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Perfect Shapes in Higher Dimensions - Numberphile

Numberphile
2016 ж. 22 Нау.
5 266 620 Рет қаралды
Жүктеу

Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions.
More links & stuff in full description below ↓↓↓
Extra footage (Hypernom): • Eating 4D Polytopes (H...
More videos with with Carlo: bit.ly/carlo_videos
Edit and animation by Pete McPartlan
Pete used Stella4D --- www.software3d.com
Epic Circles: • Epic Circles - Numberp...
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Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
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Пікірлер

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

    @000netko@000netko3 жыл бұрын

    • xD

      @andonandonov7793@andonandonov77933 жыл бұрын

    • LOL

      @mishikomishiko9088@mishikomishiko90883 жыл бұрын

    • Haaaahaaa

      @thankor@thankor3 жыл бұрын

    • Same

      @mopsbackupaccount5128@mopsbackupaccount51283 жыл бұрын

    • Most underrated comment on all of youtube for all of time. thank you.

      @theatrefirefly@theatrefirefly3 жыл бұрын

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

    @shpongle7322@shpongle73224 жыл бұрын

    • Is this clear to you? 😂

      @freddybenelli9100@freddybenelli91004 жыл бұрын

    • Remenber Nikola Tesla? Read about him.....

      @albertorivas6339@albertorivas63394 жыл бұрын

    • alberto rivas I’ve not heard Tesla touch on higher dimensions, can you give me a theory of his you have in mind?

      @lilfr4nkie@lilfr4nkie4 жыл бұрын

    • alberto rivas I have several books about Tesla.. what makes you think I haven’t heard or read about him lol. So random

      @shpongle7322@shpongle73224 жыл бұрын

    • @@shpongle7322 just another 4d mysticism delusional dude hahaha

      @azap12@azap123 жыл бұрын

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

    @minie7950@minie79503 жыл бұрын

    • No mention of the 10 sider for some reason...the forgotten solid.

      @GregtheGrey6969@GregtheGrey69693 жыл бұрын

    • Sides aren’t regular polygons :(

      @jacoblynch8844@jacoblynch88443 жыл бұрын

    • @@jacoblynch8844 *polyhedra

      @theprodigal72@theprodigal722 жыл бұрын

    • @@jacoblynch8844 they actually can be, the problem is that the vertices aren't the same.

      @realmless4193@realmless41932 жыл бұрын

    • @@theprodigal72 polygons*

      @Thiago-ck5iu@Thiago-ck5iu2 жыл бұрын

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

    @nikdoesstuff9338@nikdoesstuff93383 жыл бұрын

    • Not d12?

      @lukiepoole9254@lukiepoole92542 жыл бұрын

    • the deapot

      @daveslamjam@daveslamjam2 жыл бұрын

  • 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

    @MorningLightMtn@MorningLightMtn7 жыл бұрын

    • And so on lol...

      @threewagthepenguin9869@threewagthepenguin98697 жыл бұрын

    • and are confused at how 3D biology could even exist.

      @MuzikBike@MuzikBike7 жыл бұрын

    • 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.

      @neildhan@neildhan7 жыл бұрын

    • NusXrrnak Somewhere in 1d space, 1d scientists are wondering how they even exist.

      @TruKave@TruKave7 жыл бұрын

    • somewhere in 0D space, there is a very small speck doing nothing.

      @Misterlegoboy@Misterlegoboy7 жыл бұрын

  • This guy has the perfect accent for the word tetrahedron

    @MarkOates2@MarkOates26 жыл бұрын

    • if you know how to roll your r's then you can also say it like him

      @nanu4144@nanu41445 жыл бұрын

    • I like his pronunciation on the word square. "Sqvare" :)

      @guitargeorge1874@guitargeorge18745 жыл бұрын

    • It's like a german-scottish mix.

      @wtfduud@wtfduud5 жыл бұрын

    • 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.

      @EdoTimmermans@EdoTimmermans5 жыл бұрын

    • Tetraheedraun!!

      @protonix07gaming8@protonix07gaming85 жыл бұрын

  • 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!

    @Rune3D@Rune3D3 жыл бұрын

    • JEWS!!!!!

      @user-gr6he3hg1u@user-gr6he3hg1u Жыл бұрын

    • @@user-gr6he3hg1u??

      @snailcheeseyt@snailcheeseyt10 ай бұрын

    • It's actually one of the oldest memes in the computer feld. And it still funny to think about 💀

      @spirit_x64@spirit_x645 ай бұрын

  • 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

    @mortal19901001@mortal199010013 жыл бұрын

    • You made me think he died or something

      @rurihime4965@rurihime49652 жыл бұрын

    • He's still kicking. 79 years old!

