Cosmos - Carl Sagan - 4th Dimension

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

in “Does the Universe Have Higher Dimensions? Part 1” · View on HN

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. ▶ this video

in “Counterintuitive Properties of High Dimensional Space (2018)” · View on HN

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

in “4D Tesseract: Fourth Dimension Game” · View on HN

> 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 projected the cube into 2D! Technically this is 3D. But the 3rd dimension isn't a spacial dimension, it is a time dimension. Which itself is a helpful lesson in learning about the abstraction of dimensions! So we hallucinate a cube, rotating, and then see the projected image on a plane, which we hallucinate as a square that isn't skewed but instead has depth. This is all rather wild in of itself. The truth is that we struggle to imagine 2D! And most people will claim to be able to visualize 2D and the claim will go uncontested. If you haven't read Flatland[1], I'd encourage everyone to do so. A lot of people get it wrong. They read it as an analogy 1 dimension down. Where we 3 dimensional creatures are analogous to the 2D creatures and a 4D creature would be as baffling as a 3D creature is to the

in “New sphere-packing record stems from an unexpected source” · View on HN

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

in “Why modifying gravity doesn’t add up” · View on HN

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.

in “How to walk through walls using the 4th dimension [video]” · View on HN