Perfect Shapes in Higher Dimensions - Numberphile

Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions.
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Extra footage (Hypernom): • Eating 4D Polytopes (H...
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[@shpongle7322]

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

[@freddybenelli9100]

Is this clear to you? 😂

[@albertorivas6339]

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

[@lilfr4nkie]

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

[@shpongle7322]

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

[@azap12]

@@shpongle7322 just another 4d mysticism delusional dude hahaha

[@000netko]

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

[@andonandonov7793]

xD

[@mishikomishiko9088]

LOL

[@thankor]

Haaaahaaa

[@mopsbackupaccount5128]

Same

[@theatrefirefly]

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

[@MarkOates2]

This guy has the perfect accent for the word tetrahedron

[@nanu4144]

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

[@guitargeorge1874]

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

[@wtfduud]

It's like a german-scottish mix.

[@EdoTimmermans]

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.

[@Kunal29Chopra]

Tetraheedraun!!

[@mortal19901001]

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

[@rurihime4965]

You made me think he died or something

[@gamemeister27]

He's still kicking. 79 years old!

[@ekkekrosing8454]

@@rurihime4965 same

[@garnet1918]

Confirmed still alive!

[@PC_Simo]

@@rurihime4965 My thoughts, exactly 😨.

[@kyoai]

That guy has an amazing voice/accent mix.

[@ianedmonds9191]

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

[@highlewelt9471]

I always wonder what accent it could be

[@jarryda]

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

[@PooperScooperTrooper]

Sample it, loop it, fuck it.

[@RAL_III]

Go Switzerland! It is the best country!!!

[@chronovac]

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

[@Quetzalcoatl-Dragon_97]

That's how being smart feels

[@powerinknowledge2392]

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

[@atryan1125]

I just feel dumber

[@RedGallardo]

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

[@JonCombo]

@@alicec1533 Forth Dementia.

[@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.

[@phillipchavez1321]

Wow, same

[@MegazoneMusic23]

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

[@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.

[@pietrufarrugia9617]

@@D4narchy his wonder is beautiful

[@betteryou7hanme]

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?

[@ColinBache]

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! 🙏❤️

[@lilmarionscorner]

❌❌ ❌❌ ❌❌ ❌ FloorFloorFloorFloor It fell.

[@MorningLightMtn]

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

[@threewagthepenguin9869]

And so on lol...

[@MuzikBike]

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

[@neildhan]

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.

[@TruKave]

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

[@Misterlegoboy]

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

[@Zichfried]

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

[@colelevel2654]

Ye legit wtf

[@ez_is_bloo]

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.

[@A.Mayflower127]

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

[@lou7319]

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)

[@seandaly2211]

@@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

[@johnathonwaymire9483]

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

[@johnsaylor1583]

Mine doesn't

[@aliensasquatch7485]

@@johnsaylor1583 ok.

[@johnsaylor1583]

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

[@jobtenbosch349]

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

[@the0master200]

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."

[@nikdoesstuff9338]

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

[@lukiepoole9254]

Not d12?

[@daveslamjam]

the deapot

[@madeofbeans]

dpot

[@theayyoutube7711]

@@madeofbeans de power of two

[@DLBookTheGamer]

​@@lukiepoole9254only if you're a barbarian

[@wariouswarious9364]

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

[@tomasmieger6826]

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

[@Dexuz]

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

[@willardaustria]

@@Dexuz Underrated comment!

[@christopherochoa4145]

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

[@_skzstay1264]

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

[@AlanKey86]

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

[@pmcpartlan]

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

[@AlanKey86]

+Pete McPartlan It was indeed :)

[@pmcpartlan]

+AlanKey86 5 Stellated Polyhedra.

[@adrianhaus]

+AlanKey86 5 Thumbs up

[@__Bruh]

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

[@patwalsh9360]

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

[@alejrandom6592]

How was it

[@alejrandom6592]

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

[@justinmolanick7989]

It's your life dude and your money

[@alejrandom6592]

Anserw

[@patwalsh9360]

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

[@damienboykin7772]

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.

[@logicplague]

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

[@misanthropicisolation4013]

As opposed to figuratively?