      @gamemeister27@gamemeister272 жыл бұрын

    • @@rurihime4965 same

      @ekkekrosing8454@ekkekrosing84542 жыл бұрын

    • Confirmed still alive!

      @garnet1918@garnet1918 Жыл бұрын

    • @@rurihime4965 My thoughts, exactly 😨.

      @PC_Simo@PC_Simo Жыл бұрын

  • When I watch these videos, i simultaneously feel both smarter and dumber

    @chronovac@chronovac5 жыл бұрын

    • That's how being smart feels

      @Alex_Hernandez999@Alex_Hernandez9995 жыл бұрын

    • That's called learning, first you dont know what you dont know, then you know what you dont know, then you know

      @powerinknowledge2392@powerinknowledge23925 жыл бұрын

    • I just feel dumber

      @atryan1125@atryan11255 жыл бұрын

    • The more you know the more unknown you're able to see around you. There's a parable about that.

      @RedGallardo@RedGallardo5 жыл бұрын

    • @@alicec1533 Forth Dementia.

      @JonCombo@JonCombo5 жыл бұрын

  • That guy has an amazing voice/accent mix.

    @kyoai@kyoai7 жыл бұрын

    • He's a good lecturer. It's his job to hold your attention.

      @ianedmonds9191@ianedmonds91917 жыл бұрын

    • I always wonder what accent it could be

      @highlewelt9471@highlewelt94717 жыл бұрын

    • I thought it was some kind of Scottish, but apparently he's from Switzerland.

      @jarryda@jarryda7 жыл бұрын

    • Sample it, loop it, fuck it.

      @PooperScooperTrooper@PooperScooperTrooper7 жыл бұрын

    • Go Switzerland! It is the best country!!!

      @RAL_III@RAL_III7 жыл бұрын

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

    @scptime1188@scptime11882 жыл бұрын

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

      @Peztllence@Peztllence2 жыл бұрын

    • 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@JonathanMandrake2 жыл бұрын

    • @@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@zackbuildit882 жыл бұрын

    • ​@@zackbuildit88 Misali would be proud (maybe)

      @beetlegob@beetlegob Жыл бұрын

    • @@JonathanMandrake also, just saying, most mathematicians studying these shapes actually do allow non strictly convex solids, hence their early inclusion in the video

      @zackbuildit88@zackbuildit88 Жыл бұрын

  • 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.

    @damienboykin7772@damienboykin77723 жыл бұрын

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

    @johnathonwaymire9483@johnathonwaymire94833 жыл бұрын

    • Mine doesn't

      @johnsaylor1583@johnsaylor15833 жыл бұрын

    • @@johnsaylor1583 ok.

      @aliensasquatch7485@aliensasquatch74853 жыл бұрын

    • @@aliensasquatch7485 I don't remember commenting that. But, mine does as well. I can't fathom anything beyond the box I live in.

      @johnsaylor1583@johnsaylor15833 жыл бұрын

    • @@johnsaylor1583 or maybe you could, but then your mind broke completely and now you don't remember.

      @jobtenbosch349@jobtenbosch3493 жыл бұрын

    • 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."

      @the0master200@the0master2003 жыл бұрын

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

    @wariouswarious9364@wariouswarious93645 жыл бұрын

    • Oh kid. Just play ball, it rolls in any dimension.

      @tomasmieger6826@tomasmieger68265 жыл бұрын

    • @@tomasmieger6826 "MOM, everytime I try to roll this 3D ball it just falls over :c"

      @Dexuz@Dexuz5 жыл бұрын

    • @@Dexuz Underrated comment!

      @willardaustria@willardaustria5 жыл бұрын

    • "The fun will never end, it's Adventure Time!"

      @christopherochoa4145@christopherochoa41455 жыл бұрын

    • Mom: sure son, do you like a triangle or a cube?

      @_skzstay1264@_skzstay12645 жыл бұрын

  • Props to the animator the visuals in this were amazing

    @evank3718@evank37183 жыл бұрын

  • 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! 🙏❤️

    @ColinBache@ColinBache3 жыл бұрын

    • ❌❌ ❌❌ ❌❌ ❌ FloorFloorFloorFloor It fell.

      @lilmarionscorner@lilmarionscorner9 ай бұрын

  • *[SCREAMS GEOMETRICALLY]*

    @Abdega@Abdega6 жыл бұрын

    • Ramiel ;)

      @ksp-crafter5907@ksp-crafter59076 жыл бұрын

    • radbarij nice

      @tiagobelo4965@tiagobelo49655 жыл бұрын

    • Like when liquid metal goes down Neo's throat.

      @squareheart7077@squareheart70775 жыл бұрын

    • um..

