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If you're interested in this, you may be interested in Hyperbolica, which is a whole game about this concept: https://store.steampowered.com/app/1256230/Hyperbolica/ https://www.youtube.com/watch?v=EMKLeS-Uq_8
If you're interested in this, you may be interested in Hyperbolica, which is a whole game about this concept: https://store.steampowered.com/app/1256230/Hyperbolica/ https://www.youtube.com/watch?v=EMKLeS-Uq_8
In the meantime, the video I link is basically a video exploration of spherical geometry. One of the better ones, in my opinion, because it has "normal" objects in it, rather than floating heads or a ton of Earths or something.
(Another amusing sidebar: As you can see in the video above, an inhabitant of that space would be naturally inclined to say the space curves in above them. It would take an Einstein to assert that it's actually flat, and Spherical Einstein would have a very hard time describing "flat" to anyone. You can only make things "flat" contingent on the observer being in a very particular place. If you look at the next devlog: https://www.youtube.com/watch?v=pXWRYpdYc7Q back in Hyperbolic space, you can also see that a resident of that space would naturally believe the space they are in is a sphere (albeit one of variable radius, which is weird, but still, you can look out in the world and see the curvature, obviously it's round), and it would again take an Einstein to say that it is flat. It's flat if you are exactly on the ground, but hyperbolic space exaggerates any degree to which you are above the ground to make the horizon look round.)
Earlier quoted context omitted.
Wow, if you’re having these dreams without the aid of substances, I envy you. The most intellectual dreams I seem to be able to come up with “unenhanced” are falling off buildings and being late to college exams while having no pants on.
My favorite are the dreams I have before a semester starts: it is the end of the semester, and I've just discovered I've forgotten about an entire class for most of the semester. Then I wake up.
Does anyone know of a good visualization of a hypercube? Specifically, I'd like to be able to rotate it around various axes to see what its shadow looks like in 3D. On that note, a VR rendering might help since a 2D projection overcomplicates the shadow. It's easy to construct, just build a point, extrude the point out to make a line, extrude the line out to make a square, extrude the square out to make a cube, then…
Does anyone know of a good visualization of a hypercube? Specifically, I'd like to be able to rotate it around various axes to see what its shadow looks like in 3D. On that note, a VR rendering might help since a 2D projection overcomplicates the shadow. It's easy to construct, just build a point, extrude the point out to make a line, extrude the line out to make a square, extrude the square out to make a cube, then…
Wait, doesn't it rotate around a plane?
Earlier quoted context omitted.
Wow, if you’re having these dreams without the aid of substances, I envy you. The most intellectual dreams I seem to be able to come up with “unenhanced” are falling off buildings and being late to college exams while having no pants on.
My favorite are the dreams I have before a semester starts: it is the end of the semester, and I've just discovered I've forgotten about an entire class for most of the semester. Then I wake up.
Does anyone know of a good visualization of a hypercube? Specifically, I'd like to be able to rotate it around various axes to see what its shadow looks like in 3D. On that note, a VR rendering might help since a 2D projection overcomplicates the shadow. It's easy to construct, just build a point, extrude the point out to make a line, extrude the line out to make a square, extrude the square out to make a cube, then…
Based on the same 4D geometry concepts he's working on the game Miegakure: https://miegakure.com/
I had a dream a year ago in which I was traveling at very high speed towards an edge of our universe. In the dream I entered a null space before entering the next universe in which all star systems obeyed solid state physics type laws: stars formed an outer lattice and planets in small lattices around stars. After traveling through the second universe in my dream, I then entered a third universe that was more compact…
> everything was happening in lower dimensional manifolds curving through that space where “all the action was.” I feel like this would have to be true in a very high dimensional space, since an infinite dimensional orange is all skin. > systems obeyed solid state physics type laws: stars formed an outer lattice and planets in small lattices around stars. This sounds really fun, could you try explaining a bit more ab…
If you're interested in this, you may be interested in Hyperbolica, which is a whole game about this concept: https://store.steampowered.com/app/1256230/Hyperbolica/ https://www.youtube.com/watch?v=EMKLeS-Uq_8