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Local Versus Global Minima
A search for the lowest point can end in a valley that is low but not lowest.
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Gradient Descent: Learning by Following the Slope
To find the bottom of a valley in fog, take small steps downhill.
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Spurious Correlation: Patterns in Noise
Search enough data and you will find relationships that mean nothing.
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The Law of Large Numbers
Toss a fair coin a few times and the results are erratic; toss it many times and the fraction of heads settles near one half.
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Randomness Versus Determinism
Is the world's apparent chance real, or merely hidden order we cannot trace? The question divides deterministic systems that only look random from processes that may be random at the root.
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The Limits of Formal Systems
We build systems of axioms and rules hoping to capture a domain completely and mechanically.
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Information and the Black Hole Paradox
Throw something into a black hole and it seems to vanish, and when the hole slowly evaporates, its information appears lost forever.
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Superposition: Being in Many States at Once
A quantum system need not be in one state or another but can be in a blend of both, in a way that has no classical picture.
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The Measurement Problem
Between measurements, a quantum system evolves smoothly through many possibilities at once.