Codesota · Explainers · 7 levels deep54 paradoxes · 14 in the abyssUpdated 2026-05-23

§ 00 · Explainers

Paradoxes, ranked by obscurity.

54 paradoxes, theorems and counter-intuitive results arranged in seven concentric bands — from common-knowledge surface to the deepest metaphysics. How deep can you go?

Each entry opens as a short interactive explainer. Levels are a rough gradient of circulation: L1 is dinner-party fare; L7 is the territory where modus ponens stops working.

L1 · Surface L2 · Just below L3 · Obscure L4 · Deep L5 · Few know L6 · Frontier L7 · The abyss

§ 01 · Level 1

Surface.

Common knowledge

7 entries

L1 · Statistics / ML

Stein's Paradox

“How wheat prices help predict baseball averages.”

L1 · Causal inference

Berkson's Paradox

“Why the attractive people you date turn out to be assholes.”

L1 · Epidemiology

Low Birth Weight Paradox

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

L1 · Statistics / medicine

Will Rogers Phenomenon

“Stage 3 and stage 4 cancer survival both improved. Zero patients were helped.”

L1 · Philosophy / metaphysics

Ship of Theseus

“Replace every plank. Is it the same ship? Reassemble the old planks. Which is original?”

L1 · Measure theory

Banach-Tarski Paradox

“Cut a ball into 5 pieces. Reassemble into two identical balls.”

L1 · Social choice theory

Arrow's Impossibility Theorem

“Fair voting is mathematically impossible.”

§ 02 · Level 2

Just below.

Popular science

9 entries

L2 · Economics / AI

The Deflationary Doom Loop

“AI makes intelligence free. The trap: rent, food and fuel are still made of atoms.”

L2 · Decision theory

Newcomb's Paradox

“A perfect predictor offers you two boxes…”

L2 · Probability / decision theory

St. Petersburg Paradox

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

L2 · Probability / anthropics

The Sleeping Beauty Problem

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

L2 · Complexity / agent-based

Schelling's Segregation Model

“30% diversity preference leads to 95% segregation.”

L2 · Incentive design / Goodhart

The Cobra Effect

“Bounty for dead cobras increased the cobra population.”

L2 · AI / cognitive science

Moravec's Paradox

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

L2 · Philosophy / decision theory

The Simulation Argument

“At least one is almost certainly true: extinction, disinterest, or you are simulated.”

L2 · Anthropic reasoning

The Doomsday Argument

“You are the 100 billionth human. This is evidence humanity will go extinct soon.”

§ 03 · Level 3

Obscure.

Rationalist / EA circles

8 entries

L3 · Philosophy / epistemology

Grue Paradox

“All observed emeralds are green. They are also all 'grue'. Same evidence, opposite predictions.”

L3 · 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.”

L3 · Decision theory

Counterfactual Mugging

“'I flipped heads. But if tails, I'd have given you $10,000 if I predicted you'd pay me $100 now.'”

L3 · Game / decision theory

Absent-Minded Driver

“Two exits. You want the second. At each, you won't remember if you've passed one already.”

L3 · Decision theory

Toxin Puzzle

“You get $1M if you merely intend to drink a toxin. You don't have to drink it.”

L3 · Set theory / infinity

Ross-Littlewood Paradox

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

L3 · 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?”

L3 · Economics / finance

Grossman-Stiglitz Paradox

“Efficient markets can't exist. Here's the proof.”

§ 04 · Level 4

Deep.

AI safety deep cuts

8 entries

L4 · Decision theory / AI

Roko's Basilisk

“A future AI punishes you for not helping create it — by simulating and torturing copies of you.”

L4 · Physics / cosmology

The Boltzmann Brain Problem

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

L4 · Quantum / philosophy

Quantum Immortality

“If many-worlds is true, you cannot experience your own death. You are immortal — but horrifying.”

L4 · AI alignment

Ontological Crises

“An AI maximising 'human smiles' discovers humans are 37 trillion cells. Which ones should smile?”

L4 · Information theory

Kolmogorov Complexity

“The shortest program that outputs a string is its true information content. You can never compute it.”

L4 · 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.”

L4 · Decision theory

Satan's Apple

“Each bite is worth taking. Taking all bites kills you.”

L4 · Decision theory

The Pasadena Game

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

§ 05 · Level 5

Few know.

MIRI / FHI research

8 entries

L5 · Decision theory

Acausal Trade

“Two agents who will never meet can still cooperate across universes.”

L5 · Decision theory

Evidential Blackmail

“Pay me or I'll make it so you were always going to be the type who doesn't pay.”

L5 · Decision theory

Logical Counterfactuals

“What would happen if 2+2=5? The question is incoherent but necessary.”

L5 · Existential risk

Anthropic Shadow

“We underestimate catastrophic risks because survivors can only observe mild disasters.”

L5 · AI safety

Solomonoff Malignity

“The mathematically optimal predictor might be controlled by demons.”

L5 · AI ethics

Mind Crime

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

L5 · AI alignment

Fragility of Value

“Get 95% of human values right and you still create a dystopia.”

L5 · Anthropics

Presumptuous Philosopher

“Your existence is evidence the universe is larger. Or is it?”

§ 06 · Level 6

Frontier.

Metaphysics abyss

8 entries

L6 · Philosophy of mind

Dust Theory

“Your consciousness might be implemented by random particle collisions.”

L6 · Anthropics

UDASSA

“The measure of your existence depends on how compressible your world is.”

L6 · Metaphysics

Reality Fluid

“Some possible worlds exist more than others. Measure determines morality.”

L6 · Philosophy of science

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.”

L6 · Epistemology

Fitch's Paradox

“If all truths are knowable, then all truths are known.”

Malament-Hogarth Spacetimes

“Spacetimes where infinite computation completes in finite time.”

L6 · Epistemology

Problem of Criterion

“To know things, you need criteria. To have criteria, you need to know things.”

§ 07 · Level 7

The abyss.

The deepest questions

6 entries

L7 · Population ethics

Repugnant Conclusion

“A massive population barely worth living beats a small utopia.”

Infinitarian Paralysis

“In an infinite universe, every action has infinite consequences.”

L7 · Philosophy of mind

Combination Problem

“How do micro-experiences combine into unified consciousness?”

L7 · Philosophy of mind

Open Individualism

“There is only one consciousness experiencing all lives.”

L7 · Ethics / game theory

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.”

§ FIN

Know one we missed?

More explainers are coming. Each one is crafted, not generated. Suggest a paradox, theorem or counter-intuitive result and we’ll consider it for the next band.

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