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High-Dimensional Geometry: Where Intuition Breaks Down
Our intuitions are built for three dimensions and betray us in many.
Stories by Mahendra
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Regression to the Mean
An extreme result tends to be followed by a less extreme one, not because of any force but because extremes owe much to luck.
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Probability as Degree of Belief
What does it mean to say an event is probable? One view holds that probability is not a property of the world but a measure of our confidence.
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Infinity: Sizes Beyond Counting
Infinity is not a single vast number but a hierarchy of sizes, some larger than others.
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Gödel: Truths a System Cannot Prove
Within any sufficiently rich system of mathematics there are true statements it cannot prove.
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The Unreasonable Effectiveness of Mathematics
Mathematics, invented by contemplating abstractions, turns out to describe the physical world with uncanny precision.
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The Holographic Principle
A startling idea suggests that everything within a region of space can be described by information on its boundary.
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Wave-Particle Duality
Light and matter behave sometimes as waves, spreading and interfering, and sometimes as particles, arriving in discrete lumps.
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The Uncertainty Principle: Limits of Simultaneous Knowledge
Certain pairs of properties cannot both be known sharply at once.
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Decoherence: Why the Quantum World Looks Classical
If matter is quantum, why does the everyday world appear solid and definite, never blurred across possibilities? Part of the answer is decoherence, the leaking of quantum coherence into the environment.