The mathematics of music means piano strings can never be in perfect harmony

Unlike with guitars and violins, pianos’ strings can never be perfectly tuned to one another. The solution? As this short animation from MinutePhysics explains, the instrument’s 88 strings across more than seven octaves means tuning a piano using harmonic intervals will inevitably lead to notes being fractionally off-pitch, with the issue compounding across octaves. So instead of using harmonics, piano-tuners generally keep octaves perfect, while leaving every other interval out of tune by just a tiny fraction. This workaround forsakes the appealing mathematical patterns of harmonics, but makes it possible to keep the kind of uniformity that is so valued in an era of mass production and reproduction of music.

Cut, paste and remix your way through this century-spanning history of collage

The term collage – the artistic technique of gluing different elements together – has its origins in the early modernist movement, especially in Cubist works by Pablo Picasso and Georges Braque. But before such combining of disparate source materials became a mode of the artistic avant garde, collage had eclectic manifestations through history and across cultures – as a method of decorating, a tool for enriching scientific texts, and a means for women to engage with areas of enquiry typically reserved for men. Created to accompany the Scottish National Gallery of Modern Art’s exhibition ‘Cut and Paste: 400 Years of Collage’ in 2019, this video traces the rich roots of the technique, from the invention of paper in China in 105 CE, to its rebirth as an elevated style of modern art in the 20th century.

When home is two sisters, a houseful of vulnerable men, and a lot of tough love

After she was widowed at age 32, Grażyna Sochacka founded the Panakeja Foundation – a social-assistance centre for homeless men on Sobieszewo Island in Gdańsk, Poland. Alongside her sister Wioletta Sienkiewicz, Sochacka has dedicated her life to caring for men living on the fringes of society, and often in need of intensive care due to alcoholism and other health problems. The Polish filmmaker Filip Jacobson’s observational short Home (Dom) traces the unending daily pressures the sisters face running the centre. These include changing bed sheets, providing medical assistance, keeping up with bills, and the ever-important business of doling out cigarettes. Imbued with a deep humanity and inflections of humour, the film explores the human need for a balance between structure, freedom and respect – as well as, from time to time, heavy doses of tough love.

‘I want to take the bullet and save my friends’ – the grim reality of safety drills in US schools

A generation ago, children in classrooms in the United States prepared for natural disasters such as fires and tornadoes. Today, active-shooter drills force them to confront the grim possibility that someone – perhaps a fellow student – might open fire in their school. In this StoryCorps animation, one such drill prompts a mother and her 10-year-old son in Texas to discuss a question no child should ever have to consider – whether he would sacrifice himself to try to save his schoolmates. An affecting and troubling short, The Drill gives an aching human voice to the psychological toll of school shootings and the culture of fear they’ve created for schoolchildren and their parents in the US.

If you think that modern cosmology leaves no room for ‘god’, start using your imagination

‘We’re not so much abandoning the idea of the gods, we’re just trying to pull them all the way into the Universe.’

From the possibility of infinite universes to the prospect of panpsychism, puzzles have arisen in physics that can take science to some very counterintuitive places. According to Mary-Jane Rubenstein, assistant professor of religion and feminist, gender and sexuality studies at Wesleyan University in Connecticut, new theories and breakthroughs at the forefront of cosmology need not – and moreover, should not – elbow out theology from the conversation about our place in the cosmos. Instead, as she argues in this wide-ranging interview recorded at the HowTheLightGetsIn Festival from the Institute of Arts and Ideas in 2019, science should encourage us to build more durable myths and theologies to suit our times.