Take a moment to think about the equation in the Bayes theorem. How would you calculate it using only basic geometry?
Or, to state it more precisely: you are given the unit segment, as well as line segments of lengths equal to P(H), P(E | H) and P(E | ~H) (or the ratio of the last two, if you prefer). How do you get P(H | E) only by drawing straight lines on paper? Can you think of a way that would be possible to implement using a simple mechanical instrument?
I noticed a very neat way to solve this, which is best shown on a diagram:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRCGo49IkQx2DS9YoLYV1G0VRjzUFyme2R5eh4hfBwxu0MuGJ9hvLGdGNAFSBBxBos6JsAwsUKuP1kgGCtkwITwMJ8eo1a4kMV3v-XF5nzp-T4nqbs8M3S3HprxWAWlIN0V2FEzv3ZC2g/s1600/geom-bayes.png)
Have fun with this GeoGebra worksheet.
Your math homework is to find a proof that this is indeed correct (solution).
As an answer to a comment on LessWrong, I also made a pictograph-only version of the diagram:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8VFmAMfxOwPP2SEsLmcCcS7DMhzzOoatlFdeOYCYmLN9ipgUpU3PcrQHinst86An2a7nM1JApef2ivPa2LYXadhEda2Q7VnIWle16bd78V60VLQnM-CuhilFKORwbhyphenhyphen7iyqcWnJmKw0Y/s1600/geom-bayes.png)
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