The impossible chessboard puzzle

19 minutes

Acadiana

10 minutes

Dani

8 minutes

The physarum experiments

5 minutes

Kierkegaard’s horror of doubt

7 minutes

This puzzle is nearly impossible – but working out why is its own brain-teaser

You and a friend are prisoners with one shot at escape. A peculiarly mathematics-oriented warden has set up a puzzle that, if solved, will set you free. The rules are as follows: while the other prisoner is locked away elsewhere, you watch the warden hide a key under a single square of a chessboard. Each square has a coin flipped to heads or tails on top. You must flip just one coin to help indicate the key’s location to your puzzle partner, who will receive it in another room. Before you witness the key’s placement, you and your friend are given an opportunity to concoct a strategy together – although the warden is able to listen in, and can arrange the coins ahead of time to try and disrupt it. Is it possible to hatch a foolproof plan? The answer, in most cases, is no. But figuring out why, as guided by the mathematical wizardry of the US YouTuber Grant Sanderson, is a brain-bending exercise all of its own. In this video, part of Sanderson’s 3Blue1Brown video series, he uses the twisty prisoner puzzle as a springboard to explore how mathematical visualisation can be a useful tool for methodical problem-solving.

Video by 3Blue1Brown

The uncanny allure of the annual Cajun crawfish festival in Louisiana

Crawfish – small crustaceans also known as crayfish, crawdads or mudbugs – have long been a staple of Cajun cuisine, with the lobster-like creatures plentiful in the freshwaters of Louisiana. With an observational style and an experimental flair, Acadiana gathers scenes from a day at the state’s annual crawfish festival in Breaux Bridge. A crawfish eating competition, crawfish-inspired costumes and a float procession featuring the 2019 crowned Crawfish King and Queen are captured with a mix of anthropological curiosity and familial respect by the Québécois filmmakers Guillaume Fournier, Samuel Matteau and Yannick Nolin. While its title references the French-Canadian roots of Cajun culture in the United States, there is something otherworldly about this short film, which went on to win several awards on the Canadian film-festival circuit.

Directors: Guillaume Fournier, Samuel Matteau, Yannick Nolin

Producer: Jean-Pierre Vézina

Website: Kinomada

‘I hate giving you bad news’: when a daughter with breast cancer calls her mother

Danielle Hernandez is 30 and has Stage 4 breast cancer. As she calls her mother Violeta in Florida to deliver an update on her treatment from her home in Los Angeles, she oscillates between medical jargon and silver livings, with the more difficult pieces of information hidden in the subtext, only occasionally bubbling to the surface. This intimate conversation is captured by her roommate, the US filmmaker Lizzy Hogenson, in the short film Dani. Using a stop-motion technique that combines felt figures and claymation, Hogenson places her own veneer on the discussion, which is pierced by intermittent cracks of raw emotion, hard truths and silence. The result is at once affecting and distressing, as small moments of love, courage and pain spark and fade into uncertainty.

Director: Lizzy Hogenson

Producer: Kyle McClary

Creeping through mazes, repelling adversaries – the slow-motion smarts of slime moulds

To the naked eye, the organism Physarum polycephalum – commonly referred to as ‘slime mould’ – might seem an unexceptional creature, despite its bright-yellow glow, as its acellular existence is dedicated to tracking nutrients at a speed of 1mm per hour. But this protist’s surprising computational cunning becomes apparent when viewed in time-lapse, revealing a life form that seems to possess intelligence despite lacking a nervous system. Between 2009 and 2018, the UK artist and researcher Heather Barnett conducted a series of clever experiments in which she probed slime moulds’ capacities for forming complex tube networks and adjusting to obstacles. For this short film, Aeon Video compiled Barnett’s ‘creative collaborations’ with P polycephalum into a montage that builds in complexity, emphasising the slime moulds’ surprisingly sophisticated capacities for problem-solving.

Director: Heather Barnett

Sound designer: Graham Barton

Editor: Tamur Qutab

Want to think for yourself? Start with an agonising state of doubt, says Kierkegaard

Influenced by Socrates’ sense of irony, the Danish philosopher Søren Kierkegaard (1813-55) came to believe that a state of doubt – disorienting and horrifying as it could sometimes be – was the cornerstone of a sound philosophical practice. This scepticism of objective truth and ardent belief in thinking for oneself is omnipresent in his pseudonymous works, in which his assumed names sometimes even spar with one another. While amusing, the peculiar literary device also undercuts any sense that the works were written by a voice of authority. In this video from the London Review of Books, the British philosopher and historian Jonathan Rée traces the theme of doubt in Kierkegaard’s life and work using his unfinished, posthumously published novel Johannes Climacus: Or a Life of Doubt as a starting point.

Video by the London Review of Books

Producer: Anthony Wilks

This puzzle is nearly impossible – but working out why is its own brain-teaser

You and a friend are prisoners with one shot at escape. A peculiarly mathematics-oriented warden has set up a puzzle that, if solved, will set you free. The rules are as follows: while the other prisoner is locked away elsewhere, you watch the warden hide a key under a single square of a chessboard. Each square has a coin flipped to heads or tails on top. You must flip just one coin to help indicate the key’s location to your puzzle partner, who will receive it in another room. Before you witness the key’s placement, you and your friend are given an opportunity to concoct a strategy together – although the warden is able to listen in, and can arrange the coins ahead of time to try and disrupt it. Is it possible to hatch a foolproof plan? The answer, in most cases, is no. But figuring out why, as guided by the mathematical wizardry of the US YouTuber Grant Sanderson, is a brain-bending exercise all of its own. In this video, part of Sanderson’s 3Blue1Brown video series, he uses the twisty prisoner puzzle as a springboard to explore how mathematical visualisation can be a useful tool for methodical problem-solving.

Video by 3Blue1Brown

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Photo by Harry Gruyaert/Magnum

Essay/
Philosophy of mind
The value of uncertainty

In fiction, it grips us. In life, it can unravel us. How can brains hooked on certainty put its opposite to good use?

Mark Miller, Kathryn Nave, George Deane & Andy Clark

Study For Liberty Displaying the Arts and Sciences, or The Genius of America Encouraging the Emancipation of the Blacks (1791-92) by Samuel Jennings. Courtesy the Met Museum/New York

Essay/
History of ideas
Philosophy’s systemic racism

It’s not just that Hegel and Rousseau were racists. Racism was baked into the very structure of their dialectical philosophy

Avram Alpert