Bayes theorem, the geometry of changing beliefs

Perhaps the most important formula in probability.
An equally valuable form of support is to simply share some of the videos.

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:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example

Thanks to these viewers for their contributions to translations
Gujarati: Hitesh12358, Pragna1991
Hebrew: Omer Tuchfeld
Italian: @crampaldo

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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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Various social media stuffs:

[Andygg]

“Rationality is not about knowing facts, it’s about recognizing which facts are relevant.”

I felt this.

[distinctlyaverage]

"Evidence should not determine beliefs, but update them."
This is pure gold!

[justlooking]

I don't normally comment on youtube videos. But I must say this 15-minute video has helped me to grasp Bayes' Theorem so deeply that i was able to solve all the Bayes' Theorem-related questions in my recent math exam intuitively, with minimal plugging of formulas! It feels like magic. I am deeply grateful.

[ariadnar.]

thinking of events as "H" (hypothesis) and "E" (evidence) instead of random variables (A, B, C, ...) is definitely game changing. personally, it made the theorem much more immersive and useful. also, brilliant demonstration!

[duncanw]

hey you finally did the probability thing

[spynae]

The cool thing about Bayes' theorem as practice is that it isn't even necessarily important that your estimates are correct or accurate, but rather that the simple act of going through the motions allows for more refined guesswork.

[dimitriferresentis]

Dude, imagine every child had a math teacher as good as you... Congrats.

[moazzamjadoon]

First time in my life at age 55, I really understood Bayes Theorem. The link between the tree diagram and this box explains why the probabilities on successive branches of the tree diagram are multiplied. This is brilliant.

[truthfinder]

You will be known in the future as the father of visual mathology.

[erfannariman]

There are certain channels on youtube which have this extraordinary quality of content consistently in all of their video's. 3Blue1Brown is definitely one of those and the content on this channel is worth gold. These kind of channels should somehow be recognized by YouTube and be rewarded.

[tj]

It makes such a significant difference to one’s comprehension when something is explained in a certain way. This is one such example, in particular, the square diagram as opposed to the usual Venn diagram usually cited.

[andrewjolly]

I'm an astronomy PhD student and this is hands down the best explanation of BT I've seen on the internet. Well done.

[Baekstrom]

This is a REALLY nice presentation. I think that Bayes' theorem should be a mandatory subject in all schools and put in a wider context of epistemology. Even if you don't do the math all the time, just knowing the principles behind Bayesian inference changes the way you think. It is an awesome thinking tool!

[bluebrown]

The follow-on video mentioned here did not, er, end up getting finalized and published. At least not yet! I have a bad tendency to do this with probability videos, where there are always plans and drafts for more, but they often don't quite feel "there" once they're more fully mapped out.

[WilfredWChen]

Wow - if Youtube had a love button that depicted a greater appreciation of a video than the like button, I would be pressing it right now. I loved how this not only explained a seemingly complex probability concept, but also challenged the way we approach probability through visualisations. Thank you.

[qbtc]

I had to watch this twice to get it because of the pace but this is fantastic. Bayes theorem is usually taught as a recipe. You just go through the motions of setting up the equation and solving it not knowing how it was put together in the first place. Being able to picture the probabilities is so powerful.

[Gameboygenius]

I wonder if the misunderstanding in the question about Linda is simply a matter of language. Many people likely assume that option 1 excludes option 2, ie it's implied to say "Linda is a bank teller who is not active in the feminist movement". In that sense it may become almost a trick question for people who are not trained in logic.

[nickfausti]

This brought me to tears. I've seen Bayes theorem so many times, and just plugged in the numbers. I finally have an intuitive understanding of this now. Thank you so much.

[gaemlinsidoharthi]

I remember, when studying mathematics so many years ago, noticing how one of the top maths students would often use pictures, diagrams, and graphs to express formulae or other problems. From then on, I also did this and it made so many things easier across this field of all things mathematical.

[SIMPLETRUTHS]

I was on the dean's list in my undergrad engineering major, and graduated with high honors in my 'brand name' MBA program. This is one of the BEST explanations of a fundamental tool of analytical thinking and insight, whether for business, medicine, law, sports, online dating(!), or just clear thinking I've ever seen.

I learned and (explicitly & implicitly) used Bayes for decades, yet your preservation has given me another window into understanding/reminding me of its value in everyday thinking ... wish u were one of my prof's.

Godspeed, the world needs more of your talent.