Bertrand's Paradox (with 3blue1brown) - Numberphile
Why Hacker News recommends it
Cited in threads on random sampling as a clear illustration of how reasonable-sounding random choices can give biased results.
What it is
Numberphile interviews Grant Sanderson of 3blue1brown about Bertrand's paradox, where different reasonable ways of picking a random chord of a circle give different probabilities.
Recommended by 1 HN commenters across 1 different months, 2022 to 2024.
What Hacker News said
Recommends Dave_Rosenthal · 2022-05 · on “Uniformly Sample Points in a Disk”
So points in a circle is pretty basic, but it does remind me of a nice 3Blue1Brown video ( [this video] ) about random chords of a circle. Some of these 'generate a random sample' situations can be quite non-obvious. edit: The video is about 'Bertrand's Paradox' that another post references.
Cites zootboy · 2023-05 · on “Random(Random(Random(Random())))”
In a related vein, there's a Numberphile / 3B1B video about the pitfalls of plotting randomness in a circle: [this video]
Cites olliej · 2024-03 · on “How to generate uniformly random points on n-spheres and in n-balls”
I was always surprised at how easily you get biased sampling when generating random points despite all input - something I often saw students do was essentially normalize({2 rand() - 1, 2 rand() - 1, 2 rand() - 1}) or variations of that (where rand() is "good" not the literal rand(3)), and there are numerous other ways that are more subtly wrong. IIRC the nominally correct way for a sphere specifically is something like a=rand() b=rand() and the random point is something* like { cos(a) sin(b), sin(b), cos(a) cos(b) }[1] I think the best illustration of "reasonable choices of what random values should be used leading to biased results" is Bertrand's paradox which I was introduced to via numbe