Welcome to the quantum science podcast.

Each episode we bring you stories about developments in science and mathematics.

I'm Susan Vallett.

Two researchers have proved that penrose tilinges, famous patterns that never repeat,

are mathematically equivalent to a kind of quantum error correction.

That's next.

It's season three of the joy of why, and I still have a lot of questions.

Like, what is this thing we call time?

Why does altruism exist?

And where is Jan 11? I'm here. Astrophysicist and co-host. Ready for anything. That's right. I'm bringing in the A team. So brace yourselves. Get ready to learn. I'm Janelle Levin. I'm Steve Strogatz. And this is... Quantum Magazine's podcast, The Joy of Why. New episodes drop every other Thursday.

If you want to tile a bathroom floor, square tiles are the simplest option.

They fit together without any gaps in a grid pattern that can continue indefinitely.

That square grid has a property shared by many other tilings. Shift the whole grid over by a fixed

amount, and the resulting pattern is indistinguishable from the original. But to many mathematicians,

such periodic tilings are boring.

If you've seen one small patch, you've seen it all.

In the 1960s, mathematicians began to study

A periodic tile sets, with far richer behavior.

Perhaps the most famous is a pair of diamond-shaped tiles

discovered in the 1970s by the

polymathic physicist and future Nobel laureate, Roger Penrose.

Copies of these two tiles can form infinitely many different patterns that go on forever.

...