The Wonderful World of Mathematics The Fourth Dimension Constructing the Hypercube
ฝัง
- เผยแพร่เมื่อ 12 ม.ค. 2015
- The hypercube can be constructed by joining six cubes to the starting cube and performing a four dimensional rotation of 90 degrees along the common faces
Four dimensional rotation takes the cubes into the fourth dimension which are projected back into the original three dimensional space
Eight cubes (cells) of the hypercube: the original cube in the middle, six cubes distorted by the projection connected to each of the faces and the newly created larger outer cube.
![Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 2]](http://i.ytimg.com/vi/4URVJ3D8e8k/mqdefault.jpg)
![Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 2]](/img/tr.png)
![[Full Episode] MasterChef Junior Thailand มาสเตอร์เชฟ จูเนียร์ ประเทศไทย Season 3 Episode 4](http://i.ytimg.com/vi/e7Oqqo90x_w/mqdefault.jpg)
![A Journey into the 4th Dimension - Perspective [Part 1]](/img/n.gif)
I will never be able to listen to Metallica's song again without thinking of this hyper-cube video.
SAME
The ingenuity of memetics, never forget the great gift of the mind.
As someone who's been looking into 4D visualizations for a while, this is one of the best videos on TH-cam, because it shows clear, intuitive representations and duplicates them all for 4D rather than using shortcuts like many others.
I especially like the double rotation at the end, which is different from anything else I've seen, and really shows the rotations happening.
Same here
the best hypercube's video in youtube
Except for the fact that the video is WRONG (most of the time). The Cube unfolding shows only 5 squares when a cube has six squares, the Tesseract unfolding shows only 7 cubes when in fact the 4d-hypercube has 8 cubes. Only after 4:12 is the video correct, when the unfolding correctly shows the 8th cube. It is indeed a nice effort but must be corrected.
The first demonstration I have been able to understand in a logical way. No longer confused about the concept. Absolutely awesome!!!!!
Same 👌
Yep I used to wonder how this was even 4 dimensional at all. An ordinary picture of it just looks like a cube surrounded by trapezoidal prisms but in motion makes so much more sense. It's all really mind boggling how anyone can figure these types of things out and conceptualize them!
I read once something like: "As from a 3d perspective, you can see a square in it's entirety, from 4d perspective a cube would be visible from *all* sides."
I don't know if I understood correctly or not. But, what I think I understood was that, we're 3D conscious beings but we cannot really *"see"* or be aware of 3d. We see projections of 3d objects in our 2d retinas, and our brains processes it along with our sense of touch, and complex light and shadow information, to interpret the 3d object. We can't see behind a 3d object. We only really see what's in front of us.
But, with 4d awareness we would be able to see *all sides* of a 3d object without any distortion, there would be no "behind" because we're in a higher dimension. 4d awareness would give us true 3d vision. We would see an object from all sides at the same time, but more importantly be aware of the totality of the object, just like we see a square. There would be no above or beneath, anterior or posterior, no inside or outside.
That always, and I repeat I don't know how right or accurate it is or was, just blew my mind.
From a 4-d perspective, you could see every aspect of a 3-d object, every part of something, from the inside to the outside.
If you take a 3-d box, the 4-d being would be able to see inside it no problem.
I understood this demonstration of a rotating hypercube better than anything else I'd seen before. I feel like I can actually conceptualize it now.
Now I understand why many people consider HyperCube to be part of sacred geometry
Unfolded it is a cross
You know what that means
2.38 - the cube says 'never opened myself this way'.. while transforming into hypercube :D
2:38
This video was such a massive help in my struggle to conceptualize 4D space. I found that playing the video at 25% speed really helped a lot too.
I’ve watched so many videos and THIS ONE is the absolute best I’ve come to theoretically understanding the 4th dimension. So much makes sense now, thank you!!!
Thank you so much for this, its beautiful. Music fits perfectly and the explanation is the most clear I've found on TH-cam.
The best demonstration of hypercube in the youtube. (A melhor demonstração do hipercubo no youtube. Parabéns.
The deeply intuitive way this video was made is unique! Thanks a lot!
For the first time I'm able to wrap my mind around it (almost), thank you!!
I loved the moment the faces phased through eachother as they were folding through eachother.
3:47 'Rotating the six intermediate cubes another 90 degrees (360 degrees in total) returns to the starting cube' Which would then rotate again to become the Tesseract (720 degrees)
Electrons 1/2 Quantum spin (Angular momentum) is 720 degrees, to get back to its original shape
I am convinced that Quantum Objects are actually 4D Shapes
amazing! thank YOU for sharing ❤🙏 🙇
Beautifully done !
AWESOME DEMONSTRATION
hypercube is very complicated for 3rd dimension being
edit: wow thanks i never get this so much like before
Ha im a 4d being
@@PlzDoNotTheFade.
Ok
@@therevenge192 interesting
I’m actually 5d now
Perhaps the best visual non-verbal explanation of how a hypercube is formed. The subtitle notes are spot on. Enjoyed acappella version of Metallica's song.
