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
Difficulty
Intermediate
Comfortable with basic reasoning or arithmetic.
Written for: Curious teenagers and general adult readers.
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Goodhart's Law
The moment you measure something and start rewarding the number, the number stops telling you what it used to.
1975 (Goodhart's formulation), 1997 (Strathern's phrasing)14 min read
Pygmalion Effect
Can a teacher's expectation — with no basis in fact — make a student smarter? The data say yes. The mechanism is more unsettling than the result.
19687 min read
Schrödinger's Cat
A cat sealed in a box, neither alive nor dead until somebody looks. The story was invented to show the idea was absurd.
193514 min read
Simpson's Paradox
A treatment does better for men, and better for women, and worse for people. None of the arithmetic is wrong.
1903 (Yule), 1951 (Simpson), 1972 (named)20 min read
The Fermi Paradox
The universe is ancient, enormous, and full of ordinary stars much like ours. So where is everybody?
1950 (Fermi's remark), 1975 (Hart's argument)22 min read
The Grandfather Paradox
Travel back in time and stop your own grandparents from ever meeting. Then who was it that went back?
1943 (Barjavel's novel), with antecedents from the 1920s18 min read
The Paradox of Choice
Put out twenty-four kinds of jam instead of six and fewer people buy any jam at all. More options, fewer decisions.
2004 (the book); 2000 (the jam study)19 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 Ship of Theseus
Replace a ship's planks one at a time until not one original piece is left. Is it still the same ship?
c. 75 CE (Plutarch's report of an older dispute)20 min read
The Tragedy of the Commons
Every herder gains by putting one more animal on the shared field. The field is destroyed by people behaving reasonably.
196815 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
Benford's Law
Look at the first digit of every number in a newspaper. You'll see 1 far more often than 9 — and it is a mathematical law, not a coincidence.
19388 min read
Brooks's Law
A software project is six months late. You add more developers. Now it's eight months late. Why?
19756 min read
Conway's Law
Your software will look like your org chart. Not because you planned it, but because you couldn't plan it otherwise.
19685 min read
Dunbar's Number
You can maintain real relationships with about 150 people. Beyond that, a group becomes something different. Is this a law of human nature?
19927 min read
Flynn Effect
IQ scores rise 3 points per decade worldwide. If the tests measure intelligence, are we smarter? Or is something wrong with the tests?
19847 min read
Gabriel's Horn
A shape you can fill with a finite bucket of paint but whose inside you could never finish painting. How?
16417 min read
Matthew Effect
Two equally talented people start. One gets a small early advantage. Decades later, the gap is enormous. Where did the extra distance come from?
19688 min read
Metcalfe's Law
Double the users of a network and the value quadruples. This simple mathematics is why some networks become monopolies and others die empty.
19806 min read
Moravec's Paradox
A computer beat the world chess champion in 1997. Getting one to pick up a cup it has not seen before is still hard.
198811 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 Ellsberg Paradox
You know exactly how many red balls there are, and nothing about how many are black. Does knowing more make a bet more attractive?
19617 min read
The Jevons Paradox
Build an engine that burns less coal and the country ends up burning more coal. This was noticed in 1865 and has not stopped.
186518 min read
The Mpemba Effect
A pot of boiling water and a pot of cold water go into the same freezer. Which freezes first?
1963 (observed), 1969 (published)8 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
The Paradox of Thrift
Every family starts saving more. The economy ends up with less saving. How can everyone doing the right thing produce the wrong outcome?
19367 min read
The Two Generals' Problem
Two armies must attack at the same moment. Any message can be lost, including the one confirming the last one arrived.
1975 (proved), 1978 (named)18 min read
Zipf's Law
The most common English word is twice as frequent as the second. Why does language obey the same mathematical law as city populations?
19357 min read
Berkson's Paradox
Two things with nothing whatever to do with each other can look strongly related — purely because of who ended up in the study.
194615 min read
Galileo's Paradox
There are exactly as many square numbers as there are numbers, even though almost every number is not a square.
163813 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
Peto's Paradox
A whale has a thousand times more cells than you and lives longer. It should be riddled with cancer. It is not.
1975 (observation), 1977 (Peto's fuller statement)17 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
The Easterlin Paradox
Richer people are happier than poorer people. Yet a whole country getting richer does not seem to get happier.
197423 min read
The Grelling-Nelson Paradox
Is the word "heterological" heterological? Either answer generates a contradiction.
19087 min read
The Tristram Shandy Paradox
A man writes his autobiography but keeps falling behind. If he had infinite time, would he ever catch up?
1759 (novel), 1903 (paradox formulated)8 min read