      @HolahkuTaigiTWFormosanDiplomat@HolahkuTaigiTWFormosanDiplomat5 жыл бұрын

    • ERASE MEEEE!

      @tear728@tear7285 жыл бұрын

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

    @odinseikatsu4952@odinseikatsu49525 жыл бұрын

    • More like getting a calculator to say 2+2=5. It’s not really hard, it’s just impossible. :3

      @brysonsirus7747@brysonsirus77475 жыл бұрын

    • Although getting a movie to play in a music player is also impossible so what am I saying?

      @brysonsirus7747@brysonsirus77475 жыл бұрын

    • you can run the audio only though, that's like projecting 4D in 3D sim

      @xxCrimsonSpiritxx@xxCrimsonSpiritxx4 жыл бұрын

    • @@xxCrimsonSpiritxx So if I put a Doctor Who dvd on my cd player it would just play the audio? That's kinda cool.

      @IndigoGollum@IndigoGollum4 жыл бұрын

    • It's possible to see images in audio spectogram :p

      @loller7@loller74 жыл бұрын

  • 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

    @derekhasabrain@derekhasabrain2 жыл бұрын

  • 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

    @drustanastrophel9538@drustanastrophel95383 жыл бұрын

  • At first I was all, "OMG! PRETTY SHAPES!" but then I was like, "What even is life?"

    @wandererinthedust276@wandererinthedust2768 жыл бұрын

    • lool

      @raiden490@raiden4908 жыл бұрын

    • +Wanderer in the Dust LSD

      @Angloth@Angloth8 жыл бұрын

    • LSD is the best

      @jeroenconinx6121@jeroenconinx61218 жыл бұрын

    • hahahahahahh. love your comment

      @kozhikkaalan@kozhikkaalan7 жыл бұрын

    • 42

      @victorsousa7239@victorsousa72397 жыл бұрын

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

    @logicplague2077@logicplague20775 жыл бұрын

    • As opposed to figuratively?

      @misanthropicisolation4013@misanthropicisolation40135 жыл бұрын

    • He's granted his 3d printer eyes.

      @nicholasmolberg1043@nicholasmolberg10435 жыл бұрын

    • New torture test

      @AnymMusic@AnymMusic5 жыл бұрын

    • ΔISEPTICONS 4 EVER AHAHHAHAH

      @itsmeminime7958@itsmeminime79585 жыл бұрын

    • He can Print tears

      @UwU-wl4ep@UwU-wl4ep5 жыл бұрын

  • 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.

    @SK-vk9jf@SK-vk9jf2 жыл бұрын

  • 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!

    @loquacity4765@loquacity47652 жыл бұрын

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

    @cashbag@cashbag5 жыл бұрын

    • With a 1D time line

      @legokenobi1185@legokenobi11855 жыл бұрын

    • @@legokenobi1185 time is actually 4th dimensional structure

      @haellm9192@haellm91924 жыл бұрын

    • @@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

      @harold9924@harold99244 жыл бұрын

    • trolli gettin' roasted into inexistance

      @casualipcroboticist6336@casualipcroboticist63364 жыл бұрын

    • @@legokenobi1185 time isnt 1d

      @natedecoco615@natedecoco6154 жыл бұрын

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

    @phuturephunk@phuturephunk7 жыл бұрын

    • 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.

      @chrislynch6545@chrislynch65457 жыл бұрын

    • ***** who?

      @martingrof1685@martingrof16857 жыл бұрын

    • phuturephunk me too... but we could always try weed 😅😅😅

      @indiangrimreaper8247@indiangrimreaper82477 жыл бұрын

    • actualy we do but we don't realise it and we can't feel it

      @tonykostov928@tonykostov9287 жыл бұрын

    • That's how crazy people are made

      @ThePedroEtc@ThePedroEtc7 жыл бұрын

  • Making a 3D out of a 5D shape means that you are taking the shadow of the shadow of that 5D shape 🤯

    @toma_1225@toma_12252 жыл бұрын

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

    @AlexisTwoLastNames@AlexisTwoLastNames3 жыл бұрын

    • Go for it, Jane Street awaits

      @zyaicob@zyaicob2 жыл бұрын

  • 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.

    @BulletTheEnforcer@BulletTheEnforcer5 жыл бұрын

    • Wow, same

      @phillipchavez1321@phillipchavez13213 жыл бұрын

    • 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

      @MegazoneMusic23@MegazoneMusic233 жыл бұрын

    • 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@D4narchy3 жыл бұрын

    • @@D4narchy his wonder is beautiful

      @pietrufarrugia9617@pietrufarrugia96173 жыл бұрын

    • 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?

