Perfect Shapes in Higher Dimensions - Numberphile

  • Am Vor 6 years

    NumberphileNumberphile

    Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions.
    More links & stuff in full description below ↓↓↓

    Extra footage (Hypernom): de-film.com/v-video-unC0Y3kv0Yk.html
    More videos with with Carlo: bit.ly/carlo_videos

    Edit and animation by Pete McPartlan
    Pete used Stella4D --- www.software3d.com

    Epic Circles: de-film.com/v-video-sG_6nlMZ8f4.html

    Support us on Patreon: www.patreon.com/numberphile

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Johnathon Waymire
Johnathon Waymire

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

Vor year
Ivri chayim through the talmidim You'll find Emrys
Ivri chayim through the talmidim You'll find Emrys

Watch that and see what you should be aiming for

Vor 7 Stunden
ToastyEggs
ToastyEggs

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.

Vor 2 Tage
Zack Buildit
Zack Buildit

@Hubie Maddox what

Vor 4 Tage
CallMeBronco
CallMeBronco

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

Vor 4 Tage
CallMeBronco
CallMeBronco

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?

Vor 4 Tage
Shpongle
Shpongle

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

Vor 2 years
Mihail Milev
Mihail Milev

@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

Vor 3 Monate
Mihail Milev
Mihail Milev

@Doom Guy I'm gonna use that omg

Vor 3 Monate
Mihail Milev
Mihail Milev

@Doom Guy yesssss omg u got it so right

Vor 3 Monate
Doom Guy
Doom Guy

@Magic Mike deceptive?

Vor 3 Monate
Aegon Targaryen
Aegon Targaryen

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

Vor year
Doom Guy
Doom Guy

Lol

Vor 3 Monate
Zhaoyi CHEN
Zhaoyi CHEN

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

Vor 6 Monate
Leonilo Garrucha
Leonilo Garrucha

@Andon Andonov at

Vor 6 Monate
Brian CP
Brian CP

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

Vor 7 Monate
Z
Z

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

Vor year
Zichfried
Zichfried

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

Vor year
Nathan B
Nathan B

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

Vor 4 Monate
John Johnson
John Johnson

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

Vor 4 Monate
Josh Young
Josh Young

@Авто Люб what are you talking about?

Vor 4 Monate
Авто Люб
Авто Люб

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

Vor 4 Monate
Josh Young
Josh Young

@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.

Vor 4 Monate
Noah Heninger
Noah Heninger

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

Vor 2 years
Mateusz Szulecki
Mateusz Szulecki

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

Vor 2 Monate
Kevin Kurz’s art display
Kevin Kurz’s art display

So do I! Shapes are interesting

Vor year
Setekh
Setekh

It's a platonic kind of love :p

Vor 2 years
Riverxz01
Riverxz01

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

Vor 2 years
Derp Atel
Derp Atel

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.

Vor 3 Monate
John Johnson
John Johnson

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

Vor 4 Monate
whobitmyname
whobitmyname

Read Flatland.

Vor 5 Monate
Boyorouge Sauvage
Boyorouge Sauvage

it actually happened to Homer Simpson

Vor 7 Monate
Richard Dana
Richard Dana

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

Vor year
Ekke Krosing
Ekke Krosing

@Rurihime same

Vor 17 Tage
Brian CP
Brian CP

He's still kicking. 79 years old!

Vor 7 Monate
Rurihime
Rurihime

You made me think he died or something

Vor 9 Monate
Zulu
Zulu

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

Vor year
Mercurial Interference
Mercurial Interference

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

Vor 4 Monate
Luís Semedo
Luís Semedo

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

Vor 7 Monate
lasarousi
lasarousi

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

Vor year
SCP Time
SCP Time

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

Vor 9 Monate
Zack Buildit
Zack Buildit

@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

Vor 4 Tage
R L
R L

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

Vor 3 Monate
Pez
Pez

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

Vor 3 Monate
minie
minie

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

Vor year
Nacho Compaired
Nacho Compaired

@Thiago Poly

Vor 3 Monate
Thiago
Thiago

@99thGamer polygons*

Vor 4 Monate
Realmless
Realmless

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

Vor 9 Monate
99thGamer
99thGamer

@Jacob Lynch *polyhedra

Vor 9 Monate
Jacob Lynch
Jacob Lynch

Sides aren’t regular polygons :(

Vor year
Colin Bache
Colin Bache

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! 🙏❤️

Vor year
Symba Taylor
Symba Taylor

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!

