“One of the paradoxes of research, writes Dr. Thomas Fink, “is that, time and again, the most far-reaching discoveries are made not by focusing on the practical problems of the day but by following your curiosity.” Breakthroughs come, he explains, “when your work, and what you do to avoid it, become the same thing.”
Fink then goes on to illustrate the point with a story from Sir Roger Penrose, who won the Nobel Prize in Physics last year for the discovery that black hole formation is a robust prediction of the general theory of relativity:
‘Someone had invited me to give a talk at London South Bank University and I was really overdue with my reply. Instead of replying, all I could do was stare at the university logo on the letterhead: a pentagon with five pentagons around it.’ What bothered Penrose was that there were gaps between the external pentagons. Unlike hexagons, pentagons don’t fit together seamlessly.
He began wondering what new shapes would be required so he could fill in the gaps, and then extend the pattern without new gaps arising. It seemed it wasn’t possible with just one new shape. After a while, he had worked out a way to solve the puzzle using six new shapes. But Penrose wasn’t satisfied with six.
‘I thought, I wonder if I can do better? So I got it down to four tiles. And I was really proud of that. Then I fiddled around and I got it down to two. But my reaction was disappointment. It was just too damn easy. I felt it couldn’t be new.’
But it turned out the result of his labours, known as ‘Penrose tiling’, was new.
