Hamming, "n-Dimensional Space" (April 14, 1995)
Why Hacker News recommends it
Recommended as the source for counterintuitive high-dimensional geometry and described as an eye opener.
What it is
Richard Hamming's 1995 lecture on n-dimensional space, showing how geometric intuition about spheres and cubes breaks down in high dimensions. It is part of his course on learning to learn.
Recommended by 3 HN commenters across 3 different months, 2022 to 2024.
What Hacker News said
Strong rec bgnn · 2024-09 · on “How does cosine similarity work?”
One cannot intuitively think about higher than 3 dimensions. Even for most their intuition is often wrong in 3D space. It's quite accurate for 1D and 2D. Richard Hamming has a whole section lecture to make everyone realize precisely this [1]. This was an eye opener to me. [this video]
Recommends it_does_follow · 2022-01 · on “A high-dimensional sphere spilling out of a high-dimensional cube”
To add to this list: Richard Hamming includes a section on this in his n-dimensional spaces talk from "The Art of Doing Science and Engineering" lectures [0]. Stripe Press also recently re-published a beautiful copy of the print version of these lectures [1]. 0. [this video] 1. [LINK]
Recommends time_to_smile · 2023-05 · on “Counterintuitive Properties of High Dimensional Space”
A good chunk of this comes directly from Richard Hamming's incredible The Art of doing Science and Engineering (a video of the specific lecture on n-dimensional spaces can be found here[0]) and yet I see no mention of this talk anywhere in the article, which is unfortunate. I highly recommend checking out Hamming's lectures if you find this enjoyable. 0. [this video]