The idea that human and artificial intelligence should merge is in the air these days. The Tesla and SpaceX chief executive Elon Musk, for instance, suggests “having some sort of merger of biological intelligence and machine intelligence”. His company, Neuralink, aims to make implanting chips in the brain as commonplace as laser eye surgery.

Underlying all this talk is a radical vision of the mind’s future. Ray Kurzweil, the futurist and director of engineering at Google, envisions a technotopia where human minds upload to the Cloud, becoming hyperconscious, immortal superintelligences. Mr Musk believes people should merge with AI to avoid losing control of superintelligent machines, and prevent technological unemployment.

But are such ideas really possible? The philosophical obstacles are as pressing as the technological ones. Here is a new challenge, derived from a story by the Australian science fiction writer Greg Egan. Imagine that an AI device called “a jewel” is inserted into your brain at birth. The jewel monitors your brain’s activity in order to learn how to mimic your thoughts and behaviours. By the time you are an adult, it perfectly simulates your biological brain.