Tour 6D 

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. 😄

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.

LOL!

Excuse me but what the frick

XD Ok go watch teletubbies 😉

Enjoy @St Merkel Of Migrant Lol xD

Can I come too

{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.

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 like the analogy - if you mean that an amoeba is REALLY flat and looking at a square from edge on! :-)

Thank you! :-) It's essentially like watching the shadow of something that's behind a screen you cannot see. Glad you liked it! :-)

Baby do not deceive yourself like that

I actually tried that - but with the equivalent of a 10-D pyramid. :-) You can see it over here if you're interested: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-uuOPC55HDQE.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

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

Thanks! I'm glad you like it! :-)

WildStar2002, that is a nice screen saver

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! :-)

I've considered slowing it down - especially in the middle part. I'll prolly get to it *some*day. :-)

@@WildStar2002 7 years later-

This exact video? Thank you! :-) So glad you like it!

@@WildStar2002 Yeah! I remember it, specifically! :)

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 .

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...

Yes, that's true. It confuses me too - to be honest. :-)

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.

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.

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! ;)

Thank you! I am so glad that you like it!

Yeah, it's like a virus - keeps coming back... 🦠

+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

Oooh, thank you! :-D

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. :)

Yes. That is when I turned on the fan. >:-)

@@WildStar2002 lmao 😂 😂 😂

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. :-)

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! 😄

+Connor McDevitt That's what you get for turning the auto updates off! >:-)

Send report

Thank you! :-)

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 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.

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. :-)

Yes - the object gets doubled with all the interconnections made at each new dimension! 😄

Oooh! Me! Me!

no

Me

No

On

+Ronan Abahalovoocheskov Sounds like the start of a great pop song! ;D Glad you liked the video!

Thank you! I'm glad you liked it! :-)

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..

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. :-)

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.

Good! I'm so glad that you liked it! 😁

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! :-)

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

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. :-)

Not at all - I got a headache while *making* it! 😝😄

@@WildStar2002 oofles!

Me too! That's why I have to trust the math. :-)

+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! :-)

That's a very interesting analogy! :-) I just follow that math and see what results. :)

This comment is probably the closest thing that made me actually "visualize" the 4th dimension 'in my imagination'. I still can't fully wrap my head around of what or how would the 4D beings see while being there. I mean, I absolutely understand all the logic behind all the explanations around RU-vid, and not only (I have spent quite a good amount of time on this topic), but the difference between "understanding it" and actually "imagining it" is indescribable when it comes to this thing. I don't think there's a similar feeling to what "we" can perceive, when it comes to visualize a superior dimension, not even imagining the size of the universe itself. I guess that's what the stickman on the paper feels when it sees a line grow and shrink suddenly haha.

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 wouldn't say 0D life - not if you're watching stuff like this! :-)

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. :-)

That's one way to think of it! 😄 I'm talking purely about *spatial* dimensions here - so I've left time out of it. The 4th dimension introduces two new directions, so our creatures can now move in 'ana' and 'kata' as well as up/down, left/right, and forward/back. There are two more directions added in the 5th and another two in the 6th - for 12 total! 🤔 It would be *really* hard to get in someone's way in the sixth dimension!

Yes, that's true! There are five unique Platonic shapes in 3 dimensions, and *six* in 4D, but only three in every other dimension, 5 and up. 😄

Ahh, but you must first catch me as I slip wraith-like through higher dimensions to avoid prosecution! :-)

Yes, that is exactly right! 😄 Just like a 3D cube (from face-on angles) looks like a square connected to a smaller square inside. 🤔 Thanks for commenting!

To understand this, all you need to do is imagine projecting the four corners of a square onto a single line from one of the square's edges in 2D, then rotating it flat so only 2 corners can be projected, then rotating it one more time so that all you see is a single point on the line. Those 3 more rotations of an object take 3 dimensions, hence the need for 9D.

Very interesting! I had never considered that at all! :-) Three of the projection planes would have to be orthogonal, though, instead of perspective projections - isn't that right?

@@WildStar2002 Yes that's correct, I guess otherwise it would always show the 6D cube :P

@@WildStar2002 Although you could maybe have a warped shape or warp the thickness of the lines, so that the shape's side is bigger that's closer to the light source or have the lines closer to the shadow thicker so that in the shadow they mask the lines that are projected smaller, but that probably wouldn't end up working with all the rotations shown in the video. It's fun to both try to picture the geometry though as well as discover the geometrical analogies.

Heh day rhyme tho

Maybe next time don't take so long that your screen-saver starts up? 😄 {j/k} If this vid came up on an auto-play while you stepped out, I'll bet it was *quite* a surprise when you got back! 🤯

Steve Yorkman what about -1D

Except to mathematicians! :-)