      @betteryou7hanme@betteryou7hanme3 жыл бұрын

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

    @koalawithchaingun53@koalawithchaingun536 жыл бұрын

    • With our 1D brain

      @some1112@some11125 жыл бұрын

    • @@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.

      @garysutherland7004@garysutherland70045 жыл бұрын

    • and also with eyes which can only see 2d on their own

      @pralayhait7276@pralayhait72765 жыл бұрын

    • @Gary Sutherland r/Whooosh

      @dylanburfoot1262@dylanburfoot12625 жыл бұрын

    • OBVIOUSLY our imagination is bigger than our eyes

      @DandiLionism@DandiLionism5 жыл бұрын

  • 4d space must look terrifyingly awesome.

    @dream__soda7900@dream__soda7900 Жыл бұрын

    • trust me its beyond anything you can comprehend

      @tone618@tone618 Жыл бұрын

    • litteraly

      @tone618@tone618 Жыл бұрын

    • ​@@tone618 have you been there?

      @666thecreature@666thecreature Жыл бұрын

    • ​@@tone618 you sound so definitive, have you been there?

      @guptahaha@guptahaha11 ай бұрын

    • hes been there and so have you

      @invzmk@invzmk4 ай бұрын

  • 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. :)

    @toddmiller6232@toddmiller6232 Жыл бұрын

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

    @Zichfried@Zichfried4 жыл бұрын

    • Ye legit wtf

      @colelevel2654@colelevel26543 жыл бұрын

    • 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@ez_is_bloo3 жыл бұрын

    • @@ez_is_bloo so all movies are 4D then...

      @A.Mayflower127@A.Mayflower1273 жыл бұрын

    • 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)

      @lou7319@lou73193 жыл бұрын

    • @@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

      @seandaly2211@seandaly22113 жыл бұрын

  • I have no idea what this man is talking about, but it's damn cool!

    @EllieVaricuber@EllieVaricuber7 жыл бұрын

    • Lol!

      @RoaringTRex@RoaringTRex7 жыл бұрын

    • Lol. I love you mate! :)

      @izaakfewton7536@izaakfewton75367 жыл бұрын

    • Love u 2

      @EllieVaricuber@EllieVaricuber7 жыл бұрын

    • El Milto I'm pretending to understand it... ow my brain.

      @flinchfu@flinchfu7 жыл бұрын

    • Flinch Fu same!

      @RtsShrtFrRtthw@RtsShrtFrRtthw7 жыл бұрын

  • He is a mix of Carl Seagan and Admiral Picard, and his coolness factor a multiplication of both taken to the cube.

    @AdlerMow@AdlerMow2 жыл бұрын

  • This video: exists Me, an anime watcher: RAMIEL

    @_charademon_@_charademon_3 жыл бұрын

    • I was just looking for this comment.

      @mamalogon@mamalogon2 жыл бұрын

    • @@mamalogon lol same

      @GDSCLag@GDSCLag2 жыл бұрын

  • do a video on the Utah teapot

    @seantobin5235@seantobin52358 жыл бұрын

    • +Sean Tobin yes, please!

      @omfgmouse@omfgmouse8 жыл бұрын

    • Yes!

      @ximenabriones5040@ximenabriones50408 жыл бұрын

    • +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.

      @rich1051414@rich10514148 жыл бұрын

    • +Sean Tobin your body is ready for it, isn't it

      @frostcrackle2374@frostcrackle23748 жыл бұрын

    • +Sean Tobin Yes, please do.

      @eschelon9067@eschelon90678 жыл бұрын

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

    @sunriseavefan98@sunriseavefan985 жыл бұрын

    • You are sick

      @RJavier007@RJavier0075 жыл бұрын

    • @@RJavier007 what.

      @cjlwhite1@cjlwhite15 жыл бұрын

    • @@RJavier007 I am wondering what warranted that response...

      @michaelnortheast394@michaelnortheast3945 жыл бұрын

    • @@michaelnortheast394 he refers to people as beings as if he was not a human himself

      @RJavier007@RJavier0075 жыл бұрын

    • Or can they?

      @jacoblittmann2807@jacoblittmann28075 жыл бұрын

  • 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!

    @BIG.pisquared@BIG.pisquared3 жыл бұрын

  • 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.

    @emmanuelgiouvanopoulos8273@emmanuelgiouvanopoulos827311 ай бұрын

  • I understand some of these words.

    @tijmenvanderree487@tijmenvanderree4878 жыл бұрын

    • loool

      @milo1685@milo16858 жыл бұрын

    • Then you're doing well.

      @victorotene@victorotene8 жыл бұрын

    • I understood what cube meant

      @kawaiipotatoes2951@kawaiipotatoes29518 жыл бұрын

    • Then why use it?

