Perfect Shapes in Higher Dimensions - Numberphile
ฝัง
- เผยแพร่เมื่อ 22 มี.ค. 2016
- Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions.
More links & stuff in full description below ↓↓↓
Extra footage (Hypernom): • Eating 4D Polytopes (H...
More videos with with Carlo: bit.ly/carlo_videos
Edit and animation by Pete McPartlan
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"You can basically figure it out yourself" -Carlo Sequin on 5 dimensional polytopes
Nobody has ever believed in me as much as this guy
xD
LOL
Haaaahaaa
Same
Most underrated comment on all of youtube for all of time. thank you.
The fact that he can visualize this and explain it so clearly really shows how abstract this man can contemplate. So difficult to do
Is this clear to you? 😂
Remenber Nikola Tesla? Read about him.....
alberto rivas I’ve not heard Tesla touch on higher dimensions, can you give me a theory of his you have in mind?
alberto rivas I have several books about Tesla.. what makes you think I haven’t heard or read about him lol. So random
@@shpongle7322 just another 4d mysticism delusional dude hahaha
Ah yes those famous rpg dice...
The d4, the d6, the d8, the d10, the d20, and the dTEAPOT
Not d12?
the deapot
dpot
“this is a icosahedron”
me who plays dnd: ah yes, a d20
No mention of the 10 sider for some reason...the forgotten solid.
Sides aren’t regular polygons :(
@@jacoblynch8844 *polyhedra
@@jacoblynch8844 they actually can be, the problem is that the vertices aren't the same.
@@theprodigal72 polygons*
This guy has the perfect accent for the word tetrahedron
if you know how to roll your r's then you can also say it like him
I like his pronunciation on the word square.
"Sqvare" :)
It's like a german-scottish mix.
According to Google Translate icodahedron is pronounced as i-co-sa-hee-dron. I just had to check this after hearing him say ee-co-sa-hee-dron.
Tetraheedraun!!
I feel like my brain gets so close to imagining higher dimensions before breaking completely.
Mine doesn't
@@johnsaylor1583 ok.
@@aliensasquatch7485 I don't remember commenting that. But, mine does as well. I can't fathom anything beyond the box I live in.
@@johnsaylor1583 or maybe you could, but then your mind broke completely and now you don't remember.
Me too. I am like "yes, yes, i got it, I can imagine it, I can see it, nope. I am just too 3d for all of this."
Keep re-watching this over and over again, his explanation is so simple yet so elegant.
Sad I never got to meet him in person, he must have been a very interesting person to talk to about the World and everything surrounding us
You made me think he died or something
He's still kicking. 79 years old!
@@rurihime4965 same
Confirmed still alive!
@@rurihime4965 My thoughts, exactly 😨.
As a 3D artist, I actually find this very interesting. That was a fun bit about the Utah Teapot! It comes with every single 3D graphics software known, and I see it all the time, but I actually never knew it had a name!
JEWS!!!!!
@@user-gr6he3hg1u??
It's actually one of the oldest memes in the computer feld. And it still funny to think about 💀
When I watch these videos, i simultaneously feel both smarter and dumber
That's how being smart feels
That's called learning, first you dont know what you dont know, then you know what you dont know, then you know
I just feel dumber
The more you know the more unknown you're able to see around you. There's a parable about that.
@@alicec1533 Forth Dementia.
That guy has an amazing voice/accent mix.
He's a good lecturer. It's his job to hold your attention.
I always wonder what accent it could be
I thought it was some kind of Scottish, but apparently he's from Switzerland.
Sample it, loop it, fuck it.
Go Switzerland! It is the best country!!!
