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Issue 7 Science Shoutout

Roger Penrose

🕒 8 min

Sir Roger Penrose is one of those names in science you may see so often that you might just think it’s an adjective, especially if your interests happen to be particularly well aligned with his. Penrose’s name crops up in cosmology, quantum mechanics, various mathematical fields and even in philosophy and graphic art. He is also one of this year’s Nobel Prize laureates in physics, which is why his name has been showing up even more frequently than usual. Since his is a name and character worth remembering, we’re bringing you a short overview of his most important endeavors and contributions.

Penrose started out as a pure mathematician with a particular interest in geometry. His family initially saw mathematics as the field for the true fanatic, someone completely uninterested in the practical nature of their work. While to them this might have been a bad thing, to him it was an exact fit. He was the child who built up his answers from scratch in math class, regardless of how much time it took or the impact it had on his grade. However, he also showed a keen interest in the very nature of reality – especially the poorly understood bits.

An example of Penrose tiling.

He would often concern himself with difficult problems dismissed by his peers or with reinventing known concepts to make them more elegant or self-contained, seeing it as a sort of challenge. As a result, his ideas were often fresh takes that inspired new ways of looking at the convoluted puzzle that many problems of the time had become. This interest resulted in completely new solutions to known problems abnormally often, such as the illumination problem or, famously, the problem of tessellations with fivefold symmetry. A tessellation or tiling is a way of covering an infinite flat surface with one or more geometric shapes without gaps or overlaps, like the tiles in a bathroom. This came as a natural interest to Penrose, and out came Penrose tiling – aperiodic, with fivefold rotational symmetry. This way of covering the plane is incredibly interesting, but also just beautiful to look at, so you might want to check out this video for a quick overview or, if you have some more time, read about it from Martin Gardner or watch Penrose’s own talk, in which he touches upon something else – a somewhat unexpected application of his discovery. His aperiodic tiling was used to prove the existence of quasicrystals (non-repeating ordered crystals), bizarre structures that were thought impossible in modern crystallography.

Penrose polygons.

Some of his ideas had no immediate practical applications whatsoever, but were interesting all the same. The most famous one is probably the Penrose triangle, or the impossible tribar, which was his version of an existing impossible object. He would go on to make an entire class of impossible objects, including the so-called Penrose stairs. These were all, interestingly enough, inspired by the work of M. C. Escher and then went on to inspire the artist themselves.

However, that unintended usefulness from before became a sort of theme in Penrose’s work, considering he would engage in solving the unsolvable almost for sport, but didn’t lack interest in the breakthroughs that often followed. In fact, a similar contribution is what he is probably most famous for (and won the Nobel Prize for to boot). From an existing interest in topology, which is essentially the study of how geometric objects behave under deformations, he was attracted to astrophysics and cosmology. The problem of interest at the time was reconciling our poor understanding of curved geometry and the complex geometrical structure of spacetime, which was necessary for a complete understanding of Einstein’s general theory of relativity. Penrose was drawn to this by Cambridge cosmologist Dennis Sciama, who also introduced him to Stephen Hawking, one of his doctoral students. Hawking is perhaps best known precisely for his work on black holes, and his collaboration with Penrose was a crucial component of his success. Penrose in particular chose to study the topology of space alone and devised completely new methods of mathematically studying spacetime, which would go on to prove that Einstein’s theory and black holes were consistent. He proved the necessity of what every sci-fi enthusiast now commonly knows as a singularity, where spacetime collapses in on itself and relativity breaks down. This provided the basis for further work on black hole physics, leading to the Big Bang, the idea of the event horizon, accurate black hole simulations and, eventually, even the famous prediction and image of a real black hole and much, much more. Penrose’s venture resulted in a cascade of new knowledge in modern physics, especially cosmology, which is why many of its official terms bear his name.

