My chat with Peter Capaldi definitely exceeded my expectations. You meet a lot of characters in this business, but there's a pitch of character only a Scotsman can reach. These completely out-of-context quotes from my conversation with the current Doctor Who should give you some idea.

"… Once you get the operation it's all tidied up. I don't know what the doctors do!"

"… They're all posh blokes who say, "We had a look around and tidied things up a bit!"

LAWRENCE SMITH Peter Capaldi: 'I'll never get offered a role like this again.''

"… So the next thing is they're gonna give you a little injection. They're gonna inject little metallic earpieces so you can get your phone and listen to music and stuff like that. Which is the first step to being a Cyberman!"

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"… This table's not very good, is it. Can we get a more futuristic table!"

Capaldi with this season's Companion, Pearl Mackie.

"Australia and New Zealand. We had a lovely time there last year." Capaldi, like any good Scotsman, communicates in short, blunt sentences. "We knew Doctor Who had an historic purchase in those countries. I had no idea it was so well-known."

He's long been recognised for his epically foul-mouthed stint as Malcolm Tucker in the British political comedy, The Thick of It. People like to approach him and ask him to swear at them. Like a verbal autograph. But he had no idea what being recognised was until he became the star of one of the most enduring (and bonkers) sci-fi series of all time. "It was funny walking around Wellington and being recognised all the time," he says. "Or in Sydney, you go, Wow, I'm in Sydney! And everyone's looking at you. You think, Well there's an opera house just over there. Surely you'd rather go there!"

Maybe you can expect that kind of attention in the big smokes, but he's genuinely surprised at the reception he got from provincial New Zealand. "We drove down the North Island. And we stopped somewhere for coffee. And I couldn't believe it. The whole place recognised me. Which was lovely, but unexpected."

While he's saying this I think back to my own boyhood, and how I would have reacted if Tom Baker walked into a cafe in, say, Whakatane, I completely get it. Doctor Who is a global brand, and has been for decades.

"New Zealand's had Doctor Who since it began," he says. ''That's 50 years of … stuff."

Stuff pretty much sums it up. Few shows have as much stuff in them. From janky wheelie-bins screaming 'WE ARE THE DALEKS!' in the voice of a tannoy submerged in water; to the last season, when Capaldi's incarnation of the Doctor faced an absurdly massive CGI T-Rex stalking Victorian London. The show is both a monster and a place for monsters.

"It's a monster show. People love seeing monsters blown up and bashing through windows. There's no other show that does that. There's almost a kind of B-Movie element. If you want to see people dressed up in rubber suits, it's either this or some late-night show we shouldn't go into."

The show's monsters used to scare me, certainly. But what has always really disturbed me is the Doctor. He's a man (or possibly not a man) who can travel back and forward (and possibly sideways) through time. When he dies, he 'reanimates' in a new body, with an apparently new personality, but with all his memories. So what actually makes him him? I always wondered. It can't be his body, or his personality, because those change. It can't even be his memories, because in some episodes he purposefully loses all his memories, or gets them stolen by an enemy, and he's still the Doctor.

At the start of the last season, Capaldi's Doctor laid the Broom Paradox on a particularly nasty Frankensteinian robot who liked to regenerate himself with bits from hapless humans. If you buy a broom, the Doctor asked, and then have to replace the handle, and then have to replace the head, is it still the same broom? "That's you. You're a broom." He could as easily have been talking about himself. Or us, for that matter. Every atom in our body gets replaced every seven years. Our memories are unreliable, and our personalities are constantly changing. So who are we? That's the real horror at the heart of Doctor Who, I think.

While I'm trying to lay out this existential paradox, Capaldi is looking thoughtfully down his nose at me. "I think he's not … human,'' he finally says. "He's dressed in human bits … but he's not a human being. He's actually a creature of the universe and of the cosmos. So he's quite mysterious and romantic in that sense. He'll always present himself to the audience, and they'll always see a human being, but there's this whole hidden Doctor, which they only glimpse." Which is a pretty interesting answer, I reckon.

Capaldi is a fan who became the Doctor. For him, the magic lies in its accessible escapism. The Tardis could show up in your garage, or in your local mall, or in the bush near your house. "It can come to you, rather than being the Enterprise or something: this huge" – pronounced hyudge – "United Nations thing in space. It's more intimate. It's a mix of The Lion, the Witch and the Wardrobe and War of the Worlds. It's a mix of fairy tale and sci-fi."

He has a tradition of watching Doctor Who with his daughter. "My wife doesn't watch it. But my daughter, yes, and that was a very good Saturday evening thing to do. And then suddenly I was Doctor Who and I thought, well what do I do now? Do I maintain this ritual? And I thought, well let's do it. So that's what we do. Every Saturday night."

Capaldi won't be the Doctor for much longer. Last year's shock announcement was that both Capaldi and long-time writer and showrunner Steven Moffat will be leaving at the end of this season. Moffat will be handing over to Broadchurch creator Chris Chibnall, while Capaldi will be handing over to … well, it could be anyone really. One of our 'no-go areas' for these interviews is asking who the next Doctor will be (along with asking about their personal lives, Brexit or Donald Trump). But you get the sense, from talking to him, what Capaldi probably thinks of Trump.

For Capaldi, filming his big death scene has been an odd experience. "It was strange. A strange day. It was … explosive." He smiles ruefully. Doctors die in many ways. The first Doctor had his life force siphoned from him by the planet Mondas. Doctor Five Contracted an exotic toxaemia on Androzani Minor. Not all deaths are so dramatic. Doctor Seven died from complications during laparoscopic surgery. But Capaldi's Doctor dies a worthy death, apparently.

"He goes out fighting. Definitely."

And predictably Capaldi isn't overly sentimental about it all. "It's sad because you know you won't be Doctor Who anymore; but it's joyful because you survived it. And also because there are other things available for you to do. … It's a very special part, and you don't take it on to phone it in; you take it on to embrace it. It takes over your life to some extent. Well, completely!"

Later, in a room nearby, I tell Moffat

about my existential problem, how I've been trying to come to grips with who the Doctor is. 'He's the main character. He wears the suit with the red trim."

But he patiently lets me lay out my thoughts: how it's hard to pin down the identity of someone whose body and personality aren't fixed ideas. His answer is decisively blunt. ''I don't think his personality changes that much. He just gets a new physical form and it alters him a bit. If you look at the words on the page then the Doctors are really quite similar. He's a thrill-seeking, overgrown adolescent who thinks he comes over as Gandalf, but everyone knows he's just someone who never grew up."

Moffat's views stand out starkly against the more mystical reading of the character given to me by Capaldi, who spoke in a decidedly Gandalf-like way, at times, about the challenges of playing this iconic character, describing "a kind of ethereal element to the role that you have to conjure" and saying things like '… time moves out like ripples in a pond … the Doctor has to decide not to read the ripples."

'I'll never be asked to do this again,' Capaldi says finally. 'To be in touch with the cosmos. Perhaps I can play a down-and-out hippy next. I could be found on a beach somewhere in New Zealand. Wasted."

Dr Who, Prime, Sundays, 7.30pm.