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- Опубліковано 14 кві 2009
- This is a "tour" starting from the zeroth dimension, and moving all the way up to the sixth, and then back down to zero. It starts out with a point, which turns into a line, then a square, a cube, a tesseract (4D cube), a pentaract (5D cube), and then a hexaract (6D cube). It adds more and more complex multidimensional rotations as it gets to higher dimensions, while retaining the rotations from the lower dimensions. Then, finally, the process is reversed and it gradually morphs back down to a single point again.
Each vertex is a different color, and the edges show a color gradient between their two endpoints. Hopefully, that helps ditinguish things a bit.
The rotations and movements are painfully slow for the first and last bit, but that was needed so that it didn't get too hard to follow by the time it got to six dimensions!
Let me ask you a question in the video 11 years ago.
I can't understand because I'm not a specialist, so please tell me.
If the number of dimensions differs by two or more (more than five), how can the projection prove to be the original dimension?
I'm not certain I understand your question. 😟 As the number of dimensions being represented gets larger and larger - the object appears more and more distorted. A *huge* amount of information is lost during perspective projection! 🙃
@@WildStar2002
Thank you for your polite reply!
I am not good at English, so I use my translation software to translate my native language into English and comment.
Therefore, I would like to inform you that the nuances may not be what I originally intended.
Also, I noticed a fundamental misunderstanding.
Projection is a two-dimensional projection of an object... Correct.
And, let's get to the point, it's understandable that a lot of information is lost by projection. Then, what is the difference between the characteristics of 3D or 4D projection and 5D or 6D object projected in 2D?
@@user-ue6lj5nx4e Okay, I think I get it now! 😄
First, a projection is not necessarily two-dimensional, although it often is. It is the mapping of coordinates from one type of space onto another - like a globe to a flat map.
So, what I am doing in this video is starting with a 6-dimensional object and projecting it into a 5-dimensional space by perspective projection. I know where the 6-dimensional points are in 6-dimensional space, and I use a formula to calculate where a line drawn from a point in 6D space to your 6D viewpoint would intersect a 5-dimensional space. This leaves me with 5D points representing the original 6D object. Then I do it again from 5D to 4D. Again from 4D to 3D. Finally, I let the software calculate what the 3D points look like in 2D.
That's it! 😉 The difference between projecting from 6D to 2D is the number of times I have to run it through the formulae!
@@WildStar2002
Thank you so much for your quick answer!
You are projecting one-dimensional step by step in this video and finally outputting it as a projection on a two-dimensional plane!
That said, you said in a comment that "a lot of information will be lost if you project it", but it's good to recognize that this two-dimensional projection cannot be completely restored to six-dimensional. Wonder?
(Added below)
I think again, this may have asked a very natural question...
The answer is obvious considering the case of the map of the earth that you gave as an example.
It's the same as asking "Is it possible to return the projection map of the earth to its original shape without specifying the original shape (a sphere with a slightly collapsed latitudinal diameter)?"
I also realized that when I first asked this video, I didn't understand what I was specifically concerned about.
@@user-ue6lj5nx4e It may be a natural question, but that just makes it interesting! It also does not mean that it has been asked before - it's so much fun to discover something on your own and then find out that someone did research on it before you and came to the same conclusions!
I find it very helpful to use analogy when thinking about higher dimensions - what would a 2D person think of my 3D world - and that helps me to imagine what a 4D world might be like!
Now, doing the reverse, imagine someone in a 1D universe trying to imagine what a 3D cube looks like. In his 1-dimensional universe, *everything* he sees is just a single point with all the insides hidden behind the edge closest to him. To him, a pentagon looks the same as a cube, or an icosahedron, or his grandma. That makes me thing that extrapolating what a higher-dimensional object really is from it's 2D (or 3D) projection will be very difficult - and *impossible* in some cases. A wire-frame cube when viewed from the corner looks like a hexagon, so which is it? That is also why I use movement (rotations) in this video to help make it less ambiguous. 😄
Im too high for this im going to watch teletubbies
LOL!
