Bayes theorem, the geometry of changing beliefs

Perhaps the most important formula in probability.

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Special thanks to these supporters

Here's an interactive version of the main diagram one viewer made:

The quick proof

Interactive made by Reddit user Thoggalluth

The study with Steve:

You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.

Contents:

Thanks to these viewers for their contributions to translations

Gujarati: Hitesh12358, Pragna1991

Hebrew: Omer Tuchfeld

Italian: @crampaldo

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These animations are largely made using manim, a scrappy opensource python library

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.

Download the music on Bandcamp:

Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe

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