How to systematically approach truth - Bayes' rule

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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@3blue1brown 's explanations:

Two beautiful books containing many essays on bayesian thinking and truth-seeking:

Probability Theory, The Logic of Science, by E.T.Jaynes. This is THE book on bayesian thinking applied to science (more advanced):

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Script by:
- Matthew Barnett
- The guy with the weird accent

Animation by:
- :3

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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

[RationalAnimations]

Many of our future videos will probably be more comprehensible if you understand Bayes’ theorem and assimilate Bayesian thinking. If you found the grabby aliens’ videos somewhat confusing, try to go back to them after having understood this one! The video about prediction markets also shares the same approach of attaching probabilities to beliefs.

[MathsSciencePhilosophy]

I learnt Bayes theorem 3 years ago, understood 2 years ago, forgot 1 year ago, again understood this year when YouTube suggested me this video .❤

[nekomakhea]

"the maths of truth-seeking" is a bit more polite than the one I heard in college stats class; the one I heard was "statistics is the mathematical theory of ignorance"

[dionysianapollomarx]

Thank you for this video. Very timely, as I've been dipping into the literature on truth and rationality. Never read Bayes, or Bayesian reasoning. Thanks for the video.

[jadenearl]

Favorite channel by far, thanks to your Grabby aliens video I chose to major in statistics. My probability classes are probably my favorite

[Ultra_DuDu]

Bayes' rule saved so many peoples. Knowing the ods of false positive is really important in medecine.

[saidasaetgar]

The most accessible explanation of Bayesian thinking that I’ve encountered so far! ✨Thank you so much for creating this video! 🙏😊

[ZtereoHYPE]

This is SUCH A GOOD VIDEO! I had a hard time fully grasping the whys of Bayesian statistics but now it makes a lot of sense!

[TheFourkingluigi]

Thank you for taking the time to gift us with your amazing thought process!

[HeartOfStone.]

I appreciate that sam o'nella music in the background, excellent subject and video. Criminally underrated.

[timgabby]

An exception to the 'never say 100% or 0%' is the rule itself, which should be applied in 100% of cases. :)

[Lin_The_Cat_]

Always excited to see a new video from y’all pop up in my feed!

[gageweston]

Probably the best video I’ve seen on Bayes rule! Good job

[flyingeagle]

I find it astonishing that I don't remember ever hearing about Bayes rule until now, but despite that fact. This is precisey the way I tend to think about beleifs.
I probably simply absorbed this way of thinking through being an avid follower of various science topics, and classes that taught the scientific method without ever directly referencing Bayes.

[sulljoh]

These videos strive for clarity in a refreshing way

[inventorbrothers]

Definitely the best video I've seen on Bayes' rule. This really helped me understabd it better, snd i loved the animations!

[DingHang]

Nice, integrating a statistical formula into everyday thinking so that our reasoning is more objective.

[whitewalker]

This is a FANTASTIC video on intuitive understand on Bayes. Loved the animations. Loved that you explained the odds for of Bayesian. Loved the examples.

[shahbazsaeed]

i have watched tons of videos but none of them explain this much good, you are the best

[martindeveloper]

Only 80.000 views, that is kinda disappointing.
This video was very nice animated and clearly explained.
Thank you for also introducing the historical aspects and the idea of Bayesianism instead of just showing the formula and explaining the individual parts that most of the people do.
By introducing more about the context and background it helped understanding the content of the video.