An elusive symmetry

Take one mathematician, some tiles, a once-elusive symmetry – and suddenly Plato’s forms seem real

By Oliver Morton

Almost a quarter of a century ago, I was sitting outside the Turf Tavern in Oxford. It was a sunny late-summer day. I was a young reporter and with me, drinking a half-pint of cider, was Roger Penrose, the greatest British mathematician of his generation to apply himself to physics.

Until that drink, Plato's notion of a pure world of form to which the world perceived by humans was but a shadow was just something I had come across in books. It was familiar intellectual history, but hardly something I would expect anyone actually to believe. By the time our glasses were empty I knew that, at least to Penrose, it was an irreducible reality. The platonic world of pure form was not just as real to him as the cool gold of his drink or the sounds of my stammered questions. It was more real. For all the sunlight, I was a shadow.

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