A copy of Rembrandt's famous painting The Anatomy Lesson of Dr Nicolaes Tulp hangs prominently in the Medical School at Edinburgh. When I studied there in the early 1990s it was used by our lecturers as an introduction to anatomy, not least because it contains a major flaw. The painting shows a gaggle of 17th-century Dutch surgeons crowding round the body of Aris Kindt, a criminal hanged only an hour before. WG Sebald made much of the painting in The Rings of Saturn, meditating on the anatomical inaccuracy of the dissected left forearm, the muscles of which appear to be attached incorrectly (to the outside rather than the inside of the elbow). Rembrandt deliberately botched the arm, Sebald suggested, because he identified more closely with the wronged criminal than with the surgeons who had commissioned him. In Rembrandt's day only criminals were dissected, as it was believed the procedure denied souls the chance of a bodily resurrection. Anatomising the body was a means of dispossessing the soul.

Hugh Aldersey-Williams dedicates the prologue of Anatomies to the same extraordinary work of art. But rather than focus on the cadaver, he concentrates on the attitudes of the surgeons; how their expressions evolve from bafflement into the light of understanding, as well as the gesture Dr Tulp forms with his own left hand while elevating the tendons of the cadaver. It is a surprisingly difficult gesture to make, achievable only by using an odd combination of small muscles in the hand known as the lumbricals. One interpretation is that Tulp is demonstrating an aspect of anatomy unique to humans  the way the intrinsic muscles of the hand work with our opposable thumbs  and is therefore making a comment on the nature of our humanity. By opening his book with The Anatomy Lesson of Dr Nicolaes Tulp, the author makes it clear that it is to be as much about culture as it is about cadavers, about art as much as anatomy.

From the cover Anatomies looks as if it should be filed under "humour", with its cartoon diagrams and its fig-leafed Michelangelo. Yet although he puts himself in many potentially comic situations  an art class with nudes, a blood donor centre, a tattoo parlour  the author resists exploiting them. Anatomies is a serious work. Self-confessedly ignorant of his body's workings, Aldersey-Williams wakes one morning with the need to pee and realises that he has "no idea how my bladder works, or why it seems to work differently now from the way it worked when I was younger". This book, he tells us, will be his attempt "to find answers to these questions". But neither is Anatomies a beginner's introduction to human anatomy. When he does stumble into a functional explanation of the bladder, or the workings of the inner ear, he stops himself within a paragraph and veers instead on to some gloriously obscure anecdote about Bosch's Garden of Earthly Delights, or the mythography of Marina Warner. He assumes the reader knows nothing about the bladder, but he does assume an extensive knowledge of the works of Shakespeare. When it comes down to it, Aldersey-Williams is not that interested in how his body works; he is much more interested in the ways the body has been viewed and imagined through the centuries.

Consider the clitoris, which has been "known, lost, found, lost again and found once more during the course of 2,000 years of medical history". The ancient Greeks thought it was redundant tissue, "guarding" the entrance to the vagina the way the uvula guards the throat. Realdo Colombo, a 16th-century physician, was the first to describe its relationship to orgasm. But he was shouted down by Andreas Vesalius, the anatomical genius who was Colombo's predecessor at the University of Padua. Vesalius seems to have had little contact with the female pelvis in vivo, writing to Gabriele Falloppio, who gave his name to the Fallopian tube, "you can hardly ascribe this new and useless part as if it were an organ to healthy women" (what Vesalius's wife, Anne van Hamme, had to say on the matter goes unrecorded). Male cadavers were hard to come by in the 16th century, but female ones were even harder. Aldersey-Williams tells us that Vesalius's groundbreaking "Anatomy of the Uterus" was based solely on bits of a "monk's mistress whose body was acquired by dubious means".

Anatomies brims with fascinating details like this one. He brings us blushing and biojewellery, phrenology and phantom limbs, Vitruvius and vivisection. Though he tries to hold to a structure, his infectious enthusiasm sees him meandering around each subject like a yacht without a tiller. Thus the lungs are bypassed altogether, much of the chapter on the heart is spent discussing the kidney, and the nose is classed under "head" rather than "face". But none of this seems to matter when the terrain he covers is so richly brought to life. The chapters are executed in a rapid, breathless style with a reach more broad than deep. A couple of pages might see the narrative breeze through the Oracle of Delphi, the philosophy of Aristotle, the fiction of Gogol, and the essays of Montaigne.

Half a page is enough to give us Jesus, Muhammad, Neil Armstrong and David Hume. In the world where myriad factoids can be garnered with the click of a mouse, we're never quite sure if we're seeing the hand of Google or the eye of scholarship, but if the mark of a science writer is how well those facts are brought together in an innovative and perspective-altering way then Aldersey-Williams has succeeded, creating an impressionistic but relentlessly entertaining cultural history of the human body.

Rembrandt's painting was of a condemned man who, by forfeiting his soul, enabled the rest of us to move towards a greater understanding of our humanity. In examining our bodies so closely, Aldersey-Williams doesn't want us to forfeit our souls. Four centuries after Rembrandt we are still gazing under the skin to try to understand the nature of our selves, and now submit our over-investigated bodies to increasing numbers of scans and blood tests, as well as the gaze of superspecialists. The book concludes with an examination of what might lie over the horizon; what prostheses, transplants and robotic body parts we might one day have to incorporate into our ideas of the self. Some studies have claimed that, in western societies at least, as our understanding of the body increases, anxieties about our health rise. By helping to put those anxieties in context, and showing us just how far we've come, Anatomies puts a humane case for making peace with our bodies just the way they are.

 Gavin Francis's Empire Antarctica is published by Chatto.