      @enderman6777@enderman67777 жыл бұрын

    • That's the joke.

      @Samstar369@Samstar3697 жыл бұрын

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

    @AlanKey86@AlanKey868 жыл бұрын

    • +AlanKey86 Thanks Alan, was that your lovely twinkly stuff over the polyhedra?

      @pmcpartlan@pmcpartlan8 жыл бұрын

    • +Pete McPartlan It was indeed :)

      @AlanKey86@AlanKey868 жыл бұрын

    • +AlanKey86 5 Stellated Polyhedra.

      @pmcpartlan@pmcpartlan8 жыл бұрын

    • +AlanKey86 5 Thumbs up

      @adrianhaus@adrianhaus8 жыл бұрын

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

      @__Bruh@__Bruh5 жыл бұрын

  • " Could you show to a NON-mathematician in an intuitive way." That is the right approach...

    @feraskiki655@feraskiki6553 жыл бұрын

  • 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...???

    @AntoanetaDD@AntoanetaDD3 жыл бұрын

  • The idea of 1D honestly scares me more than 4D

    @Jack.Strait@Jack.Strait5 жыл бұрын

    • JackStrait *scares in 0D*

      @SalveSandWonk@SalveSandWonk5 жыл бұрын

    • @@SalveSandWonk *screams on *point**

      @mauz791@mauz7915 жыл бұрын

    • The band or the dimension?

      @SoluKissin@SoluKissin5 жыл бұрын

    • @@SoluKissin The band obviously

      @Jack.Strait@Jack.Strait5 жыл бұрын

    • Thanks for that horrifying vision. This video contextualized that statement.

      @BrettChungus@BrettChungus5 жыл бұрын

  • I have my unit 3 and 4 English and Psychology exams tomorrow but this is far more important

    @patwalsh9360@patwalsh93605 жыл бұрын

    • How was it

      @alejrandom6592@alejrandom65925 жыл бұрын

    • I need to know you can't leave half of a story

      @alejrandom6592@alejrandom65925 жыл бұрын

    • It's your life dude and your money

      @justinmolanick7989@justinmolanick79895 жыл бұрын

    • Anserw

      @alejrandom6592@alejrandom65925 жыл бұрын

    • yo sorry dude. went well 👍🏼 will be getting into uni!

      @patwalsh9360@patwalsh93605 жыл бұрын

  • His accent mixed with talking math stuff is quite a soothing experience tbh

    @braydenfrederick7879@braydenfrederick78792 жыл бұрын

  • 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

    @masterspark9880@masterspark98803 жыл бұрын

  • So far I am just enjoying the shapes.

    @williamaleman5460@williamaleman54605 жыл бұрын

    • 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.

      @Alwis-Haph-Rytte@Alwis-Haph-Rytte5 жыл бұрын

    • Mr Rytte Excuse me..what exactly are you saying? “to make themselves FEEL smart?” That is just a doosh thing to say..

      @brysonsirus7747@brysonsirus77475 жыл бұрын

    • Enjoying the shapes... That's something I do on pornhub XD

      @davidmurvai40@davidmurvai404 жыл бұрын

  • People in 4D space are writing down notes in 3D

    @r0b0tiks@r0b0tiks5 жыл бұрын

    • Le funny 😜

      @neymarjr4566@neymarjr45665 жыл бұрын

    • love it lol reminds me of a movie

      @tea5316@tea53164 жыл бұрын

    • And people in 2D are writing in 1d

      @Soilad@Soilad4 жыл бұрын

    • Which movie..??

      @electro-magnetik528@electro-magnetik5284 жыл бұрын

    • can't imagine that though

      @saharshbehal8766@saharshbehal87664 жыл бұрын

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

    @charbelazar686@charbelazar6862 жыл бұрын

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

    @nyanates@nyanates3 жыл бұрын

  • Don't be ashamed of yourself if you're confused. It took Super Mario 11 years to figure out 3D.

    @bibasik7@bibasik76 жыл бұрын

    • Really underrated comment.

      @xRyann_@xRyann_5 жыл бұрын

    • *N I C E*

      @NickLM2008@NickLM20085 жыл бұрын

    • Yeah but 11 years our time is only like 35 minutes 4D time, so...

      @SineEyed@SineEyed5 жыл бұрын

    • When Mario dies in the 3d world, does he jump out in a 4th dimension?

      @donovanmahan2901@donovanmahan29015 жыл бұрын

    • Bibasik another dipshit comment, searching for praise while providing stupidity without intelligence..

