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Physical Theorem

Heisenberg Uncertainty Principle

Fundamental limit of measurement. Not about instruments but nature itself.

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Discover connections across different types of entities

Mathematical Theorem

Banach-Tarski Paradox

Uses axiom of choice. Demonstrates measure theory limits.

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Philosophical Concept

The Precautionary Principle

Principle that actions with uncertain but potentially catastrophic outcomes should be avoided. When harm is …

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Einstein on the nature of reality

Einstein on the nature of reality

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Philosophical Concept

Simulation Hypothesis

Modern philosophical hypothesis that reality might be a computer simulation. Nick Bostrom's argument: if civilizations …

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Wittgenstein on the limits of language

Wittgenstein on the limits of language

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Mathematical Theorem

Central Limit Theorem

Why normal distribution ubiquitous. Statistics foundation.

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Mathematical Theorem

Intermediate Value Theorem

Intuitive but powerful. Guarantees roots exist.

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Book

The Singularity Is Near

Kurzweil's futurist manifesto predicts that exponential technological growth will lead to the Singularity—a point where …

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Mathematical Theorem

Gödel's Incompleteness Theorems

No system can prove all truths about arithmetic. Limits of formal systems.

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Philosophical Concept

Determinism

Philosophical view that all events are determined by prior causes. Hard determinism denies free will—every …

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