Love your 4D videos!
Beautiful demonstration, thanks!
Really good video on hypercubes. I'm going to show this to my year 8s tomorrow as they were asking about 4D objects. I'll let you know how it goes. Would love to watch a similar video to this on 4D spheres.
A 4D sphere... is...
has an area of pi(r to the power of 4)
Good illustration. Superb Music!
Amazing Video ... Great music... very clear presentation ! (Wonder if metallica while writing the original song ever thought that their song would fit so well to a Tesseract )
i love this song and presentation, fantastic work.
It is mind blowing!
Beautiful explained
Wonderfull!!
This was absolute amazing
Very, very beautiful. It'll need a few more watchings before I really can feel what's going on. But the logic is clear! Many thanks.
THIS IS WHAT IVE BEEN SEARCHING FOR
Really.........mind blowing !!!!
Great Music & Voice
BTW - Scala & Kolacny Brothers - Nothing Else Matters
Thank you so much.
That is the best vídeo to undestand. And I have seen a lot of them!
This is incredible but the entire concept terrifies the hell outta me
That was beautiful
ahhh excellent video and awesome song!!!!!! I mean 10/10
That was about the freakiest song I've ever heard.
On a video, we have to try to understand the 4th spatial dimension with 2 dimensions.
I think it could be great to create a three-dimensional experience to represent the 4 dimensions of the hypercube.
I don't know if it's possible with, laser, for exemple. You create a modeling of the hypercube with laser, and each cube of the hypercube has a different color.
We would still see it as 2D
@@Ken-no5ip true, we would need three dimensional vision
Try VR. Technically it's still 2D but your brain almost processes it as 3D.
@@andrewramlall3560 We don't have three dimensional vision? Can you explain the difference between the two? Pretty curious.
@@Killertiller01 our eyes are three dimensional spheres, but their surface is 2 dimensional. Therefore, it follows graphical perspective, like how a picture or mirror looks like it has depth, when it really is only an illusion. So, with a dimension shifted up we would need to see both the surface and inside of everything, as if it were a glass sculpture, instead of just the surface with "2d vision"
Before I knew hypercube can fold, I thought it's just two cubes connected for some reason, now I know it all just a distorted 8 cubes that make up a hypercube, just like a square that make up cubes
Thank you.
Wtf, the animation was so good my brain misinterpreted the deformation as an actual rotation transformation. It feels wrong, but somehow a lot more realistic now
At 4:20 you can see that the hypercube is made up of 8 cubes, not of 6. Therefore the depiction that shows only 6 cubes cannot be accurate (for all 8 cubes simultaniously).
yes, I agree! , also I see what you did there ❤
Thank you
The music makes me feel sad that my puny mind can’t grasp the 4d spacetime.
3:52 is amazing
Gods Evolutionary systematic process in geometric design.
There is a cell missing. The eighth cell which is not warped but enlarged in the 3d projection was implied but not included in the object so it does not appear when the object is rotated. This is most apparent at 180 degree rotation
yes, for the initial part that is true. But you can actually see it at the very end, when its compared to the Salvador Dalí's painting and as the hypercube collapses again ❤
Woow excelente es el mejor explicado que he visto😨😨no estoy segura pero creo q entendi😅😅😅
What would a projection of a 4D mirror look like?
What is the cover for that song? It's so beautiful tbh.
Like the background music
What software did you use to create this animation? POV-Ray?
Yes, POV-Ray and Wolfram Mathematica
The square hammer, look at how a 4th dimensional object moves.. and if you can wrap you mind around it. You may begin to understand what I'm doing here and the mechanisms I'm using.
I subscribed before liking, which is a first.
When rotating each face of a cube by 90°, why does the size of the face change ?
Actually the Tesseract doesn't do a inside-out movement but it's ju rotating as a normal Cube:
In fact, it isn't two cubes connected inside but actually two cubes connected through the Fourth Dimensional Axis that we can't and won't never be able to discover
a lot better than Carl Sagan's video
Unfathomable
The side of a square is a line. The side of a cube is a square. The side of a tesseract is a cube.
Or all common sides are basically hinged and can rotate or form other shapes.......
4D hurts my thoughts. Imagine a 4D TV or Rubiks Cube? 🤯
4:13 trippy...
now we need a hypersphere
wonder what a 2 dimentional shape looks like to a 4 dimentional being
what happens if a forth dimension creature show up in front of us ? and in what shape we see him?
We see a 3d projection of him. Looks like it happens already, sometimes.
yes pls explain it in COMIC SANS
I don't know but is this related?
A Line has 2 point on its edge
A Square has 4 line on its edge
A Cube has 6 square on its edge
.
.
And
A Tesseract has 8 Cube on its edge?
A room where all walls are mirrors including food and ceiling
Ok, so now we need a *penteract.*
That's a 5D *tesseract*.
