as others have mentioned, this is a 3D (perspective) projection of a 4D object. a slice would be just a cube (at least in the case of an axis aligned cube. it gets a but trippy when rotations are introduced)
@@angeldude101 with which the brain then tries to recreate the 3D projection in order to try and intuit the true 4D object. and it's all done using a salt powered lump of jelly :P
It is absolutely correct that we can see cross sections of a 4D object. But what we all forget, even myself, is that even a photography or an image can be a cross section (projection into the surface). Take for example the tree at 0:14 in the video, which is not a cross section of a 3D object, but an image of the whole object. The same also applies to the rotating cube, which the 2D guy sees. On the other hand, if the tree or cube had not been an image, but a 3D object, then he would have seen cross sections of the cube or tree. Good video anyway! You are a great teacher!
I always despise these kinds of videos. Not because I find them uninteresting or stupid, but because I hate the idea of never being able to fully visualize a 4D object. Every time I'm reminded of that, I feel frustrated...
I would consider myself decent at math, but this just feels so odd to wrap my head around. I find that quite interesting since I have a "fine" time understanding both the logic and abstract math of things like DEs both PDEs and ODEs, or even complex analysis :)
If you want to get REALLY nerdy it’s actually the 3d shadow of the hyper cube with one of its ‘w’ sides removed because including that side would overlap all other sides and making it look like a cross section (a cube). (remember, there are two ‘w’ sides just like there are 2 x y and z sides on a cube)
0:44 this is not the cross section of a hypercube. That would look just like a regular solid cube to us. If I asked you to quickly draw a 3d cube on a piece of paper, you would simply outline the cube by drawing its 1d edges. Now imagine your perspective changed so you are directly facing the front of the cube. No other faces would be visible, and it would look like this: _______ | | | | |______| All you see is a square (the cube’s front face) as none of the other faces are visible from your perspective. The edges comprising those other faces are behind this front face. If you were to make the front face completely transparent, you would see the edges behind it, and it would look like this: _______ | \ _ / | | |_| | | /___\ | You can now see another smaller square inside a larger square, connected to the larger square’s corners. This is the cube shown in the video, just in 2 dimensions. It is the shadow of a 3d cube’s edges being directly projected onto a 2d plane. If it were the shadow of a 4d cube’s edges being directly projected onto a 3d plane, you get the shape seen in the video.
Sir, I think you're confusing cross sections with projections. What you were calling cross sections of 4D or 3D objects were actually 3D or 2D projections of 4D and 3D objects. A cross section would be if I cut out a 2D slice out of a 3D cube. Projections are flattening a 3D cube until it fits into a 2D space. They are not the same thing. Example: An image of a cube is a 2D projection of the 3D object. A slice of that cube is a 2D cross section of a 3D object.
I am not too familiar with the mathematics of this, but is there a generalized method of turning polygons into their 4th dimensional counterpart? What about any continuous shape?
I'm not sure about a generalised mathod (hehe get it, math method) but I just used basic reasoning for the cuboid -> hypercube thing. I imagine someone out there has found one but I'm not aware of it.
that's like saying "how do you turn any 2d shape into a 3d one". think about that. to make a cube, you extrude a square along the 3rd dimension. to make a cylinder, you rotate a rectangle around a line on the 2d plane. to make a pyramid, you take the shape you want and extrude it, but shrink it to a point gradually while you extrude. extrude (extend along a direction) rotate (self-explanatory) resize (make bigger or smaller, usually combined with others) move (in case you want the shape elsewhere too but not extruding along that movement) and more, or for some shapes, just use a mathematical function since it would be more complicated to make them from these operations. the 2d to 3d to 4d analogy works here.
Yep and that's exactly what this video is doing, except it's doing 2 projections (4d -> 3d -> 2d) In fact, if you had special eyes that could see a full volume of space at once (insides and all) you would be able to make out 4d space just as well as you can make out 3d space now
i recently seen a video where a guy made minecraft in desmos, check that out im pretty sure he made 3d movements in desmos. something with matrices i cant remember
Just use calculus mentally piece by piece by parts in previous dimension or this case your current dimension in 3D then you can visualize higher dimensions better.
When should we tell him 3D Desmos already exists and it could be slightly easier?
You only get like 2 views in the 3d graph though, if you use 2d and make your own projections, you can make very wacky things
@ Fair enough and point, I respect your point.
Shhh, its a canon event
He brain built incorrectly
I actually already made 4d desmos myself using 4d rotation matrixes and I saw someone on Reddit make 5d desmos once
as others have mentioned, this is a 3D (perspective) projection of a 4D object. a slice would be just a cube (at least in the case of an axis aligned cube. it gets a but trippy when rotations are introduced)
yeah i didn't really like it when he said that wrong thing, because now many clueless people will believe it
It's a 2D perspective projection of a 3D perspective projection of a 4D object.
@@angeldude101 with which the brain then tries to recreate the 3D projection in order to try and intuit the true 4D object. and it's all done using a salt powered lump of jelly :P
Yeah I'm triggered by this too
The dark mode desmos was from the Reverse Contrast setting in case anyone is wondering
The cheery "don't forget to piss right off" really got me this time. 😀
It is absolutely correct that we can see cross sections of a 4D object.