      @jfern6673@jfern66735 жыл бұрын

  • 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.@mg222.7 жыл бұрын

    • MG222 super mega Omni ultra nega pneumono hyper alternative meta ultra polyvoxel

      @matshbocks@matshbocks6 жыл бұрын

    • 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

      @thewhitefalcon8539@thewhitefalcon85396 жыл бұрын

    • MG222 Super Kami Isocahedron

      @loveless8241@loveless82416 жыл бұрын

    • Not when I shift into MAXIMUM OVERDRIVE

      @hydrathermal9030@hydrathermal90306 жыл бұрын

    • Erm... That would be incredibly weird.

      @flyingspacebrainedidiot@flyingspacebrainedidiot5 жыл бұрын

  • 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.

    @vivianwilfred1768@vivianwilfred17683 жыл бұрын

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

    @engrdendenkadil1147@engrdendenkadil11473 жыл бұрын

  • I love the Platonic solids, but only as a friend.

    @theRealPlaidRabbit@theRealPlaidRabbit8 жыл бұрын

    • +theRealPlaidRabbit that's offensive, yo.

      @burpie3258@burpie32588 жыл бұрын

    • +burpie Love can be between one rabbit and a bunch of polytopes. Even if it's not that kind.

      @theRealPlaidRabbit@theRealPlaidRabbit8 жыл бұрын

    • theRealPlaidRabbit Can it also be between a rabbit and... a polar bear? :-D

      @burpie3258@burpie32588 жыл бұрын

    • burpie A snowshoe hare-- until the bear gets hungry! :)

      @theRealPlaidRabbit@theRealPlaidRabbit8 жыл бұрын

    • +theRealPlaidRabbit Platonic Solids can be renamed the "Friendzoned" Solids... XD

      @perirana1078@perirana10788 жыл бұрын

  • 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.

    @SyphistPrime@SyphistPrime7 жыл бұрын

    • nice one

      @Orakwan@Orakwan6 жыл бұрын

    • So are we just shadows of 4d beings? And are they shadows of 5d beings? What is the shadow of an infinite dimension being?

      @IamKingofInternet@IamKingofInternet6 жыл бұрын

    • Imagine watching TV in the 4d universe

      @semi-mojo@semi-mojo6 жыл бұрын

    • 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).

      @Nejvyn@Nejvyn6 жыл бұрын

    • 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.

      @avigindratt7608@avigindratt76085 жыл бұрын

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

    @evabeyza@evabeyza2 жыл бұрын

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

    @mahdinoroozi1614@mahdinoroozi16143 жыл бұрын

  • mathematicians: there are only five platonic solids utah teapot: 😤😤😤😤😤

    @siddiqislam4035@siddiqislam40355 жыл бұрын

    • @Jason Lee Its not just pissed its steaming

      @TheLegend-jp1vg@TheLegend-jp1vg5 жыл бұрын

    • The Legend27 name checks out

      @eldnahym@eldnahym5 жыл бұрын

    • @@eldnahym it's actually a freesian teapot but whateffs

      @BrutusAlbion@BrutusAlbion4 жыл бұрын

    • 😂😂😂

      @harrisonsimmons5256@harrisonsimmons52564 жыл бұрын

    • utah teapot: hold me tea...

      @deouro@deouro4 жыл бұрын

  • It's almost like he making up those big word to make his speech appear more photosynthesis

    @IceX92@IceX927 жыл бұрын

    • Icex Aoki he is a professor tho, technically he's just osteoporosis.

      @sinatraforeign@sinatraforeign7 жыл бұрын

    • Icex Aoki great he's trying to make his speech more cycle where plants make their food

      @Ray-hx3rm@Ray-hx3rm7 жыл бұрын

    • These comments are so dodecylbenzenesulfonate.

      @geckertim5126@geckertim51267 жыл бұрын

    • Icex Aoki lol

      @hero_py@hero_py7 жыл бұрын

    • laundry sauce

      @literallyeverything7264@literallyeverything72647 жыл бұрын

  • 6:17 That honestly looks really cool

    @skullmastergamer@skullmastergamer3 жыл бұрын

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

    @VansangluraVanchhawng@VansangluraVanchhawng3 жыл бұрын

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

    @the_phoe@the_phoe6 жыл бұрын

    • Or maybe the questions are pre-scripted?

      @Alexisasful@Alexisasful5 жыл бұрын

    • I think the questions are scripted.

      @r_____________________@r_____________________5 жыл бұрын

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

      @Eicee-yg6jh@Eicee-yg6jh5 жыл бұрын

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

    @noahheninger@noahheninger4 жыл бұрын

    • It's a platonic kind of love :p

      @stylis666@stylis6664 жыл бұрын

    • So do I! Shapes are interesting

      @KevinKurzsartdisplay@KevinKurzsartdisplay3 жыл бұрын

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

      @mateuszszulecki5206@mateuszszulecki52062 жыл бұрын

    • @@stylis666 Get out

      @horrorspirit@horrorspirit Жыл бұрын

    • @@stylis666 Now; *_THAT’S_* a solid pun 👍🏻!

