Actually after thinking about the topic a bit more, and then thinking back to the story of flatland. If I saw this floating and morphing in my living room in 3 dimensional space, I would be seeing the shadow of a 4 dimensional shape that is outside my 'plane' of existance (cube of existance is more accurate I suppose.) Would it be a shadow or 'slices' of the 4d shape passing through my 3d 'plane', similar to a finger appearing like a morphing circle when passing through flatland.
I have a quick question before I ask a more in depth question: At the beginning and end the shape appears like a 3d torus. Is it possible to rotate this 4d shape such that it would rotate in on itself in the same fashion as a 3d torus like a vortex? Think like how smoke rings move. In what ways could we make this 4d shape behave like a smoke ring?
Ok, from what I'm understanding from this (besides the part where I'm getting high all the time from this) is that considering the lack of knowledge the human brain has, will only allow us to see a certain dimension (2D) but imagine 3D? So if the human used more than 10%, wouldn't that allow us to see in more dimmensions?
Saying it's impossible to visualise is highly underestimating yourself, four isn't much harder than three. This looks about right but I hate perspective in 4D, it makes me feel like I need more eyes. (Which is probably why you think it's impossible to visualise)
Said WildStar: "it's hard to visualize because of the loss of information with the step down to 3D."
Indeed, it's even harder to visualize than that, because what we're actually seeing is a TWO-dimensional representation, so even more information is lost.
@ChrisCDXX You're right - just because it's rotating doesn't make it 4D, and it's hard to visualize because of the loss of information with the step down to 3D. Well, actually, it's *impossible* to visualize - but I trust the math behind it. This is what the shadow of a 4D torus would look like. The rainbow colors are to help in the visualization: +x = red, +y = green, +z = blue, and +w axis = gray. :-)
@WildStar2002 dude, you need to put that in the description. makes a lot more sense now that you said that, I bet a lot of ppl would benefit from an explanation.
@MrNitt True - but in this case, I had no idea what it would look like, I trusted the math. I created a program that revolved a sphere around an imaginary axis perpendicular to the volume in which it was created (like revolving a circle around an axis in it's plane). Then I used a perspective projection technique from an imaginary 4D viewpoint, and rotated the object along various random axes - and here it is! :-)
@cRaSHaCk i could rotate it in just one direction at a time. I think I did that for one of the hypersphere vids I put up here. Unfortunately, it's going to have to be a project for a future time. Lotsa schoolwork besetting me at the moment! ;-)
Well, I'm not sure you'd call this a polychoron. :-) Is a circle a polygon? Is a sphere a polyhedron? Functionally, it is a polychoron, I just didn't show all the interconnect edges, and I used enough of them to give the illusion of a curved shape. :-)
It -should- look like a torus! :-) It's a sphere revolved through the 4th dimension around a central plane. Just like a traditional torus is a circle revolved around a line.
At least one variation of one - yes. Consider. What is a torus revolved around a circle? What is a torus revolved around a torus? Higher dimensions start to get complicated and fun! :-)
@Meb8Rappa It's like connecting the ends of a spherical cylinder...there're multiple types of 4d tori, and i can't rly ask wildstar which type it is because he's not on anymore.
@SharkRetriver a 3-torus is defined as what you get when you try to fold the opposite sides of a cube together. So it is more like a 2-torus revolved around a circle.
I knew people could easily project hypercubes, but I thought projecting a rounded object with a hole through the center would be physically impossible for a human being to do! Do you use a special tesseract forming program?
I used 3D Studio Max and a MaxScript program I wrote. Imagine creating a torus shape by projecting a circle through another circle at right angles to it. Instead of making it solid just show enough intersections to give the idea. That's exactly what I did, only it was a sphere instead of a circle. Then, to get a curved shape, I cheated... I made a whole bunch of little spheres representing discrete points, and then connectect them with very short cylinders. it looks round, but it isn't.
You probably shouldn't watch this if you have motion sickness...
MrPianoman6651 1 month ago
Is this a duocylinder or what kind of hypertorus is this?