Excuse me but what the frick
XD Ok go watch teletubbies 😉
Enjoy @St Merkel Of Migrant
Lol xD
Can I come too
I'm pretty sure the only reason this is confusing is because a 6D still image is trying to be projected by a 3-D simulator shown in a 2-D screen. Picture this; you're Mario in a 2-D side-scroller. As mario, all you can see is a very thing line because you are restricted by dimension. Now say a 3-D person (that Mario can't see because the person is to you're right, which is out of your field of vision.) takes a sphere and slowly puts it through the plane. Imagine putting an apple on a piece of paper, except it goes through the paper. Yeah, that's whats happening. As Mario, you see a small line as the sphere enter, and that line gets bigger as the ball gets further in. Once the sphere gets at the halfway mark through the plane the line will start getting smaller until Mario can't see it at all. Moral of the story is that a 2-D creature can only see a slice of a 3-D thing same for us. When the 4-D part comes up. We only see a slice of it. And when the 5-D cube comes we only see a point. We see nothing for the 6th as far as I can tell.
Do you think that a being in the 4th dimension could see "a cube" from the 5D space, a plane from the 6D, a line from the 7D and a point of 8D? Or do you think it is somehow limited to three dimensions, so that he wouldn't see a 0D point?
Colin Maier Well, to be fair, I don't know for sure. We have no evidence of other dimensions, so we have nothing to worry about :p
All I know is you can't completely visualise an object within a higher dimension.
Giovanna Porto Very true, very true. In the end, none of us really know. It's sort of sad how there are so many questions we won't know the answer to, but at the same time it's nice to know that we're a smart enough species to ask these questions.
Giovanna Porto maybe it has to do with group theory representation symmetries...like SO(3), SO(4) in barycentric coordinate system ect :p or not
If I were a 6-dimensional person I would see that as a perfectly normal shape rotating.
I feel like an ameba staring at a square
I like the analogy - if you mean that an amoeba is REALLY flat and looking at a square from edge on! :-)
00:44
The point at which all minds were blown.
{sigh} Also the point where my shop vac got clogged. :-)
It wasn't easy to follow, was it?
0:49 "the chaotic cube"
Fun fact: the lines never touch each other and are always at 90° from each other
@@manuelramirezwork IF we were in a 6D universe.
Since this a projection, the lines have to ditch their 90° fun.
WHY DID YOU HAVE TO ADD THE OTHER ONES SO FAST?
I think it just appears faster because there are more dimensions being rotated through in the same amount of time as the video progresses.
Use playback speed if it’s too fast?
Strife Rixa 1:10
Вот именно, почему он добавил 5-е и 6-е измерение так быстро, не дав прочувствовать разницу между 4 , 5 и 6 измерениями....
I didn't even see the 4th dimension and it jumps to 5. And I don't know 5 yet.
I may not understand what is happening here, but I find it satisfying.
Thank you! :-) It's essentially like watching the shadow of something that's behind a screen you cannot see. Glad you liked it! :-)
now imagine 10d
I actually tried that - but with the equivalent of a 10-D pyramid. :-)
You can see it over here if you're interested: ua-cam.com/video/uuOPC55HDQE/v-deo.html
what is that thing XD
I know - the 10-D pyramid doesn't look like much, eh? That's why I did this instead. :-)
Tesseract but there is 10 cubes in it
Nice screensaver.
Thanks! I'm glad you like it! :-)
WildStar2002, that is a nice screen saver
I have seen other models of 6D but this is the first time I've really been able to wrap my consciousness around it.....thank you to whomever made this video, and thanks to Wildstar 2002 for posting it.
Baby do not deceive yourself like that
If i don't have enough leg room , i'll just have to move to the 6th dimension , it's either comfy or i fall off the world .
Very comfy - unless someone else on the plane has the same idea and you get your feet tangled in the fourth dimension! :-)
@@WildStar2002 oh no .