Mathematicians: there are 5 regular polygons in 3d space
jan Misali: 48, take it or leave it.
jan Misali
It's a toki pona thing where only names are capitalized
To be fair, the difference is the definition: Jan misali also accepts polygons that aren't strictly convex, which allows for self intersection, planar tiling and the other things he shows, but if you were to actually define it, most mathematicians would probably restruct them to be strictly convex, and call the other ones semi-polygons or something like that. They're still interesting, but also different. It's actually quite similar to how some people say 0 is prime, while most mathematicians define primes as natural numbers (excluding the 0, should it be considered a natural number in this system), and 0 acts quite different than the other primes
@@JonathanMandrake it’s not Jan Misali, it’s jan Misali, “jan” is just the toki pona word for person, it’s not his actual first name
@@zackbuildit88 Misali would be proud (maybe)
@@JonathanMandrake also, just saying, most mathematicians studying these shapes actually do allow non strictly convex solids, hence their early inclusion in the video
The 6D Hypercube structure really looks like a Metatron Cube. And the 5D polytope, when he tilted it at an angle, made pentagrams with the negative space.
Meanwhile in a higher dimension:
"Mom, can you buy me some real toys... I'm tired of playing with these Rhombic Triacontahedrons"
Oh kid. Just play ball, it rolls in any dimension.
@@tomasmieger6826
"MOM, everytime I try to roll this 3D ball it just falls over :c"
@@Dexuz Underrated comment!
"The fun will never end, it's Adventure Time!"
Mom: sure son, do you like a triangle or a cube?
Somewhere in 4D space, there are 4D idiots like us gawking at 4D mathematicians trying to imagine common 4D shapes crunched into unimaginable 5D hypershapes
And so on lol...
and are confused at how 3D biology could even exist.
Have any of you ever read Flatland by Edwin A. Abbott. I admit, to my shame, that I never finished it.
Nonetheless, I think you might find it very interesting given these comments.
NusXrrnak Somewhere in 1d space, 1d scientists are wondering how they even exist.
somewhere in 0D space, there is a very small speck doing nothing.
Awesome video!! I’ve been searching for ages for an answer to why there are only 5 Platonic solids in 3 dimensions. Not only is this the first explanation that I find instantly intuitive and concise, it’s also demonstrated beautifully. The extension into the higher dimensions and reference to fewer dimensions is also a wonderful way to contextualise the whole concept of perfect solids. Thanks so much! 🙏❤️
❌❌
❌❌
❌❌
❌
FloorFloorFloorFloor
It fell.
Props to the animator the visuals in this were amazing
*[SCREAMS GEOMETRICALLY]*
Ramiel ;)
radbarij nice
Like when liquid metal goes down Neo's throat.
um..
ERASE MEEEE!
I bet your 3D printer would literally cry if it could lol.
As opposed to figuratively?
He's granted his 3d printer eyes.
New torture test
ΔISEPTICONS 4 EVER AHAHHAHAH
He can Print tears
14:08 is the projection that somehow really clicked with me. I felt like I "see" this and that was a huge moment of joy.
The hyper cube alone made my head hurt, by the time he reached the 600-cell I felt my brain trying to burst out of the top of my skull
Trying to picture 4D is kinda like trying to play a movie in a music player
More like getting a calculator to say 2+2=5. It’s not really hard, it’s just impossible. :3
Although getting a movie to play in a music player is also impossible so what am I saying?
you can run the audio only though, that's like projecting 4D in 3D sim
@@xxCrimsonSpiritxx So if I put a Doctor Who dvd on my cd player it would just play the audio? That's kinda cool.
It's possible to see images in audio spectogram :p
Watching 4D objects represented in 3D projections on a 2D screen.... seems legit
With our 1D brain
@@some1112 You don't perceive the world with only your brain. Logic is one dimension you can use to observe what you perceive with the five senses. That is perceiving with six dimensions.
and also with eyes which can only see 2d on their own
@Gary Sutherland r/Whooosh
OBVIOUSLY
our imagination is bigger than our eyes
A petition for us to upgrade our simulation to 4d.
It was so satisfying that I was able to understand some semblance of 4D space when he was describing why the "smaller cube" isn't inside the "bigger cube", because in 4D all of the edges and faces would be exactly the same, but the perspective and warping of them as a projection would make it look like this
This gentleman has managed to engender two emotions within me simultaneously: feelings of absolute childlike wonder and confusion. Interestingly enough, even though I was lost at times, I still felt that what he presented in this video is learnable and, thus, possible to understand. I enjoyed myself immensely.
