# Sir Roger Penrose: physicist and mathematician

Exactly a year ago, I was lucky enough to meet Sir Roger Penrose after a talk he gave in Oxford on his book *Fashion, Faith, and Fantasy in the New Physics of the Universe. *This was a huge deal for me because I've been so inspired by Penrose over the years. I was recently digging through some old files and found this biographical essay I wrote on Penrose in 2013, which I thought I would share in honor of the occasion. Funnily enough, I contacted him when writing this essay to see if I could get some quotes but never got a response!

Also, sorry in advance for the informal writing and referencing. Hopefully the information is still interesting and useful, if incomplete.

## The makings of a mathematician

Roger Penrose comes from a family of competitive overachievers. His mother Margaret was a doctor, and his father Lionel was a renowned medical geneticist and elected Fellow of the Royal Society. His older brother Oliver went on to study statistical physics, teaching primarily at Heriot-Watt University in Edinburgh, and his younger brother Jonathon was the British Chess Champion ten times, later becoming a psychology lecturer.

Penrose’s father Lionel was particularly influential. His Quaker background led to a strict household, where Penrose reflects, “I don’t think we were even allowed to read novels, certainly not on Sundays.” However, scientific inquiry, problem-solving, and puzzles were always encouraged. Though Lionel’s genetics research was focused on Down syndrome, he brought many scientific and mathematic interests home to his children. He would make puzzles and toys for them in a wood shed out back, developing wooden models that could reproduce themselves. Penrose writes, “It was very hard to talk to my father about anything personal. We talked about science. We used to go for long walks. He would describe how things grow. It was fascinating. He was certainly a great inspiration to me on the scientific side,” and in a different interview, he added, “The important thing about my father was that there wasn’t any boundary between his work and what he did for fun. That rubbed off on me.” As Roger Penrose developed as a mathematician and theoretical physicist, he replicated this attitude through an unwavering enthusiasm and commitment to his work.

Lionel’s influence also shaped some of Penrose’s most memorable work—Penrose tiles. Though not the most useful of discoveries, Penrose tiles are remarkably beautiful repeating shapes that fit together in solids with pentagonal symmetry. Penrose’s interest in the tiles “has to do with the idea of a universe controlled by very simple forces, even though we see complications all over the place…It was an attempt to see how the complicated could be satisfied by very simple rules that reflect what we see in the world.” This geometric discovery was sparked by early talks with his father. Penrose reflects, “I remember asking him—I was around 9 years old—about whether you could fit regular hexagons together and make it round like a sphere. And he said, ‘No, no, you can’t do that, but you can do it with pentagons,‘ which was a surprise to me.”

As influential as his parents were, they were unable to persuade Penrose to follow in their footsteps and become a medical doctor. His fate was decided at age sixteen in London, England, after living in Canada during World War II. With two years left of the British equivalent of high school, students had to choose certain subject areas to specialize in. Unable to combine Biology, a necessity for a medical career, with his true passion Mathematics, Penrose infuriated his parents and sealed his fate. He told his story:

“I remember an occasion when we had to decide which subjects to do in the final two years. Each of us would go up to see the headmaster, one after the other, and he said, ‘Well, what subjects do you want to do when you specialise next year?’ I said, ‘I’d like to do biology, chemistry, and mathematics’ and he said ‘No, that’s impossible—you can’t do biology and mathematics at the same time, we just don’t have that option.’ Since I had no desire to lose my mathematics I said ‘Mathematics, physics, and chemistry.’ My parents were rather annoyed when I got home; my medical career had disappeared in one stroke.”

“Rather annoyed” might have been an understatement, as two years later, the Penrose family still remained divided as to what path Roger should take. Roger’s father Lionel had been appointed a human genetics professor at University College, London, enabling Roger to attend the university for free. However, when Roger proposed pursuing a Mathematics degree, he reflected, “My father didn’t approve at all. Mathematics might be right for people who couldn’t do anything else, but it wasn’t the right thing to make a real career of.” Lionel and Roger were both fiercely stubborn, so they resolved the conflict in the most objective way they could—through an aptitude test. Lionel asked one of the University College’s mathematicians to create a special test for Roger. The test had twelve difficult questions. While the mathematician had expected Roger to solve one or two over the course of the entire day, Roger was able to solve all twelve, correctly, in just a few hours. Convinced, Lionel gave his son his blessing to study mathematics, and Roger proceeded to spend the next four years at University College, London, achieving his B.Sc. degree with First Class Honours in Mathematics.

