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
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.
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
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?
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! 🙏❤️
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.
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
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!
@AlanKey86 - there would only be four stars in three dimensions - the stellar dodekahedron, great dodekahedron, great stellar dodekahedron, and great icosahedron.
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.
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.
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.
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
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.
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
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
@@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.
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.
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
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
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.)
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!
you can have other shapes of dice and still have them be equally weighted, they just start becoming cylinders with shaped faces on the sides, or weird shapes with some sides you dont land on.
You can take care of that by repeating some of the labels. Some games using 3d dice already do that, for instance cube dice with only 3 numbers (each number repeated twice).
@@kirillmed1 I'm no expert, but you may get problems with the dice landing on the "flat side" in the same way that 2d dice would land on their flat side in 3 dimensions. You could always extrude out and put smooth caps on the ends which you don't want the die to fall, but it's starts to feel less "dicey" at that point.
@@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
@@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.
+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.
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.
20:16 you are watching a projection of a 4D object that represents a 5D object in a 3D space flattened to a 2D space aka your screen. How cool is that?
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!
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
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?
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...???
Bryson Sirus Mate do you not understand the use of the phrases “hope(s) for” and “future technology”, particularly when used at the same time? It completely disregards what is possible now, or what we believe to be possible now. I don’t ask you to explain, because it is irrelevant. My statement takes into account nothing about reality but for the fact that it isn’t possible at this moment or in the past. In short, regardless of your theories and ideas, the infinity of the future allows unlimited hope.
This guy is so easy to listen to and explains things in such an engaging, easy to understand way. I have to admit, I literally don't know much past the basic 3D shapes, but the fact that he seems so happy to explain makes me want to enter the 4th and 5th dimensions.
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 also, just saying, most mathematicians studying these shapes actually do allow non strictly convex solids, hence their early inclusion in the video
In 3D, you can get a sphere by making a circle curve in all directions, or a cylinder from extruding a circle. In 4D you should be able to get a hypersphere from making a sphere curve into the new dimension, and another two shapes from extruding a sphere and extruding a cylinder.
Just think of the cross-section that a 3D sphere has in 2D. It’s just a bunch of circles, other than its ability to grow and shrink it would seem no different than a 2D circle to an inhabitant of 2 dimensions. A 4D Circle (or hypersphere) would be similar to us. Just a sphere that would grow and shrink.
jogiff It would grow and shrink to our eyes. Buy we cannot comprehend its true form. Since all we see is a 3D slice. But thank you for your comment, it really helped me to understand something
You can do it the same way a circle. Infinite circles of different sizes = 3D sphere (2D slices) infinite spheres “inside” each other, like the smaller cube in the larger cube in the hyper cube , only with spheres and there isn’t those lines connecting them.
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.
No matter how hard we try to imagine what a polygon would look like in the 4th dimension, I don't think we could ever truly be able to show any kind of representation of how that shape would appear. If you were restricted to 2 dimensions & there was a shape in front of you, no matter what you try to imagine, how far you rotate around the shape, where you go within your 2 dimensions or how long you stand there observing the shape, there is an entire level of data which is unavailable to you & possibly way beyond your comprehension. This same principle would have to be applied to a shape in front of you when being restricted to 3 dimensions too. So unless you bordered on insane genius, whilst ever you lived here you'd probably never be truly able to appreciate what this extra dimension actually means to the shape in front of you. But the idea that time is our 4th dimension could give us a glimpse into how we have to think - if we currently live in 4 dimensions but only have control over 3 (as we are 'dragged' involuntarily through the 4th), extending this idea down to living in 2 dimensions but being dragged involuntarily through the 3rd dimension would be like staring at individual 'slice' photos of an MRI scan of a shape, watching it change as you travel through your 3rd dimension. This would possibly be perceived as watching something change in time, yet moving up to our level & seeing it from up here 'outside' that 3rd dimension, we know it's not time they're traveling through but moving through the object itself. And taking this down to 2 dimensions (living in 1 & being dragged through the second), the concept of the existence of a 3rd dimension of top of that would be inconceivable at that level - not even with the grasp of such a limited scope of perception. If this idea is correct, then no matter how many dimensions you live in, the dimension above you will always be perceived as what we currently call time, & the dimensions that you DO have control over will clearly become obvious as just another layer of information only available (or able to be understood) to those living in that dimension or higher. So you can only imagine what information is available to those living in the 4th dimension & above... does that make sense?!?!??? Or did I just brain my damage?
