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Bayes' rule: the maths of truth-seeking

The philosopher Gottfried Wilhelm Leibniz had a dream. He hoped that progress in philosophy and mathematics would eventually yield a method to systematically figure out the truth. This video explores an approach to that dream that takes us some of the way there: Bayesianism. The basic idea of Bayesianism is to represent beliefs as probabilities and update them using the formal rules of probability theory to the best of our ability. In particular, Bayes' rule tells us how to update our degree of belief in a hypothesis after observing some evidence. Bayes' rule has many consequences that we can recognize as central to scientific reasoning, such as Cromwell's rule, which tells us with the language of probability theory that our beliefs shouldn't be absolute dogmas, but always potentially put into question when new evidence comes in. ▀▀▀▀▀▀▀▀▀PATREON, MEMBERSHIP, KO-FI▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 🟠 Patreon: https://www.patreon.com/rationalanimations 🔵 Become a member of the channel: https://www.youtube.com/channel/UCgqt1RE0k0MIr0LoyJRy2lg/join 🟤 Ko-fi: https://ko-fi.com/rationalanimations ▀▀▀▀▀▀▀▀▀SOCIAL & DISCORD▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Twitter: https://twitter.com/RationalAnimat1 Discord: https://discord.gg/hxWBm6sBNU ▀▀▀▀▀▀▀▀▀LINKS & READINGS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Arbital's guide to Bayes' rule: https://arbital.com/p/bayes_rule/?l=1zq The bayesian view of scientific virtues: https://arbital.com/p/bayes_science_virtues/ @3Blue1Brown 's explanations: 1. https://youtu.be/HZGCoVF3YvM 2. https://youtu.be/U_85TaXbeIo 3. https://youtu.be/lG4VkPoG3ko 4. https://youtu.be/ZA4JkHKZM50 5. https://youtu.be/8idr1WZ1A7Q @Julia Galef's explanation of bayesian thinking: https://youtu.be/BrK7X_XlGB8 Two beautiful books containing many essays on bayesian thinking and truth-seeking: 1. Map and Territory, by Eliezer Yudkowsky: https://www.amazon.com/Map-Territory-Rationality-AI-Zombies/dp/1939311233/ref=sr_1_2?crid=2EFD6G3N09W7Y&keywords=eliezer&qid=1645017447&sprefix=elieze%2Caps%2C156&sr=8-2 2. How to Actually Change Your Mind, by Eliezer Yudkowsky: https://www.amazon.com/Actually-Change-Your-Mind-Rationality/dp/1939311276/ref=sr_1_5?crid=2EFD6G3N09W7Y&keywords=eliezer&qid=1645017447&sprefix=elieze%2Caps%2C156&sr=8-5 Probability Theory, The Logic of Science, by E.T.Jaynes. This is THE book on bayesian thinking applied to science (more advanced): https://www.amazon.com/Probability-Theory-Science-T-Jaynes/dp/0521592712/ref=sr_1_1?crid=3263961XQEYON&keywords=jaynes+probability+theory&qid=1645017539&sprefix=jaynes+probability+theory%2Caps%2C135&sr=8-1 ▀▀▀▀▀▀▀▀▀OTHER STUFF▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Share this video with a friend or on Social Media: https://youtu.be/4hHA-oqpNig Playlist with all the animated videos: https://www.youtube.com/watch?v=GgyX-MnRAuY&list=PL1Nr7ps7wyYo-0AOYd6lfKp-6Czh4p5On Bitcoin address: 1FX4iepZfh1yuMNYtvYf2CWL7gha8cakuf Ethereum address: 0xDa8463494Dd233c3aBe59bc42Abc4D50823A5f3 ▀▀▀▀▀▀▀▀▀PATRONS & MEMBERS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ BIG thanks to our patrons & members from the simple adder tier and above: Lexi X רם רינגל Ana Tomasovic Ashten The Platypus Bryan Egan Calvin McCarter Chris Chapin Craig Ludington Dan Wahl David Mc Florian Gabriel Ledung hr101 Jacob Van Buren Jeroen De Dauw JHeb John S Lars Osborne Logic Luke Freeman Meade Marmalade Nathan Nathan Fish Nicholas Kees Dupuis Nick Sharp noggieB Raphaël Lévy Roborodger Sephiths Superslowmojoe Tim Duffy Udo Austin Cluff Connor Dang Griffith FusionOak Mark Gongloff Matthew Brooks Neel Nanda rictic Robin Hanson Ryouta Takehiko Scott Alexander YouAyePee Bleys Goodson Dawson Francisco Lillo marverati Matt Parlmer Michael Zimmermann no special person Trevyn Case William Deng Gabriel Fair Thomas Farago ▀▀▀▀▀▀▀CREDITS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Script by: - Matthew Barnett - The guy with the weird accent Animation by: - :3 Narration by Robert Miles: https://www.youtube.com/c/RobertMilesAI ▀▀▀▀▀▀▀MUSIC▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Brandenburg Concerto No4-1 BWV1049 - Classical Whimsical by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/ Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100303 Artist: http://incompetech.com/ ▀▀▀▀▀▀▀CHAPTERS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Chapters: 0:00 - Mathematicizing truth-seeking 1:55 - Conditional probability 3:39 - Explanation of Bayes' rule 10:34 - The odds form 14:54 - Cromwell's rule 17:36 - The bayesian view of truth-seeking