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Hamming, "n-Dimensional Space" (April 14, 1995)

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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 as the source for counterintuitive high-dimensional geometry and described as an eye opener.

Pure mathematicsUniversity lectures & courses#hamming#n-dimensionalspace#hypersphere#curseofdimensionality

3 comments from Hacker News

@bgnn2024-09 · in “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

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@time_to_smile2023-05 · in “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

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@it_does_follow2022-01 · in “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

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