The Weekend's TV: Sherlock, Sun, BBC1<br/>Amish: World's Squarest Teenagers, Sun, Channel 4

Did you know that Sherlock Holmes is completely clueless in some regards?

Dr Watson tells us so in A Study in Scarlet, the very first Sherlock Holmes story: "His ignorance was as remarkable as his knowledge," he writes. "Of contemporary literature, philosophy and politics he appeared to know next to nothing." Which is not something you'd guess from the countless film and television adaptations of the Holmes persona, and a reminder that however overworked a legendary character may be there's almost always a fresh angle from which to observe him. A bit of cluelessness would have worked very well in Sherlock, Steven Moffat and Mark Gatiss's bold updating of Holmes to contemporary London. You can easily imagine the character looking utterly blank when Big Brother was mentioned or the talk turned to David Cameron, but (so far at least) they've passed on that under-exploited character detail. It hardly matters, though, because their Sherlock is a triumph, witty and knowing, without ever undercutting the flair and dazzle of the original. It understands that Holmes isn't really about plot but about charisma.

It's easy to think of reasons why it wouldn't work. How can this pre-emptive genius of forensic science stand out in a world where forensic science is a commonplace, for one thing? Back in the 1890s, CSI: Baker Street was an almost unique franchise, now every local policeman can call up a DNA trace and take a short cut to a conviction. A nervous adapter might shy away from the technology entirely, and make Holmes into a self-conscious Luddite, a contradiction to modern notions of command. Instead, Gatiss and Moffat embrace it so wholeheartedly that it leaves its mark on screen – as Holmes's peremptory phone-texts swim into view over the action – in particular during a Scotland Yard press conference at which Holmes unhelpfully undermines the official version with a mass-mailing to everyone present. They've visualised his thought processes too, so that his inspirations tag the crime scene like an internet word cloud. And they relish every mismatch between Conan Doyle's canonical details and modern manners. When Watson (very nicely played by Martin Freeman as a man with PTSD, after a tour of duty in Helmand Province) finds Holmes lying in a swoon in his flat he assumes he's a junkie. Holmes rolls back his sleeve to reveal three nicotine patches on his arm. This, he announces, is a three-patch problem.

You'd diagnose Benedict Cumberbatch's Holmes as high-functioning Asperger's these days, and the script has a lot of fun with that too. Holmes notices instantly that a female lab assistant has furtively applied some lipstick, but crushingly fails to grasp that she's put it on because she fancies him. When she returns having wiped it off again he compounds the problem. "What happened to the lipstick?" he asks. "It wasn't working for me," she replies, humiliated. "Really," Holmes says, "I thought it was better. Your mouth's too small now." There are good running gags about Mrs Hudson's status as landlady ("I'm not your housekeeper, you know," she keeps saying) and judicious borrowings from Conan Doyle. Fans will recognise at once that the close-reading Holmes applies to Watson's mobile phone is drawn from an almost identical analysis of a pocket watch. More slyly oblique is the conversion of the lost ring that Holmes uses to lure the killer in A Study in Scarlet into a lost "ring", a mobile phone that can be used to contact the killer directly. If you want a quibble I suppose you might note that Holmes appeared a bit slow when listing the attributes of his mystery killer – which rather obviously suggested a London cabbie – but if you want a quibble I really suggest you look somewhere else. Flagrantly unfaithful to the original in some respects, Sherlock is wonderfully loyal to it in every way that matters.

You hardly need Holmes's powers of deduction to know that the teenagers in Amish: World's Squarest Teenagers are a long way out of their comfort zone, not that they'd have the faintest idea what a comfort zone is, having grown up almost entirely insulated from the modern world. Like Holmes, their grasp of some areas of common knowledge is foggy. It was revealed that they'd never heard of Marilyn Monroe or JFK. They do, however, have a matchless grasp of obscure Old Testament patriarchs. For Channel 4's series, five of them had left their homes in the Midwest to spend time with British teenagers, and they began by travelling to a south London council estate.

They were shocked by London, naturally. "Creepy," said one, asked to give her response to Soho sex shops, "... it seems like the devil's territory." Others were troubled by the alienation of London commuters: "It's kind of amazing how you can be in such a big crowd and be totally isolated." And in everything they said it was clear that they felt they were the privileged ones, and British teenagers were to be pitied. Some of this was a failure of imagination on their part. They simply couldn't conceive that another way of life might contradict or compete with their own. But their innocent bafflement at a society in which teenagers stab each other also had its chastening elements. One of them, Jerry, was in no great rush to end his Rumspringa – the name the Amish give to a period of worldly experiment that precedes adult baptism – but even he appeared to have a serenity that would have been enviable, if it came without the spiritual brainwashing.

t.sutcliffe@independent.co.uk