This is what my friends love life looks like
Sounds complicated - perhaps your friend should consider a 1D love life - just two points connected by a single bar. :-)
@@WildStar2002 Wow...that's beautifully poetic...
imagine how awesome it would be if you could see from the point of view from a 6D creature even for 1 second
I'm glad that your imagination has grown (handing you back your eyes). That's always a good thing isn't it?
This video was created in 3D Studio Max using MaxScript. I've been interested in geometry and the 4th dimension since around 8th or 9th grade. Never really taken any formal classed, just learned on my own as I followed my particular interests. :-)
Me at grade 12th thinking that knowing many programming languages makes me smart and then you entered.
cool
@@adheesh2secondsago630 when I was in 12th grade I didn't know a single programming language lol. I still don't, I only studied the basics of C. don't look down on yourself, you're ok
"Would you like to see my six dimensional dice?"
Very nice job representing all those dimensions in a 2d format. Mind blowing stuff. Hard to wrap ones head around the concept. Easy to see how a 4d (or higher) being would be preceived as godlike to us lowly 3d folks.
A nice, worthwhile video. I suggest adding an audio explanation as one is proceeding through the various dimensions.
Thank you! I have considered doing exactly that - and slowing it down or stopping it at key points. Ah, when will I have the time, though? Someday! :-)
it's comprehensible but the dimensions are switching too quickly.
I've considered slowing it down - especially in the middle part. I'll prolly get to it *some*day. :-)
@@WildStar2002 7 years later-
This was 1 of my favorite videos, Back in the Day.
Glad to see it, again! :)
This exact video? Thank you! :-) So glad you like it!
@@WildStar2002 Yeah! I remember it, specifically! :)
When it hit 0:45 shit got crazy
Yes. That is when I turned on the fan. >:-)
@@WildStar2002 lmao 😂 😂 😂
THINGS GOT VERY CONFUSING VERY QUICKLY
Yes, that's true. It confuses me too - to be honest. :-)
Welcome back guys its being recommended again after 4 years
Yeah, it's like a virus - keeps coming back... 🦠
I could watch this all day long!
Thank you! I am so glad that you like it!
You can't show something that is 6D in a 3D perspective. It just looks to us like a bunch of cubes going through each other. Its kinda like trying to look at something 3D in a 2D perspective. You just can't do it.
Very true. This is (at 6D) the shadow of the shadow of the shadow of the original. :-)
+WildStar2002 You have no idea what dimensions are...
+WildStar2002 you spent the time show people wrong informadtion about 6D
+Dave Roxby You are, of course, welcome to believe anything that you like.
Kind of. Then again, we render 3D shapes to a 2D screen all the time. It doesn't give a completely accurate perspective of the 3D object, but it is enough to understand it conceptually. Adding more dimensions just makes it more convoluted, but not wrong. Everything you see is what it would look like from a single POV. These shapes are accurately graphed.
My blanket when I'm trying to find the long side:
I remember seeing a video like this when I was a lad. My kid brain didn't understand it then, and my more matured, more developed brain still doesn't understand it. Nice to run into it again.
God bless.
To understand this 2D of sort of 3D projection of a 6D dimension you need lots of imagination. That imagination tells me that before the single point you started and after that 6D in which you ended, there are infinite more dimensions. Good animation Wildstar, Thanks a megaton.
Thank you! :-) You're quite right. *So* much information is lost when stepping down the dimensions that it starts to just look like a meaningless mass of lines and color pretty quick. I'm thinking about figuring out some different projection techniques (stereographic and sectioning) and then displaying the same object in three or four different ways at the same time. Maybe that will help to visualize it better! :-)
That's a great idea. You'd decode the images and separate them, then you can start joining them together till the whole complex structure keeps in people's minds, so they can imagine the inner structures while seeing the whole together, but after it's been put back. Cheers!
We'll see what I can come up with. It *might* make things even *more* incomprehensible! ;)
I'm really glad you enjoyed it! :-)
Glad you liked it! :-)
You could pause it and count how many lines converge at a corner two - if there are 4 lines there, it's 4-dimensional. You can see the edges sort of double up as it's transitioning to the next higher dimensions. :-)
Stunning Tour 6D
Thank you! I'm glad you liked it! :-)
Gotta admit I like the part where there's only the line. It's so simple and yet it's the stepping stone for something so awesome as the 6D.
