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Oh yes, a 4D print casting a 3D shadow
Found the 3d print file for those interested
Isn’t “3rd dimensional plane” an oxymoron?
I mean typically people refer to planes as hyperplanes once you go past 3D, but I’ve definitely heard them just called “planes” too
Hyperplanes are just a generalization of planes to higher dimensions. Often you hear the term when working with vectors because, like in 3D, you can define an n-dimensional hyperplane by a surface normal vector and a point. All lines perpendicular (orthogonal) to that normal vector which pass through the point form the plane.
It’s a useful concept and since we already have a word for that kind of structure in 3D space we just use the same term for it in other dimensions
Hmmm. I don’t think so but I do think it is incorrectly used here. To me, the 3rd dimensional plane would just be the z axis. If you were talking about the entire 3D shape which they are here, I would just say 3rd dimension.
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.
It’s worse. It’s the projection of a 3d shape onto a 2d shape, which is then captured on a different 2d shape to be displayed to us.
It also has a brief 4d dimension, sliced at the second the picture was taken.
Rolling shutter, my beloathed…
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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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.”
His full presentation on this:
Can I buy this chandelier?
In the Beyond section of Bed Bath and Beyond
Next an Tesseract dice
