To all intensive purposes, you might have another think coming about how idioms work

Human language is, of course, far from static. Our vocabularies are constantly being influenced by cultural movements, migrations, new technologies and much, much more. Indeed, even good old-fashioned mixups can shape the way we speak, write and think. As this animation from BBC Ideas explains, there’s a long and rich history of commonly misheard sayings eventually becoming widely accepted, and even replacing the original phrase. So if you’ve ever deployed ‘duck tape’ or spent an afternoon ‘biting your time’, worry not: you might just be on the idiomatic cutting-edge.

Can you solve this slippery maths puzzle that doubles as a morality tale?

The International Mathematical Olympiad (IMO) is an annual competition for the brainiest of high-school maths whizzes in the world. This animation from the US YouTuber Grant Sanderson, who creates maths videos under the moniker 3Blue1Brown, breaks down a question from the 2011 IMO that proved especially challenging to competitors. Between Sanderson’s methodical analysis and the nifty animations, the maths-minded might convince themselves that they would have come up with the answer all on their own. But Sanderson, ever the savvy instructor, crafts his lesson around how to find the solution as well as being mindful of how knowledge is obtained. In doing so, he transforms an algebra puzzle into a lesson on empathy, pedagogy and the nature of discovery.

‘I know it looks barbaric.’ Can a fight club curb street violence?

Chris ‘Scarface’ Wilmore has spent much of his life in Virginia facing violence and jail time. Despite an early opiate addiction and running with gangs, he’s made it to 40 years old. Many others haven’t been so lucky, getting caught up in small disputes that turned deadly. Hoping to curb the violence in his community, Wilmore has taken a unique, controversial approach: from his backyard in Harrisonburg, he runs ‘Streetbeefs’, a makeshift fight venue where disagreements can be settled in a controlled environment, with Mixed Martial Arts referees keeping watch. Wilmore believes in acknowledging and controlling the violence that the state-sanctioned alternatives fail to address; if his efforts save even two lives, it will have been worth it, he says. However, Streetbeefs isn’t condoned by local officials, nor is it clear if it has succeeded in reducing local homicides. The US director Paul Hairston’s short documentary profiles Wilmore and his unconventional fight club, raising broader questions about human nature and the role of violence in society.

Watch Charles and Ray Eames put their 1969 spin on one of the world’s oldest toys

The oldest spinning top ever discovered dates back some 5,500 years, meaning that we’ve been entranced by these toys for nearly as long as human civilisation has existed. And if there’s any doubt about the contemporary appeal of all things centrifugal, look no further than the recent – and depending on your tolerance for flash-in-the-pan retail trends, annoying – ubiquity of the small handheld toys known as fidget spinners. In this short film from 1969, the legendary husband-and-wife US designers Charles and Ray Eames celebrate the crosscultural, millennia-spanning appeal of all things small, simple and spinnable. With an appropriately playful score from the celebrated US film composer Elmer Bernstein, the Eameses offer us 123 tops from around the world, a reminder of the simple satisfaction of watching something spin from initial twirl to final topple.

How a scientific attempt to demystify Buddhist meditation yielded astounding results

In 1981, Herbert Benson, a cardiologist at Harvard Medical School, set out to study the ancient meditation practices of Buddhist monks on the Tibetan Plateau. With the Dalai Lama’s blessing, Benson spent roughly a decade in remote regions of the Himalayas in northern India researching an especially intense technique known as tummo, as well as the physiological effects of other advanced forms of meditation. Rather than debunking the seemingly tall tales of advanced practitioners capable of raising their body temperatures to dry cold, wet sheets around their bodies, Benson’s work actually confirmed and expanded upon these anecdotes. In particular, by tracking vital signs and body-heat output during meditation sessions, Benson found that these monks possessed remarkable capacities for controlling their oxygen intake, body temperatures and even brainwaves. In 2013, a second study conducted on advanced Tibetan tummo meditators by Maria Kozhevnikov, a cognitive neuroscientist the National University of Singapore, corroborated much of what Benson had observed, including practitioners’ ability to raise their body temperatures to feverish levels by combining visualisation and specialised breathing.

This extended trailer for the UK filmmaker Russ Pariseau’s feature documentary Advanced Tibetan Meditation: The Investigations of Herbert Benson MD relays portions of Benson’s landmark research, which ultimately signalled a seismic shift in how Western science views Buddhist meditation. Simultaneously, the material makes evident the disparate ways that Western scientists and Tibetan Buddhists understand the self.