Anyone who has experienced vertigo while wearing a new pair of specs will be at a distinct advantage when it comes to enjoying Raymond Tallis's book. I've had it myself a few times - the sensation that, like poor Alice in Lewis Carroll, one's neck has suddenly stretched like a giraffe's, detaching the head from the body. “What am I doing up here?” is the confused reaction. “Look how far away my feet are! Goodbye, feet!” The unpleasantness passes quite quickly once the specs are familiar. But for a short while, you are reminded of the unsteadying fact that you don't see the world from some vague, internal “you” perspective. No. You see it, specifically, from the eyes in your head, which are located, somewhat weirdly, and without visible means of support, at least 5ft up in the air - “hoisted up on 5ft or 6ft of meat”, in Tallis's own vivid phrase; “a bust on a long plinth”.

This is an amazing book about the human head, and since its chief stated purpose is to amaze, there can be no higher compliment. One needs to be warned at once that Tallis is a bit of a brainbox, so it isn't all plain sailing, style-wise. Having a medical and academic background (he was professor of geriatric medicine at Manchester University), Tallis is also a poet, literary critic and philosopher, and it is his unique ability to synthesise hard biological fact, wide philosophical inquiry and piercing poetic incontrovertibility that makes his book so original. The effect on his prose of all these rigorous academic disciplines is to make it extremely mentally stimulating, of course, but I think he wouldn't mind my saying that it also means he has never met a polysyllabic compound that he didn't want to shake warmly by the hand. What is a “harrumph”? It is a “protolinguistic Ur-phoneme”. Meanwhile, tears are “manganese-rich ocular saline”; the returned gaze in a mirror represents “a chaste, ocular auto-copulation”; a make-up bag is really an “armamentarium”.

The mission of the book is clear enough, however. Tallis wants to challenge the prevailing notion of the brain as the lone site of consciousness (“the brain is absurdly over-rated,” he writes). Deliberately challenging the orthodoxies of our day, he wants to remind us of what an astonishing range of stuff goes on in our heads besides neural activity, because he sincerely believes that the brain's two excellent hemispheres don't add up to a whole world.

Inside this unnaturally elevated head of ours are crammed organs and orifices that interact in complex ways with the world beyond. “I want to celebrate the mystery of the fact that we are embodied,” he writes; also, that our consciousness is beyond us, in every way. “We are not to be understood, as animals may be understood, as stand-alone organisms; even less are we to be understood as stand-alone brains.”

Of course, what has already drawn attention to the book in some quarters are its delightful discussions of the head's various disgusting secretions (snot, saliva, ear wax), and its under-appreciated everyday activities such as smiling, yawning, masticating foodstuff, vomiting it up again, and breathing. Making strange the familiar is a special gift, and Tallis seems to know which facts we will sniff at, which we will swallow, which will inspire nausea, and which will make us simply stretch our eyes. We produce a quart of mucus every 24 hours, apparently. We will yawn, in the course of our lives, a quarter of a million times. If our hair had feeling, we'd have to have a local anaesthetic when we had it cut. The mouth is “the anus of the face” (or so says Samuel Beckett). Drink a cold glass of orange, and you feel its progress beyond the windpipe and gullet: “It is a torch, momentarily lighting up the darkness within the body.”

The section on saliva (30,000 litres in a lifetime, incidentally) is a good example of his cross-disciplinary approach: we start with a vivid fictional passage from Jean-Paul Sartre, then do the biology and chemistry (“during its passage down the secretory ducts, sodium and chloride are abstracted”), then start to consider the mystery of involuntary swallowing, and then our attitude to our own saliva, which changes radically once it's outside the body in the form of spit. Would you drink a glass of your own saliva? Why is spitting at someone such a terrible insult? When did casual spitting become socially unacceptable? Taking in atrocity anecdotes and a quote from Handel's Messiah along the way (“He hid not his face from shame and spitting”), Tallis reaches the end of his journey through spittle with the comforting thought that sometimes we just lick stamps - although he doesn't consider the benefits of licking one's wounds, which I wouldn't have minded learning the truth about, while we were on the subject.

It is no criticism of the book, incidentally, to say that, quite frequently, one wishes one had Tallis's telephone number, because he seems to have missed something. Personally, I want him to tell me precisely how dangerous boxing is, and whether it should be banned. I am disappointed to have nothing on phrenology (the 19th-century “science” of analysing character by feeling and observing the shape of the head), and I also think it hilarious that the saliva section has no mention of Pavlov (although maybe that's a bit Pavlovian of me?). The chapter on blushing doesn't mention Christopher Ricks's famous book Keats and Embarrassment. However, this urge to send him parcels of books is not because Tallis doesn't cover things adequately, of course. It's because quite the opposite is the case.

The beauty of The Kingdom of Infinite Space is that, while Darwinians may disapprove of its “we are not animals” stance, and neurophilosophers will be dismissive of its “we are not brains on sticks” position, to an outsider such academic concerns are comfortably secondary to the thrilling way that Tallis is able to demonstrate exactly how his own consciousness happens to work. The mental energy is neatly gymnastic: each sequence of thoughts starts with a confident deep breath and arms outstretched, then runs up, does a roll, a leap, a twist and a double-somersault, and lands on its own two sturdy feet without the faintest wobble at the far diagonal corner of the mat. I've never seen anything like it.

The irony of The Kingdom of Infinite Space, of course, is that it sets out to draw attention to everything other than the brain, yet in the process makes the reader bury his face in his hands and moan, “It hurts, I tell you; it hurts!” But the pleasure of this book is that, at the same time - and in all the best senses - it is a very, very heady experience.

The Kingdom of Infinite Space by Raymond Tallis
Atlantic £19.99 pp324

Times Recommends

• The Sunday Times 100 best holiday reads
• What will we be reading this summer: the booksellers predict
• Literary festivals: a survivor’s guide