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PublicSep 28, 2026
Bayes rule and belief updates
Evidence changes belief through both how expected it was and how plausible the hypothesis was beforehand.
PublicSep 28, 2026
Small world networks
A few long-range links can connect tight local clusters without erasing their local structure.
PublicSep 28, 2026
Godel and the limits of proof
A consistent, effectively axiomatized theory rich enough for arithmetic cannot settle every arithmetic statement.
PublicSep 28, 2026
Infinity comes in sizes
The whole numbers and real numbers are both infinite, but there is no one-to-one pairing between them.
PublicSep 28, 2026
Symmetry and conservation
Under the conditions of Noether's theorem, a continuous symmetry of a physical action yields a conserved quantity.
PublicSep 28, 2026
Exponential growth and doubling
When growth is proportional to the current amount, equal time steps multiply the total rather than add a fixed amount.