The Barber Paradox
The barber shaves every man in town who does not shave himself, and no one else. So who shaves the barber?
1918 (Russell's lectures); the story circulated earlier11 min read
Nature
Apparent contradiction
The contradiction comes from an unstated assumption or an equivocation. Once named, the paradox resolves without abandoning anything important.
Looks contradictory, dissolves under careful analysis.
16 entriesFilter these further →
Beginner
Ages 8+, no background needed.
Intermediate
Curious teenagers and general adult readers.
Achilles and the Tortoise
The fastest runner alive can never catch a tortoise with a head start. The argument is airtight. So where does it go wrong?
c. 450 BCE15 min read
The Paradox of Tolerance
A society that tolerates absolutely everything, including those working to end it, does not remain tolerant for long.
19458 min read
The Twin Paradox
One twin flies away and comes home younger than the other. Yet each of them saw the other's clock running slow.
1905 (implicit in Einstein), 1911 (Langevin's traveller)20 min read
Olbers' Paradox
If the universe is infinite and full of stars, every line of sight should end on one. So why is the night sky dark?
1610 (Kepler), 1744 (de Chéseaux), 1823 (Olbers)17 min read
The Boy or Girl Paradox
A family has two children and one of them is a boy. What are the odds the other is a girl? It depends on how you found out.
1959 (posed), 1961 (retracted in part)13 min read
The Paradox of the Court
A student agrees to pay for his lessons the day he wins his first case. He never takes a case. His teacher sues him for the money.
c. 420 BCE (traditional); earliest surviving account 2nd century CE20 min read
Meno's Paradox
How can you search for something you don't know? And how would you recognise it if you found it?
c. 380 BCE9 min read
The C-value Paradox
An onion carries five times more DNA than you do. A single-celled amoeba carries a hundred times more. Nobody expected that.
1971 (named), 2001 (renamed the C-value enigma)17 min read
Advanced
Undergraduate level in the relevant field.
Maxwell's Demon
A tiny creature sorting fast molecules from slow ones appears to make heat flow the wrong way, for free, forever.
1867 (letter to Tait), 1871 (published in Theory of Heat)18 min read
Zeno's Dichotomy Paradox
To cross a room you must first cross half of it, then half of what is left, and so on without end. So how does anyone move?
c. 450 BCE18 min read
The St. Petersburg Paradox
A coin-flipping game whose average winnings are infinite. How much of your own money would you actually pay to play?
1713 (posed by Nicolaus Bernoulli), 1738 (published by Daniel Bernoulli)19 min read
The Two Envelopes Problem
One envelope holds twice as much money as the other. The arithmetic says swap — then says swap back, forever.
1953 (Littlewood, crediting Schrödinger), 1989 (envelope form)19 min read
Levinthal's Paradox
A protein has more possible shapes than the universe has atoms, yet it finds the right one in less than a thousandth of a second.
1968–196917 min read
The Ladder Paradox
A ladder too long to fit inside a barn fits inside it — and also does not — depending entirely on who is watching.
1905 (the physics), 1961 (first prominent published version)19 min read
Expert
Graduate level or specialist readers.
The EPR Paradox
Measure one particle here and you instantly know something about its partner light-years away. Einstein thought this proved physics was unfinished.
1935 (argument), 1964 (Bell's theorem), 2015 (loophole-free tests)21 min read