And the owner of the phantom limb is not suffering straightforward pangs for the one that was lost. Children born without hands can still feel their fingers. A phantom may be an intruder, something wholly new. An artist, Alexa Wright, has collaborated with amputees to produce images that satisfy their idea of the invisible limb - arms that fade out below the elbow and start again just before the hand; feet that float under a stump of leg; a stick of arm ending in a flattened hand and swollen, splayed fingers.
Sometimes these ghosts haunt their victims in terrible ways. A man who had not lost his arm, but only lost all sensation in it, was racked by pain for months. The final crushing, wrenching moment, when the arm was wrecked in a motorbike accident, stayed with him, imprinted on his nervous system in much the same way that, so they used to believe, a dead man's eye would retain the last thing it saw.
Dr Ramachandran, a rather charming and impressive-sounding neuroscientist from San Diego, has developed a way of treating that sort of pain with a mirror box, which creates the visual illusion of two functioning limbs. Once the eye has something to latch on to, the phantom is often soothed, and is sometimes exorcised altogether. Dr Ramachandran has theorised that other body parts begin to usurp the area of the brain previously devoted to the missing limb (the bit of the brain that deals with the genitals is next to the bit that deals with the feet: touching the genitals can conjure up a phantom foot, and sometimes a sexually aroused foot).
This is controversial - another scientist was called on to rubbish Ramachandran - but may be evidence that the connection between the brain and the body is more flexible, more open to change, than had been realised.
A few months ago I dislocated my thumb; the pain was nothing to the weirdness of seeing a part of my body in an utterly strange position. There was something of this weirdness in Peter Webber's film, with people changed into unexpected machines, working in ways that didn't quite make sense. As scientific exposition it sometimes lacked clarity, but its hints of a new view of humanity, aliens stranded in our own bodies, gave it a certain unnerving power.
An excellent film by Hamish Mykura for Reputations (BBC2) examined the life of Eamon de Valera - a compromiser who threw Ireland into civil war, a republican hero who turned on the IRA; a mathematician whose high-romantic vision of Ireland left him, in the Second World War, blind to the concrete struggle going on about him. When Hitler killed himself, De Valera went in person to offer his sympathy to the German representative in Dublin. Like any substantial programme on Ireland, this was a dispiriting reminder of how history and myth won't let go: some limbs just keep on twitching.Reuse content