[@Illegiblescream]

He's granted his 3d printer eyes.

[@AnymMusic]

New torture test

[@itsmeminime7958]

ΔISEPTICONS 4 EVER AHAHHAHAH

[@UwU-wl4ep]

He can Print tears

[@Abdega]

*[SCREAMS GEOMETRICALLY]*

[@ksp-crafter5907]

Ramiel ;)

[@tiagobelo4965]

radbarij nice

[@squareheart7077]

Like when liquid metal goes down Neo's throat.

[@TaigiTWeseFormosanDiplomat]

um..

[@tear728]

ERASE MEEEE!

[@SyphistPrime]

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.

[@Orakwan]

nice one

[@IamKingofInternet]

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

[@semi-mojo]

Imagine watching TV in the 4d universe

[@Nejvyn]

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).

[@avigindratt7608]

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.

[@minie7950]

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

[@GregtheGrey6969]

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

[@jacoblynch8844]

Sides aren’t regular polygons :(

[@theprodigal72]

@@jacoblynch8844 *polyhedra

[@realmless4193]

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

[@Thiago-ck5iu]

@@theprodigal72 polygons*

[@cashbag]

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

[@legokenobi1185]

With a 1D time line

[@haellm9192]

@@legokenobi1185 time is actually 4th dimensional structure

[@harold9924]

@@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

[@casualipcroboticist6336]

trolli gettin' roasted into inexistance

[@natedecoco615]

@@legokenobi1185 time isnt 1d

[@the_phoe]

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

[@Alexisasful]

Or maybe the questions are pre-scripted?

[@r_____________________]

I think the questions are scripted.

[@Eicee-yg6jh]

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

[@Rune3D]

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!

[@AMORTEDEYAHWEHDEMIURGOS]

JEWS!!!!!

[@snailcheeseyt]

@@AMORTEDEYAHWEHDEMIURGOS??

[@spirit_x64]

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

[@williamaleman5460]

So far I am just enjoying the shapes.

[@Alwis-Haph-Rytte]

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.

[@brysonsirus7747]

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

[@davidmurvai40]

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

[@EllieVaricuber]

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

[@RoaringTRex]

Lol!

[@izaakfewton7536]

Lol. I love you mate! :)

[@EllieVaricuber]

Love u 2

[@flinchfu]

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

[@RtsShrtFrRtthw]

Flinch Fu same!

[@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

[@matshbocks]

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

[@thewhitefalcon8539]

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

[@loveless8241]

MG222 Super Kami Isocahedron

[@hydrathermal9030]

Not when I shift into MAXIMUM OVERDRIVE

[@flyingspacebrainedidiot]

Erm... That would be incredibly weird.

[@derekhasabrain]

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

[@Jack.Strait]

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

[@SalveSandWonk]

JackStrait *scares in 0D*

[@mauz791]

@@SalveSandWonk *screams on *point**

[@SoluKissin]

The band or the dimension?

[@Jack.Strait]

@@SoluKissin The band obviously

[@BrettChungus]

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

[@koalawithchaingun53]

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

[@some1112]

With our 1D brain

[@yalnayal]

LOL

[@garysutherland7004]

@@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.

[@pralayhait7276]

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

[@dylanburfoot1262]

@Gary Sutherland r/Whooosh

[@sunriseavefan98]

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

[@RJavier007]

You are sick

[@cjlwhite1]

@@RJavier007 what.

[@AnathematizedMage]

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

[@RJavier007]

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

[@jacoblittmann2807]

Or can they?

[@SK-vk9jf]

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.

[@dhoffman4994]

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

[@jfern6673]

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

[@ericcricket4877]

@@jfern6673 Revolutionary.

[@Fermion.]

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.

[@duchyre]

@@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.

[@r0b0tiks]

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

[@tea5316]

love it lol reminds me of a movie

[@Soilad]

And people in 2D are writing in 1d

[@electro-magnetik528]

Which movie..??

[@saharshbehal8766]

can't imagine that though

[@PhoenixMF1986]

This is kinda terrifying. What if we 3D are just notes of a 4D being?

