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Thinking outside the 10-dimensional box

3Blue1Brown · explainer · Watch on YouTube

Recreational & visual mathPure mathematics

What it is

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.

Why Hacker News recommends it

HN recommends it as the go-to intuitive visualization of high-dimensional geometry, relevant to machine learning, optimization and sphere packing.

  • 6 people recommended it
  • 6 different months
  • 3 strong recommendations
  • first 2017, last 2025

What HN commenters said

  1. “A trick for visualizing higher dimensions”

    Trick for visualizing higher dimensions

    sillysaurus3, 2017-10 · Strong recommendation · in “What Is a Neural Network?”

  2. “incredible video about visualizing higher dimensions[1]”

    Visualizing higher dimensions

    jedimastert, 2018-07 · Strong recommendation · in “Random Points on a Sphere”

  3. “There's a great 3blue1brown video that demonstrates this unintuitive result in a relatively intuitive way”

    Intuitive demonstration of unintuitive high-dimensional result

    kibwen, 2025-07 · Strong recommendation · in “New sphere-packing record stems from an unexpected source”

  4. “is a great complement to your article”

    Complements intuition about high-dimensional geometry for optimization

    gilbetron, 2018-03 · Recommendation · in “Counterintuitive Properties of High Dimensional Space”

  5. “This 3Blue1Brown video addresses enough related stuff that the rest should become reasonably comprehensible”

    Explains high-dimensional sphere geometry and surface concentration

    jerf, 2022-01 · Recommendation · in “Geometry from Another Universe”

  6. “has a decent video which perhaps helps get a handle on how one can use higher-dimensional spaces”

    Approach to using higher-dimensional spaces without visualizing them

    NeoTar, 2024-05 · Recommendation · in “Strangely Curved Shapes Break 50-Year-Old Geometry Conjecture”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: high dimensions, spheres, 3blue1brown, visualization, sphere packing

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