But what we all forget, even myself, is that even a photography or an image can be a cross section
(projection into the surface).
Take for example the tree at 0:14 in the video,
which is not a cross section of a 3D object, but an image of the whole object.
The same also applies to the rotating cube, which the 2D guy sees.
On the other hand, if the tree or cube had not been an image, but a 3D object,
then he would have seen cross sections of the cube or tree.
Good video anyway!
You are a great teacher!
what you would be seeing is the tree surface embedded in 3d space. if we are assuming some kind of euclidean space, it has to be a planar section
I understand this, but I'm still sitting here like "Any sufficiently advanced science is indistinguishable from magic"
Nice job of 4D in 2D
I always despise these kinds of videos. Not because I find them uninteresting or stupid, but because I hate the idea of never being able to fully visualize a 4D object. Every time I'm reminded of that, I feel frustrated...
I would consider myself decent at math, but this just feels so odd to wrap my head around. I find that quite interesting since I have a "fine" time understanding both the logic and abstract math of things like DEs both PDEs and ODEs, or even complex analysis :)
very nice!!
there's slightly wrong imformation though,
that's actually the shadow of the tesseract and not the cross sectiono!!
Yes. That part of the video caught me off guard.
If you want to get REALLY nerdy it’s actually the 3d shadow of the hyper cube with one of its ‘w’ sides removed because including that side would overlap all other sides and making it look like a cross section (a cube). (remember, there are two ‘w’ sides just like there are 2 x y and z sides on a cube)
0:44 this is not the cross section of a hypercube. That would look just like a regular solid cube to us.
If I asked you to quickly draw a 3d cube on a piece of paper, you would simply outline the cube by drawing its 1d edges. Now imagine your perspective changed so you are directly facing the front of the cube. No other faces would be visible, and it would look like this:
_______
| |
| |
|______|
All you see is a square (the cube’s front face) as none of the other faces are visible from your perspective. The edges comprising those other faces are behind this front face. If you were to make the front face completely transparent, you would see the edges behind it, and it would look like this:
_______
| \ _ / |
| |_| |
| /___\ |
You can now see another smaller square inside a larger square, connected to the larger square’s corners. This is the cube shown in the video, just in 2 dimensions. It is the shadow of a 3d cube’s edges being directly projected onto a 2d plane.
If it were the shadow of a 4d cube’s edges being directly projected onto a 3d plane, you get the shape seen in the video.
This seems like the projection of the 4d onto 3d then onto 2d, not a slice of 4d in 3d then projected onto 2d.
Sir, I think you're confusing cross sections with projections. What you were calling cross sections of 4D or 3D objects were actually 3D or 2D projections of 4D and 3D objects. A cross section would be if I cut out a 2D slice out of a 3D cube. Projections are flattening a 3D cube until it fits into a 2D space. They are not the same thing.
Example: An image of a cube is a 2D projection of the 3D object. A slice of that cube is a 2D cross section of a 3D object.
I am not too familiar with the mathematics of this, but is there a generalized method of turning polygons into their 4th dimensional counterpart? What about any continuous shape?
I'm not sure about a generalised mathod (hehe get it, math method) but I just used basic reasoning for the cuboid -> hypercube thing. I imagine someone out there has found one but I'm not aware of it.
that's like saying "how do you turn any 2d shape into a 3d one". think about that.
to make a cube, you extrude a square along the 3rd dimension.
to make a cylinder, you rotate a rectangle around a line on the 2d plane.
to make a pyramid, you take the shape you want and extrude it, but shrink it to a point gradually while you extrude.
extrude (extend along a direction)
rotate (self-explanatory)
resize (make bigger or smaller, usually combined with others)
move (in case you want the shape elsewhere too but not extruding along that movement)
and more, or for some shapes, just use a mathematical function since it would be more complicated to make them from these operations.
the 2d to 3d to 4d analogy works here.
Ok you beat me on this race
Prob Speedrun this if I have the time to memorize
4D nikocado avocado when?
If you can display 3d on a 2d screen, cant you display 4d on a 3d world?
Yep and that's exactly what this video is doing, except it's doing 2 projections (4d -> 3d -> 2d)
In fact, if you had special eyes that could see a full volume of space at once (insides and all) you would be able to make out 4d space just as well as you can make out 3d space now
Have you watched hypercubist math's 2 videos on visualizing the 4th dimension? They're great and I'm eagerly awaiting the third video.
What if you didn’t set wc to 0 would see a more complete visual of the 4d shape?❤
Was looking for 3d in 2d desmos and got 4d😭
you have any old videos on tutorials on how to make 3d movements in 2d desmos and stuff?😓😅😅
He mentioned it in the video, yes
i recently seen a video where a guy made minecraft in desmos, check that out im pretty sure he made 3d movements in desmos. something with matrices i cant remember
You called it a cross section, but you showed a projection. 2 very different things
Just use calculus mentally piece by piece by parts in previous dimension or this case your current dimension in 3D then you can visualize higher dimensions better.
avocado broke me lmao
2:45
speech.exe is not responding
I always wonder if there 4D
This is not a crosssection! It's a projection, a crosssection is a 0 unit thin slice out of a shape!
make 4D doom
Desmos is the new gd 2.1 as 2.2 has beacome to powerful and nothing is impressive anymore
hey like my comment too
ofcourse bbg