[@bibasik7]

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

[@xRyann_]

Really underrated comment.

[@NickLM2008]

*N I C E*

[@SineEyed]

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

[@donovanmahan2901]

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

[@jfern6673]

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

[@scptime1188]

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

[@Peztllence]

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

[@JonathanMandrake]

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

[@zackbuildit88]

@@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

[@beetlegob]

​@@zackbuildit88 Misali would be proud (maybe)

[@zackbuildit88]

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

[@fakecubed]

Whatever version of D&D they play in the 5th dimension must be really boring having only three kinds of dice.

[@popstarrowlet1636]

👍

[@drawapretzel6003]

you can have other shapes of dice and still have them be equally weighted, they just start becoming cylinders with shaped faces on the sides, or weird shapes with some sides you dont land on.

[@OverpepperedSoup]

You can take care of that by repeating some of the labels. Some games using 3d dice already do that, for instance cube dice with only 3 numbers (each number repeated twice).

[@kirillmed1]

Or, actually use dice of lower dimension

[@skulleeman]

@@kirillmed1 I'm no expert, but you may get problems with the dice landing on the "flat side" in the same way that 2d dice would land on their flat side in 3 dimensions. You could always extrude out and put smooth caps on the ends which you don't want the die to fall, but it's starts to feel less "dicey" at that point.

[@tijmenvanderree487]

I understand some of these words.

[@milo1685]

loool

[@victorotene]

Then you're doing well.

[@kawaiipotatoes2951]

I understood what cube meant

[@enderman6777]

Then why use it?

[@Samstar369]

That's the joke.

[@loquacity4765]

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!

[@mx7718]

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

[@phuturephunk]

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

[@chrislynch6545]

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.

[@martingrof1685]

***** who?

[@indiangrimreaper8247]

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

[@tonykostov928]

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

[@ThePedroEtc]

That's how crazy people are made

[@wandererinthedust276]

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

[@raiden490]

lool

[@Angloth]

+Wanderer in the Dust LSD

[@jeroenconinx6121]

LSD is the best

[@kozhikkaalan]

hahahahahahh. love your comment

[@victorsousa7239]

42

[@evank3718]

Props to the animator the visuals in this were amazing

[@Harrow_the_Ninth]

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

[@syahmiqawiem]

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

[@thefamousarthur]

What?

[@natedecoco615]

@Audy Simon flat earther shush

[@chicassoproductions8527]

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?

[@gavinbrown216]

Chicasso Productions atmosphere

[@matildadunkley6084]

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

[@CheeseTruffles]

who else felt extremely satisfied watching the animations

[@Ioganstone]

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

[@jktube5143]

me

[@stromboli183]

This channel is pure gold.

[@Sth3ll]

As a 3d artist, you made my day by mentioning the teapot. Thank you !

[@noahheninger]

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

[@stylis666]

It's a platonic kind of love :p

[@KevinKurzsartdisplay]

So do I! Shapes are interesting

[@mateuszszulecki5206]

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

[@horrorspirit]

@@stylis666 Get out

[@PC_Simo]

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

[@marconapoleone]

20:16 you are watching a projection of a 4D object that represents a 5D object in a 3D space flattened to a 2D space aka your screen. How cool is that?

[@MerpIsMe]

Marco Napoleone Huh.

[@iBlaze1232]

On your 1D brain

[@That_One_Guy...]

With the comprehension level of 0D

[@iBlaze1232]

With the -1d iq

[@ArvoAnimi]

And the video is at it's core a one dimensional array of ones and zeros

[@Gumpy719]

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!

[@stellarfirefly]

Another shout-out to the animator(s) for this video. That's excellent, high-quality work right there. (Narrators, editors, etc. were also great of course, but they have always been so.)

[@siddiqislamyoutube]

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

[@TheLegend-jp1vg]

@Jason Lee Its not just pissed its steaming

[@eldnahym]

The Legend27 name checks out

[@BrutusAlbion]

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

[@harrisonsimmons5256]

😂😂😂

[@deouro]

utah teapot: hold me tea...

[@seantobin5235]

do a video on the Utah teapot

[@omfgmouse]

+Sean Tobin yes, please!