After completing his first university degree, Roger decided to continue his pure mathematics studies at the University of Cambridge. He began studying algebraic geometry under the tutelage of Hodge, but ended up working under John Todd for his second two years. Penrose and Hodge were unable to see eye-to-eye due to Penrose’s unique way of approaching mathematics—he did every problem geometrically, using pictures and images to assist him. While this novel approach became a great strength as Roger transitioned to physics, it caused his mentorship relationship with Hodge to break down. Penrose humorously recounted:

“I think part of the reason Hodge threw me out, if I can use that term, was that I decided that the problem he suggested had no solution… He was always terribly polite, although he didn't believe me. He never quite said so in so many words, you see. He just said ‘Oh that sounds interesting. Would you like to explain it to me?’ And I tried to show him this funny notation I had developed. I was writing tensors in terms of blobs, with arms and legs... And then I developed this diagrammatic quotation…and it was totally incomprehensible to him. I think he thought I was a bit mad or something.”

Though Penrose did achieve his Ph.D. for research in algebra and geometry under Todd from Cambridge in 1957, the most important outcomes of his Cambridge experiences were not his mathematical works—papers like “A Generalized Inverse for Matrices,” “A Note on Inverse Semigroups,” and “On the Best Approximation Solutions of Linear Matrix Equations”—but his new interest in physics and his new mentor Dennis Sciama.

## A Student of Sciama's

Penrose attributes his original interest in physics to a series of radio presentations on astronomy and cosmology by Fred Hoyle that he heard during his last year as a student at University College in London. The talks started local, regarding planets and stars, and then stretched into cosmological theories. Though this was his first real exposure to the subject, Penrose already questioned what he was hearing. “In the steady state model, as he [Hoyle] was describing it, the galaxies would disappear from view. The idea was that when they exceeded the speed of light, the light wouldn’t get here. I remember being very puzzled by this and drawing various pictures and so on.”

He first met Dennis Sciama that same year on a trip to visit his older brother Oliver at Cambridge. Oliver was currently studying at Cambridge, and he and Sciama were friends and fellow research students. When Roger learned Sciama was a cosmologist, Roger eagerly showed Sciama the spacetime diagrams he drew refuting Fred Hoyle’s disappearing galaxy conjecture. Sciama was amazed at Roger’s geometric approach to the problem and quickly saw that he was right, and they became fast friends.

When Roger attended Cambridge as a pure mathematics student, mentored by Hodge and then Todd as mentioned above, he continued to pursue his physics interests on the side. He often cites the two most inspiring lectures he ever attended to be Hermann Bondi’s general relativity course and Paul Dirac’s quantum theory course, both of which he took during his first year at Cambridge and which had nothing to do with his major. During this time, Sciama also became an incredibly important mentor for him. Though Penrose was committed to finishing his mathematics work, Sciama prepared Penrose to apply these mathematical skills to the worlds of physics and cosmology without any formal training in these fields. Penrose reflects:

“When I did go to Cambridge as a research student, in quite a different area (in pure mathematics), I think Dennis felt it was his duty to look after me…He somehow took me under his wing and [we] had lots of discussions about physics, cosmology, and all sorts of things. Although I was officially a pure mathematics research student at Cambridge, I learned an awful lot from Dennis. Certainly not just cosmology, but physics generally, and a kind of excitement and enthusiasm for the subject that was very important to me.”

## A flourishing physicist

After achieving his Ph.D. in mathematics, Roger Penrose was prepared for a lifetime of serious work in mathematics, physics, and cosmology. Over the course of his academic career, he has held temporary positions at many universities in England and the United States, including Bedford College, King’s College, and Birkbeck College all in London, and Princeton, Syracuse, and the University of Texas-Austin in America. He has spent the most time at the University of Oxford, where he is currently the Emeritus Rouse Ball Professor of Math. Along the way, he had earned numerous accolades; most notably, he was knighted in 1994 for his scientific accomplishments.

His academic interests have stretched from the farthest edges of our universe to the smallest acts of consciousness. While many scientists jump on the latest band-wagon, Penrose always carves his own path, however unfashionable. He mused:

“It was important for me always, if I wanted to work on a problem, to think I had a different angle on it from other people. Because I wasn't good at following where everybody else went. I wasn't the kind of person who could pick up the prevalent arguments and knowledge of the time. Other people were good at that. They could suck it all out and put it together and make advances. I was the kind of person who'd have some kind of quirky way of looking at something on my own, which I would hide away and work at. So it meant that I had to have some way of looking at a problem that was my own.”

