Ideas & Philosophy

1,886 cards. Each one is a 40-second story with a five-minute read behind it. Page 32 of 32.

Andersen wrote one hundred fifty-six fairy talesHans Christian Andersen (1805–1875) turned a poor Odense childhood into stories that now exist in more than 125 languages. Nine volumes hold 156 fairy tales that stuck in Western …
A spin of a rigged wheel changed people's guesses about Africa.Researchers spun a wheel that landed on 10 or 65, then asked people what share of UN members were African countries. Those who saw 10 guessed around 25 per cent; those who saw 65 …
The donkey that starved to death between two identical piles of hay.Place a hungry donkey exactly halfway between two equal bales of hay. With no reason to prefer either, a perfectly rational animal never moves and starves. The joke was aimed at a…
A Chinese sage dreamed he was a butterfly, then wondered which was real.More than 2,000 years ago, Zhuang Zhou dreamed he was a butterfly, flitting about happily. He woke up and asked: was he a man who had dreamed of being a butterfly, or a butterfly …
Can a machine that speaks perfect Chinese understand a single word of it?Picture a man locked in a room, following an English rulebook to answer Chinese notes slipped under the door. His replies are flawless, yet he understands none of it. In 1980 the …
The philosopher who lived in a jar and told Alexander the Great to move.When the most powerful man in the world asked Diogenes if he wanted anything, the ragged philosopher reportedly replied: yes, stand out of my sun. Diogenes slept in a storage jar,…
The Dunning–Kruger effect doesn't say what most people think it says.It's usually quoted as 'stupid people are too stupid to know it'. The 1999 study said something narrower: people who do badly at a specific task tend to overrate how well they did…
Descartes imagined a demon faking the whole world, to find one certainty.What if a powerful, malicious being were feeding you a perfect illusion of sky, earth and even your own body? René Descartes took the idea seriously, to strip away every belief th…
You learn a new word, then suddenly see it everywhere. Why?Buy a new car and the roads seem full of the same model. Learn an unusual word and it pops up all week. The world hasn't changed; your attention has. Psychologists call it the fre…
A three-page paper from 1963 broke philosophy's definition of knowledge.You glance at a clock reading two. It is two o'clock, and you have every reason to trust the clock. But it stopped exactly twelve hours ago. Your belief is true and justified, yet…
'This sentence is false.' Five words that logicians still can't tame.If the sentence is true, then what it says holds, so it's false. If it's false, then it's true. Thinkers in ancient Greece, fifth-century India and the medieval Islamic world all …
A scientist who knows everything about colour sees red for the first time.Mary has spent her life in a black-and-white room, learning every physical fact about colour and vision. One day she walks out and sees a red tomato. Does she learn something new?…
About 10,000 readers told a columnist her maths was wrong. She was right.Three doors, one car, two goats. You pick a door; the host, who knows where the car is, opens another to reveal a goat. Should you switch? Switching wins two times in three. When …
One box or two? A simple choice that splits philosophers down the middle.A near-perfect predictor has filled a closed box with a million dollars only if it foresaw you taking that box alone. A second, open box holds a thousand. The money is already the…
William of Ockham never wrote the famous line named after his razor.'Entities must not be multiplied beyond necessity' is the classic wording of Occam's razor. The 14th-century friar it's named after never used those words, and the idea is far old…
A 17th-century mathematician treated belief in God as a bet.Blaise Pascal argued that reason can't settle whether God exists, yet we can't avoid choosing how to live. So weigh the stakes: a finite cost against a possible infinite reward. H…
The simplest strategy in a famous contest was just four lines of code.Two prisoners each do better by betraying the other, yet both end up worse off than if they had kept quiet. That's the prisoner's dilemma. When Robert Axelrod ran a tournament of …
The chicken fed every morning has no idea what tomorrow brings.The sun has risen every day of your life, so you're sure it will rise tomorrow. But why? David Hume argued in 1739 that there's no non-circular way to justify learning from the pa…
One letter in 1902 wrecked a logician's plan to build arithmetic from logic.Consider the set of all sets that are not members of themselves. Is it a member of itself? If yes, then no; if no, then yes. Bertrand Russell found this contradiction in 1901 and …
Remove one grain at a time. When does a heap stop being a heap?A million grains of sand is a heap. Take one away and it's surely still a heap. Repeat that step enough times and logic forces you to call a single grain a heap. This 2,400-year-o…
A former slave wrote the oldest self-help rule that still works.Epictetus was born enslaved in the first century and became one of Rome's great Stoic teachers. His core idea: some things are up to us, our judgements and actions, and most thing…
The most important data is often the data that never came back.In the Second World War, statisticians studied bullet damage on planes returning from missions. The catch: the planes that were shot down never came back to be counted. Survivorsh…
If you replace every plank of a ship, is it the same ship?The ancient Greeks said Theseus's ship was preserved in Athens, its rotting planks swapped out one by one until none of the originals remained. Philosophers have argued ever since…
The trolley problem was never really about trolleys.Philippa Foot introduced it in 1967: a runaway tram will kill five people unless you divert it onto a track where it will kill one. Most people say pull the lever. Change it so yo…
Design a fair society without knowing who you'll be in it.Imagine choosing the rules of your society before you know whether you'll be born rich or poor, healthy or ill, or what you'll believe. John Rawls called this the veil of ignoranc…
A Greek philosopher 'proved' that the fastest runner can never catch a tortoise.Give a tortoise a head start, said Zeno of Elea, and Achilles must first reach where it was. By then it has crept ahead, so he must reach that point too, and so on forever. The ar…