There were so many ear-catching moments in Peter Hennessy’s series for Radio 4, Winds of Change, adapted from his new book by Libby Spurrier and produced by Simon Elmes. Harold Wilson answering a journalist’s question after a sleepless night while awaiting the results of the 1964 election, quizzical, cheeky and so quick off the mark. When asked if he felt like a prime minister, he replied: ‘Quite honestly, I feel like a drink.’ Later he was waylaid at Euston station having just got off the morning train from Liverpool and was still unsure of the result. (Labour won by just four seats after 13 years of Conservative rule.) At 3.50 that afternoon, Wilson, sitting by the phone in Transport House, at last received a message from the Palace. ‘Would it be convenient for you to come round and see Her Majesty?’

Earlier, in 1962, in the build-up to the Cuban missile crisis, Nikita Khrushchev was away from Moscow at his summer residence on the Black Sea coast. ‘What do you see?’ he bellowed at his advisers. ‘I see US missiles in Turkey, and aimed at my dacha.’

Hennessy’s most timely series takes us back to the 1960s following Harold Macmillan’s speech in South Africa predicting the transition of Britain’s colonies to independence. It’s stuffed full of characters — General de Gaulle’s advice to the young Queen Elizabeth on what her role should be: ‘In that station to which God has called you, be who you are, Madam.’ The young President Kennedy speaking on primetime TV not long before the East Germans began building the wall across Berlin and declaring that ‘our rights there are clear and deep-rooted’. Macmillan, then PM, leaving London to spend the day shooting on the grouse moors of Yorkshire as the wall was going up through those anxious August days in 1961.

In 1960, we discovered, in an episode about Stockwell, the government’s secret nuclear bunker in the Cotswolds, constructed at the height of very real fears about a third world war, this time nuclear, that the PM’s driver was told to carry four pennies for use in a public telephone box in case of a surprise attack. How else was the PM to make contact with Whitehall?

We might think we are living in uncertain times but Hennessy reminds us of those years of imminent apocalypse as the Cold War set in and a 104-mile wall was built round a European city not that far from London. Surprisingly, very few of the political giants he describes have made it on to Radio 4’s Great Lives series, another staple of the schedule that is always sharp and revelatory as Matthew Parris’s guests are challenged to convince him that their choice of great life is worthy of the title. Last week Philippa Perry chose Maria Montessori, the Italian doctor and educator whose theories about child development and system of education have been adopted in countries across the world. Parris, ever sceptical, forces his guests to make a clear and persuasive argument.

Perry first encountered Montessori’s work when looking for a nursery for her daughter. She was struck by the unusual teaching methods, children of different ages in the classroom, each pursuing their own tasks, everyone allowed to learn at their own pace, in their own way. Let’s see what the child is interested in, Montesorri recommended, and follow that. While working with children with special needs in her native city, Rome, in the 1890s she had seen how many of them had gifts that could be brought out and made useful if the right environment was provided for them.

‘Never interrupt a concentrating child,’ she taught, even if all the child was doing was steering a toy truck across the carpet. But what about disruptive children, Parris interjected. How does a teacher with 30 children in her class allow each individual to learn in their own way? It’s often intelligent children who are the most disruptive, he was reminded. Montessori, argued Perry, was remarkable because she allowed children to teach her.

The inspiration behind The Sound Odyssey on Radio 4 (produced by Jax Coombes) is somewhat in the mould of Montessori, taking one musician and introducing them to a style of composition and performance very different from their own. It’s about making connections and becoming creative through what you don’t know rather than what you do. This week Gemma Cairney took Kate Stables, a banjo player and singer, to Casablanca to meet Asmaa Hamzaoui, daughter of a famous Gnawa musician. Gnawa, we learned, came out of the sub-Sahara. It is trance-like, meditative music that uses just three instruments — the guembri (a stringed instrument), metal castanets and drums. Unusually, Hamzaoui’s father encouraged her to become the first female guembri player in Morocco; she also has a wonderful singing voice.

The challenge set by Cairney was for Stables and Hamzaoui to come up with a new piece of music that combined both musical traditions in just two days. We could hear Stables’s discomfort as she found herself improvising a vocal line. It’s edgy, even dangerous as each musician exposes themselves to failure. But what emerges is a positive connection, a human exchange, the music of change.