Cosmos - Carl Sagan - 4th Dimension

What Hacker News said

Strong rec lgl · 2021-04 · on “Does the Universe Have Higher Dimensions? Part 1”

Good answer, a 4th dimension and the shadow projection analogy is brilliantly exemplified by Carl Sagan in this popular video: [this video]

Recommends CodeCube · 2014-02 · on “4D Tesseract: Fourth Dimension Game”

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: [this video]

Recommends travisjungroth · 2024-10 · on “Counterintuitive Properties of High Dimensional Space (2018)”

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

Cites smtddr · 2014-08 · on “How to walk through walls using the 4th dimension [video]”

I've been watching this vid on repeat trying to fully comprehend what's happening. This is another vid trying to explain the same thing - [this video] I really want to believe this is possible and this is how we'll be able to travel far into space. Like how we have to spend time walking around a very long wall when a bird can just fly over it in a fraction of the time, we wouldn't have to think about traveling light-years because there would something else we can do that's faster than a straight line.

Cites vyrotek · 2022-10 · on “Why modifying gravity doesn’t add up”

A fun way think about it is pressing on a filled balloon from the outside. Inside the balloon is our whole reality/dimension. Everyone is poking inwards and bending the rubber is what we see and how we interact with each other. But we're completely locked into our current senses. In some ways, it sounds awfully... "spiritual", right? The challenge is there's no point in trying to imagine what existence or thought outside of our reality looks like. Carl Sagan's FlatLand helps illustrate how stuck we really might be. [this video]

Cites godelski · 2025-07 · on “New sphere-packing record stems from an unexpected source”

> how weird large-dimensional space is It's rather crazy that we humans can't really even intuit about a single extra dimension. Or even a single fewer! There's a lot of people who will say that they can visualize things in the 4th dimension but I've yet to find someone who can actually do this. This includes a large number of mathematicians (it's never the mathematicians that claim this...) I really like the animation in this Math Overflow post[0], because it has a lot of hidden complexity that most people don't think about. The animation is actually an illusion, and you are "hallucinating". That top image projecting a cube down onto a plane? Well... that isn't a cube. We've already project

Critical nyc111 · 2024-10 · on “Counterintuitive Properties of High Dimensional Space (2018)”

"This video might help. [this video] " Sagan's video proves that it's always helpful to investigate abstract concepts with an experiment. But the video also raises an important question: Can we derive true conclusions from wrong assumptions? Here the assumption that the "flatlanders" are really flat is wrong. Sagan notices that too and he says that his objects are not really flat, but they have thickness. Now these little cutouts have some little height but let’s ignore that, let’s imagine that these are absolutely flat. So the thickness of his objects are never zero. His flatlanders has a notion of third dimension because they have the third dimension. Their height is not zero. This is the typic