      @PC_Simo@PC_Simo Жыл бұрын

  • 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.

    @jhosp89@jhosp893 жыл бұрын

    • 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.

      @patrickogier7419@patrickogier741911 ай бұрын

  • This is the best video I’ve ever seen for trying to visually contextualize higher dimensionality.

    @giusepperesponte8077@giusepperesponte807710 ай бұрын

  • First time in my life I properly understood 4+ dimensions.

    @northwind6199@northwind61997 жыл бұрын

    • NorthWind Achievement get!

      @jamzsmp@jamzsmp7 жыл бұрын

    • Dude... thats a bigass claim but if you say it must be true. Gratz. Im still on it!

      @davidl.fernandez2940@davidl.fernandez29406 жыл бұрын

    • same before I thought that it was just nonsense!

      @czechm4te@czechm4te6 жыл бұрын

  • who else felt extremely satisfied watching the animations

    @CheeseTruffles@CheeseTruffles6 жыл бұрын

    • Hark! Indeed. The motion feature segmentation of this piece was rather the most symbolic yet inert, inscrutably binomial for one to grasp.

      @Ioganstone@Ioganstone6 жыл бұрын

    • me

      @jktube5143@jktube51436 жыл бұрын

  • This channel is pure gold.

    @stromboli183@stromboli1833 жыл бұрын

  • I have always been browsing KZhead for 4d and higher and you are one of the videos that have taught me something

    @ShellyChambers-jk9en@ShellyChambers-jk9en4 ай бұрын

  • 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

    @MaRiahhTurnerPoliticalMakeup@MaRiahhTurnerPoliticalMakeup4 жыл бұрын

  • I minimally understood, but I definitely feel smarter. Thanks!

    @dhoffman4994@dhoffman49946 жыл бұрын

    • 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@jfern66735 жыл бұрын

    • @@jfern6673 Revolutionary.

      @ericcricket4877@ericcricket48775 жыл бұрын

    • 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.@Fermion.5 жыл бұрын

    • @@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.

      @duchyre@duchyre5 жыл бұрын

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

    @THC800@THC8003 жыл бұрын

    • Yes; and tesseracts (4D-hypercubes), as its cells, and penteracts (5D-hypercubes), as its hypercells. However; the Rhombic Triacontahedron is only the convex hull of that particular projection, not the object, itself (Rhombic Triacontahedron is actually a 3D-object, as is evident from the suffix: ”-hedron”); the real deal is a 6D-hypercube.

      @PC_Simo@PC_Simo Жыл бұрын

  • Amazing explanations! This really helped me understand the complexity of other dimensions. Very informative video.

    @alyssatortora7156@alyssatortora7156 Жыл бұрын

  • 24:23 "like an evil twin" "nice twins actually" Few seconds later "EVIL TWIN"

    @DiceDecides@DiceDecides5 жыл бұрын

    • Scrolled down just to find this lol my favorite part

      @Sirrwinn@Sirrwinn5 жыл бұрын

    • DiceDecides looks like thats his only speech

      @francisruizyamba6149@francisruizyamba61494 жыл бұрын

    • Yeah i like eminem too

      @MohammadAli-iz9ld@MohammadAli-iz9ld4 жыл бұрын

  • Hats off to the animator! And to professor Séquin, of course.

    @Harrow_the_Ninth@Harrow_the_Ninth8 жыл бұрын

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

    @RooiGevaar19@RooiGevaar193 жыл бұрын

  • I think of the measure polytope duals to be the "bipyramid" series. The line bipyramid is the square, then the square bipyramid is the octahedron, then the octahedral bipyramid is the 16 cell, and so on.

    @TM-wn6fj@TM-wn6fj2 жыл бұрын

  • Please let this guy narrate more videos!

    @user-go5ri2yg5f@user-go5ri2yg5f8 жыл бұрын

  • My brain shut down at 18:27 and everything lost its semantic value.

    @Proxyincognito@Proxyincognito8 жыл бұрын

    • +Gazeth Sonica RIP

      @theodoros_1234@theodoros_12348 жыл бұрын

    • Same

      @yoruneko34@yoruneko348 жыл бұрын

    • +Gazeth Sonica Hehehe semantics :drooolz: I haz losst it.

