Discover the secret geometry of beauty – the mathematics of form and pattern

In ‘The Study of Mathematics’, Bertrand Russell wrote: ‘Mathematics, rightly viewed, possesses not only truth, but supreme beauty.’ This is the idea underlying Ars Qubica by the Spanish 3D animator and illustrator Cristóbal Vila. A fluid sensory experience that unites music, mathematics, art and design, the video deconstructs patterns and motifs in art to reveal how beauty emerges from ‘geometric skeletons’.

Historic street view: an image for each of the 181 years since the dawn of photography

Just a decade after the first surviving photograph was taken, photography became widespread enough that, today, the Canadian film archivist and YouTuber Guy Jones could assemble this parade of streets worldwide – one photograph for each year from 1838 to 2019. The resulting montage offers a scattershot urban history of modernity, chronicling seismic shifts in transportation methods and fashions, as well as the more subtle evolutions of storefront signage and roadway surfaces. The video also provides a meaningful window into the history of the medium itself. At the dawn of photography, the black-and-white images are deliberately framed, with the camera often drawing the attention of its subjects. In recent photos, as the camera has become more ubiquitous, it’s often less artfully employed, and its presence goes mostly unnoticed by the people whose lives it freezes in discrete moments. 

What wrapping a rope around the Earth reveals about the limits of human intuition

If you tied a rope tight around the Earth’s equator and then added a single yard of slack, would the extra material make any noticeable difference to someone standing on the ground? Yes, actually. The answer comes as a surprise to most people, but the additional bit of rope raises it high enough off the ground for our eyes to easily discern it, and our feet to easily trip over. That fact might seem trivial, but the early 20th-century philosopher Ludwig Wittgenstein believed that this chasm between human intuition and physical reality revealed something important about the fallibility of our thinking. After all, if something that seems obvious to almost everyone can be totally false, what else might we be wrong about? This video from the Center for Public Philosophy at the University of California, Santa Cruz breaks down the mathematics behind Wittgenstein’s knotty example, and asks whether it should make us all feel a bit less certain about even our most deeply held beliefs.

Spoiler alert: does knowing how it ends make fiction more fun?

‘It’s not the journey, it’s the destination’ might seem like trite advice, but when it comes to storytelling, the worn adage actually seems to hold up to scrutiny. Just ask Nicholas Christenfeld, professor of psychology at the University of California, San Diego: in a 2013 study, he put our cultural obsession with so-called ‘spoilers’ to the test. After sneakily revealing the end of short stories when describing them to test subjects, he found that their enjoyment of the fictional narratives actually increased – a conclusion that perhaps isn’t so surprising if you think about how many times you’ve watched your favourite movie or read your favourite book. However, Christenfeld still found that there was a forceful knee-jerk aversion to the idea of having a story spoiled, so you might still want to restrain yourself before blurting out the latest Game of Thrones twist to friends and insisting it’s for their own good.

Meet the jazz pianist who improvises in tandem with a piano that plays itself

‘How can I be free in this particular cage?’

From synthesizers replacing real instruments in the studio to the rise of musical compositions written entirely by AI, it’s not surprising that many professional musicians have been resistant to the ascendent role of technology in the music industry. However, the French-American jazz pianist and composer Dan Tepfer has developed a creative way of leveraging the rise of musical machines using what he calls ‘improvisational algorithms’.

On his digital player piano, his notes are sent through a computer, which then automatically plays back notes that correspond to commands he’s written. And although the idea of predetermined ‘rules’ might on its surface seem to cut against the spirit of musical improvisation, Tepfer finds that they actually fuel his playing, leading him down paths he wouldn’t otherwise find. This video from NPR’s Jazz Night in America series details how Tepfer mines new musical ideas from his improvisational algorithms, which culminated in his album Natural Machines (2019) and a series of performances with visuals generated from the compositions. Read more about Dan Tepfer at NPR’s website.