Professor Gunther von Hagens from Heidelberg, who produced the exhibition of bodies and body parts is clear that his aim is to increase people's knowledge and understanding of the body. But there is an aesthetic element and to my mind some of the displays are as beautiful and arresting as any work of art. The bodies go through a process known as plastination – a unique invention of von Hagens'. The body is frozen to halt decomposition and a fixing agent is injected into the blood vessels. The vessels are injected with contrasting plastics then dehydrated using acetone; the bodies are then placed into a container of a silicon or epoxy plastic; following this, in a vacuum chamber the acetone trickles out and the plastic is sucked into every cell. The result is a body whose anatomy can be displayed with complete visibility.

The exhibition starts gently with hands and ankles and other limbs, but the most impressive items are the full figures. They are arranged in striking poses with the anatomy fully visible, the body sometimes halved, sometimes skinless, so that the muscles and organs are fully displayed. A man playing chess leans forward at the board, with his cranium suitably exposed; there is a swimmer, flying like an angel, and a swordsman split in three ways so that every muscle involved in the swordplay is seen. The most impressive is the man riding a rearing horse. One of the most beautiful exhibits is the complete arterial system, feathery in blood red. In line with the motive to instruct, there are diseased organs, a liver shrivelled from alcohol abuse, lungs disfigured by cigarette tar, the misshapen brain of an Alzheimer's sufferer.

The exhibition has been enormously successful in Germany and Japan – and on the afternoon I saw it in London it was well attended, especially by young people. The desire to learn was I would guess as strong as the desire to be moved. But it is impossible to spend time there and not reflect on human mortality, also to muse on "What a piece of work is man" (a Shakespearean view influenced by Renaissance anatomy?).

The tension between art and anatomy has a long tradition from the anatomist Vesalius, whose public demonstrations were given the dramatic title 'Anatomical Theatre', to Leonardo da Vinci, rather curiously described in the accompanying brochure as a scientist rather than artist. The figures are also in the tradition of the Enlightenment anatomist Fragonard, who was influenced by the Enlightenment desire to understand the purely human. I found the exhibits here had as much fascination and beauty as anything presented for the Turner prize in recent years.

Earlier exhibitions in Germany have been strongly criticised by church leaders, who attacked von Hagens for "playing with the dead". But von Hagens argues that all the bodies have been freely donated; he vigorously denies the use of some Siberian peasant bodies without prior consent. This is a way of attaining a sort of immortality – it extends physical existence beyond death. This is a precise reason why it is not easy to believe in an afterlife, when the body can survive without any demonstrable life or personality. Von Hagens says that he no longer fears death and that whether or not we continue into an afterlife "this exhibition gets much closer to the soul than the church because you are so close to the body." I don't follow that, but I agree with him that the effect of the exhibition "goes beyond education because feelings and emotions are involved".

This is an exhibition which is fascinating and illuminating, instructive and astonishing and quite unique.

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