      @Jossandoval@Jossandoval8 жыл бұрын

    • +Gazeth Sonica defintely takes some practice to keep up with the more abstract topics in mathematics

      @kunstderfugue@kunstderfugue8 жыл бұрын

    • Energy Core Very true, but thats also what makes it so much fun xD

      @Proxyincognito@Proxyincognito8 жыл бұрын

  • I just love the way this man talks

    @Dragongaga@Dragongaga9 ай бұрын

  • This is truly amazing … thx for sharing

    @hallur7523@hallur75232 жыл бұрын

  • We all live in 3 dimensional sphere earth while this guy live in his 6 dimensional rhombic triacohedron earth

    @syahmiqawiem@syahmiqawiem5 жыл бұрын

    • What?

      @thefamousarthur@thefamousarthur4 жыл бұрын

    • @Audy Simon flat earther shush

      @natedecoco615@natedecoco6154 жыл бұрын

    • 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?

      @chicassoproductions8527@chicassoproductions85274 жыл бұрын

    • Chicasso Productions atmosphere

      @gavinbrown216@gavinbrown2164 жыл бұрын

    • @@gavinbrown216 we live under the atmosphere not in it.

      @matildadunkley6084@matildadunkley60844 жыл бұрын

  • 4d liquid would be the trippiest thing imaginable

    @tenletters5889@tenletters58897 жыл бұрын

  • Nice teacher! Great explanation, thank you a lot

    @cristhian8518@cristhian85183 жыл бұрын

  • The animation is amazing!

    @zeniousspy4609@zeniousspy46093 жыл бұрын

  • Imagining 4d figures in your 3d head while watching it being illustrated on a 2d screen... My brain: *Nope*

    @rithikkumars1676@rithikkumars16767 жыл бұрын

    • i feel ya

      @diamondpixelators475@diamondpixelators4755 жыл бұрын

    • And processing it with your 1d brain

      @user-ky7mf2kp2v@user-ky7mf2kp2v5 жыл бұрын

    • @@Corgi_fax no. we should instantly colonise mars

      @ninamilosavljevic8kg@ninamilosavljevic8kg5 жыл бұрын

  • his voice is so soothing, combined with the maths...altogether this video is the stuff of my dreams

    @mx7718@mx77187 жыл бұрын

  • 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

    @cathie_486@cathie_4862 жыл бұрын

  • Great upload! The universe is filled with wonder

    @mauritzventer2092@mauritzventer20923 жыл бұрын

  • You really have to be a mathematician to be able to make proverbial chocolate out of something that is not just invisible, but also unimaginable...

    @martijnvanweele6204@martijnvanweele62047 жыл бұрын

    • or be HP Lovecraft

      @Ghorda9@Ghorda97 жыл бұрын

    • martijn van weele WTF does that even mean?

      @sambarillas1062@sambarillas10626 жыл бұрын

  • I love how he says “squere”

    @brianb.8028@brianb.80285 жыл бұрын

    • 🐿

      @samerinaa@samerinaa4 жыл бұрын

    • He is Swiss, that is how it sounds with a Swiss accent!

      @robertarthropthesecond@robertarthropthesecond3 жыл бұрын

    • I love the icosa

      @cupiter7864@cupiter78643 жыл бұрын

  • nice job pal... just when I thought I might get some sleep tonight... but thanks too, that was explained quite well. I now have a better understanding.

    @paradisemike1582@paradisemike15823 жыл бұрын

  • You are blowing my mind on Pi Day! ,My spiritual guides led me to your channel. Thank you sir!

    @branchestarot@branchestarot Жыл бұрын

  • His voice is perfect for telemarketing I expected at the end of every sentence to end with "only for $19.99".

    @alexz635@alexz6357 жыл бұрын

    • Alexis Zikas Dude 😂😂

      @usamazaheer3507@usamazaheer35075 жыл бұрын

    • I think he's better suited for a science documentary.

      @davecrupel2817@davecrupel28175 жыл бұрын

  • So, there would be more DnD dice in 4 dimensions?

    @BinyaminTsadikBenMalka@BinyaminTsadikBenMalka8 жыл бұрын

    • D600

      @Adraria8@Adraria88 жыл бұрын

    • +Adraria8 all hail the D666

      @reallygoodbook7258@reallygoodbook72588 жыл бұрын

    • Exactly

      @laxxius@laxxius8 жыл бұрын

    • +A light switch I bet you came from YIAY lol

      @Adraria8@Adraria88 жыл бұрын

    • +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??

      @hellNo116@hellNo1168 жыл бұрын

  • This man made it possible for me to be able to "see" the fourth dimension for the first time.. holy moly, I thought it impossible yet here I am, trying to see the fifth one. I wonder if there could ever be a way to represent it digitally one day, somehow, in VR or something

    @jekytck@jekytck2 жыл бұрын

  • 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

    @vutrongquyen2796@vutrongquyen27962 жыл бұрын
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