Dunning-Kruger Effect
The less you know, the more confident you feel. The more you know, the more you see how much you don't. Why?
19996 min read
Type
Knowledge
What can be known, proved, or announced.
35 entriesFilter these further →
Beginner
Ages 8+, no background needed.
Occam's Razor
When two explanations fit the evidence equally, which should you believe? The one that assumes less.
c. 13206 min read
The Monty Hall Problem
Three doors, one car. The host opens a losing door and offers you the swap. Does it make any difference whether you take it?
1975 (posed), 1990 (made famous)9 min read
Amara's Law
Every major technology is overhyped on arrival and underestimated a decade later. Why does intuition fail in the same direction twice?
19776 min read
Baader-Meinhof Phenomenon
You learn a new word. Within a week, you hear it three times. Did the world start using it when you did — or did you just stop filtering it out?
20066 min read
Brandolini's Law
A tweet spreads a false claim to a million people. Correcting it requires essays and citations. Why does the truth always have to work harder?
20137 min read
Chesterton's Fence
You find a fence in the middle of a field with no obvious purpose. Remove it? Chesterton says no — and the reason reveals something about reform.
19297 min read
Hanlon's Razor
They didn't do it to hurt you. Probably they just didn't think. How much does it matter?
19806 min read
Semmelweis Reflex
A doctor proved handwashing saved lives. He had the data. The medical profession ignored him for twenty years. Why does evidence trigger resistance?
18476 min read
Bertrand's Box Paradox
You reach into one of three boxes and pull out a gold coin. The chance the other coin in that box is gold is not one half.
188910 min read
Intermediate
Curious teenagers and general adult readers.
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
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
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
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
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 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
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
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
Russell's Paradox
Consider the set of all sets that do not contain themselves. Does that set contain itself? Either answer is wrong.
1901 (discovered), 1902 (letter to Frege), 1903 (published)19 min read
The Halting Problem
No program can ever be written that reliably tells you whether another program will finish running. This is not a limit of our cleverness.
193620 min read
The Liar Paradox
"This sentence is false." Decide whether you are looking at something true or something false, and see how far you get.
c. 600 BCE (the Epimenides line); c. 350 BCE (Eubulides' paradox)26 min read
Cantor's Diagonal Argument
There are more numbers between 0 and 1 than there are whole numbers in all of eternity. Both lists are infinite.
189116 min read
Newcomb's Problem
The boxes are already filled. Does choosing one still change what is in them?
c. 1960 (posed), 1969 (published)10 min read
The Byzantine Generals Problem
Several generals must attack together or be destroyed. They can only send messengers, and some of the generals are traitors.
198222 min read
The CAP Theorem
A system spread across several machines can give you consistent answers, or always answer at all. The network makes you choose.
2000 (conjectured), 2002 (proved)23 min read
The Sleeping Beauty Problem
Woken with no memory of having been woken before, how confident should you be that the coin came up heads?
1997 (posed), 2000 (named and popularised)24 min read
The Sorites Paradox
One grain of sand is not a heap. Adding a single grain never turns a non-heap into a heap. So heaps do not exist.
c. 350 BCE20 min read
The Unexpected Hanging Paradox
A prisoner is told he will hang next week, on a day he cannot possibly predict. He proves it cannot happen. It happens.
1943 (in circulation), 1948 (first in print)21 min read
Berry's Paradox
"The smallest number that cannot be described in fewer than twelve words." That description is eleven words long.
1906 (published by Russell, crediting Berry); communicated c. 190419 min read
Expert
Graduate level or specialist readers.
Gödel's Incompleteness Theorems
In any system of arithmetic strong enough to be useful, there are true statements it can never prove. Including this one.
193125 min read
The Black Hole Information Paradox
Physics insists information can never be destroyed. Black holes appear to destroy it. Both of those cannot be true.
1974/75 (Hawking radiation), 1976 (the paradox stated)24 min read
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
The FLP Impossibility Result
A handful of computers cannot be guaranteed to agree on a single value if even one of them might be slow. Not merely hard — impossible.
198523 min read