All above the third dimension are mere shadows of the other dimensions as we cannot actually see them, but we can see a fourth dimensional shadow on a 3 dimensional ground. Like seeing a 3 dimensional cube shadow on the ground, it would appear to be in 2 dimension.
well, technically this video never goes above the 2nd dimension, since it's on your computer screen.
Emily Shonk They are definitely cool, however they are 2 and 3 dimensions respectively.
Emily Shonk For checking out the Mandelbrot Set I recommend Xaos, for the Mandelbulb I recommend Mandelbulber.
That's one hell of a rollercoaster :O
Beautiful video
long story short...we can't perceive higher dimension than we are living in ...this case 3D
True. So, I make a 3D projection of a 4D projection of a 5D projection of a 6D object. :-)
WildStar2002 that is awesome BTW
Thank you! :D
technically we can't perceive three dimensions; only two.
That's true, technically, but we visualize and think in three dimensions and we're so used to the interpretation from the two flat images we get (plus other tricks) that it's nearly 3D perception. :-)
Very true. :-) It's hard to imagine (impossible in my view, really) what the original object must look like from just the projection of it's 3D shadow. A cube, for example, can cast a hexagonal shadow if it is oriented properly. If you didn't know what a cube was, how could you reconstruct it from a hexagonal shadow?
Absolutely mindblowing.
Thank you! :-)
really very mind blowing !!!
This is like an animated depiction of my hypothesis! For every dimension, just draw two of the previous dimension's cubes and connect all the vertices!
So relieved when it changed back to a cube!
+Slick Persian Hehheh - I know, right? Thanks for watching and commenting! :-)
yea np... I actually just saw Interstellar, that's why i was watching this lol
I can't comprehend this man!! I'm freaking out!!
Oooh, I *love* M.C.Escher! My favorite artist! :-)
Большое спасибо!
it would help if you labeled which demension it was on the screen at what time
There were only 3 depicted on there. What you saw are projections of higher-dimensional objects onto pseudo- 3 dimensions (pseudo becausethey are actually 2 dimensions but we're used to visualizing 3d as 2d.)
Summer Thurlow If it helps it's 0D right at the beginning and immediately starts to lengthen into 1D. 2D starts at 0:10, 3D at 0:20, 4D at 0:30, 5D at 0:40, and 6D at 0:50. I've thought about annotating it, but I've never got around to it. Those are the representations anyway, crazygoat85 is right to say that it's pseudo 3D and that we can't really see the higher dimensional objects. :)
looks like a fun ride
This is beautiful
Thank you, I am delighted that you like it! 🥰
Could you create another video where you display on-screen an axial indicator for each dimension's rotation? Or a numerical indicator for each? It would help tremendously
Yes, I have thought of this. It is *definitely* something that I would like to do, just needa get the time! 😋 Thanks for the suggestion! 😄
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Everyone will say: wow this is amazing!!!
But no one will wonder how it works
It's okay if people don't understand how it works - I just hope they like it. :-) I am happy to explain it to anyone who is interested!
I understand it, and it is beautiful
Guys, hey guys. Now watch this again while listenning to Only Time by Enya. It feels like a unicorn is licking your brain.
I tried it and I had to visit a rape center after.
Thanks Enya, the shame of that unicorn's horn will never wash away.
Good call. I found myself getting sad at the end when the dimensions reduced back down to 1, then gone.
So… who here has read Flatland?
Oooh! Me! Me!
no
Me
No
On
I can't stop watching this video
Oooh, thank you! :-D
Mind blown, eyes popped, and imagination grown
Heh day rhyme tho
Don't you realize it still a 3D object?
just more complicated plus motion
4:th d=time
time=motion........
so a single 1D point on a paper moving around is 4D? it has motion, time and direction also.
Israel Alvarez If it moves around on the papers that is in 2d. Then the 3:rd D is the time axel.....