Wow, same
I certainly did as well. Ive always been fascinated with these topics of dimensions. And I even chuckled when he mentioned its a great toy for kids! 23:10
I like how he corrected the "so they're like evil twins" to "they're more like nice twins actually!" like he loves these shapes.
@@D4narchy his wonder is beautiful
But we can also perceive all 3 of the physical dimensions of our reality, which can only be achieved by observing from at least one dimension higher.
Can't see a point unless you're beside it. Can't view a line unless you are behind it. Can only view 2d shapes, by hovering above them.
Where does our consciousness reside?
People in 4D space are writing down notes in 3D
Le funny 😜
love it lol reminds me of a movie
And people in 2D are writing in 1d
Which movie..??
can't imagine that though
Making a 3D out of a 5D shape means that you are taking the shadow of the shadow of that 5D shape 🤯
He is a mix of Carl Seagan and Admiral Picard, and his coolness factor a multiplication of both taken to the cube.
The idea of 1D honestly scares me more than 4D
JackStrait
*scares in 0D*
@@SalveSandWonk *screams on *point**
The band or the dimension?
@@SoluKissin The band obviously
Thanks for that horrifying vision. This video contextualized that statement.
I really wish, if only for a moment, I could actually experience perceptive awareness of an additional spatial dimension.
Perhaps one day we will have this opportunity. You could conceivably teach yourself to conceptualize in four dimensions if you provided your brain with 4-d input. You'd need a computer wired directly into your brain. Computers have no trouble with higher-dimension geometry.
***** who?
phuturephunk me too...
but we could always try weed 😅😅😅
actualy we do but we don't realise it and we can't feel it
That's how crazy people are made
Thank you very much, Numberphile and Carlo Sequin. I have always struggled with this level of mathematics beyond "you can't imagine a 4D shape" so I was astonished to find myself grasping the concepts (with some rewinding). Sequin's style is intuitive and captivating and I can't believe that I now have not only a page of notes, as if I were at school again, but an appreciation of the beauty and mystery of these forms. You've made my day!
This video: exists
Me, an anime watcher: RAMIEL
I was just looking for this comment.
@@mamalogon lol same
Don't be ashamed of yourself if you're confused. It took Super Mario 11 years to figure out 3D.
Really underrated comment.
*N I C E*
Yeah but 11 years our time is only like 35 minutes 4D time, so...
When Mario dies in the 3d world, does he jump out in a 4th dimension?
Bibasik another dipshit comment, searching for praise while providing stupidity without intelligence..
The diagrams, the colours, the animations are all just wonderful!
5 stars!
or should that be "5 Platonic Solids!"
+AlanKey86 Thanks Alan, was that your lovely twinkly stuff over the polyhedra?
+Pete McPartlan It was indeed :)
+AlanKey86 5 Stellated Polyhedra.
+AlanKey86 5 Thumbs up
@AlanKey86 - there would only be four stars in three dimensions - the stellar dodekahedron, great dodekahedron, great stellar dodekahedron, and great icosahedron.
this channel is making me realize i want to study this kind of conceptual math along with financial math and quantitative analysis
Go for it, Jane Street awaits
4d space must look terrifyingly awesome.
trust me its beyond anything you can comprehend
litteraly
@@tone618 have you been there?
@@tone618 you sound so definitive, have you been there?
hes been there and so have you
And this is why they shouldn't call "4D movies" the 4D movies. Excellent video. Thank you!
Ye legit wtf
Nahh..
Dimensions could mean multiple things. And 4D movies add another dimension to the watching experience.
Our universe itself is 4D because it also has 1 temporal TIME dimension.
@@ez_is_bloo so all movies are 4D then...
Movies depict 3d images on a 2d screen. The moment a third dimension is involved in displaying the movie, in the movie's universe this is 4d. (There is no screen protruding out of the screen but visually it appears that way so I do consider that an extra dimension in presentation)
@@A.Mayflower127 not necessarily. All "3D" movies are technically 4D, but 2D movies are only 3D because its 2 dimensions of space plus one dimension of time
I have my unit 3 and 4 English and Psychology exams tomorrow but this is far more important
How was it
I need to know you can't leave half of a story
It's your life dude and your money
Anserw
yo sorry dude. went well 👍🏼 will be getting into uni!
