One of Thomson's motivating interests here is the paradoxical demand on all actors "to be real and fake, at the same time". He recalls as a schoolboy watching Laurence Olivier play Archie Rice on the London stage in 1957. Olivier had hitherto been the English theatre's Shakespearean god, with his triumphant incarnations of Hamlet, Henry V and Richard III. Back then, the young Thomson knew would be a stretch for an actor so steeped in the aristocratic and burnished by his success on screen. But Olivier's pathetic Archie got to him: "I could feel something I wasn't able to articulate: that this glittering wreck only a few feet away was as vital as one's father in life, drunk or sober."

Olivier is a mystery Thomson keeps trying to unravel, principally by setting him as one point of a triangle between two rivals: his wife Vivien Leigh and his American foil, Marlon Brando, the only actor who approached him in terms of presence and grandeur. Leigh fell apart doing Blanche every night in , while Brando (who starred opposite her in the film) sabotaged his career through a basic distrust of acting. Olivier just kept going, armoured with a self-love and a self-belief that steamrollered doubt.

Daniel Day-Lewis' breakdown when he played Hamlet on stage in 1989 has become famous theatre folklore - when Hamlet confronted the ghost, the actor allegedly saw his own father. (Day-Lewis now denies it.) One can't imagine Olivier, who died that same year, being troubled by visitations from the otherworld. A reputation for coldness and treachery dogged him; he seemed to have been barely interested in people beyond what he could borrow from them as material for imitation. But if, as he once said, acting is just lying, he made himself one heck of a convincing liar.

Thomson, like some of the performers he admires, has a wayward streak. His weird imagining of David Garrick (1717-79) and Brando in the back of a New York taxi playing a scene from does little to illuminate the personality of either - though the taxi driver could have dined out on it for a while. And his tendency to reference footballers out of the blue - Ronaldo, Pelé, Cruyff - is whimsical. I'm not sure Sarah Miles would thank him for this metaphor on her dalliance with Olivier: "She was a ball that a George Best could not help playing with."

He later dips into fiction, or a fictional scenario of a couple of actors who get married and involve themselves in the long, rivalrous struggle to "make it". Does he secretly hanker to write a novel? His imaginative reach as a critic suggests that he might be a brilliant portraitist. Here he is on Olivier (again): "He wanted to be loved, and admired. He wanted applause. And he guessed he was an awful person." It sounds like the opening of a short story.

Even allowing for the missteps here and there, this book has a nugget of interest on almost every page. I didn't know John Gielgud helped the young Brando with the verse on the set of , or that director Francis Ford Coppola considered both Olivier and Brando for the title role of . I didn't know Clark Gable killed a woman in a drunk-driving accident.

Thomson is good on the contrast between British and American acting, and the latter's transformation under the sway of the Actors Studio and the Method. He speculates plausibly on the difference between "the grand gestures" of acting in Garrick's day (though Garrick himself was said to be "quiet and natural") and the gradual lessening of effects to the point where the greatest actors dared to do "nothing". He can clinch such an argument with an epigrammatic terseness worthy of Dr Johnson: "Every master of underplaying looks like a ham 30 years later."

As much as Thomson enjoys the mysterious alchemy of acting - the way that it can be both rehearsed and spontaneous, risky and yet disciplined - he sees beyond its purpose as mere entertainment. In the latter stages of the book, he examines acting as it overlaps with real life, and how it may be a skill to project the best version of ourselves. But what if we're only playing extras? It's the quandary of Prufrock: we are the lead player in our consciousness, but to the world we are all but invisible.

So it may be that "the process of acting becomes more necessary as an assurance that we exist".

Will it save us from anonymity? We each of us think we're unique, special, one of a kind, but "the world has you typed", and like certain actors you get stuck in a long run, "doing the same thing every night until it seems stupid". Yul Brynner played 4,625 times, according to Thomson. He must have learned to live with it. Yet others did not.

I remember, as a child, loving an actor named Pete Duel. He was briefly famous as Hannibal Heyes, one of a duo of desperadoes in the TV western series . He was the dark and good-looking type with a wry manner. Duel shot himself on New Year's Eve, 1971. (Duel: his name always sounded like he carried a gun.) When, in shock, I asked my mum why he had done this, she told me (how did she know?) that he had been unhappy about being typecast.

For years afterwards I thought "typecast" was a kind of condition, like having Parkinson's or epilepsy. Having read I'm wondering if I was right.