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.
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.
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
The description hurts my brain, it doesn't make any sense to me at all, it just seems to be filled with irrelevant words that sound sciency to someone who doesn't know what they mean. Like a bad sci fi script.
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.
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."
Um, hypothetically speaking, for a ah friend, if I wanted to STOP slipping into the ever deepening abyss of further levels of hell, how might I, oh I mean my friend, accomplish this?
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.
Hiu
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
Isn't the description dumbed down to fit thosoe of us with less than mathematician level brains? :-)
The description hurts my brain, it doesn't make any sense to me at all, it just seems to be filled with irrelevant words that sound sciency to someone who doesn't know what they mean. Like a bad sci fi script.
🙄
AI slop
It's not AI is it though?
Organic slop™
Can I buy this chandelier?
In the Beyond section of Bed Bath and Beyond
Oh yes, a 4D print casting a 3D shadow
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.
So, Earth is actually flat
I thought it was carbonated?
when described in a Euclidean manner, yes
In euclidian metric (which we usually use) it's not, in spherical it is.
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.
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."
Um, hypothetically speaking, for a ah friend, if I wanted to STOP slipping into the ever deepening abyss of further levels of hell, how might I, oh I mean my friend, accomplish this?
That's the main timeline you're experiencing, it's totally normal
That's what I was terrified that
the Eldritchian voices inside my head, and alsoyou would say.His full presentation on this:
https://youtube.com/watch?v=iqTLQ0T-MxU
Found the 3d print file for those interested
https://www.thingiverse.com/thing:202774
Will it work on my 4d printer or will I have to project it down to 3d first?
Make sure it has enough time filament to load a snapshot from the past and still print in the present.
yapping alert
Next an Tesseract dice
got xmas ornaments do that 🪩