he formulated his ideas here in geometric, topological terms. One of the fundamental properties of quantum particles is called “spin,” which is somewhat—but not quite—like the familiar spin of a cricket ball. Spin is about “angular momentum,” which in the case of a cricket ball basically means how fast the ball is spinning. Try and think about quantum spin the same way, however, and you find that the particle seems to rotate twice to return to where it started from: it’s almost as if the object is spinning in twisted space. This motion can be described using mathematical objects called spinors.
Since the late 1960s Penrose has been developing a theory that literally adds a new twist to spinors, positing objects called twistors that reveal deep connections between quantum theory and the shapes of spacetime, and which he thinks might point the way to a theory of “quantum gravity,” attaining the long-sought goal of reconciling quantum theory and general relativity. It’s a niche field, not least because it’s so difficult. What most physicists associate with Penrose’s work on quantum mechanics, however, is his allegiance to two related and unconventional ideas.
The least controversial is a belief that quantum mechanics as we know it might break down when confronted with gravity. He suspects that the reason we don’t see the counter-intuitive properties of quantum particles—most notably the way they seem to exist simultaneously in two or more states, or “superpositions”—in the everyday world is that when objects get big enough to “feel” significant gravitational force, quantum mechanics needs modifying if it’s to describe them. Because general relativity says that gravity is caused by masses bending spacetime, a quantum superposition of a large object—crudely, seeming to put it in two places at once—would have to superimpose two simultaneous structures of spacetime. That can’t be countenanced, Penrose says.
So in the standoff between quantum mechanics and general relativity, Penrose thinks that the former will crack first. The trouble is, quantum theory as it stands has been repeatedly tested and never yet found wanting. This has led to a strong belief—the “Faith” of his book’s title—that it must be correct without modification. But that faith wasn’t shared by several of the theory’s early proponents, including Einstein. The paradoxes that result when quantum-style descriptions are applied to objects of everyday size was what Schrödinger was illustrating with his cat.
So Penrose thinks that there is some real, physical “collapse” of a quantum superposition as objects grow big enough for gravity to become a significant part of the picture. It’s still a minority view, although Penrose says experimentalists are very close to being able to test it—and he confidently predicts they will find discrepancies with the standard theory.
Penrose’s thoughts about the collapse of superpositions led him to propose, on the basis of recondite reasoning, that quantum effects might be responsible for consciousness. Having put the idea forward in his 1989 book The Emperor’s New Mind, Penrose and anaesthesiologist Stuart Hameroff went on to claim that protein strands in the brain called microtubules might host the superpositions of quantum vibrations demanded by their theory. Penrose thinks that the collapse of these superpositions could enable the brain to solve problems that are formally “non-computable,” that is, uncrackable by any digital computer.
The details are vague and the biophysics unconvincing. Had virtually anyone else put forward this theory, they’d have been dismissed as a crank. One might say Penrose’s eminence gives him licence, but this is the wrong way to see it. He concedes his ideas are “crazy,” but they are not random speculations. They draw from the same well of profound feeling for the rules and the shapes of nature, guided by an uninhibited spirit of inquiry that has been lucky enough never to have to worry about job security, and is too free to obsess about prizes. (Hawking, in contrast, seems increasingly preoccupied with his Nobel prospects.)
Applying the “We shall never see their like again” rhetoric to Roger Penrose should not be taken to imply that today’s scientists are all feeble-minded bean-counters. But the significance of his career isn’t merely as a sentimental bridge to a lost age. He is a living link to a time when science really was done differently: a time when young researchers could wander, wonder, blunder—and still succeed. A young Penrose would probably thrive in any environment; in today’s world, however, he would have to do so in spite of everything else.