Vor year
ChaoticKill248
ChaoticKill248

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!

Vor year
Vivian Wilfred
Vivian Wilfred

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.

Vor year
Cristhian
Cristhian

Nice teacher! Great explanation, thank you a lot

Vor year
Master Spark
Master Spark

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

Vor year
cashbag2012
cashbag2012

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

Vor 3 years
Eiden D'Elia
Eiden D'Elia

With a one dimensional brain

Vor 16 Tage
Alessandro Pizzica
Alessandro Pizzica

@Nathaniel Zhan time is 4d

Vor 20 Tage
Mateusz Szulecki
Mateusz Szulecki

To a 1D brain Where your knowledge is 0 dimensional

Vor 2 Monate
No One
No One

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.

Vor 3 Monate
loquacity
loquacity

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!

Vor 4 Monate
MaRiahh Walker / Political-Makeup
MaRiahh Walker / Political-Makeup

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

Vor 2 years
Evank
Evank

Props to the animator the visuals in this were amazing

Vor year
John Brian Simms
John Brian Simms

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).

Vor 2 years
Odin Seikatsu
Odin Seikatsu

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

Vor 3 years
Derp Atel
Derp Atel

well said.

Vor 3 Monate
Thiago
Thiago

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

Vor 4 Monate
Silver
Silver

Ever listen to an audio play?

Vor 4 Monate
Jonathan West
Jonathan West

like getting an mp3 to play an .mp4 file.

Vor 5 Monate
Eric’s Animated Shorts
Eric’s Animated Shorts

@Crimson Spirit like a shadow

Vor 9 Monate
Damien Boykin
Damien Boykin

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.

Vor year
mahdi noroozi
mahdi noroozi

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

Vor year
Engr Denden Kadil
Engr Denden Kadil

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

Vor year
Gamers_mate
Gamers_mate

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.

Vor year
RiverSticks
RiverSticks

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

Vor 5 years
Silver
Silver

You just reinvented Flatland.

Vor 4 Monate
Flaming Pi
Flaming Pi

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)

Vor 7 Monate
Bowiefan88
Bowiefan88

Hahahaha totally :)))

Vor 8 Monate
Satyam Tekriwal
Satyam Tekriwal

r/me_irl multi-dimensional

Vor 8 Monate
Oni
Oni

Bruh

Vor 10 Monate
Citizen Of Earth
Citizen Of Earth

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

Vor 4 Monate
Multiverse
Multiverse

Beautifully explained. Thankyou sir

Vor 2 years
Miguel Angel Quinteiro Piñero
Miguel Angel Quinteiro Piñero

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.

Vor year
Eva Beyza
Eva Beyza

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

Vor 4 Monate
Rayan Sattar Khan
Rayan Sattar Khan

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

Vor 2 years
Charbel Azar
Charbel Azar

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

Vor 3 Monate
Carbon Eight
Carbon Eight

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?

Vor year
Jazz
Jazz

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.

Vor 2 years
BulletTheEnforcer
BulletTheEnforcer

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.

Vor 3 years
Stuart Parnell
Stuart Parnell

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

Vor year
KJ7QLV
KJ7QLV

@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.

Vor year
Levi Workman
Levi Workman

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?

Vor year
Pietru Farrugia
Pietru Farrugia

@D4narchy his wonder is beautiful

Vor year
D4narchy
D4narchy

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.

Vor year
SK
SK

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.

Vor 7 Monate
Let your Light shine
Let your Light shine

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!

Vor 11 Monate
SCP Time
SCP Time

I think i get you.

Vor 9 Monate
Kris Montgomery
Kris Montgomery

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

Vor 2 years
Drustan Astrophel
Drustan Astrophel

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

Vor year
AnnoyedPenPen
AnnoyedPenPen

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

Vor 3 years
Vali_BG
Vali_BG

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

Vor year
Darveysh
Darveysh

O

Vor 2 years
TARA Construction
TARA Construction

Because we have soul

Vor 2 years
Ferenc Rarosi
Ferenc Rarosi

@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? ;)

Vor 3 years
IIINEMESESII
IIINEMESESII

@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.

