3Blue1Brown
6 HN recommenders · recommended in 8 months, 2017–2025
25:13 · 3.2M views · Aug 11, 2017
3Blue1Brown visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow. It builds geometric intuition for counterintuitive properties of high-dimensional space.
HN recommends it as the go-to intuitive visualization of high-dimensional geometry, relevant to machine learning, optimization and sphere packing.
9 comments from Hacker News
A trick for visualizing higher dimensions: this video Only 383k subscribers. Hmm. Remember to subscribe, comment, and smash that like button. Real Engineering is another great channel. And of course Veritasium and Numberphile.
Don't forget 3Blue1Brown's incredible video about visualizing higher dimensions[1]. He's getting to xkcd levels of "Of course there's a relevant video" [1]: this video
There's a great 3blue1brown video that demonstrates this unintuitive result in a relatively intuitive way: this video
As you increase the dimensionality of a sphere, an ever-increasing proportion of the sphere is within epsilon of the surface. This 3Blue1Brown video addresses enough related stuff that the rest should become reasonably comprehensible: this video This particular result is tossed in as a side note around 23:25, so it's not addressed directly, but it'll help.
Great article! I've been thinking about this on and off recently, as I wonder if we might be having intuitive issues when it comes to gradient descent optimization. 3 Blue,1 Brown had a video recently that kicked off my head scratching and is a great complement to your article: this video