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 can inform many central tenets of scientific reasoning. One example is Cromwell's rule, which tells us with the language of probability theory that our empirical beliefs shouldn't be absolute dogmas, but always potentially put into question when new evidence comes in.
ERRATA:
- At 8:37, there should be P(H|e) on the left-hand side.
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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
@measureofdoubt'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
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Script by:
- Matthew Barnett
- The guy with the weird accent
Animation by:
- :3
Narration by Robert Miles: https://www.youtube.com/c/RobertMilesAI
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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
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▀▀▀▀▀▀▀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