Vor 3 years
Tahlia Grant
Tahlia Grant

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

Vor 2 years
Zenious Spy
Zenious Spy

The animation is amazing!

Vor year
JP
JP

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?

Vor year
Lee Shallis
Lee Shallis

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

Vor year
phuturephunk
phuturephunk

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

Vor 5 years
Jeremiah Barnes
Jeremiah Barnes

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

Vor 4 Monate
GOOGOL
GOOGOL

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

Vor 4 Monate
Luis Perez
Luis Perez

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.

Vor 2 years
ukiitm
ukiitm

Mescaline

Vor 2 years
Yang Kong
Yang Kong

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

Vor 2 years
Riley 225
Riley 225

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

Vor 3 Monate
W Cactus
W Cactus

Very interesting and well explained

Vor 6 Tage
AntoanetaDD
AntoanetaDD

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...???

Vor year
Heri Joensen
Heri Joensen

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

Vor 2 years
MarkOates
MarkOates

This guy has the perfect accent for the word tetrahedron

Vor 4 years
Wolfman HCC
Wolfman HCC

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

Vor year
alissa mower clough
alissa mower clough

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

Vor year
Nintendoprogamer12
Nintendoprogamer12

I love how he says “icosahedron”

Vor year
Guilherme Antão
Guilherme Antão

extremely accurate

Vor year
Arthipex
Arthipex

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

Vor year
Isaac
Isaac

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.

Vor 2 years
Ranibow Sprimkle
Ranibow Sprimkle

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

Vor 2 years
Tony
Tony

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

Vor year
TomtheMagician21
TomtheMagician21

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

Vor year
Syphist
Syphist

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.

Vor 4 years
GOOGOL
GOOGOL

@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.

Vor 4 Monate
GOOGOL
GOOGOL

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.

Vor 4 Monate
Can Çalı
Can Çalı

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

Vor 3 years
Trainwreck
Trainwreck

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

Vor 3 years
TREY XIII
TREY XIII

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

Vor 3 years
Trazyn the Infinite
Trazyn the Infinite

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

Vor year
Nik does stuff
Nik does stuff

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

Vor year
dave slam jam
dave slam jam

the deapot

Vor 5 Monate
Lukie Poole
Lukie Poole

Not d12?

Vor 8 Monate
Cathie Korowa
Cathie Korowa

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

Vor 3 Tage
Jayyy Zeee
Jayyy Zeee

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

Vor 2 years
GTA and Apple channel
GTA and Apple channel

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

Vor 11 Monate
Afonso Bucco
Afonso Bucco

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

Vor year
Warious& warious
Warious& warious

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

Vor 3 years
MinecraftMilkCraft
MinecraftMilkCraft

@김현인_SKZstay Son: it just falls through the earth

Vor 6 Monate
Caio Marcio Rodrigues
Caio Marcio Rodrigues

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

Vor 7 Monate
Dexuz
Dexuz

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

Vor year
TOMAS MIEGER
TOMAS MIEGER

@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.

Vor year
nyetloki
nyetloki

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

Vor year
Sarabjot Makkar
Sarabjot Makkar

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.

Vor year
Vincent Cutignola
Vincent Cutignola

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

Vor 2 years
Drew Lester-Nieves
Drew Lester-Nieves

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

Vor 4 Monate
Maysam Mirzakhalili
Maysam Mirzakhalili

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. ✌💝

Vor 2 years
Nya Nates
Nya Nates

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

Vor year
Tasha
Tasha

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

Vor year
Vansanglura
Vansanglura

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

Vor year
Sharvil Patel
Sharvil Patel

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

Vor Monat
Logic Plague
Logic Plague

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

Vor 3 years
Blizzard_the_seal
Blizzard_the_seal

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

Vor year
Sasha Green
Sasha Green

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

Vor year
yus3dp
yus3dp

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

Vor 2 years
Bakerygo
Bakerygo

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

Vor 2 years
DogMcMeow
DogMcMeow

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

Vor 2 years
SpaceMario2
SpaceMario2

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

Vor year
Jordan Thompson
Jordan Thompson

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

Vor year
Sil Marillian
Sil Marillian

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

Vor year
StonerBill420
StonerBill420

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?

