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No. He shows how non euclidean (spherical) space translates to euclidean (flat) space. Description is bullshit.
There is the cool idea of showing how different dimensions, in our situation where fully visualizing a fourth dimension is fundamentally impossible, could potentially look. Like, yes this is obviously not going to show us a fourth dimension but looking at how a 2D plane can actually be a 3D space if you have the capacity to see it is kinda neat. It’s as close as most people are going to get to visualizing a fourth dimension.
You’re so focused on how this isn’t a literal representation of something fundamentally impossible to represent that you forgot to exercise your imagination even a little bit.
What if I were to tell you you’re supposed to extrapolate the concept instead of taking it absolutely literally?
There’s nothing to extrapolate here. The description is BS. There’s no such thing as ‘linear plane’ there’s a flat plane and curved plane (with positive and negative curvatures). There’s a thing called linear algebra but it’s not the same. Also planes are 2 dimensional spaces. When you have more dimensions name ‘plane’ doesn’t apply. If you extrapolate BS you’ll get even more BS
🙄
Seems to me like it’s demonstrating the projection of a complex three dimensional shape which produces a simple pattern on a two dimensional plane.
thatsthejoke.jpg
But what’s the time equivalent flashlight?!
Manifolds such as these are actually defined by the maps used from a linear space. Two manifolds (i.e. two sets of maps) are considered the same (isomorphic) if the maps of one set can be “morphed” into the other and vice versa.
The flashlight demonstrates how the manifold’s map projects into the linear space. See stereographic projection.
That’s kind of part of a larger point actually: There is no 3d vector space in reality. It’s a made up construct used to make sense of the world around us.
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Hiu
Can I buy this chandelier?
In the Beyond section of Bed Bath and Beyond
This is like me laying naked on my back with an erection and saying the shadow cast by the sun is a complex timekeeping device.
If you can keep time for more than 4 hours, be sure to go to the doctor.
So, Earth is actually flat
I thought it was carbonated?
when described in a Euclidean manner, yes
Isn’t “3rd dimensional plane” an oxymoron?
Neat. How does this help me violate causality or skip over to a different planet? “Scientists discover we are trapped in an even deeper infinite fractal of hell from which there is no escape.”
Found the 3d print file for those interested
Will it work on my 4d printer or will I have to project it down to 3d first?
Next an Tesseract dice
got xmas ornaments do that 🪩