All you need to do to easily visualize 4D objects is to slice it up into 3D slices. For example, you could slice a 3D cube into many 2D slices. Each slice would be a square. Similarly, a hypercube would be sliced into many 3D cubes. A 4-simplex would be sliced into many tetrahedrons that get smaller and smaller.
something i was thinking about while reading this.. You can draw a 3D cube on a 2D sheet of paper. But if we only lived in a 2D world, would we even know what to draw for the 3 dimension.
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. :)
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
"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.
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!!!
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 😨.
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?
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!!
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.
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.
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."
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!
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
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!!!!!
@@AMORTEDEYAHWEHDEMIURGOS??
It's actually one of the oldest memes in the computer feld. And it still funny to think about 💀
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.
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.
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?
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.
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
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
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.
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.
his voice is so soothing, combined with the maths...altogether this video is the stuff of my dreams
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
*[SCREAMS GEOMETRICALLY]*
Ramiel ;)
radbarij nice
Like when liquid metal goes down Neo's throat.
um..
ERASE MEEEE!
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
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.
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
Ah yes those famous rpg dice...
The d4, the d6, the d8, the d10, the d20, and the dTEAPOT
Not d12?
the deapot
dpot
@@madeofbeans de power of two
@@lukiepoole9254only if you're a barbarian
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.
Hats off to the animator! And to professor Séquin, of course.
“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*
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!
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...
@@AnathematizedMage he refers to people as beings as if he was not a human himself
Or can they?
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.)
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!
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.
Whatever version of D&D they play in the 5th dimension must be really boring having only three kinds of dice.
👍
you can have other shapes of dice and still have them be equally weighted, they just start becoming cylinders with shaped faces on the sides, or weird shapes with some sides you dont land on.
You can take care of that by repeating some of the labels. Some games using 3d dice already do that, for instance cube dice with only 3 numbers (each number repeated twice).
Or, actually use dice of lower dimension
@@kirillmed1 I'm no expert, but you may get problems with the dice landing on the "flat side" in the same way that 2d dice would land on their flat side in 3 dimensions. You could always extrude out and put smooth caps on the ends which you don't want the die to fall, but it's starts to feel less "dicey" at that point.
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
Props to the animator the visuals in this were amazing
As a 3d artist, you made my day by mentioning the teapot. Thank you !
Watching 4D objects represented in 3D projections on a 2D screen.... seems legit
With our 1D brain
LOL
@@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
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.
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
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.
this stuff is so mind boggling... it is so fascinating and seemingly impossible to even try to imagine...
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
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.
20:16 you are watching a projection of a 4D object that represents a 5D object in a 3D space flattened to a 2D space aka your screen. How cool is that?
Marco Napoleone Huh.
On your 1D brain
With the comprehension level of 0D
With the -1d iq
And the video is at it's core a one dimensional array of ones and zeros
People in 4D space are writing down notes in 3D
love it lol reminds me of a movie
And people in 2D are writing in 1d
Which movie..??
can't imagine that though
This is kinda terrifying. What if we 3D are just notes of a 4D being?
Please let this guy narrate more videos!
This is the best video I’ve ever seen for trying to visually contextualize higher dimensionality.
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..
4d liquid would be the trippiest thing imaginable
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
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!
the animations for this video were amazing!
It's almost like he making up those big word to make his speech appear more photosynthesis
Icex Aoki he is a professor tho, technically he's just osteoporosis.
Icex Aoki great he's trying to make his speech more cycle where plants make their food
These comments are so dodecylbenzenesulfonate.
Icex Aoki lol
laundry sauce
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
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
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!
This is a real nice sounding accent. Really easy to understand...😄
Dutch?
@@davidh9844 no, he is swiss.
Like me😂
subtitles buddy
His accent does sound distinctly Dutch.
Yeah, we all love those squeers. :D
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.
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...???
