I feel like my brain gets so close to imagining higher dimensions before breaking completely.

Watch that and see what you should be aiming for

That’s what annoys me. If I look at projections of 3D objects in the 2d plane and projections of 4d objects into the 3rd dimension, it makes intuitive sense but I just can’t fully fathom it. I always feel so close to fully understanding the 4d geometry of the shapes but it’s never enough.

@Hubie Maddox what

have you actually done them? this really fascinates me and there seems to be very little serious discussion about. based on the artwork ive seen based on psychedelic trips it makes me suspect you have somehow 4D mental images going on. id love to hear your thoughts

what makes you so sure we "are not meant to know" it ever? whose to say we arent done evolving and future human brains might be able to see and live in 4D?

The fact that he can visualize this and explain it so clearly really shows how abstract this man can contemplate. So difficult to do

@Phantom4545 45 well I was just saying the the theory u or someone else was saying is "different", actually *includes* your theory, and has more. So this theory is just your theory +. But also this "theory" has physical evidence

@Doom Guy I'm gonna use that omg

@Doom Guy yesssss omg u got it so right

@Magic Mike deceptive?

"You can basically figure it out yourself" -Carlo Sequin on 5 dimensional polytopes Nobody has ever believed in me as much as this guy

Lol

Thats when I stopped the video. He's not talking to me for the whole time :)

@Andon Andonov at

And you deserve it! I'm sure you could if you really wanted to!

@Mop's backup account they are at 668 now hehe

And this is why they shouldn't call "4D movies" the 4D movies. Excellent video. Thank you!

@Josh Young Thank you! Saved me the effort and a long explanation! Really though, I see a clock as times "ruler".

"4D" movies add another sense to the movie. Most often it's smell.

@Авто Люб what are you talking about?

@Josh Young a 4d hypercube dows not move when in a picture. Does that make a stale hypercube not 4d?

@Авто Люб getting tired of repeating this... nah just kidding, I love correcting pedants who are wrong. Dimensions are not only spatial. Something doesn't have to be spatial to be considered a dimension of something, because dimension is also a synonym for a quality or facet.

Interview: Like an evil twin. Guy: Like a nice twin actually. This guy really loves shapes.

Thanks to this im gonna consider the octahedron and the cube as friends

So do I! Shapes are interesting

It's a platonic kind of love :p

Imagine a 2D being trying to understand the platonic solids.

Imagine if our view is just 4d shadows. We're in a cave, looking at the wall. If we were to ever leave, we would break our minds and those who resided in the cave with us would call us crazy.

The 2D would only see a cross section of the 3D. It has no concept of up and down.

Read Flatland.

it actually happened to Homer Simpson

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

@Rurihime same

He's still kicking. 79 years old!

You made me think he died or something

Title: educational stuff Thumbnail: the angel that screams geometrically.

@Luís Semedo wasn't leliel a 2d thing with a 3d shadow?

@lasarousi well, Leliel certainly was, it's not farfetched to think so

I clicked this just to confirm Ramiel is in fact a 4D being moving in our 3D world

Mathematicians: there are 5 regular polygons in 3d space jan Misali: 48, take it or leave it.

@R L 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

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

jan Misali It's a toki pona thing where only names are capitalized

“this is a icosahedron” me who plays dnd: ah yes, a d20

@Thiago Poly

@99thGamer polygons*

@Jacob Lynch they actually can be, the problem is that the vertices aren't the same.

@Jacob Lynch *polyhedra

Sides aren’t regular polygons :(

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! 🙏❤️

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!

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!

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.

Nice teacher! Great explanation, thank you a lot

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

Trying to understand 4D in a 3D world through a 2D screen.

With a one dimensional brain

@Nathaniel Zhan time is 4d

To a 1D brain Where your knowledge is 0 dimensional

Lol 😆, there is a diy youtube video on how to do a homemade 3D image using your phone and some materials. Might have to go to arts and crafts store to get materials. I havent tried it yet to see if it works.

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!

