An Engineer’s Take on Bertrand’s Paradox
TL;DR: Draw a picture. Probability should always correspond to a length, area, or volume.
I show off an example from a real project I'm working on. In this case I'm mapping probabilities onto the surface of a sphere.
If you're not familiar with Bertrand's Paradox, don't overthink it. Imagine any "word problem" with at least two variables. Bertrand's examples and mine all talk about probabilities. This family of problems comes up a lot. Most of the time you don't even need a sphere!
I was inspired by Grant's videos on the subject: https://www.youtube.com/results?searc... Grant spends a lot of time delving into Alice and Bob's heads, explaining how they could get confused. That was interesting, but I just take it for a given that people will frequently misinterpret "word problems."
This is the paper I'm working on: https://tradeideasphilip.github.io/hi... This paper is far from complete. I'm only showing it off because the sphere analogy is such a perfect example of what I'm discussing. Feel free to read the paper but I'm hoping it will make a lot more sense when it's done. 😜
This video is my entry in the SoMEπ community edition, summer 2024 contest: https://some.3b1b.co/?utm_source=subs...
And the "director's commentary": • SoME'r is back! Bertrand's Paradox #somepi
0:00 Intro
0:12 My take on Bertrand’s paradox
0:47 The sound of one hand clapping
0:55 My solution to Bertrand’s paradox
1:21 Randomly pick latitude and longitude
1:38 Clarity and precision
2:03 Real example (work in progress)
3:22 Behind the scenes
3:33 Raison d'être