Picture prisoners in neighbouring cells who can only knock on the walls. A knock carries no words — only the fact that it happened. It sounds hopeless, yet it is enough: as long as any two prisoners are linked by two separate routes, say with the cells arranged in a ring, knocks alone let them elect a leader and, in principle, carry out any computation a full conversation could. Tiny sensors that can only emit a pulse, and living cells that signal with a single chemical, live with the same limits. I study networks like these, where devices can only beep or every message loses its content on the way, and what they can still achieve.

In the children’s game of telephone, a whispered message is passed down a line and comes out garbled at the end. Real networks play this game all the time: noise flips bits, adversaries tamper with messages, and computers crash halfway through a job. In a data centre, where thousands of machines work on one task, some are always failing. My research shows how a group of computers can keep going regardless — catching and repairing mistakes in the middle of a long exchange instead of starting over, working around the parties that have failed, and still finishing the task correctly. Much of it builds on interactive coding, the theory of protecting entire conversations rather than single messages, which I surveyed in a monograph.

Generals surrounding a city must agree whether to attack, but they can only send messengers — and some of the generals are traitors, and some messengers never arrive. This old puzzle captures a modern problem: hospitals that want joint statistics without revealing any patient’s record, or computers that must agree on a shared history while some of them lie. Cryptography solves such problems assuming the network itself is perfect. My research drops that assumption, showing that computations can keep their inputs private and their results correct despite both noise and adversaries, without adding much communication compared with the original computation.