Cosmos - Carl Sagan - 4th Dimension

carlsagandotcom · 5.4M views · 2009-03-24 · 7:24

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Overview

A segment from Carl Sagan's original Cosmos explaining the fourth spatial dimension through analogy with a two-dimensional world and shadow projection.

On Hacker News

HN recommends it as the clearest intuitive introduction to thinking about a fourth dimension.

Recommended by 3 HN people across 3 months · HN mentions 2014–2025

Topics

Pure mathematics Recreational & visual math Fundamental physics

What people said

lgl · 2021-04 · Strong recommendation
Good answer, a 4th dimension and the shadow projection analogy is brilliantly exemplified by Carl Sagan in this popular video: [VIDEO]
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travisjungroth · 2024-10 · Recommendation
In 3 dimensional space, you can’t. Draw a square on paper. The lines will be orthogonal. Draw a cube. The third dimension won’t be orthogonal. It can’t be. But, that doesn’t mean a third dimension doesn’t exist or can’t exist. The same thing happens with a hypercube. The fourth dimension won’t be orthogonal on paper. It won’t be orthogonal in three dimensions (you can build a 3D projection of a hypercube). This doesn’t mean it isn’t real or can’t be real. Whether you think of 4D space as something real we don’t have access to or something imaginary isn’t really too important. It’s just very helpful to realize it won’t have the concreteness of 3D objects in 3D space for you because you don’t have direct access to it. This video might help. [VIDEO]
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CodeCube · 2014-02 · Recommendation
For those trying to wrap their heads around this ... I find this segment by Carl Sagan from the original Cosmos to be pretty well presented on the topic: [VIDEO]
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Sources

Video by carlsagandotcom, played through YouTube.

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