One of my greatest hopes for future technology is the ability to truly visualize 4D space and shapes
Bryson Sirus
Mate do you not understand the use of the phrases “hope(s) for” and “future technology”, particularly when used at the same time? It completely disregards what is possible now, or what we believe to be possible now.
I don’t ask you to explain, because it is irrelevant. My statement takes into account nothing about reality but for the fact that it isn’t possible at this moment or in the past.
In short, regardless of your theories and ideas, the infinity of the future allows unlimited hope.
@@mekafinchiwait what... *brain.exe not responding
As long as the 4th spatial dimension spaces isn't found, i don't think that's possible
Two words: Virtual Reality, there’s a 4D toybox simulator that’s looks pretty dope
Impossible for the human brain to comprehend no matter what
This guy is so easy to listen to and explains things in such an engaging, easy to understand way. I have to admit, I literally don't know much past the basic 3D shapes, but the fact that he seems so happy to explain makes me want to enter the 4th and 5th dimensions.
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...
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
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
And where are the higher dimension polytopes made out of teapots??!!!
Ashton Fortenbacker You clearly didn't perceive my sarcasm
Hyperpot
4-teapot
That needs 42 dimensions
we do not know if 4 dimensional beings drink tea
@@God-ch8lq They drink Te4
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
I love the way he pronounces "tetraheedrron" and "sqvares". And overall films with him are marvellous
My brain is melting try to picture a hypersphere or a 4D sphere.
In 3D, you can get a sphere by making a circle curve in all directions, or a cylinder from extruding a circle. In 4D you should be able to get a hypersphere from making a sphere curve into the new dimension, and another two shapes from extruding a sphere and extruding a cylinder.
Just think of the cross-section that a 3D sphere has in 2D. It’s just a bunch of circles, other than its ability to grow and shrink it would seem no different than a 2D circle to an inhabitant of 2 dimensions.
A 4D Circle (or hypersphere) would be similar to us. Just a sphere that would grow and shrink.
jogiff It would grow and shrink to our eyes. Buy we cannot comprehend its true form. Since all we see is a 3D slice.
But thank you for your comment, it really helped me to understand something
You can do it the same way a circle. Infinite circles of different sizes = 3D sphere (2D slices) infinite spheres “inside” each other, like the smaller cube in the larger cube in the hyper cube , only with spheres and there isn’t those lines connecting them.
Try to picture a 6 dimensional Calabi-Yau manifold... your brain will disintegrate like a supernova lol
OMG 26 minute numberphile video, yeeeeeeeeeeeeeeees!!
I love how he says “squere”
🐿
He is Swiss, that is how it sounds with a Swiss accent!
I love the icosa
He is a mix of Carl Seagan and Admiral Picard, and his coolness factor a multiplication of both taken to the cube.
1) woah
2) how does he edit these vids with those graphics!?!?
3) how do they 3d print those props!?!?
... 3D printers ? =3
Prout this guy either didnt notice they are made out of 2d polygons or living in 4D world
4D printers are existing in the 4D world.. they look the same as those wireframes
Answer to 3: 3D printers.
1) yes
2) with software
3) with a 3d printer
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 👍🏻!
i really like this guy, the way he explained everything made it so clear
This is the best demonstration of Platonic solids I’ve seen yet.
Thanks for these videos.
one of my favorite youtubers is watching one of my favorite youtubers. ❤ love your videos Eugene
I Agree, It Helped Me My Video ruclips.net/video/gnuRA6uCjjU/видео.html
wow! you are my favorite video maker! you have taught me almost everything I know about electronics and physics.
Physics Videos by Eugene Khutoryansky I just love your videos.
Physics Videos by Eugene Khutoryansky I
His voice is perfect for telemarketing I expected at the end of every sentence to end with "only for $19.99".
Alexis Zikas Dude 😂😂
I think he's better suited for a science documentary.
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
This channel is pure gold.
the "bewmmm" sound when the animation combines shapes is so satisfying to me.
I just realized if we could see 4d, geometry in school would be so damn crazy
A 2d person is saying The Same about us... itd still be boring cause itd be normal to them.
Yeah but 4 dimensional beings would have 4 dimensional brains making them able to comprehend more.
and more tests
yeah or imagine how crazy it would be if we could see 2D
@@wrcz give him a minute to figure it out
Imagine a 4D kid drawing in a 3d paper a house that is a Cross polytope on top of a Hypercube
Yes that's it. I lost you at the 3d paper !