It changes when you have diffrent bases of dimention^^
ps:sorry for bad English^^
yea it's true
The original object starts at zero dimensions and goes up to six before returning to zero. Once it gets past three dimensions, though, you can't see the extra dimensions. That makes it look like there is motion - like it is changing shape - but really it's just rotating. :-)
I can see everything!!!!!!!
+Ronan Abahalovoocheskov Sounds like the start of a great pop song! ;D Glad you liked the video!
Watching and understanding 3D on a 2D screen is hard enough sometimes, but beginning at 4D on a 2D screen, it's a complete mindfuck
The sad truth is that we cannot even comprehend truly higher dimensions. Except mathematically
It is a sad truth. I wish I could actually *really* see 4D and higher objects - but I still like watching the shadows of higher dimensional objects. :-)
HELP, My brother says the 4d-6d is moving into it self, and for me, it looks perfectly fine, HELP
You are correct. The object is perfectly rigid and is rotating in 4D-6D space. It *looks* like it's moving into itself because we cannot see the 4th, the 5th, or the 6th dimensions. If you look at the shadow of a clear cube made from 12 sticks (one for each edge, three joined at each corner), the shadow would *appear* to be crossing into itself - but that is because a shadow is essentially 2D. This is exactly the same reason why 4D-6D look the way they do in this video. :-)
@@WildStar2002 but it doesn't look like that for me? it's rotating perfectly, but my brother says, its moving into its self. so uh, thats wierd
@@Haze_Nexus_real you must be from the 4th dimension lol
@@JordanLitNZ ohhhhhhhh that makes sense..
i couldnt tell where the 4th ended and the 5th began lol
It's really hard to see - so I timed it precisely when I created the video. At 0:20 it starts to expand into the 3rd dimension. It begins to expand into 4 dimensions at 0:30, into 5 dimensions at 0:40, and the 6th dimension is introduced at 0:50. If you watch the corners and edges very carefully, they appear to double when it has expanded into a new dimension. :-)
Wow THIS makes everything clear to me
Good! I'm so glad that you liked it! 😁
you sir, made my day
I know I can't touch it, so why did I feel like I could.
At about 4d shapes stop making sense.
Wait, let me get this right... We are watching a 2d video of a 2d program displaying the 2d representation of the 3d shadow of a 4d shadow of a 5d shadow of a 6d object...?
Exactly. :)
And the computer is doing this in a 3d reality by theoretically creating this 6d entity. ;)
There are no 4D or 5D shadows present or needed, it's just a 3D shadow of a 6D object rotating in 9D space with light projected from that 9D space into 3D space and all displayed on 2D image displayed in 3D space.
Damn, just what i've been looking for
Don't mind me, I'm just on a watch-all-the-UA-cam-videos-you-incessantly-watched-as-a-kid marathon.
Really? 🤔 You watched videos like this as a kid!? 😲
Yeah, pretty much anything to do with higher dimensions, infinity, that sort of stuff. Not that I understood any of it. (In fact, I still don't.) But I find it interesting.
@@lightningfirst689 me too! Glad you like it as well!
I have no Idea what I just saw
It's a geometric progression of square and cubic shapes from 0, to 1, to 2, all the way up to 6 dimensions and back. :-) I hope you liked it - even if it's an esoteric geometrical concept! :-)
WildStar2002 thanks. I DID like the video
Am I the only one who got a headache while looking at this?
Not at all - I got a headache while *making* it! 😝😄
@@WildStar2002 oofles!
Thanks for the great screen saver!
Great Soundtrack!
1 dimensional
2 dimensional
3 dimensional
4 dimensional
5 dime- WHOAH THIS MAKES NO SENSE
I'm glad you at least made it past four before you got confused! I find this video to be visually confusing also - but I trust the math that generated it. :-)
なるほど
４次元５次元６次元は認識できないな・・・
+takayuki nitta I'm not sure that I understand your comment, so I'll answer to what I *think* you mean. :-)
This is just math - we can't *see* anything beyond the third dimension - since we're 3-dimensional beings. However, there are no such limits to math. We can extend the patterns we see in lower dimensions to higher ones - mathematically. That's what I've done here. :-)
+WildStar2002
数学は面白い
６次元を２次元の動画で見れるのも面白い
素晴らしい動画をありがとう
Thank you for a splendid animation！
+takayuki nitta Thank you! :-)
this is awsome!