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

Props to the animator the visuals in this were amazing

I honestly feel that this video has done more to make me feel sane than any other teaching I've ever received. What Sequin is speaking about makes so much sense to me (experientially, not mathematically).

Trying to picture 4D is kinda like trying to play a movie in a music player

well said.

Well you can just make it 3D sound experience to compensate and imagine, but never see the actual movie, which is a great comparison you got

Ever listen to an audio play?

like getting an mp3 to play an .mp4 file.

@Crimson Spirit like a shadow

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.

amazing ,great works, thanks for putting together such an instructive illustration

This has better explanation than the other. Much clearer. ❤️

This is really cool I always thought 4th Dimensional shapes were cool I knew about the Tesseract for a while but I think the 24 cell is my new favourite.

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

You just reinvented Flatland.

But then the old 4d guy is saying So 5d Platonic solids aren’t as interesting, not that many We’re in a sort of sweet spot (Imagine that with his accent)

Hahahaha totally :)))

r/me_irl multi-dimensional

Bruh

Awesome video. Mr. Sequin is a brilliant guy. Great teacher.

Beautifully explained. Thankyou sir

Excellent video Professor. I need your help. How many faces of nine vertices exist in a 6-hypercube with p=6, that is, in a 6-dimensional hypercube with 46656 vertices. Could you give me an equation to calculate the characteristics of that hypercube.

That is absolutely amazing. I have just learned polyhedrons and the video comes up within a few time

The best video I've ever watched on dimensions and geometry, loved it ♥️ and understood it.

Now that's a proper science lesson, thank you very much for conveying such important knowledge in the most simplistic realistic fun way!

With the projection of the 600 Cell, I wonder if the mass of tetrahedrons on the inside could be comparable to a solid of constant width?

This was very interesting and cool and I loved the excitement and energy while explaining this complex subject in a layman's way of understanding.

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.

Welcome to the trip feels when you break through to the higher dims!

@Levi Workman You actually see in two dimensions. Your brain just processes the stereoscopic image from both of your eyes and guesses how far things are in front of you.

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?

@D4narchy his wonder is beautiful

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.

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.

This is freaking amazing! So since in the analogy of flat land (2D) they can only move in length and width, in 3D we can move length width, and height. In 4D space, it would stand to reason then that they can move on some 4th dimensional plane of space? To us it would appear as if they were phasing in and out of existence, and yet to them it would simply be moving in the 4th plane. Much the same as we can move up and down. 4th dimensional space would have to be larger than 3D space? One thing perplexing me though is this: suppose their were other being in this 4D space. Would we not observe them in our 3D space? All these polytopes are attached to each other so we would see them much as flat landers would see us as a line, we would see them as a 3D object. Some are suggesting that the UFO phenomenon is really beings from a higher dimensional space. But how in the world would they hide themselves from us? Do the reside inside the polytope? How would that be possible. Another way to consider this is that we reside in all three dimensions of space. Wouldn’t they also reside in all 4 dimensions of space? We do not have the ability to shift ourselves into 2D space, other than say taking a flat photograph. But that is an artifact of our existence, not actually our existence. I hope my musings and questions about this make sense to someone with more understanding than myself. If you have any thoughts or ideas about how to answer any of these questions, please reply!

I think i get you.

I really like the explanation along with the range of visuals.

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 fact that three dimensional beings can even figure out the properties of four dimensional objects amazes me.

@Javier Rodriguez "maybe you are just delusional" maybe you don't get people goofing around

O

Because we have soul

@IIINEMESESII IMO "Light cone" is part of physical reality regardless if there are intelligent beings in the universe or not. ;) So that is why time indirectly part of reality. IMO. The question is similar to numbers. Do numbers exist? What do you mean exist? ;)

@Ferenc Rarosi i thought time was man made concept used to measure things moving in a space. as in if humans never were, would there still be time? does the universe need time to function? yes things would still be moving but if there is no observer of objects then what does an infinite universe need time for? idk if im making any sense but i seen somewere about time if its real. i mean obviously to us it is. or to a concious being time is perceived but is it 'real' and needed by the universe for anything? just wondering no disrespect. bc that to me would be a huge reason we can never time travel backwards in time. bc its our concept of something happening. things moved and you cant make them rewind if time was a real thing there should be a way to interact with it? right? we can interact with everything else in the universe. but never with time.

