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?
39 Comments
CannonFodder@lemmy.world · 233 pts · 138d
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.
Rhaedas@fedia.io · 116 pts · 138d
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.
verdare@piefed.blahaj.zone · 45 pts · 138d
Rolling shutter, my beloathed…
Speculater@lemmy.world · 22 pts · 138d
thatsthejoke.jpg
But what's the time equivalent flashlight?!
mathemachristian@lemmy.ml · 21 pts · 138d
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.
fossilesque@mander.xyz · 1 pts · 138d
a_non_monotonic_function@lemmy.world · 1 pts · 137d
Hiu
BlackLaZoR@lemmy.world · 151 pts · 138d
No. He shows how non euclidean (spherical) space translates to euclidean (flat) space. Description is bullshit.
Soup@lemmy.world · 8 pts · 137d
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.
DragonTypeWyvern@midwest.social · 1 pts · 138d
What if I were to tell you you're supposed to extrapolate the concept instead of taking it absolutely literally?
BlackLaZoR@lemmy.world · 42 pts · 138d
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
87Six@lemmy.zip · 0 pts · 138d
Isn't the description dumbed down to fit thosoe of us with less than mathematician level brains? :-)
bearboiblake@pawb.social · 10 pts · 138d
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.
DragonTypeWyvern@midwest.social · -3 pts · 138d
🙄
wrinkle2409@lemmy.cafe · 88 pts · 138d
Zron@lemmy.world · -2 pts · 138d
AI slop
shane@feddit.nl · 21 pts · 138d
It's not AI is it though?
Golden@lemmy.blahaj.zone · 2 pts · 137d
Organic slop™
grau0wl@lemmy.world · 44 pts · 138d
Can I buy this chandelier?
Trex202@lemmy.world · 71 pts · 138d
In the Beyond section of Bed Bath and Beyond
ChaoticNeutralCzech@feddit.org · 37 pts · 138d
Oh yes, a 4D print casting a 3D shadow
BigBenis@lemmy.world · 33 pts · 138d
Isn't "3rd dimensional plane" an oxymoron?
AnarchoEngineer@lemmy.dbzer0.com · 38 pts · 138d
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
traxex@lemmy.dbzer0.com · 4 pts · 138d
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.
RevolverSly@lemmy.world · 22 pts · 138d
So, Earth is actually flat
lengau@midwest.social · 10 pts · 137d
I thought it was carbonated?
DarkSurferZA@lemmy.world · 8 pts · 138d
when described in a Euclidean manner, yes
justme@lemmy.dbzer0.com · 6 pts · 138d
In euclidian metric (which we usually use) it's not, in spherical it is.
58008@lemmy.world · 20 pts · 138d
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.
FunStuffIsFun@eviltoast.org · 30 pts · 138d
If you can keep time for more than 4 hours, be sure to go to the doctor.
TherapyGary@lemmy.dbzer0.com · 15 pts · 138d
His full presentation on this:
https://youtube.com/watch?v=iqTLQ0T-MxU
timeghost@lemmy.world · 15 pts · 138d
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."
OpenStars@piefed.social · 6 pts · 138d
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?
BanMe@lemmy.world · 6 pts · 138d
That's the main timeline you're experiencing, it's totally normal
OpenStars@piefed.social · 4 pts · 138d
That's what I was terrified that
the Eldritchian voices inside my head, and alsoyou would say.craigers@lemmy.world · 11 pts · 138d
Found the 3d print file for those interested
https://www.thingiverse.com/thing:202774
Silic0n_Alph4@lemmy.world · 13 pts · 138d
Will it work on my 4d printer or will I have to project it down to 3d first?
Sylvartas@lemmy.dbzer0.com · 6 pts · 138d
Make sure it has enough time filament to load a snapshot from the past and still print in the present.
Zerush@lemmy.ml · 3 pts · 138d
Next an Tesseract dice
Tetragrade@leminal.space · 3 pts · 138d
yapping alert
m3t00@lemmy.world · 1 pts · 138d
got xmas ornaments do that 🪩