Just as he described, Penrose’s unique background led him to one of the greatest breakthroughs of his career. As physicists began to question what was inside black holes, Penrose approached the problem from an angle nobody had considered before—topology. Topology analyzes connections and not shapes or curvatures. At the time, it was an obscure branch of mathematics that most physicists had never even heard of. However, Penrose’s mathematical background helped him realize the power of asking topological questions like “Does spacetime come to an end?” From this angle, Penrose was able to use topological tools to prove his revolutionary singularity theorem. Penrose’s singularity theorem states that if any star imaginable implodes far enough to form an apparent horizon, which means it won’t let outgoing light escape, then gravity will grow so strong that it will create a singularity, a point with infinite density and zero volume. Because all black holes have apparent horizons, Penrose’s singularity theorem proved that every black hole must have a singularity inside of it.

This is just one of many examples of important contributions Penrose has made to black hole research, and to the progress of science and mathematics in many fields. In 1969, he discovered that spinning black holes store rotational energy in the swirl of space around them, and that this energy can be extracted because it is outside the hole’s horizon. Applying his love of geometry to physics, he also developed Penrose diagrams as a way to pictorially map the region of spacetime around a black hole. Penrose also invented twistor theory, a revolutionary, intensely mathematical attempt to unite general relativity and quantum physics in an effort to better understand the physics at points like singularities.

As he continued to publish pure mathematical and physics papers, Penrose also delved into brain science and authored two controversial books that argued that unknown quantum mechanical processes are necessary to understand consciousness, *The Emperor’s New Mind *(1989) and *Shadows of the Mind* (1994). While his recent books are less controversial—*The Road To Reality *(2004) is a critically acclaimed foundation of mathematics and physics and *Cycles of Time* (2010) argues for a cyclic cosmology—Penrose still believes that quantum mechanics is not exactly right. An old man now, the search for the truth belongs to the younger generation. But Penrose believes the answers are out there:

“I don't think our understanding removes the point. You see, in a sense, understanding nature is making it more mathematical. That's what we are doing all the time. Mathematics is logical structure, a disembodied logical structure, and you might think that when you put your physical problem into that disembodied mathematical structure, you have removed its point…But my view is: once you have put more and more of your physical world into a mathematical structure, you realize how profound and mysterious this mathematical structure is. How you can get all these things out of it is very mysterious, and, in a sense, gives the universe more of a point.”

Sir Roger Penrose has lived a full life, committed to using mathematics to understand the world around him and the universe he can only imagine. His unique approach has led him to crucial breakthroughs for the progress of science, and he continues to propose new and controversial ideas to this day. Through his enthusiasm and unwavering commitment to his work, his lifetime of never settling can inspire us to courageously keep questioning. Penrose’s contributions to the progress of science are small, significant steps in the human race’s larger search for reason and meaning in a mysterious, beautiful universe.

## References

Al-Khalili, Jim. *Black Holes, Wormholes & Time Machines*. 2nd ed. Bristol, UK: Institute of Physics Pub., 2011. Print.

"Interview with Dr. Roger Penrose." Interview by Alan Lightman. *Neils Bohr Library & Archives*. American Institute of Physics, 24 Jan. 1989. Web. 2 Dec. 2013. <http://www.aip.org/history/ohilist/34322.html>.

Kruglinski, Susan. "The Discover Interview: Roger Penrose." *Discover* 30.8 (2009): 54-57. *Academic Search Complete*. Web. 18 Nov. 2013.

Kuhn, Robert. "Roger Penrose." *Closer to Truth*. Getzels Gordon Productions. Web. 02 Dec. 2013. <http://www.closertotruth.com/participant/Roger-Penrose/75>.

Kuhn, Robert. "Why This Universe?" *Skeptic* 13.2 (2007): 28-39. *Academic Search Complete*. Web. 18 Nov. 2013.

O'Connor, J.J., and E.F. Robertson. "Roger Penrose." *School of Mathematics and Statistics*. University of St. Andrews. Web. 02 Dec. 2013. <http://www-history.mcs.st-and.ac.uk/Biographies/Penrose.html>.

Penrose, Roger. "What Is ‘reality’?" *The New Scientist* 192.2582 (2006): 31-39. *Academic Search Complete*. Web. 18 Nov. 2013.

Rowe, David E. "Remembering an Era: Roger Penrose’s Paper on “Gravitational Collapse: The Role of General Relativity”." *The Mathematical Intelligencer* 30.1 (2008): 27-36. *Academic Search Complete*. Web. 18 Nov. 2013.

"Sir Roger Penrose." Encyclopaedia Britannica. Encyclopaedia Britannica Online. Encyclopædia Britannica Inc., 2013. Web. 02 Dec. 2013. <http://www.britannica.com/EBchecked/topic/450252/Sir-Roger-Penrose>

Thorne, Kip S. *Black Holes and Time Warps: Einstein's Outrageous Legacy*. New York: W.W. Norton, 1994. Print.