Bayes' Theorem
Thomas Bayes (published by Richard Price) · 1763
"Belief should update in proportion to evidence — Bayes' theorem is the exact math for how much a new piece of evidence should move your confidence."
Bayes never published this in his lifetime — a friend found it in his papers and printed it in 1763. It's the exact formula for how much a new piece of evidence should change what you believe.
Bayes' theorem relates the probability of a hypothesis given evidence to the probability of that evidence given the hypothesis, weighted by the hypothesis's prior probability. The prior matters more than intuition suggests: a positive test for a rare disease can still mean you probably don't have it, if false positives from the healthy majority outnumber true positives. Updating correctly means multiplying prior by evidence, not replacing it.
Why can a positive result on an accurate test for a rare disease still mean you probably don't have it?
Read more about the topic
The explanation above is written with AI assistance. These are the originals — go to them to check it.
- Bayes' TheoremStanford Encyclopedia of Philosophy
Deterministic Chaos
"Fully deterministic systems — with no randomness anywhere in their equations — can still become practically unpredictable, because tiny differences in starting conditions grow exponentially over time until prediction becomes impossible."