Last Night's TV - Britain's Greatest Codebreaker, Channel 4; The Boarding School Bomber, BBC3

Britain's Greatest Codebreaker

There's always a question, with drama-documentary, as to which is the crutch and which the invalid.

Is this a play that needed a prop, in other words, or a documentary that felt unable to stand on its own two feet? In Britain's Greatest Codebreaker, a tribute to the mathematician and cryptographer Alan Turing, the documentary material far outweighed the dramatised sequences, but you were still left with a sense that what it really wanted to be was a play; a clever, Michael Frayn sort of affair, in which the intellectual biography was raided for metaphors for the life. In fact, it got a little heavy-handed with that desire: "You want my dreams because you say that dreams are a cipher and you say that you are able to render them into plain text and find in them the content that I secretly wish to convey to you," said Turing to his Dr Greenbaum. Later, he glumly concluded that he might be uncrackable: "I've tried to decode myself, but I can't get outside myself to do it." Dr Greenbaum, meanwhile, a lot more garrulous than you might expect from an old-school Freudian, did his bit in return, discussing Turing's ideas about artificial intelligence. "How can it be called thinking if it's drained of all this fragile broken-heartedness," he asked, suggesting that it isn't logic that makes us human but its opposite.

These scenes were quite nicely played by Ed Stoppard as Turing and Henry Goodman as Greenbaum. And they carried a fair amount of information about Turing's sentimental life, including his idealised devotion to a boyhood friend called Christopher Morcom and the criminal charge that eventually ruined his life. But they couldn't entirely be trusted to convey the real message of the programme, which was that we – as inhabitants of a computer-dependent world – owe Turing everything. For that we needed testifying experts, including Steve Wozniak (who founded Apple with Steve Jobs) and Turing's biographer David Leavitt. Without Turing's ground-breaking paper, "On computable numbers, with an application to the Entscheidungsproblem", they implied, no iPad, no smartphone, no internet, nothing.

I'm not sure how true that is. Was the computer one of those inevitable inventions, towards which human knowledge was inexorably driving? Or was it a fork in the road we might have sailed past if Turing hadn't spotted the turning? Either way, his genius and originality were undeniable, and the cruelty with which he was eventually treated decidedly shaming. After a pick-up had robbed his house, Turing guilelessly reported the matter to the police, who turned out to be far more interested in buggery than burglary. He was eventually offered the choice between a prison sentence and a crude form of chemical castration and fatally opted for the latter. Depressed by the effects on his body, and continuing harassment by the police, he's believed to have committed suicide by eating a cyanide-doped apple (Snow White was one of his favourite films). In 2009, Gordon Brown apologised on behalf of the British government: "We're sorry. You deserved so much better." It was a hazardous quote on which to end a biographical documentary, but, despite the film's shortcomings, I think they just about got away with it.

When Andrew Ibrahim's mother got a telephone call from him to say that he'd converted to Islam her first reaction was "Oh God, not again... another fad." Andrew, now Isa, had already been through skateboarding, alcohol and heroin, but religion proved the most dangerous fad – a gateway drug to the jihadi extremism that eventually led him to plan a bomb attack on a Bristol shopping centre. The Boarding School Bomber was a bit like Four Lions without laughter to ease the discomfort – a sad account of a troubled teenager looking for somewhere to belong, and saddest of all when his mother was on screen. He never got to set off his bomb, but he'd blown up her life.