Vor 2 years
AlanKey86
AlanKey86

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

Vor 6 years
B
B

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

Vor 3 years
Klapaucius Fitzpatrick
Klapaucius Fitzpatrick

Love your music mate

Vor 5 years
Adrian Häußler
Adrian Häußler

+AlanKey86 5 Thumbs up

Vor 6 years
Pete McPartlan
Pete McPartlan

+AlanKey86 5 Stellated Polyhedra.

Vor 6 years
AlanKey86
AlanKey86

+Pete McPartlan It was indeed :)

Vor 6 years
VTS [RU]BiK
VTS [RU]BiK

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.

Vor 7 Monate
Freyaday
Freyaday

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...

Vor 2 years
The Biblical Prophet Brando
The Biblical Prophet Brando

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

Vor 2 years
Vali_BG
Vali_BG

I want to see it.

Vor year
ThePinkBunnyEmpire
ThePinkBunnyEmpire

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

Vor year
MG222
MG222

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

Vor 5 years
A Hitler
A Hitler

morgan freeman cube

Vor 3 years
Maximilian Finkler
Maximilian Finkler

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....

Vor 3 years
HueHanaejistla! Inc.
HueHanaejistla! Inc.

Brooke Carrie what did it look like describe

Vor 3 years
B
B

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

Vor 3 years
Dabbing Flight
Dabbing Flight

Erm... That would be incredibly weird.

Vor 3 years
Scarekrow
Scarekrow

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

Vor 2 years
Isaac T
Isaac T

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

Vor year
ChangedNames
ChangedNames

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

Vor 2 years
Erenea5
Erenea5

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 :

Vor 2 years
メカフィンチ
メカフィンチ

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

Vor 2 years
Ivri chayim through the talmidim You'll find Emrys
Ivri chayim through the talmidim You'll find Emrys

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

Vor 7 Stunden
TheIndieGamesNL
TheIndieGamesNL

you can visualize these shapes their very common in dmt experiences

Vor 10 Monate
Dr M
Dr M

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

Vor 11 Monate
Aurelia
Aurelia

Not gonna happen in this universe, I'm afraid

Vor year
メカフィンチ
メカフィンチ

@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

Vor year
Random Highlights
Random Highlights

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

Vor 9 Monate
Lisa Quagliozzi
Lisa Quagliozzi

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

Vor 2 years
Zack Buildit
Zack Buildit

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

Vor 4 Tage
Colten Jackson
Colten Jackson

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

Vor year
snair
snair

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

Vor 4 years
Dennis de Jong
Dennis de Jong

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

Vor 3 years
Neymar Jr
Neymar Jr

Le funny 😜

Vor 3 years
Gary Sutherland
Gary Sutherland

@Ty Doan Does not compute fellow human.

Vor 3 years
Chrstphre Campbell
Chrstphre Campbell

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

Vor 3 years
Mattis Grotegerd
Mattis Grotegerd

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

Vor 4 Monate
David
David

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.

Vor 2 years
Jeremy Toman
Jeremy Toman

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

Vor 3 Monate
S_man
S_man

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.

Vor year
Phoenixis
Phoenixis

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

Vor 4 years
Eicee1989
Eicee1989

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

Vor 3 years
TitanFallout
TitanFallout

I think the questions are scripted.

Vor 3 years
Axel
Axel

Or maybe the questions are pre-scripted?

Vor 3 years
Alexis TwoLastNames
Alexis TwoLastNames

this channel is making me realize i want to study this kind of conceptual math along with financial math and quantitative analysis

Vor year
yaicob.com
yaicob.com

Go for it, Jane Street awaits

Vor 10 Monate
IT
IT

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 ?

Vor year
Vũ Trọng Quyền
Vũ Trọng Quyền

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

Vor 5 Monate
RooiGevaar19
RooiGevaar19

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

Vor year
Physics Videos by Eugene Khutoryansky
Physics Videos by Eugene Khutoryansky

Thanks for these videos.

Vor 6 years
InfinitySoul
InfinitySoul

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

Vor year
Nia Schimnoski
Nia Schimnoski

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

Vor 3 years
Jim Brown
Jim Brown

Physics Videos by Eugene Khutoryansky I

Vor 4 years
Pulak Das
Pulak Das

Physics Videos by Eugene Khutoryansky I just love your videos.

Vor 4 years
Kyle Glarum
Kyle Glarum

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

Vor 4 years

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