Last updated 2 weeks ago by Michael Darmanin
In 1955, Albert Einstein passed away, not quite believing in the existence of black holes.
Almost exactly 10 years after that, in January 1965, 33-year-old Roger Penrose proved that black holes can form and could be shown to be a robust prediction of Einstein’s General Theory of Relativity.
In 2020, 55 years down the line, that seminal piece of work has earned Penrose the Nobel Prize for Physics.
Of course Penrose’s brilliant career has seen more than that one piece of work. Terms such as Penrose Inequalities, Penrose Interpretation of Quantum Mechanics, Dolsi-Penrose Model, Penrose Formalism, Penrose Diagram, the brilliant Penrose-Hawking Singularity Theorems litter diverse fields of mathematics and physics.
At the same time Roger Penrose perhaps comes closest to being a polymath in the modern era. He demonstrates versatility in multiple fields that was common in ancient times but has been rendered near-impossible by the extent of specialisation in every current-day domain.
Penrose is not only a scientist and a prolific writer on scientific topics. His contribution transcends the world of physics and mathematics and enters the domain of art. Alongside all those theories that bear his name in the scientific world, we have the Penrose Tiling, the Penrose Cube, he Penrose Stairs and the Penrose Triangle, all of which cut across into the world of art as well.
And in a curious way, his worlds across the scientific and artistic world do intersect.
Worlds before Big Bang
Roger Penrose visited Utrecht in July 2018. As a part of the 19th UK and European Meeting on the Foundation of Physics, he gave a public lecture on Conformal Cyclic Cosmology at the Utrecht Science Park. The topic under discussion was “What happened before the Big Bang?”
While most cosmologists would reply that time did not exist before the Big Bang rendering the question meaningless, Sir Roger had a different idea. Under the title Worlds Before Big Bang: Colliding Black Holes and Creation of Dark Matter, he spoke of his work on cosmology.
He explained his theory in which the universe goes through an endless sequence of cycles, each of which starts with a Big Bang. Unlike other theories, the cycles do not end with a crunch. Penrose predicts that the universe keeps on expanding and expanding. As the last stars and galaxies fade away and the black holes evaporate, it becomes conformally symmetric. Avoiding the technical terminologies, it can be summed up by saying there remains no difference between big and small and only angles are preserved.
The Dutch Connection
This idea of conformal symmetries is closely linked to Penrose’s interest and work in art. And curiously, the intersection has a significant Dutch connection.
In 1954, as a second year graduate student of mathematics at Cambridge, Penrose visited Amsterdam for the International Congress of Mathematicians. While getting on a bus, he ran into Sean Wylie, a lecturer at Cambridge.
Wylie was carrying a print of Night and Day, the famous MC Escher woodcut. Till then Penrose had never heard of the Dutch artist. Finding the print fascinating, he asked Wylie for more information. That was how he ended up accompanying Wylie to the Van Gogh Museum, where an Escher exhibition was being held.
“I was blown off my feet,” Penrose later said in an interview given to Nicos Starreveld and Raf Bocklandt of the University of Amsterdam. The pictures were fascinating, and he was particularly struck by the one called Relativity.
Triangle, staircase and waterfall
The experience started Penrose off in experimenting with rivers, bridges, roads etc going off in different directions into the realms of impossibility. His father, Lionel Penrose, was a medical geneticist, a professor or eugenics at University College London. Deeply interested in mathematics, he now found his son’s experiments fascinating, particularly the impossible triangle he had come up with. Penrose senior became hooked, and soon produced an impossible staircase.
Father and son decided to write a paper on their experiments. While it was difficult to categorise this work into a particular field of science, Lionel Penrose knew the editor of the British Journal of Psychology. It was to this journal that the paper was duly submitted and accepted. It gave credit to Escher and a copy was sent to the artist. Soon Lionel Penrose and Escher were communicating. The impossible triangle of Penrose was used by Escher repeatedly in his famous Waterfall.
Meeting of minds
Later, Roger Penrose even met Escher. On another visit to Netherlands, he was driving across the country with his wife when he passed Baarn. Escher lived in this town, some 24 km from Utrecht. Penrose stopped in the town, rang the artist up, and was invited to have tea.
According to Penrose, “I was expecting staircases going out of the windows in all directions, but no it was just a very ordinary house.” It was a very pleasant meeting. In fact, Escher also invited Penrose to take any print he wanted from a pile. The one Penrose chose was Fish and Scales.
In return Penrose sent Escher some cardboard pieces of a puzzle. They were identical shapes which would tile in a plane, but after some manipulation with the orientations. After solving the puzzle, Escher wanted to know the underlying logic. When Penrose explained, the artist, with his splendid intuitive grasp of geometry, developed a painting of ghosts. That was one of the last works of art Escher produced.
The puzzle with tiles later evolved into the famous Penrose tilings. These tile an entire plane in a non-periodic way. However, Escher passed away before that. He would have surely loved this curiosity.
Circle limit and conformal symmetries
In that same Amsterdam conference, geometer Harold Coxeter was also impressed by Escher’s work. He introduced the artist to the Poincaré disc model of the hyperbolic plane. It was with this model that Escher came up with his Circle limit paintings, experimenting profusely with conformal symmetries.
And this fascination with conformal symmetries helped Penrose along in his field of cosmology. Conformal cosmology suggests that the beginning and the end of the universe are in effect the same, since these two phases of its evolution contain only massless particles. According to the ultra-sophisticated mathematics of Penrose, as time ends in the era of massless particles, the fate of our universe can actually be reinterpreted as the big bang of a new one: “Our universe is what I call an aeon in an endless sequence of aeons.”
It is close to a model Escher would have loved.