Snowflake formulas, dice odds and other satisfying maths of the everyday

Mathematical properties underpin everything in our world, even if our minds tend towards noting their effects rather than their functions. This mesmerising video from the Paris-based design studio Parachutes investigates the maths hidden in our everyday lives – from the swirling patterns of storm clouds to the binary code behind computer screens.

How the philosophical paradox of aspiration is resolved by a new theory of self-creation

Let’s say you’ve decided to enrich yourself by learning to appreciate classical music, even though you didn’t have much previous interest in it. Such a resolution is hardly uncommon, but acting on the aspiration requires you to value an activity that you don’t yet know how to. In this video, Agnes Callard, associate professor of philosophy at the University of Chicago, borrows from her book Aspiration: The Agency of Becoming (2018) to put forth a solution to this paradox centred on understanding our current and future selves as inexorably bound through the act of aspiration. Further, she argues, in resolving this paradox, we can understand ourselves as responsible for the act of self-creation – and, by extension, for our own morals and values. This video is part of the series Into the Coast, which sets out to capture philosophy as a ‘living discipline’ through interviews with leading academic philosophers.

The violinist staging a concert of unity at the border between North and South Korea

The South Korean violinist Hyung Joon Won has held a singular – and perhaps quixotic – dream for the past seven years: a joint concert by North and South Korean musicians at the world’s most contentious border. At 160 miles long and 2.5 miles wide, the Korean Demilitarised Zone (DMZ) separates the two countries at the 38th parallel. On this narrow strip, the threat of all-out war hangs heavy – and anyone with a violin case or a film camera gets short shrift. The South Korean-born filmmaker Catherine Kyungeun Lee follows Hyung Joon as his plan for a show of peace at the border teeters between success and collapse, at great personal cost to him. Filmed in 2015, her documentary traces the confluence between fraught geopolitics and all-too-human struggles on the peninsula.

Lee is now directing two documentaries in East Africa. One tells the story of a child-soldier who became a Harvard graduate and activist who was jailed in South Sudan, and the other follows the woman in charge of realising Somalia’s first democratic election in 50 years, despite seemingly insurmountable opposition.

Basic healthcare and clean needles is all in a day’s work at a roving addiction clinic

Marc Lasher works as an addiction medicine specialist but, between his regular appointments, he oversees a clean-needle exchange on the streets of Fresno County in California, out the back of a modified school bus. Lasher’s decades-long dedication to public health is all the more impressive considering that his programme was illegal in the state until 2012. In the wake of the opioid epidemic, his approach – addressing drug addiction as a matter of public health rather than criminality – has only recently come into favour in much of the United States. In this acclaimed documentary, the US filmmaker Elivia Shaw follows Lasher and a team of young volunteers as they provide people coping with addiction with clean needles, as well as basic medical care and referrals to specialists and detox centres. The result is both a moving testament to Lasher and his team’s selfless work and a damning indictment of a healthcare system in which unaddressed health issues, costs and the physical and emotional tolls of poverty compound each other relentlessly.

Jim Hall, 78, has a blue body – but his outlook on life is more unusual still

‘I decided it was OK to have fun with my body … I probably have more balls than anybody!’

Jim Hall worked in urban development for four decades before retiring as the principal city planner of Baltimore. Aged 78 and beginning to feel some of his faculties slip, he is planning a move to Texas to live out his final years. These unremarkable details of his biography might seem at odds with his unique look – most conspicuously, the blue tattoo covering almost every inch of his skin. But despite the unusual choices he’s made to modify his body – including some unusual, intimate augmentations hidden from view – Hall’s outlook on life is deeply practical, centred on playfulness and an enduring sense of gratitude for what he sees as the incredible gift of being a human. With a palette that complements Hall’s own chosen colours, this short documentary from the US directors Jonathan Bregel and Steve Hoover finds wonder and wisdom in a man who is as hard to define as he is plain-spoken and pragmatic.