That's a 4D cube.
what song is playing in the background? I know it is nothing else matters but who covers it? also I know it is NOT Darude
here ya go watch?v=kTvN4pExX7g
BTW - Scala & Kolacny Brothers - Nothing Else Matters
Benny Benassi - Satisfaction
River forever
4:35 Tried the best i could to focus on the red cube as it starts to spin, but i always loose it. I can't comprehend this. My brain won't let me.
The brain is capable of comprehending, but it takes a long time and a lot of practice. However, once you are able to perceive 4D forms as they truly are, you will be able to comprehend hyperdimensional forms not as mere shadows or awkwardly amorphous projections, but as rigidly rotating objects just the same as you do for 3D shapes. There really are no words to express the immense joy and bliss that comes with this ability. It's like learning how to ride a bike for the first time again, that feeling when the training wheels come off and the bike becomes an extension of your body.
@@williamwesner4268 It is impossible for us to imagine something in the 4th dimension. As much as it's impossible for a being of 2nd dimension to understand ours.
It took me a while to understand why I can't understand.
When we draw a cube on paper it's still 2d because the draw has no "thickness".
It's worth to watch 4th dimension video. The hypercube is not as well explained than here but the other stuff is f***** up.
All cubes are the same size. Its the projection that distorts the shape.
Wow. That can only happen in a non physical realm! Where is that dimension extending out to?!?! I’m going to call it the dimension of focus.
Wow. Think about it, for my people that believe in God if the Holy Bible and Jesus. They are in a higher dimension. They're dimension goes in and out of ours . Looks like many but all is ONE. The Father Son and Holy Spirit. It's funny we all bump head science guys and spiritualist, but everything we present to each other doesn't at all debunk the other but SUPPORT each other. Wow wow wow. This is amazing. I love yall for we are all the same you are me and I am you.
Q cancion sera esa? 😮😮😮
DeltaWrong!!! the video is WRONG (most of the time). The Cube unfolding shows only 5 squares when a cube has six squares, the Tesseract unfolding shows only 7 cubes when in fact the 4d-hypercube has 8 cubes. Only after 4:12 is the video correct, when the unfolding correctly shows the 8th cube. It is indeed a nice effort but must be corrected.
I agree. been strugling to understand the EIGHT cube missing here. this other video helped me a lot th-cam.com/video/BVo2igbFSPE/w-d-xo.html
Does a cube have 6 sides?
?
A cube has 6 faces, 12 edges and 8 vertices.
Ohhhhhhhhhhhhhhhhhhhh METALLICAAAAAAA!!!!!!!!!!!!!!!!!!!!!!!!!!
It appears to me that the 4 th dimension is basically like being in a house of mirrors.......
Oh
Metallica - Nothing Else Matters (Song in the background, only a different version)
there are secrets in the shadows 🤫
Think like a Chinese finger puzzle
My head hurts
¿Y luego?
Bro what is this cover
only 286 views, damn shame
I find it odd that there's so much speculation and attempt to explain a fourth spacial dimension when we don't even know if such a thing exists. Are we trying to understand a concept for no reason? Is there any actual point? I probably just don't understand the subject well enough to know the answers to these questions. It just seems strange.
If I were to take a guess I would say the idea of higher dimensions probably has the greatest effect on astrophysics and the study of the universe. One such reason to look into these higher dimensions and whether or not they exist is that their existence is needed in some of our biggest theories. One example is String Theory, which unifies Einstein's General Relativity and Quantum Mechanics. The issue is that for gravity to work in String Theory there needs to be 11 dimensions minimum (IIRC). Please take what I am saying here with a grain of salt as my knowledge is really surface level at best. But yeah understanding these dimensions can help lead to testing our theories of them, which in turn can point towards their existence, which would literally change our view on reality.
We don’t know? No sir you don’t know we do
man, the teseract is make whith a 8 cubes?
I know 8 cubes clearly, but the away it is constructed in the animation 1 cube + 6 connected cubes to each face with the eighth cube at the end
> How is it that this has been around for 5 years & I'm only aware of it now?
★★★★ --> 🎶 🎶 🎶 🎶
You would have to show it .369
At least this video makes some sense for me even though I still cannot understand what explicitly is that fouth dimension( how can a line be penpendicular to a three dimentionnal space and phrase differently this line is perpendicular to any single line in this space).
wisbetwilsion A 2d creature would say the same about a cube ;-)
Jim Mcbobason you mean a flatlander 😏
for make a cube, 6 squares, for make a hypercube, 8 cubes
For line: 2 points
For square: 4 lines
For cube: 6 squares
For hypercube: 8 cubes
See the pattern?
For a 5D cube... 10 hypercubes?
Naaaaaah thanks to this video I could understand
Who was that covering metallicas nothing else matters?
👍🏻💐🤜🏼🤛🏽🐱🕺☀️🌈
Um, a cube has six sides, not four
faces*
@@TerryPlays thx
You can look at it the way you want but it’s still 3d. You can’t show a 4th dimensional thing in a 3d world. The concept of a 4d cube is just a cube in a cube
na it is a 3d shadow of a 4d cube. the cube inside isnt actually inside. it is behind in the fourth dimensional direction.