Penrose was evidently a prominent figure in 20th century physics and mathematics, but – more recently – he has also contributed to broadening the non-scientist’s understanding of science. He has written several books that could be classed as popular science (more on that later), some in collaboration with his colleagues and some on his own. He frequently tried to tackle the difficult, overarching principles that inspired his work and a lot of modern physics, but without dumbing them down. His interviews and talks are much the same – if you don’t pay close attention, his explanations might just go over your head. There is a line from one of his books which explains why he often leaves it to his audience to work things out themselves, like he used to in his school days:

It is always the case, with mathematics, that a little direct experience of thinking over things on your own can provide a much deeper understanding than merely reading about them.

Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe

This sentiment is certainly expressed across the board in his popular work. However, this should not discourage you from giving it a go if you’re interested. Quite the opposite – there is always something to gain from truly trying to understand a new concept, even if it is foreign. Penrose seems to believe that anyone can grasp even obscure, unintuitive ideas if they are given a thorough enough explanation and the opportunity to think, and that might just be what he set out to do.

The Road to Reality is a beast of a book, for the seriously interested. It is intended as a comprehensive introduction to serious mathematical physics for the lay reader, one who necessarily needs to be willing to ponder over extremely difficult concepts as they go through it. The book lies somewhere between popular science and textbook material. It does not refrain from showing the formulas and diagrams behind the concepts it covers. It is also not a quick read by any means, comprising over 1000 pages of math and theoretical physics. However, it is an excellent introduction to something most popular science books simply cannot get across and that is how exactly people like Penrose see reality. He tries to get across not just what mathematical and physical concepts occupy his mind, but also how he perceives them. The reader who completes the gargantuan task of mindfully reading the entirety of The Road to Reality will no doubt come out of the experience having an entirely different perception of reality, as the title might suggest.

Another immensely interesting book, this time with a completely different goal, is Cycles of Time. Fittingly subtitled An Extraordinary New View of the Universe, this book covers another one of Penrose’s attempts to answer the most difficult questions there are, this time the origin and fate of the universe. It describes a rival theory of the origin of the universe, positing that the universe goes through cycles – beginning ultra-smooth and infinitely small, going on to expand and generate matter and eventually become completely uniform again, after the last of its black holes evaporates through Hawking radiation, which serves as the perfect foundation for a new universe to form. Essentially, he proposes that the heat death of our universe might just be the Big Bang of another. Like any cosmological model, it is not without faults, but the book is a compelling read and quite accessibly written. Anyone with an interest in the “Big Questions” of the cosmos should read it and approach it with the same critical eye that brought Penrose the idea in the first place.

Two of the books pictured above, The Emperor’s New Mind and Shadows of the Mind, detail his (joint) effort to understand the nature of the mind. Specifically, they lay out a quantum theory of consciousness, all while explaining the origin and properties that arise from it.

If this sounds intriguing, you might want to check out this podcast, where Penrose himself explains his theories and why he finds them so captivating.

Fashion, Faith, and Fantasy in the New Physics of the Universe is the last of his solo popular science projects, where he criticizes and warns against succumbing to the attractiveness of new theories. Among his many collaborative writings, The Nature of Space and Time might be the most interesting to anyone who knows him mostly from his work with Stephen Hawking. In it, Hawking and Penrose debate physics and the philosophy behind it, inspired by the famous Bohr-Einstein debates.

Overall, it is not without reason that people follow and admire people like Sir Roger Penrose. He has contributed so much, both in minute and significant ways, to modern science over his long career, and all because he is simply interested in understanding whatever there is to understand. If you decide to watch some of his interviews, you will see that he leaves an impression of youthful curiosity, always going on tangents about the things that sparked his interest. He is a man who has learned – and taught – so much, but continues to live by the Socratic idea of accepting one’s own ignorance and growing from it.


If you’re reading this when it first came out, you can watch the Nobel Prize ceremony live if it interests you. Sir Roger Penrose will be receiving his own Nobel Prize on December 8th!

Did you enjoy learning about Roger Penrose? Are you planning on reading some of his publications or have you done so already? Let us know in the comments!

By Laura Busak

Laura is a physics student with a love for all things cosmic. She enjoys making and listening to music, reading books that make her think, and generally doing whatever random things she thinks of, often until 2 am.

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