By Pat Sheil
BIOGRAPHY
The Impossible Man: Roger Penrose and the Cost of Genius
Patchen Barss
Atlantic, $55
In September 1964, mathematician Roger Penrose crossed a road near his office in Birkbeck College, London, deep in conversation with cosmologist Ivor Robinson. Thankfully, they had paused at the kerb to await a break in the traffic because by the time they’d reached the other side, Penrose had had an epiphany that would debunk the accepted wisdom of the impossibility of “singularities”, or black holes.
He’d realised that the recently discovered quasar 3C 273 was a point in spacetime where Einstein’s equations did not so much break down as follow their inevitable course into cosmic oblivion. Penrose wrote up his ideas in a paper published the following year. Fifty-five years later, aged 89, it would win him the Nobel Prize for Physics.
Roger Penrose was born in 1931 in Colchester, England, one of four children of geneticist Lionel Penrose and physician Margaret. His father was a domineering man who suffered fools not at all, was cruel to his wife and impatient with his children. But when Roger and Lionel’s interests coincided, his father’s encouragement would shape his thinking. Decades later, Penrose vividly recalled coming across a sundial while on a childhood walk with his father, who explained its workings in detail. How the untouchable shadow’s predetermined march was driven by the rotation of the Earth, its orbit around the sun, the rhythm of the seasons.
“With such low expectations of his father,” Patchen Barss writes, “Roger found their shared discovery of the sundial strange and exhilarating.”
Nobel Laureate in Physics Roger Penrose in 2020 with his medal.Credit: AP
On September 3, 1939, the day war was declared, the Penrose family moved into a house by the Thames in London. London, Ontario, to be precise, Canada being a haven for many British families of means as war loomed. Lionel had secured a position at the University of Western Ontario, and the family did not return to England until 1945.
Escher and Penrose found inspiration in each other’s work.
In 1952, University College London awarded Penrose a bachelor of science with first-class honours in mathematics. A PhD in algebraic geometry from Cambridge followed in 1957. In 1959, he married Joan Wedge. Their first child was stillborn, and Joan never fully recovered from the depression that this brought on. Though they went on to have three healthy children, the marriage was a deeply unhappy one for all concerned.
The Penroses didn’t own a car, so Roger cut through a wooden floor in their London home, and installed a trapdoor and ladder leading to the garage/study underneath the house. “Whenever he wanted to escape from his wife and children, which was most of the time,” writes Barss, “he would lift the lid and vanish into his private silent universe of tensors, twistors and singularities.”
The couple separated and divorced. In 1988, Penrose married a student, Venessa Thomas, 34 years his junior. They, too, have separated.
In the early 1960s, Penrose had sent Dutch artist M.C. Escher two-dimensional drawings of impossible three-dimensional structures, most notably “the Penrose triangle”. While holidaying in Europe in 1962, he called the artist from a public phone, and invited himself over to his studio. The two geometric conjurers had a wonderful evening, the visit ending with Escher inviting Penrose to select a print from his workbench. He chose Fish and Scales, which still hangs on the wall of his study.
Penrose’s optical illusion of an “impossible triangle”, inspired by a visit to an Escher exhibition.Credit: emmgunn
Penrose and Escher also shared a fascination with what may seem a rather pedestrian aspect of geometry – tiling. The endlessly repeating ceramic pattern that might waterproof one’s bathroom is periodic, meaning that no matter how big the floor, every step taken across it will reveal the same pattern. But Penrose, inspired by Escher (who was in turn fascinated by the intricate Islamic mosaics of the Alhambra in Spain), came up with various “non-periodic” tiling patterns, using pentagons, stars, and diamonds, such that baffled pedestrians could never know what configuration would next appear under their feet.
The cover of Scientific American magazine in 1977 featured M.C. Escher’s Penrose tiling.
The hypnotic appearance of “Penrose tiling” on the cover of Scientific American in January 1977 was to make Roger Penrose famous far beyond the cloistered world of theoretical maths. Escher would later write of his encounter with him: “I am often struck by the simplicity and childish playfulness of these learned scientists and that is why I like them, and feel more at ease with them than with my own colleagues.”
Indeed, it was the “playfulness” of Penrose’s approach to mathematics that allowed him to make his most astonishing breakthroughs. Yes, there was pioneering maths of the most impenetrable and challenging kind underpinning his work, but at heart he remained a boy fascinated by a sundial’s shadow, twisting the shape of spacetime just to see what would happen if he changed a number here or there.
And there was no shortage of numbers. Real numbers, imaginary numbers, complex numbers; the elements of a beguiling mathematical chemistry begging for investigation.
Penrose has long been of the view that mathematics has an “external reality”, as Barss puts it. He describes his belief in the stand-alone existence of mathematics as “a very common feeling among mathematicians”, and that their pursuit is “more like exploration than invention. They’re discovering things that are already out there in nature and the Platonic world”.
It is this sense of the independence of mathematics from the universe it describes, and how this philosophy plays out in the life of one of the greatest mathematicians of all, that lies at the core of this enlightening portrayal.
The separation of thought from substance, the notion that mathematics exists irrespective of matter and energy, unfolds before the reader as Penrose’s career carries on, metaphorically separated from the nuts and bolts of everyday life.
Penrose with one of M.C. Escher’s works.Credit: AP
He weaved magic to astonish his elite fellow travellers in this conceptual world. During a mathematical conference in Poland in 1962, “few people in the world could have appreciated Roger’s geometric treatment of null infinity. And almost all of them were in the room with him”. Yet his wife’s depression and the chaotic nature of parenthood baffled him.
You don’t need a PhD in mathematics to appreciate Barss’ illuminating biography, though anyone with a fascination with maths as an inquiry into nature, or as recreational enjoyment, will revel in it.
Penrose and Escher took the triangle to places that would have perplexed Pythagoras, but Barss captures the mathematician – still working at age 93 – in his own, real world, and shows that while maths may well have an independent existence from the physical universe, it is practised by people. People with families, frustrations, triumphs and tragedies. And he does it brilliantly.
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