I love the way he pronounces "tetraheedrron" and "sqvares". And overall films with him are marvellous
This man is, honestly, a very cool guy. He knows and loves his shapes (polytopes) in 2d, 3d and higher dimensions. He was a cool collection of them, and his relation with them is VERY wholesome.
So far I am just enjoying the shapes.
Yeah because the rest is just imaginary mathematical BS to make themselves feel smart. Sure it's math theory, but since it's outside what we/they can see, feel, experience in a 3D world, it's speculation on mathematical theory. But the shapes are unique.
Mr Rytte Excuse me..what exactly are you saying? “to make themselves FEEL smart?”
That is just a doosh thing to say..
Enjoying the shapes... That's something I do on pornhub XD
Trying to understand 4D in a 3D world through a 2D screen.
With a 1D time line
@@legokenobi1185 time is actually 4th dimensional structure
@@legokenobi1185 And I'm having a 0D thought about how arrogant you are.
Edit edit edit: THE INSULT WAS MENT FOR THE GUY RIGHT ABOVE ME SORRY TROLLI I LIKE YOUR COMMENT
trolli gettin' roasted into inexistance
@@legokenobi1185 time isnt 1d
" Could you show to a NON-mathematician in an intuitive way."
That is the right approach...
There’s this toy I have that would really help this guy explain polyhedra. It’s a bunch of equilateral triangles and squares with the same side lengths, and every side has a magnet so you can stick them together to make 3D shapes
At first I was all, "OMG! PRETTY SHAPES!" but then I was like, "What even is life?"
lool
+Wanderer in the Dust
LSD
LSD is the best
hahahahahahh. love your comment
42
6:56 man im so used to these crazy seamless segueways nowadays i almost thought mans was gonna try to sell me a tea pot
I just did a project on 4-dimensional regular polytopes, and there are actually 19 of them (that I could find). These include the regular star 4-polytopes and the 4D honeycombs.
Additionally, there are definitely more than three regular polytopes in dimensions higher than the fourth, due to the existence of hypercube honeycombs. So that makes at least four. Whether the star polytopes are applicable to the fifth, sixth, etc. dimensions I'm not sure of. Some sources say no.
In the end, this just comes down to how we define a regular polytope. This video makes the assumption that regular polytopes are convex, finite, do not have any holes, aren't self-intersecting, etc. Without these assumptions, more becomes possible. :)
His accent mixed with talking math stuff is quite a soothing experience tbh
The fact that three dimensional beings can even figure out the properties of four dimensional objects amazes me.
You are sick
@@RJavier007 what.
@@RJavier007 I am wondering what warranted that response...
@@michaelnortheast394 he refers to people as beings as if he was not a human himself
Or can they?
I have no idea what this man is talking about, but it's damn cool!
Lol!
Lol. I love you mate! :)
Love u 2
El Milto I'm pretending to understand it... ow my brain.
Flinch Fu same!
6:17 That honestly looks really cool
What a wonderful explanation! Thank you for helping us to learn something that is so fascinating in such a fun way. Professor, this has been a true delight!
Also fun idea to think about, in 4D space all shadows would be 3D if you had 4D lighting. Try to wrap your head around that.
nice one
So are we just shadows of 4d beings? And are they shadows of 5d beings? What is the shadow of an infinite dimension being?
Imagine watching TV in the 4d universe
Well, you actually do. You live in a 3D space and travel through time, so you move through four dimensions. A TV screen in this very 4d universe has two dimensions in space plus the passage of time, making it 3d. So an actual 2d TV could look like a moving line (1 dimension in space and 1 in time) or like a picture (2 dimensions in space, but no in time).
And what would 4d light look like? It would still be pure energy. One photon of that light would be, what, like infinitely more energetic than a photon in 3 dimensions, am I right? Insane.
do a video on the Utah teapot
+Sean Tobin yes, please!
Yes!
+Sean Tobin I think the '6th platonic solid' is only a honorary title. It does not actually earn it. Its just extremely common. Its like the 'hello world' model of 3d rendering engines.
