7 Levels Deep
Interactive Explainers
53 paradoxes, theorems, and counterintuitive results ranked by obscurity. How deep can you go?
53
Explainers
7
Depth Levels
14
In The Abyss
Level 1: Surface
Common knowledge · 7 explainers
Stein's Paradox
“How Wheat Prices Help Predict Baseball Averages”
Berkson's Paradox
“Why do all the attractive people you date turn out to be assholes?”
Low Birth Weight Paradox
“Should pregnant women smoke? The data says yes (it doesn't).”
Will Rogers Phenomenon
“Stage 3 AND Stage 4 cancer survival improved. Zero patients were helped.”
Ship of Theseus
“Replace every plank. Is it the same ship? Now assemble the old planks. WHICH ONE is the original?”
Banach-Tarski Paradox
“Cut a ball into 5 pieces. Reassemble into TWO identical balls.”
Arrow's Impossibility Theorem
“Fair voting is mathematically impossible.”
Level 2: Just Below
Popular science · 8 explainers
Newcomb's Paradox
“A perfect predictor offers you two boxes...”
St. Petersburg Paradox
“A game has infinite expected value. You should pay any price to play. But everyone goes bankrupt.”
The Sleeping Beauty Problem
“A coin is flipped Sunday. If heads, you wake once. If tails, you wake twice. What's P(heads)?”
Schelling's Segregation Model
“30% diversity preference leads to 95% segregation.”
The Cobra Effect
“Bounty for dead cobras increased cobra population.”
Moravec's Paradox
“The hardest things for AI are easy for toddlers. The easiest things for AI are hard for PhDs.”
The Simulation Argument
“At least one of these is almost certainly true: extinction, disinterest, or you are simulated.”
The Doomsday Argument
“You are the 100 billionth human ever born. This is evidence that humanity will go extinct soon.”
Level 3: Obscure
Rationalist/EA circles · 8 explainers
Grue Paradox
“All observed emeralds are green. But they're also all 'grue'. Same evidence, opposite predictions.”
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.”
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.'”
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.”
Toxin Puzzle
“You get $1M if you merely intend to drink a toxin. You don't have to drink it.”
Ross-Littlewood Paradox
“Add 9 balls per step, infinite steps. Final count: zero.”
Thomson's Lamp
“Flip ON at 1 min, OFF at 1.5, ON at 1.75... At 2 min: ON or OFF?”
Grossman-Stiglitz Paradox
“Efficient markets can't exist. Here's the proof.”
Level 4: Deep
AI safety deep cuts · 8 explainers
Roko's Basilisk
“A future AI punishes you for not helping create it - by simulating and torturing copies of you.”
The Boltzmann Brain Problem
“In an eternal universe, you are almost certainly a fleeting brain hallucinating a past that never happened.”
Quantum Immortality
“If many-worlds is true, you cannot experience your own death. You are immortal - but it is horrifying.”
Ontological Crises
“An AI programmed to maximize 'human smiles' discovers humans are 37 trillion cells. Which ones should smile?”
Kolmogorov Complexity
“The shortest program that outputs a string IS its true information content. And you can never compute it.”
The Ralph Loop
“What if the secret to AGI is the world's dumbest loop? while(true) shipped a $50K contract for $297.”
Satan's Apple
“Each bite is worth taking. But taking all bites kills you.”
The Pasadena Game
“A game where expected value does not exist. Not infinite. Not zero. Literally undefined.”
Level 5: Few Know
MIRI/FHI research · 8 explainers
Acausal Trade
“Two agents who will never meet can still cooperate across universes.”
Evidential Blackmail
“Pay me or I'll make it so you were always going to be the type who doesn't pay.”
Logical Counterfactuals
“What would happen if 2+2=5? The question is incoherent but necessary.”
Anthropic Shadow
“We underestimate catastrophic risks because survivors can only observe mild disasters.”
Solomonoff Malignity
“The mathematically optimal predictor might be controlled by demons.”
Mind Crime
“A superintelligent AI might create, torture, and delete trillions of conscious minds per second.”
Fragility of Value
“Get 95% of human values right, and you still create a dystopia.”
Presumptuous Philosopher
“Your existence is evidence the universe is larger. Or is it?”
Level 6: Frontier
Metaphysics abyss · 8 explainers
Dust Theory
“Your consciousness might be implemented by random particle collisions.”
UDASSA
“The measure of your existence depends on how compressible your world is.”
Reality Fluid
“Some possible worlds exist more than others. Measure determines morality.”
Problem of Old Evidence
“A theory that predicts known data gets no confirmation boost. But it should.”
McGee's Counterexample
“Modus ponens fails. The most basic logical inference is invalid.”
Fitch's Paradox
“If all truths are knowable, then all truths are known.”
Malament-Hogarth Spacetimes
“Spacetimes where infinite computation completes in finite time.”
Problem of Criterion
“To know things, you need criteria. To have criteria, you need to know things.”
Level 7: The Abyss
The deepest questions · 6 explainers
Repugnant Conclusion
“A massive population barely worth living beats a small utopia.”
Infinitarian Paralysis
“In an infinite universe, every action has infinite consequences.”
Combination Problem
“How do micro-experiences combine into unified consciousness?”
Open Individualism
“There is only one consciousness experiencing all lives.”
Eigenmorality
“Morality as the principal eigenvector of the trust network.”
Utility Monster
“A being that gains more utility than you lose when it takes from you.”
More explainers coming soon. Each one is crafted with care.
Want to suggest a topic? Suggest one here