Honestly this is pretty cool. I wonder how living being would look if they were projected in the fourth dimension...

The animation is amazing!

Question, if the 4th dimension is our time dimension. Does placing the three (or eight?) cubes in the same spot one after the other cause them to fold into to forming a 4th dimensional shape, in the same way folding over the squares makes a cube?

for the 4th dimension I image something with a hinge, imagine 2 cube connected at the corner but only one cube should be visible in the 3d plane while the other cube only becomes visible when the other is invisible, both can be invisible at once but neither can be visible at the same time as the other

I really wish, if only for a moment, I could actually experience perceptive awareness of an additional spatial dimension.

@Chris Lynch but they do though, because they conpute in 3 dimensions

@TootTootMcbumbersnazzle what if you are very unstable and psychotic? Nothing can break your mind if its already broken eh?

Have fun being possibly insane. If you are lucky, you could be a mathematician and could try explaining these shapes to other 3 dimensional beings In a seemingly expertly way.

Mescaline

Well, first don’t look at any living being. You will see their insides. This is because 4d people see in 3D, we see in 2d , 2d beings see 1d , and 1d sees a point (0d) 0d beings see nothing

It’s insane how I understood the 6D hyper cube and insanely saw how it was gonna look before he showed the model🤯🤯🤯 understanding higher dimensions will make me a better abstract painter

Very interesting and well explained

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...???

This video blew my mind 10 times! I love this stuff :)

This guy has the perfect accent for the word tetrahedron

Got an ad and was going to leave, til I seen this.

It's a strangely sexy accent. Or, at least as sexy as you can get while talking about the fifth dimension...

I love how he says “icosahedron”

extremely accurate

@Carmen Reggediesch Well, I am. Can confirm it ;)

It would be nice to see a 4D object made where the fourth dimension is also illustrated through varying colour or shade. It's hard to understand what is closer/farther in the 4th dimension.

Some things that blow my mind when it comes to 4 dimensions, are that knots are impossible, there are 6 principle planes of rotation, gravity abides to F = (G*M*m)/r^3 and two perpendicular planes can intersect at just 1 point

That Rhombic Triaconthahedron (22:58) is a mind blowing 6D shape. It has cubes as its faces!

I tried to actually visualise the tesseract in 4d and my brain exploded! So far I can only do the simplex but still in 4d though

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.

@Random thoughts & theories there is possibly an infinite amount but its out of my knowledge to know that and even the smartest people on earth dont know.

Well.. That means that the entire space inverted and stretched from varying distances will cloak the entire space in a 3d shadow basically you will be moving through sludge and then light would possibly be plasma bent and constructed inside and around the multifaceted and complex shapes of thw 4th dimension.

@Trainwreck I think you don't have shadows in 1st dimension.

If you were in the 1st dimension, would shadows be in 0 dimensions or the 1st?

Basically you would have a 3 Dimensional shadow kind of how in our world we see shadows in 2 Dimensions on a flat surface

As a person with an affinity for higher dimensions, I see this as a VERY interesting video

Ah yes those famous rpg dice... The d4, the d6, the d8, the d10, the d20, and the dTEAPOT

the deapot

Not d12?

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

Him: "Print objects in 4D and beyond." 3D Printer: "Nope."

@Afonso Bucco No like 2D to 3D Unlimited will be more than enough for to print out a 4D hyber-cube

also you would spend lots of plastic printing in 4D. Actually infinite 3D plastic is not enough to fill (or hyperfill) any 4D object.

Meanwhile in a higher dimension: "Mom, can you buy me some real toys... I'm tired of playing with these Rhombic Triacontahedrons"

@김현인_SKZstay Son: it just falls through the earth

This is the best of all comments here. Undoubtedly ! Congrats.

@TOMAS MIEGER Of course, I was just having fun.

