"The Hypercube: Projections and Slicing" 1978 Award-winning computer animation
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- Опубликовано: 26 окт 2024
- "The Hypercube: Projections and Slicing" 1978 Award-winning computer animation.
Fantastic tutorial of how to visualize hypercubes.
I cleaned up the audio. Original was BETAMAX. Copied from web.
"The Hypercube: Projections and Slicing"
by Thomas Banchoff and Charles Strauss, Brown University, was awarded the Prix de la Recherche Fondamentale at the International Congress of Scientific Films in Brussels in 1978, the year it was produced. It was featured in a plenary lecture at the International Congress of Mathematicians in Helsinki in that same year.
this is mind blowing.
Sadly more then 40 years laters it is still the best visual representation.
It really is. I've looked around for improvements to it - or at least someone who imitated it - and found nothing. That's why I cleaned this one up best I could but hopefully someone can do better.
@@KENNETHUDUT i think it is due to the limitation of the 2d screen and our eye.
First we should be able to see every particle of a 3d object. We can not even see the surface of the thing properly. We can not read deepth from the screen. If someone ever did 3d moddeling they know tracking a hole inside of your mesh is a huge pain.
So first we should fix that to get what is going on in 4d.
I think VR could help us. The gear can track your eyes movement and where you are focusing at. So if you are focusing into a cube the rest of the part could be transparent.
And if you can not see trough something you know it is a 4d object and you can not see further than the cells.
My biggest problem was about understanding 4d is I couldn't tell from the lines what you couldn't see. You see lines you couldn't see from scanning a 4d object without x-ray vision.
So I had to draw it, I did animations and I did 3d models, I can understand now. But it is messy. If I wasn't the one who created it, I couldn't follow it. And I only understand the tesseract wich is the simplest platonic solid in 4d.
Why sadly? I thought you meant happily.
Thanks I am the Robot of this... it's not so high Super For Babys... Auaaua. Amen I Love Y'ous, Amen Y'ous Jesus Christus, Wiktor Witas Kuhn... in Lak'ech Amen
4D Minecraft is a pretty cool recent representation
ruclips.net/video/u8LMyWcKL_c/видео.html
I wonder: would 2-dimensional people call a cube a "hypersquare"?
greetings from 2-dimensional world, it's actually called a 3-dimensional hypercube
@@yuchencai7554 You are 2-dimensional? Wow! I'm please to meet you.
@@yuchencai7554 Greetings, Flatlander! Are you too a disciple of the higher orders?
@@yuchencai7554 Just like we call it a hypercube a 4-dimensional tesseract?
Totally makes sense.
Thanks All
room sized computer nearly died displaying this
Nonsense. This was produced on a single DEC PDP-11, a rack-sized 16-bit minicomputer.
I'm sure of the specifics of this animation. Though it wasn't common for computers to display these kinds of things in real time in that era. With Flight of the Navigator for instance the computer they used literately ran at one 1 frame a week and printed the CGI elements directly to 35mm film then they had to manually register the negatives the film crew made and the negative the computer made to make the final product. Captain Disillusioned did a good video explaining it.
This is cool, especially for 1978. Most tesseract videos / animations only show the stereographic projections, but the cross section visualization actually shows concretely what a 4D cube would look like if it intersected with 3D Space at various angles.
I got my brain to understand it not as it folding in on itself and as actually rotating, that's w e I r d d
This is _the video_ that did that for me too - no idea what it was doing inside of my brain when it succeeded but it's like it was moving neuron clusters around that weren't used to moving together or something
@@KENNETHUDUT yeah, it really was something weird
If you follow the edges it breaks my adhd brain enough to see it r o t a t e
I was sick as hell and so my brain kinda screwed so I guess it kinda just *went*
You know what’s mind blowing? The 3D cube rotates in different directions depending on how your brain wants it to rotate, just like the black ballerina turning left or right, I hope it’s not just me
Ye it happens when u look at its 2d projection
i thought i was going insane suddenly seeing the rotation shift
And by the way,
I'm not sure anyone will see this ant time soon, but the book "Hyperspace," by Michio Kaku, has a really nice way of explaining higher-dimensional physics in an easier to grasp manner.
I'm sure anyone will thoroughly enjoy it.
Still haven't finished it, but picked it back up after ten years and I am really REALLY enjoying it. 🙂👍
I see it John Snow. I enjoyed cleaning this film up a little. It's absolutely brilliant graphics for the time and it deserved all of its awards. anybody capable of explaining higher dimensional physics has my respect. If Michio Kaku did a great job of it then i'll look for it in my library. thank you!
4:07 is just genius. Of course I cant say „easy to understand“ but the explaination is so great
That's also one of my favorite parts of this.
@@KENNETHUDUT Personally, I can't see the difference in representation, since you can literally see this inside the stereographic one
[inside not front facing, how is this confusing to some people?],
but if you have trouble perceiving all of the extra space aside from the singular plane shown here then I can see that!
