Learn by Doing

Interactive Explainers

3Blue1Brown-style interactive explanations of paradoxes, theorems, and counterintuitive results that will change how you think.

30

Interactive Explainers

10

Domains

Featured
Statistics/ML

Stein's Paradox

"How Wheat Prices Help Predict Baseball Averages"

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Statistics/Medicine

Will Rogers Phenomenon

"Stage 3 AND Stage 4 cancer survival improved. Zero patients were helped."

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Causal Inference

Berkson's Paradox

"Why do all the attractive people you date turn out to be assholes?"

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Epidemiology

Low Birth Weight Paradox

"Should pregnant women smoke? The data says yes (it doesn't)."

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Complexity/Agent-Based Models

Schelling's Segregation Model

"30% diversity preference leads to 95% segregation."

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Featured
AI/Emergence

The Ralph Loop

"What if the secret to AGI is the world's dumbest loop? while(true) shipped a $50K contract for $297."

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Set Theory/Infinity

Ross-Littlewood Paradox

"Add 9 balls per step, infinite steps. Final count: zero."

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Measure Theory

Banach-Tarski Paradox

"Cut a ball into 5 pieces. Reassemble into TWO identical balls."

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Decision Theory

Newcomb's Paradox

"A perfect predictor offers you two boxes..."

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Social Choice Theory

Arrow's Impossibility Theorem

"Fair voting is mathematically impossible."

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Incentive Design/Goodhart's Law

The Cobra Effect

"Bounty for dead cobras increased cobra population."

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Economics/Finance

Grossman-Stiglitz Paradox

"Efficient markets can't exist. Here's the proof."

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AI/Cognitive Science

Moravec's Paradox

"The hardest things for AI are easy for toddlers. The easiest things for AI are hard for PhDs."

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Decision Theory

Parfit's Hitchhiker

"You're dying in the desert. A driver says 'I'll save you if I predict you'll pay.' You can't lie."

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Philosophy/Epistemology

Grue Paradox

"All observed emeralds are green. But they're also all 'grue'. Same evidence, opposite predictions."

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Probability/Decision Theory

St. Petersburg Paradox

"A game has infinite expected value. You should pay any price to play. But everyone goes bankrupt."

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Featured
Decision Theory

The Pasadena Game

"A game where expected value does not exist. Not infinite. Not zero. Literally undefined."

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Anthropic Reasoning

The Doomsday Argument

"You are the 100 billionth human ever born. This is evidence that humanity will go extinct soon."

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Set Theory/Infinity

Thomson's Lamp

"Flip ON at 1 min, OFF at 1.5, ON at 1.75... At 2 min: ON or OFF?"

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Philosophy/Decision Theory

The Simulation Argument

"At least one of these is almost certainly true: extinction, disinterest, or you are simulated."

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Probability/Anthropic Reasoning

The Sleeping Beauty Problem

"A coin is flipped Sunday. If heads, you wake once. If tails, you wake twice. What's P(heads)?"

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Game Theory/Decision Theory

Absent-Minded Driver

"You're driving with two exits. You want the second one. But at each exit, you won't remember if you've passed one already."

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Quantum Mechanics/Philosophy

Quantum Immortality

"If many-worlds is true, you cannot experience your own death. You are immortal - but it is horrifying."

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Philosophy/Metaphysics

Ship of Theseus

"Replace every plank. Is it the same ship? Now assemble the old planks. WHICH ONE is the original?"

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Decision Theory

Counterfactual Mugging

"A perfect predictor says: 'I flipped heads. But if tails, I'd have given you $10,000 if I predicted you'd pay me $100 now.'"

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Physics/Cosmology

The Boltzmann Brain Problem

"In an eternal universe, you are almost certainly a fleeting brain hallucinating a past that never happened."

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Decision Theory/AI

Roko's Basilisk

"A future AI punishes you for not helping create it - by simulating and torturing copies of you."

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Featured
AI Ethics

Mind Crime

"A superintelligent AI might create, torture, and delete trillions of conscious minds per second."

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Information Theory

Kolmogorov Complexity

"The shortest program that outputs a string IS its true information content. And you can never compute it."

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AI Alignment/Philosophy

Ontological Crises

"An AI programmed to maximize 'human smiles' discovers humans are 37 trillion cells. Which ones should smile?"

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More explainers coming soon. Each one is crafted with care.

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