+Sean Tobin your body is ready for it, isn't it
+Sean Tobin Yes, please do.
That Rhombic Triaconthahedron (22:58) is a mind blowing 6D shape. It has cubes as its faces!
Yes; and tesseracts (4D-hypercubes), as its cells, and penteracts (5D-hypercubes), as its hypercells. However; the Rhombic Triacontahedron is only the convex hull of that particular projection, not the object, itself (Rhombic Triacontahedron is actually a 3D-object, as is evident from the suffix: ”-hedron”); the real deal is a 6D-hypercube.
I think of the measure polytope duals to be the "bipyramid" series. The line bipyramid is the square, then the square bipyramid is the octahedron, then the octahedral bipyramid is the 16 cell, and so on.
Hats off to the animator! And to professor Séquin, of course.
4d liquid would be the trippiest thing imaginable
Never had it better and clearer explained... an amazing way about it, dear professor... Truly thankful I am for such a smooth transition from 2D to 3D, 4D, ..., into infinity... and perhaps further...???
Even though I could only understand some parts of the explanation, the explanation was amazing for someone with such less knowledge on higher dimensions. If you can do more videos on higher dimensions on how to comprehend them, it would be great.
I love the Platonic solids, but only as a friend.
+theRealPlaidRabbit that's offensive, yo.
+burpie Love can be between one rabbit and a bunch of polytopes. Even if it's not that kind.
theRealPlaidRabbit Can it also be between a rabbit and... a polar bear? :-D
burpie A snowshoe hare-- until the bear gets hungry! :)
+theRealPlaidRabbit Platonic Solids can be renamed the "Friendzoned" Solids... XD
They need to start giving these higher dimensional polytropes more creative names like Maximum Overdrive Ultra Hyper Cube because you can never have too many epic adjectives
MG222 super mega Omni ultra nega pneumono hyper alternative meta ultra polyvoxel
I'm sure they'll end up named like the radio frequency bands.
point: ultra low cube
line: very low cube
square: low cube
cube: medium cube
tesseract: high cube
5d hypercube: very high cube
6d hypercube: ultra high cube
7d hypercube: super high cube
8d hypercube: extremely high cube
9d hypercube: tremendously high cube
10d hypercube: light cube
11d hypercube: ridiculous cube
12d hypercube: ludicrous cube
MG222 Super Kami Isocahedron
Not when I shift into MAXIMUM OVERDRIVE
Erm... That would be incredibly weird.
This is the best demonstration of Platonic solids I’ve seen yet.
This channel is pure gold.
I understand some of these words.
loool
Then you're doing well.
I understood what cube meant
Then why use it?
That's the joke.
24:23 "like an evil twin" "nice twins actually"
Few seconds later "EVIL TWIN"
Scrolled down just to find this lol my favorite part
DiceDecides looks like thats his only speech
Yeah i like eminem too
i managed to have a visualization of 4d space through the eyes of 3d, which is that in 4d we add a new axis and that new axis makes it so when you look at 3d cubes being attached, in 4d there's a new axis, which makes the cubes not entirely attached, which is how we can fold it, because of the new axis creating more space
11:50. The fact the yellow cube is not actually inside the blue cube as it would appear and is also in fact the same size as the blue cube but just appears to be smaller due to our perception as he said is just amazing and mind boggling! I wish we could find a way to visualize the 4th dimension in its entirety! I try so so hard to see it in my mind which I know you can't but I'm so fascinated by it I have to try.
If the fourth dimension is time, then the movement of the cube from one position to the other as your perception changes due to the movement would explain it. The time that it takes to move is actually the fourth dimension.
Please let this guy narrate more videos!
I like the question the young guy asks, he's smart enough to make these kind of interviews actually interesting
Or maybe the questions are pre-scripted?
I think the questions are scripted.
Well... He couldn't answer the first question
This is the greatest video on dimensions on TH-cam that I've watched (many times).
I have always been browsing TH-cam for 4d and higher and you are one of the videos that have taught me something
his voice is so soothing, combined with the maths...altogether this video is the stuff of my dreams
I minimally understood, but I definitely feel smarter.
