Imagine you’re holding two equal-size dice. Is it possible to bore a tunnel through one die that’s big enough for the other to slide through? It is — but what about other shapes? In a paper posted online in August, two researchers describe a shape with 90 vertices and 152 faces that they’ve named the Noperthedron, the first convex polyhedron that definitely cannot pass through itself.

In this episode, Quanta contributor Erica Klarriech tells host Samir Patel about how the researchers discovered the shape, and how it solves a centuries-old geometric mystery.

Audio coda courtesy of the Gemsmen Renaissance Consort.

Studies of neural metabolism reveal our brain’s effort to keep us alive and the evolutionary constraints that sculpted our most complex organ.

The story How Much Energy Does It Take To Think? first appeared on Quanta Magazine.

Ask ChatGPT how to build a bomb, and it will flatly respond that it “can’t help with that.” But users have long played a cat-and-mouse game to try to trick language models into providing forbidden information. Just as quickly as these “jailbreaks” appear, AI companies patch them by simply filtering out forbidden prompts before they ever reach the model itself.

Recently, cryptographers have shown how the defensive filters put around powerful language models can be subverted by well-studied cryptographic tools. In fact, they’ve shown how the very nature of this two-tier system — a filter that protects a powerful language model inside it — creates gaps in the defenses that can always be exploited. In this episode, Quanta executive editor Michael Moyer tells Samir Patel about the findings and implications of this new work.

Audio coda courtesy of Banana Breakdown.