@Dexuz - Dude - by saying a "ball" I mean of course a "higher dimensional ball" - a geometric body in wich every point of the (N-1) "surface" is in exact same distance to the main "middle point" in a N-Space. Understood.

@TOMAS MIEGER no mom, I'm tired of running both backwards and forwards in time AND space to catch it. Its exhausting!

fantastic video! 0d point, 1d line, 2d flat, 3d space, add time in 4d (hypercube), add probability/choice 5d (basically a parallel world), add movement between all probable outcomes (allowing for a rapid shift on the 3d level) (rapidly transitioning hypercube), 7d consider natural laws and scientific constant variations 8d extend 7d as a line allowing movement between variations 9d extend movement of natural law variation as a space, 10d summation of all spacetime probabilities with movement between probable outcomes/choices and natural law variation.

The reason why you have to rotate the icosahedron 36° is so that you could actually put the gyro elongated band in between that pentagonal bipyramid if you don't know what gyro elongation is it's pretty much whenever you elongated shape not with squares but with equilateral triangles so you could call the icosahedron a gyro elongated pentagonal bipyramid

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

Thank you very much. I am very excited that you are working on these importance. How ever you are faceing other every day problems like me but you have a great mind to put them aside and think about these importance too. Great people , great managers. ✌💝

This is the best demonstration of Platonic solids I’ve seen yet.

You made this so easy to understand, thank you so much, I have learned a lot!

This is the greatest video on dimensions on YouTube that I've watched (many times).

I always require '"the string theory"' to understand higher dimensions. And you are more genius. 🤗🤗

I bet your 3D printer would literally cry if it could lol.

@Misanthropic Isolation poor printer, tortured by being forced to create objects outside its realm of existence

Try using ball and cylinder magnets to make hypercube wireframes. That is a real way to elicit tears.

i was actually thinking about 3d printing or sculpting a hypercube ;}

I feel sorry for the guy that had to program those objects for the 3D printer.

@John Stevonson i have a 0D printer but i cant seem to find what it prints

Are there also 4D analogues to the non-platonic regular polyhedra like the great dodecahedron?

This was a great video, and starting a list of education videos like this to refer to. Thanks!

Didnt understand it all untill I watched it twice great presentation by a man that can bring such things to the non mathematical of us hello from Australia

My question is: At what dimensional point does the simplex meet the hypercube, where, when looking at a graph, we find it can be comprised of either simplexes or cubes?

The diagrams, the colours, the animations are all just wonderful! 5 stars! or should that be "5 Platonic Solids!"

@AlanKey86 - there would only be four stars in three dimensions - the stellar dodekahedron, great dodekahedron, great stellar dodekahedron, and great icosahedron.

Love your music mate

+AlanKey86 5 Thumbs up

+AlanKey86 5 Stellated Polyhedra.

+Pete McPartlan It was indeed :)

Very useful video. I did understand it all when i begin solving 4D..7D twisty puzzles - Magic Cube 4D..7D, Magic 120 Cell. Cool experience.

I wonder if there's a pattern to which polytopes can be projected into a lower dimension such that their outline matches their unit polytope...

Thank you for teaching me. I want to learn more.

I want to see it.

What about in hyperbolic space? Could you cram more triangles/squares/etc around each other in 3D and make more of these solids?

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

morgan freeman cube

Great question, and great thought exercise, i think that from a mathematical point of view, music is 2D and the 3D music wold soud like some background noise to us, and the 4D like a backgound noise with a high pitch and so on... I guess....

Brooke Carrie what did it look like describe

The 10-dimensional analogue to the Octahedron or dual to the Dekeract has the name "Chiliacosicosikatetraxennon".

Erm... That would be incredibly weird.