It makes sense,When they sliced the 4D cube from corner to corner and formed the 4 Triangles and 4 Octagons 1/2 through (The shape was beautiful) and then the 8 equilateral triangles formed the "Platonic Solid"..blew my mind.
Also Slicing a 3D cube corner from corner,face to face,edge to edge was interesting and helpd me "sort of" percieve 4D a lil better.
Excellent video"!!👏👏👏
The best visualization, ever - amazing.
Still mind blowing in 2024
To put into perspective how old this computer animation is, when it was first released, there was only one Star Wars film (Unless you count the Holiday Special), and Iran was still under a king
Tesseract illustrations seem best when the coloring helps give and add to the depth perception. That was my biggest challenge finally wrapping my head around it. Still a bit foggy but I think I have it. Although I really wish I could see the real four dimensional object. 😓
Me too... Amen
Nobody can. Our brains have the physical ability to visualize the fourth dimension, but if it hasn't seen something similar to x thing, it just can't imagine that x thing. For example, our brains have never seen any fourth 90° axis, so we can just visualize only 3 of them.
this video is profound
Oh god they knew this in 1978 what do we know now
They knew this long before 1978! It just first became possible to show it with computer graphics then.
My favorite modern video on higher-dimensional shapes (spot the joke about early computer graphics!) is this Numberphile video with Carlo Sequin: ruclips.net/video/2s4TqVAbfz4/видео.html It describes the analogues of Platonic solids in EVERY number of dimensions. The most complicated case is 4 dimensions and then, strangely, it actually gets simpler beyond that.
Gotta love vector gràphics.
Let us suppose that each of the two cubes have discreet numeric bases. Cube A uses base 10 and Cube B uses base 9. (arbitrary and interchangeable) Whereas, all distances match the volume exactly, the scaling of any point taken in isolation would have a different locale when taken in isolation as compared to the identical placement in the other base. That difference accounts for frequency as a waveform. It also allows two objects to occupy the same space simultaneously-- unless you observe the phenomenon in isolation.
Who else was really looking forward to a rotation of the sliced 4D cube in 4D space, but was disappointed to it ending with just a rotation in 3D space?
The best video ever about it! Or... Is there any better? I am loving those videos.
I just had to understand more about hypercubes after watching that Cube 2: Hypercube movie.
So Slicing a Dimension brings it down 1 dimension "interesting"!.
Slicing 3D brings up 2D shapes.
Slicing 4D brings up 3D shapes.
I just want to assume slicing a 5D cube would bring up 4D shapes.
It worked that way because when you "slice a dimension", it means that you intersect a n dimension subspace with a (n-1) dimension subspace. Example: you slice a cube (3D) with a square/flat plane (2D) to get a 2D cross section
Waiting for this vid to be recommended to the rest of youtube
At 1:20 i can see it spinning in different axis every time i rewatch. Am I the only one?
😀😀😀 yesss
WHAT THE HELL IS THIS TRICKERY
THANK YOU TEACHER.
Finally getting a better picture of what 4d is
My key is to focus on the corners
LilBrownieD thats a good strategy!!
@@KENNETHUDUT thank you!
might not sync up with darkside of the moon but its very educational
Hilarious that this won a prize 40 years ago but anyone with a crappy 3d software could do it today, we've come a long way
Just imagine how stupid our achievements will look in 40 years.
In 40 years, Skynet will have purged the planet of us lesser beings in order to fulfil its higher purpose. And we will probably be convinced that we purged ourselves.
Animation is great.
Audio cuts out a lot with words that are only half or a third of the word.
So this could be done with a new narrator.
Yes the audio was rather poor unfortunately and I tried to clean it up but it had problems. There's a link to the original though if you can do a better audio cleanup that would be great
@@KENNETHUDUT I cannot help you, but I have a suggestion.
Do some searches for DJ blogs, or Radio Sound Engineers blogs. Ask politely for a pro to listen to this to get the words that cut out so much it is hard to parse. So you want a written version of this; add your guesses or guesses from people like Numberphile on the missing words you cannot figure out. Then when you have a full script; a human can do the narration at the same speed as the video so it matches. Or there are AI narration programs that might be free or very cheap, but I never researched them so dunno. Good luck! Ummm if you already attempted to fix the audio? I think contacting Numberphile or similar Math Nerds to have them just guess at the missing words would be better than DJs or Sound Engineers. However I have no idea if you have a basic ability or if a Sound Engineer could do better than your own results.
If you can convince the guy who does 20 second songs?
Anthony Vincent is great, and he really pays attention to voices...which is part of his ability to copy many music styles.
Did nobody notice the audio and video pausing in sync? All you need to do is cut out the pauses and stitch the rest together. There is nothing missing.