Thanks!
im guessing 4d is a bunch of 3d space stuck together, and in order to get another 0.00001% increase in an idea of what 4d actually is, we would need to be outside our 3d universe, which is a 4d universe, looking back in
@@jfern6673 Revolutionary.
What I find impossible to wrap my mind around, is that a 4d being could take something from a locked safe, without touching the sides.
@@Fermion. not if you take dimension compactification into consideration. The safe would still have a side in the 4th dimension, it would just not be symmetrical in size with the others.
Now that's a proper science lesson, thank you very much for conveying such important knowledge in the most simplistic realistic fun way!
That is absolutely amazing. I have just learned polyhedrons and the video comes up within a few time
mathematicians: there are only five platonic solids
utah teapot: 😤😤😤😤😤
@Jason Lee Its not just pissed its steaming
The Legend27 name checks out
@@eldnahym it's actually a freesian teapot but whateffs
😂😂😂
utah teapot: hold me tea...
Another shout-out to the animator(s) for this video. That's excellent, high-quality work right there. (Narrators, editors, etc. were also great of course, but they have always been so.)
whoa! his 4d object collection is awesome
the image of the heptagon shoving the other one away with the sound affect is absurdly funny
So, there would be more DnD dice in 4 dimensions?
D600
+Adraria8 all hail the D666
Exactly
+A light switch I bet you came from YIAY lol
+Binyamin Tsadik i dont think all the dnd dice are platonic objects. isnt it one that is spinning which is not symetrical in the xx' zz' field??
We all live in 3 dimensional sphere earth while this guy live in his 6 dimensional rhombic triacohedron earth
What?
@Audy Simon flat earther shush
First qurstion I would have personally is in respect to his use of the word "in". So we don't live ON the sphere? We live IN the sphere? This is Hallow Earth theory right? Why then hush the flat earther?
Chicasso Productions atmosphere
@@gavinbrown216 we live under the atmosphere not in it.
This has better explanation than the other. Much clearer. ❤️
I know I am not smart enough to understand these things but still I cannot stop watching videos like this one
who else felt extremely satisfied watching the animations
Hark! Indeed. The motion feature segmentation of this piece was rather the most symbolic yet inert, inscrutably binomial for one to grasp.
me
My brain shut down at 18:27 and everything lost its semantic value.
+Gazeth Sonica RIP
Same
+Gazeth Sonica Hehehe semantics :drooolz: I haz losst it.
+Gazeth Sonica defintely takes some practice to keep up with the more abstract topics in mathematics
Energy Core
Very true, but thats also what makes it so much fun xD
This is the best video I’ve ever seen for trying to visually contextualize higher dimensionality.
amazing ,great works, thanks for putting together such an instructive illustration
Interview: Like an evil twin.
Guy: Like a nice twin actually.
This guy really loves shapes.
It's a platonic kind of love :p
So do I! Shapes are interesting
Thanks to this im gonna consider the octahedron and the cube as friends
@@stylis666 Get out
@@stylis666 Now; *_THAT’S_* a solid pun 👍🏻!
First time in my life I properly understood 4+ dimensions.
NorthWind Achievement get!
Dude... thats a bigass claim but if you say it must be true. Gratz. Im still on it!
same before I thought that it was just nonsense!
Eyoooo what’s Ramiel doin here 😂👌
**SCREAMS GEOMETRICALLY IN ANGEL**
This is making me tired like my math class but unlike my math class I don't want it to stop :D
My brain blue screened half way through
+invalidusername do not use win for rendering higher dimensions
invalidusername Try using 4D Ram and a floppy disk
Imagining 4d figures in your 3d head while watching it being illustrated on a 2d screen... My brain: *Nope*
i feel ya
And processing it with your 1d brain
@@Corgi_fax no. we should instantly colonise mars
The animation is amazing!
my mind .....is blown!!!! loved this video.
As a 3d artist, you made my day by mentioning the teapot. Thank you !
the animations for this video were amazing!
I always require '"the string theory"' to understand higher dimensions.
And you are more genius.
🤗🤗
The most beautiful thing I’ve ever seen.