Absolute satisfication
The problem with the video that there is no way to visualize higher dimension objects in 3d. The higher dimension objects not egzactly looks like those. To visuslize a 5d object you really need 5d. So the video is pointless.
While I agree with your first point, obviously I disagree with your second point. It's true that the step down into a lower dimension loses a LOT of information, yet we represent 3D objects in 2D all the time. Pointless? Perhaps not ideal, but still useful! And, of course, I'm not trying to show these objects as they truly are - I know that's not possible. I find the representations to be strange and wonderful - like a postcard from a place I can never visit. It's not the same as going there - but it's still fun to look! :-)
May I don't used the word "pointless" correctly because english is not my native language.
Oh, it's all okay! I wasn't offended or anything! :-) Thanks for watching and for commenting! :-)
Otherwise it was interesting so I have to say thanks for the uploading.
You're welcome - thanks again for stopping by! :-)
U lost me at 3.
Me too! That's why I have to trust the math. :-)
It's very confusing, I know. I'm considering redoing it and slowing down the middle sections. It changes dimensions every 10 seconds, approximately. It starts from at 0 and immediately starts into the 1st dimension - then starts the 2nd at around 0:10, 3rd at about 0:20, 4th at about 0:30, 5th at around 0:40 and sixth at 0:50. It's fully into the next dimension after about 5 seconds of "growing" into it, so it's fully 5D at around 0:35 (for example).
As timey-wimey goes on, the thing becomes more and more wibbly-wobbly.
You sir, are doing it right.
I could be wrong, but it seems to me I remember reading somewhere that the human brain maps objects fully in three dimensions - although you are quite correct that we infer depth from the differences detected in the two 2D scenes our eyes provide, I think it's actually reconstructed and filled in as 3D inside our brains. :-)
my mind just got blown out of this world
I didn't understand 5d & 6d at all but I understand the 4d very much better than any other video in UA-cam.
I've been some scary roller coaster in my life time without getting sick, This however, almost made me chunder all over my screen.
Good explanation. Also, a BTTF fan Just rewatched the series this weekend with my son.
This is a video that describes 6D shapes and why 5D shapes will never be seen in a 4D space. I am watching this video in a 3D world, on a 2D screen with my 1D brain and 0D life.
I wouldn't say 0D life - not if you're watching stuff like this! :-)
i guess that a simpler way to understand this is noticing how layers just get added
Yes - the object gets doubled with all the interconnections made at each new dimension! 😄
Thank you. I've thought about rendering it a again in some kind of a stereoscopic format, but which one? I want to preserve color the color, so I don't want to use the red/blue or red/green techniques (besides people would have to get the glasses). Doing images side-by-side do I do the cross-eye version or the parallel version? I dunno, may still do it at some point, but at least it's accessible this way. ;-)
That is so true! Thanks for your comment! :-)
Basically, the collapse of all possible futures and their flows in time. The way something can be smaller or bigger in many different directions. This is basically the observation of the past and future in one as well as other possible pasts and futures alligned into a condensed concept.
Cool! Respect!
Awesome video.
Thank you! :-)
thanks for f*cking up my mind this day
How serene.
Cool, thanks for breaking my brain.
Technically correct, although the coloring, shadows, and movement give enough information for us to correctly reconstruct the 3D shape in our minds.
looks like the best tivoli ride ever..
Its a magneto flex witch is traveling in a dimensional axis so its rotating in a 2d axis but visualized in a 3d shape and so the 1d dimension axis is impossible to see. But if its flipped and moves by rotating you'll be able to sense the 1d dimension.
if you old an 6d cuba and if its rotating, do you see youre hands inside and outside of the cube?