Meb8Rappa 3 months ago
Actually after thinking about the topic a bit more, and then thinking back to the story of flatland. If I saw this floating and morphing in my living room in 3 dimensional space, I would be seeing the shadow of a 4 dimensional shape that is outside my 'plane' of existance (cube of existance is more accurate I suppose.) Would it be a shadow or 'slices' of the 4d shape passing through my 3d 'plane', similar to a finger appearing like a morphing circle when passing through flatland.
oaney 4 months ago
I have a quick question before I ask a more in depth question: At the beginning and end the shape appears like a 3d torus. Is it possible to rotate this 4d shape such that it would rotate in on itself in the same fashion as a 3d torus like a vortex? Think like how smoke rings move. In what ways could we make this 4d shape behave like a smoke ring?
oaney 4 months ago
Ok, from what I'm understanding from this (besides the part where I'm getting high all the time from this) is that considering the lack of knowledge the human brain has, will only allow us to see a certain dimension (2D) but imagine 3D? So if the human used more than 10%, wouldn't that allow us to see in more dimmensions?
lilrocker1053 7 months ago
Saying it's impossible to visualise is highly underestimating yourself, four isn't much harder than three. This looks about right but I hate perspective in 4D, it makes me feel like I need more eyes. (Which is probably why you think it's impossible to visualise)
KoenZyxYssel 7 months ago
This has been flagged as spam show
@KoenZyxYssel "Saying it's impossible to visualise is highly underestimating yoursel"
No it isn't. It's telling the truth.
If you think you can visualise 4D then whatever you are visualising is wrong.
BlueCosmology 7 months ago
So im looking at this one point then im like..."i thought you were...right here...".
BillyTheMilkMan 7 months ago
everything looks fine until 0:11
chamington 8 months ago
everything looks fine until 0:10
chamington 8 months ago
This has been flagged as spam show
Thumbs up if you got lost after 0:10
Wiintendoh 8 months ago
you need to make a video with all your crap you made in one shape(ish) type thing (: ... not saying all your work is crap i think its pretty coolio.
LIAMpants 9 months ago
i'm really high
thousandthys 10 months ago
@ZanoxTheSecond: Right, but a YouTube video is a two-dimensional image. (Regardless of how many eyes we have!) :-)
Milesco 10 months ago
Said WildStar: "it's hard to visualize because of the loss of information with the step down to 3D."
Indeed, it's even harder to visualize than that, because what we're actually seeing is a TWO-dimensional representation, so even more information is lost.
Milesco 1 year ago
wow! thanks for this! :D
jack390 1 year ago
this should be called the silly rainbow wire frame torus, just because its rotating doesnt mean its 4d lol
ChrisCDXX 1 year ago
@ChrisCDXX You're right - just because it's rotating doesn't make it 4D, and it's hard to visualize because of the loss of information with the step down to 3D. Well, actually, it's *impossible* to visualize - but I trust the math behind it. This is what the shadow of a 4D torus would look like. The rainbow colors are to help in the visualization: +x = red, +y = green, +z = blue, and +w axis = gray. :-)
WildStar2002 1 year ago 6
@WildStar2002 dude, you need to put that in the description. makes a lot more sense now that you said that, I bet a lot of ppl would benefit from an explanation.
ChrisCDXX 1 year ago
@ChrisCDXX Good idea - done! :-)
WildStar2002 1 year ago
Just because we can make a fancy illusion doesn't necessarily mean it's the fourth dimension.
MrNitt 1 year ago
@MrNitt True - but in this case, I had no idea what it would look like, I trusted the math. I created a program that revolved a sphere around an imaginary axis perpendicular to the volume in which it was created (like revolving a circle around an axis in it's plane). Then I used a perspective projection technique from an imaginary 4D viewpoint, and rotated the object along various random axes - and here it is! :-)
WildStar2002 1 year ago 7
*homer's voice*hmmmm fourth dimension
PABLOthunderforce5 1 year ago 10
@PABLOthunderforce5 hmmmm, forbidden 4-dimensional donut...