If you look at the waveform, it's pretty obvious what to cut out. The background noise even helps with that. However, you want to do this perfectly, to avoid any pops and clicks from the waveform not lining up.
I could do this in probably under an hour, just based on the audio. Sadly I don't think any of my audio software can do video at the same time (to keep things in sync), but to be fair I've never checked.
Best vide that is ever i see on youtube
awesome ! same here
I'm getting Tempest flashbacks.
This would also work with less dimensions, if there is a line connecting. 2 0d shapes make a 1d, and it would seem rotating though it has no width, due to if you imagine a pencil spinning with the camera locked in one perspecting, it would seem to change length. 2 1d would also make a 2D, and the square would also seem to change length as rotating
4:44 that is just a shadow of 4D object , I thought it is a 4D object model
Wonder what computer and monitor was used for this. Looks like a vector display - with more colours, even!
Amazing!!!
hyper dimensional objects really aren't that bewildering of a concept but people make it so. some shapes have two dimensions, {a,b} some have three {a,b,c} some have 5 {a,b,c,d,e}. the monster has millions.
Amen
This is excellent. Thank you.
Here's the link to the original. it's still there 7 years later.
mediaburn.org/video/the-hypercube-projections-slicing-others/
wow, way before the #internet, #screensavers, #facebook etc.
?
@@tannerfry1412 Only boomers will understand.....
#2manyHashtags
@@graffiti9145 lol disagree what's wrong with hashtags?
Be careful, that is an infinite crease
I found a treasure.
2:25 I'm confused, I don't see any flat facets here, can someone care to elaborate?
The simplicity of the hyper cube is that it is limited to the form of a cube, and so could also be permutated beyond and within the teseract because it needs to be a cube to function as one - so you could add and take away continuously a quarter of it, then it becomes energy and a beyond within the cube permutation - now the cube and tesseract becomes a way to create energy, being both hyper in teseract and in cube. The reason it is so simple is that the form is perfectly man made, so it can be perfectly grinding or made to grind rather on the natural shape of wave. So it could be made to create within cube while it is teseract - ing. With a little help. Superconcentrated man made fire of strange unnatural form.
tesseract at 3:36 and following
I think hallucinogens should be explored and taken more seriously.
Helps you too see the laws of the universe at work and their underlying mathematical representations in real time.
Unfortunately you can perceive a little too much and it just stumps you. Getting carried away too quickly before being able to have even an inkling of understanding. Just before we grasp anything, the perspective of reality changes so greatly and we are so in awe, that we forget what it was we were even thinking about. Too beautiful not to be experienced. Time seems to mean nothing there. All things feel eternal somehow.
Looking at the moon, we miss all the heavenly glory.
It's just too much. But not beyond the realm of possibility.
Would be nice to visual see in a virtual environment what others perceive. Kind of like experiencing another person's dream.
The detail of our universe seems infinite. Unattainable. Just to be experienced.
I don't think anyone could ever truly understand the mind of God without being God himself, but I sure love the journey.
So awesome. 🙉
The journey on this planet is such a spectacular gift that's easy to forget. I can be mesmerized by a tiny gap in the wall and take an imaginary journey that I have no idea how. sometimes I forget to appreciate but I think that's why we have each other. Thank you for the reminder!
Was that a color vector monitor from 1978?
Indeed I think it is. beautiful
you can make a entire 3d movie by using 4d considered time in 3d for example cube spinning
That's a great. I love this kind of stuff. There's so much hiding "just beyond" the surface of things, like, what's the world like between the paint on a wall and the wall (for any little creatures living in there)?
What if we could reach into the glass of the phone and go into the world we see on the screen?
Sometimes it feels like we almost can
7:10 trippy asf
As good as this is, I still don't think it's actually able to be visualized.
@@sk8erz6721 well, it's shadows. it's like looking at your shadow on the ground and trying to figure out what casting it and having no idea what a person looks like except for the shadow
This is cool and hurts my brain. 😆
The feeling when your 3D brain cannot properly process a 4 dimensional object, let alone its movements...
2020 soon
Wormhole?
6:40 the bestagon
9:00 enter Ramiel!
Who came here after watching "Interstellar" movie to learn more about a tesseract.
😊
FUTURE
MADE OUT
VIRTUAL INSANITY
Edge dynamics is broken in flat illustration
soold.
they are called cells not 3 dimensional faces
🤓🤓
... what
how did this win an award? the math isnt too much more complex than 3d, so were people just dumber back then?
@@trinityy-7 1976. they didn't have displays doing this kind of thing
@@KENNETHUDUT how did they do this with no display then
nonsense
This makes absolutely no sense. Anybody that claims to have a grasp on this visualization is full of it
clearly you're just stupid and have the IQ of a pencil lmao
Literally just imagine squishing 8 cubes together
"You're not thinking fourth dimensionally." -- Doctor Emmett L. Brown, 1885 and 1955