7:43 - 8:50 ---- THANK ! YOU! SIR! that was the only explanation i could follow on a 4D model! now i understand it! :)

Some names for regular polytopes are so insane toungetwisters! Here are a few: For 2D, we have: icosadodecagon tricontatrigon tricontatetragon tricontapentagon tricontahexagon tricontaheptagon tricontaoctagon tricontaennagon ... you get the piont. all 2d polygons where E => 32 3d stops at the icosahedron, so no touge twsters there 4D: hecatonicosahedroid hexacosihedroid

Alright so in 3D some might view the teapot as another plotonic, so does that mean that maybe in higher dimensions there might be platonic that are just as different

Carlo Sequin is a great teacher and his insights are well arranged and easily conveyed in an understandable way, I wish I could teach so well :

One of my greatest hopes for future technology is the ability to truly visualize 4D space and shapes

@メカフィンチ why are you relying on technology? Heaven is already inside you.

you can visualize these shapes their very common in dmt experiences

Only higher beings from other dimensions can cross over to lower dimensions although they are forbidden from doing so

Not gonna happen in this universe, I'm afraid

@MrSayines yes you can do that, but as you said it wouldn’t be very interesting and you wouldn’t be actually seeing the 4d shape, just slices

Once I fully understand 4D I will break out of the flesh that bounds me to 3D and become more powerful than you could ever imagine

This is ART my friends. My HS students are using similar concepts to construct an open cube mobile sculpture. This is critical thinking at it's finest. We need to encourage more of this thought in K-12 EDUCATION. Lisa Daly, Highland HS, SLC UT

Aren’t there technically more regular polyhedra than the 5 Platonic solids? Due to stuff like polygrams and the like? The only difference is that many are either not strictly convex or have no interior

I love how this guy says “you’ll just have to believe me” when the 3D visual aids stop being useful

Watching 4D objects represented in 3D projections on a 2D screen.... seems legit

Well if you imagine to watch 3d objects represented in 2d projections on an 1d whatever. Maybe you can know how much salt is needed for having an idea about 4d represented in 3d

Le funny 😜

@Ty Doan Does not compute fellow human.

No, they're wong. ( ! ) an (xD model will distort wildly when squished down to a 2D ( screen ) Projection of an apparently 3D object !

Imagine playing a dice game with four-dimentional hyperdice, and having to calculate the amount of vertices you have rolled simultaneously. Finally some fun for my physic's colleagues :D

If we actually lived in 2-dimensions, we wouldn't even be able to see the 2-D shadow of the cube. We'd only be able to see one straight line. Imagine what that says about how much of the 4th dimension we're really seeing when we look at a 3-D shadow of a hypercube from the third dimension.

Could a simplex ever have enough vertices to resemble a sphere?

Just thought of something: look at one side of the hyper cube head on. If you think about it, it looks like the shadow of a normal cube drawn on a 2D plain.

I like the question the young guy asks, he's smart enough to make these kind of interviews actually interesting

Well... He couldn't answer the first question

I think the questions are scripted.

Or maybe the questions are pre-scripted?

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

Hi I have a question: How are those extra dimensions (ex.4rth, 5th etc) linked to the higher dimensions of physics if linked at all? In physics fourth dimension isn't conceivable by observation but takes place in the subatomic level ( it can be linked with time , providing different possibilities at the same spatial dimension). In the fifth dimension, we would see a world slightly different from our own that would give us a means of measuring the similarity and differences between our world and other possible ones. In the sixth, we would see a plane of possible worlds, where we could compare and position all the possible universes that start with the same initial conditions as this one and so on.. until the 11th ( by the way in physics things dont go beyond the eleventh while in geometry it seems you can have infinite dimensions.. So is there any link between those geometrical extra dimensions that you present in this video and the extra dimensions of physics ?

I have learned about 4d for months but now i do really acquire the concept and catch the precise definition also visualization of a 4d cube

I love the way he pronounces "tetraheedrron" and "sqvares". And overall films with him are marvellous

Thanks for these videos.

*d o u b l e t h e d o t s a g a i n*

Physics Videos by Eugene Khutoryansky Your videos are like a hidden gem of youtube, I am so glad I found them❤

Physics Videos by Eugene Khutoryansky I

Physics Videos by Eugene Khutoryansky I just love your videos.

wow! you are my favorite video maker! you have taught me almost everything I know about electronics and physics.