WildStar2002 1 year ago 7
Imagine a rollercoaster like that.
shredcity12345 1 year ago
@shredcity12345 Oooh, that would be cool! I wonder if I could model it so we could see that it would look like! :-)
WildStar2002 1 year ago
This absolutely ROCKS! Wow...I watched it 4 times...
Holy Crap, I want a screen saver made of this.
This should have music put to it, big time.
hardhitter0421 1 year ago
@hardhitter0421 Thank you! :-) This one is one of my personal favorites too.
WildStar2002 1 year ago
0:20 is a fat person eating a very skinny person.
SharkRetriver 1 year ago
@SharkRetriver Heheh - so it would seem! :-)
WildStar2002 1 year ago
Cant you rotate it in just one direction.
I mean when you rotate it in 4d, dont rotate it also in 3d.
I confused :))
cRaSHaCk 1 year ago
@cRaSHaCk i could rotate it in just one direction at a time. I think I did that for one of the hypersphere vids I put up here. Unfortunately, it's going to have to be a project for a future time. Lotsa schoolwork besetting me at the moment! ;-)
WildStar2002 1 year ago
iz dis a 4d dohnut?,
make a 4d homer to.
BHMatrix 2 years ago 2
Doh! It IS a 4D donut! Mmmmmm - forbidden donut...
WildStar2002 2 years ago
Any polychoron that have circles in them make my head explode
SharkRetriver 2 years ago
Well, I'm not sure you'd call this a polychoron. :-) Is a circle a polygon? Is a sphere a polyhedron? Functionally, it is a polychoron, I just didn't show all the interconnect edges, and I used enough of them to give the illusion of a curved shape. :-)
WildStar2002 2 years ago
wait! it looks like a torus!
SharkRetriver 2 years ago
It -should- look like a torus! :-) It's a sphere revolved through the 4th dimension around a central plane. Just like a traditional torus is a circle revolved around a line.
WildStar2002 2 years ago
a circle revolved around another circle is a torus, so a hypertorus is a sphere around a sphere?
SharkRetriver 2 years ago
Nearly so. This hypertorus is a circle revolved around a sphere (or a sphere revolved around a circle - which amounts to the same thing.)
WildStar2002 2 years ago
so a sphere around a sphere is a 5d torus!
SharkRetriver 2 years ago
At least one variation of one - yes. Consider. What is a torus revolved around a circle? What is a torus revolved around a torus? Higher dimensions start to get complicated and fun! :-)
WildStar2002 2 years ago
@SharkRetriver it more looks like a sphere around a circle but i don't know.
Meb8Rappa 2 months ago
@Meb8Rappa It's like connecting the ends of a spherical cylinder...there're multiple types of 4d tori, and i can't rly ask wildstar which type it is because he's not on anymore.
SharkRetriver 2 months ago
@SharkRetriver a 3-torus is defined as what you get when you try to fold the opposite sides of a cube together. So it is more like a 2-torus revolved around a circle.
Meb8Rappa 2 months ago
it looks cool lol
KingOfAceZ1 2 years ago
Thank you. ;-) This one is probably one of my favorites. :-)
WildStar2002 2 years ago
I thought the 24-cell was ur favourit
SharkRetriver 2 years ago
The 24-cell is my favorite 4D figure - but this is one of my favorite videos. :-)
WildStar2002 2 years ago
I knew people could easily project hypercubes, but I thought projecting a rounded object with a hole through the center would be physically impossible for a human being to do! Do you use a special tesseract forming program?
Flemburg 3 years ago
I used 3D Studio Max and a MaxScript program I wrote. Imagine creating a torus shape by projecting a circle through another circle at right angles to it. Instead of making it solid just show enough intersections to give the idea. That's exactly what I did, only it was a sphere instead of a circle. Then, to get a curved shape, I cheated... I made a whole bunch of little spheres representing discrete points, and then connectect them with very short cylinders. it looks round, but it isn't.
WildStar2002 3 years ago
Is that a faceted hypertorus then?
kristiaaaan 2 years ago
It is. The idea (like in most modeling programs) is that if you have enough facets it appears smooth.
WildStar2002 2 years ago