Brilliant lol
welll uhh i ummm you seee uh
The picture will actually be a regular 3D house like yours now. Maybe We are all just pictures of some 4D’s..
We call that Minecraft
I have always been browsing RUclips for 4d and higher and you are one of the videos that have taught me something
One of the boxes in the back should have "Time travel stuff" written on it
Those animations are so cool, and useful
Thank you Sir for the clear explanation and visualization. Now I almost understand what 4D look like.
Guys don’t tell him
Hate to break it to you but those are just projections
@@AMan-xz7tx
But hey, at least we live in a 4d world.
It is not perfectly euclidian unfortunately.
Alllmost!
Making a 3D out of a 5D shape means that you are taking the shadow of the shadow of that 5D shape 🤯
my brain got a blue screen error and had to shut down to prevent damage
another dipshit comment, searching for praise while providing stupidity without intelligence..
same :D
@@jfern6673 why are you so triggered just don't read the comment why bother ? xd
Mine:
What
J Fern Well someone is salty.
Wow awesome job on the editing!!
Love this channel!!
Totally agree
+Nitya Sharma I agree it was really great =D!
they missed the seventh three dimensional platonic solid: kissing your homie goodnight
What is the sixth?
@@ukiitm the Utah teapot
😂 cute
😂 cute
r/SuddendlyGay
(Ironic)
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.
If only my grade school teachers could have had some tactical instruction like this, I might have a better understanding of geometry..
Which geometry? ... They only tried teaching you one, didn't they?
No matter how hard we try to imagine what a polygon would look like in the 4th dimension, I don't think we could ever truly be able to show any kind of representation of how that shape would appear.
If you were restricted to 2 dimensions & there was a shape in front of you, no matter what you try to imagine, how far you rotate around the shape, where you go within your 2 dimensions or how long you stand there observing the shape, there is an entire level of data which is unavailable to you & possibly way beyond your comprehension.
This same principle would have to be applied to a shape in front of you when being restricted to 3 dimensions too. So unless you bordered on insane genius, whilst ever you lived here you'd probably never be truly able to appreciate what this extra dimension actually means to the shape in front of you.
But the idea that time is our 4th dimension could give us a glimpse into how we have to think - if we currently live in 4 dimensions but only have control over 3 (as we are 'dragged' involuntarily through the 4th), extending this idea down to living in 2 dimensions but being dragged involuntarily through the 3rd dimension would be like staring at individual 'slice' photos of an MRI scan of a shape, watching it change as you travel through your 3rd dimension. This would possibly be perceived as watching something change in time, yet moving up to our level & seeing it from up here 'outside' that 3rd dimension, we know it's not time they're traveling through but moving through the object itself. And taking this down to 2 dimensions (living in 1 & being dragged through the second), the concept of the existence of a 3rd dimension of top of that would be inconceivable at that level - not even with the grasp of such a limited scope of perception.
If this idea is correct, then no matter how many dimensions you live in, the dimension above you will always be perceived as what we currently call time, & the dimensions that you DO have control over will clearly become obvious as just another layer of information only available (or able to be understood) to those living in that dimension or higher.
So you can only imagine what information is available to those living in the 4th dimension & above... does that make sense?!?!??? Or did I just brain my damage?
I skipped to the end of your post but I'm pretty sure your brain was just already broken.
+Kyle Rotterdam ya know, ya probly right
All you need to do to easily visualize 4D objects is to slice it up into 3D slices. For example, you could slice a 3D cube into many 2D slices. Each slice would be a square. Similarly, a hypercube would be sliced into many 3D cubes. A 4-simplex would be sliced into many tetrahedrons that get smaller and smaller.
something i was thinking about while reading this.. You can draw a 3D cube on a 2D sheet of paper. But if we only lived in a 2D world, would we even know what to draw for the 3 dimension.
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??
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. :)
I love these geometry heavy videos.
the teapot killed me. that damn teapot.
yea, wtf was that? how is it a Platonic solid? Just because some people like it or use it a lot?
As a man who works in 3D I love the teapot, it’s a preset in 3Ds Max, like the unifying symbol of my kind.