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Strange Spheres in Higher Dimensions - Numberphile

Numberphile

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  • Recommended by 2 people: 2 on Hacker News.
  • A classic. People kept recommending it from 2020 to 2025.
  • Presented by Matt Parker, mathematician and author

Intermediate. Assumes working knowledge.

767K views9 years ago2 recommendations

Computer scienceMath for programmersComputation and complexity

Matt Parker explains the counterintuitive properties of spheres in higher dimensions and how they relate to high-dimensional geometry.

Squarespace (including 10% off): squarespace.com/numberphile Video features Matt Parker. More links & stuff in full description below ↓↓↓ Parker CIRCLE T-Shirts and Mugs (torment Matt at his live shows!): teespring.com/stores/parker-circle Parker Square: bit.ly/ParkerSquareTshirt More from this interview: youtu.be/RLZCpMPIeMc More Matt on Numberphile: bit.ly/Matt_Videos Matt Parker's own channel: youtube.com/user/standupmaths Matt's book on 4D stuff:bit.ly/Matt_4D_US or bit.ly/Matt_4D_UK Brady's new show, The Unmade Podcast: unmade.fm/ The man who loved circles: youtu.be/AzmUCL1OHhs Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: numberphile.com/ Numberphile on Facebook: facebook.com/numberphile Numberphile tweets: twitter.com/numberphile Subscribe: bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: patreon.com/numberphile Brady's videos subreddit: reddit.com/r/BradyHaran/ Brady's latest videos across all channels: bradyharanblog.com/ Sign up for (occasional) emails: eepurl.com/YdjL9

Why it's here

2 people recommend this

What people say. Recommended for building intuition about high-dimensional spaces and the curse of dimensionality in vector embeddings.

magicalhippoon Hacker News • Recommends

On “Volume of a Sphere”

Generalizations to higher dimensions1 also have some fun properties. For one, the volume of a n-dimensional sphere (ball) goes to zero as n goes to infinity. But not in a trivial way: given a radius r, you can find the number of dimensions n that maximizes the volume of the n-sphere. For r=1 it's 5 dimensions, but for r=3 it's 55 dimensions. Numberphile2 has a video on higher dimensional spheres which talks about this weirdness. 1: link 2: link to this video
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ithkuilon Hacker News • Recommends

On “A visual exploration of vector embeddings”

There is a good numberphile video about that link to this video It contains also a hilarious reference to the "parker circle:.
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ithinksoon Hacker News • Mentions

On “A mathematician's guided tour through higher dimensions”

Oh they are very spike-y, well, my point in the above post is to just solve the eq but easier 'visualization' would be 0 By the way, this is a similar phenomena to the 'curse of dimensionality' 1 0 link to this video 1 link
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hn_throwaway_99on Hacker News • Mentions

On “Tadayuki Watanabe disproved a major conjecture about spheres”

Also not a topologist, but thought it was interesting after watching the video from the current top comment, link to this video , where if you look at the size of the "contained sphere", 4D is the only place where the contained sphere is exactly tangent to the containing box. Lower than that, and it's easy to visualize how the contained sphere is smaller, higher than that, the contained sphere is always bigger. So seems like it might be a natural consequence that techniques that work at higher or lower dimensions don't work for the case in 4D where the sphere is exactly tangent.
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