Impossible Cookware and Other Triumphs of the Penrose Tile
Patchen Barss
Patchen Barss
Quote:Given that Fibonacci seems to appear everywhere in nature—from pineapples to rabbit populations—it was all the more odd that the ratio was fundamental to a tiling system that appeared to have nothing to do with the physical world. Penrose had created a mathematical novelty, something intriguing precisely because it didn’t seem to work the way nature does. It was as if he wrote a work of fiction about a new animal species, only to have a zoologist discover that very species living on Earth. In fact, Penrose tiles bridged the golden ratio, the math we invent, and the math in the world around us.
Quote:It was as though Penrose’s fanciful mathematics had forced itself into the natural world. “For 80 years, a crystal was defined as ‘ordered and periodic,’ because all crystals studied from 1912 on were periodic,” Shechtman says. “It wasn’t until 1992 that the International Union of Crystallography established a committee to redefine ‘crystal.’ That new definition is a paradigm shift for crystallography.”
Quote:Nobody knows how the story of forbidden symmetry ends. Mathematicians continue to explore the properties of Penrose tiles. Quasicrystals remain the subject of both basic and applied research. But it has been an incredible journey so far. In the past 40 years, five-axis symmetry has gone from impractical to valuable, from unnatural to perfectly natural, from forbidden to mainstream. It’s a transformation for which we can thank two scientists who pushed past conventional wisdom to uncover a remarkable new form of infinite variation in nature.
'Historically, we may regard materialism as a system of dogma set up to combat orthodox dogma...Accordingly we find that, as ancient orthodoxies disintegrate, materialism more and more gives way to scepticism.'
- Bertrand Russell
- Bertrand Russell