[@ximenabriones5040]

Yes!

[@rich1051414]

+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.

[@frostcrackle2374]

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

[@eschelon9067]

+Sean Tobin Yes, please do.

[@emmanuelgiouvanopoulos8273]

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.

[@DiceDecides]

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

[@Sirrwinn]

Scrolled down just to find this lol my favorite part

[@francisruizyamba6149]

DiceDecides looks like thats his only speech

[@MohammadAli-iz9ld]

Yeah i like eminem too

[@matin563]

And where are the higher dimension polytopes made out of teapots??!!!

[@matin563]

Ashton Fortenbacker You clearly didn't perceive my sarcasm

[@Dexuz]

Hyperpot 4-teapot

[@rodschmidt8952]

That needs 42 dimensions

[@God-ch8lq]

we do not know if 4 dimensional beings drink tea

[@rolandpahi3079]

@@God-ch8lq They drink Te4

[@6c3333]

Please let this guy narrate more videos!

[@AlexisTwoLastNames]

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

[@zyaicob]

Go for it, Jane Street awaits

[@TonyMacaroni69_]

This is a real nice sounding accent. Really easy to understand...😄

[@davidh9844]

Dutch?

[@TonyMacaroni69_]

@@davidh9844 no, he is swiss. Like me😂

[@paulrunner1048]

subtitles buddy

[@AirCicilia]

His accent does sound distinctly Dutch.

[@tomosko2669]

Yeah, we all love those squeers. :D

[@northwind6199]

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

[@jamzsmp]

NorthWind Achievement get!

[@davidl.fernandez2940]

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

[@festivite]

same before I thought that it was just nonsense!

[@googoofeesmithersmits4536]

this stuff is so mind boggling... it is so fascinating and seemingly impossible to even try to imagine...

[@toddmiller6232]

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. :)

[@IceX92]

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

[@sinatraforeign]

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

[@Ray-hx3rm]

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

[@geckertim5126]

These comments are so dodecylbenzenesulfonate.

[@hero_py]

Icex Aoki lol

[@literallyeverything7264]

laundry sauce

[@rithikkumars1676]

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

[@diamondpixelators475]

i feel ya

[@user-ky7mf2kp2v]

And processing it with your 1d brain

[@ninamilosavljevic8kg]

@@Corgi_fax no. we should instantly colonise mars

[@Trevurie]

My brain is melting try to picture a hypersphere or a 4D sphere.

[@MuzikBike]

In 3D, you can get a sphere by making a circle curve in all directions, or a cylinder from extruding a circle. In 4D you should be able to get a hypersphere from making a sphere curve into the new dimension, and another two shapes from extruding a sphere and extruding a cylinder.

[@jogiff]

Just think of the cross-section that a 3D sphere has in 2D. It’s just a bunch of circles, other than its ability to grow and shrink it would seem no different than a 2D circle to an inhabitant of 2 dimensions. A 4D Circle (or hypersphere) would be similar to us. Just a sphere that would grow and shrink.

[@Eternalmars1]

jogiff It would grow and shrink to our eyes. Buy we cannot comprehend its true form. Since all we see is a 3D slice. But thank you for your comment, it really helped me to understand something

[@weirdkid4166]

You can do it the same way a circle. Infinite circles of different sizes = 3D sphere (2D slices) infinite spheres “inside” each other, like the smaller cube in the larger cube in the hyper cube , only with spheres and there isn’t those lines connecting them.

[@Advection357]

Try to picture a 6 dimensional Calabi-Yau manifold... your brain will disintegrate like a supernova lol

[@giusepperesponte8077]

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

[@tenletters5889]

4d liquid would be the trippiest thing imaginable

[@EugeneKhutoryansky]

Thanks for these videos.

[@malm7arb]

one of my favorite youtubers is watching one of my favorite youtubers. ❤ love your videos Eugene

[@magventure1019]

I Agree, It Helped Me My Video kzbin.info/www/bejne/nZ_Yg3RsqqidoLc

[@Your_Daily_Scroll]

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

[@pulakdas8998]

Physics Videos by Eugene Khutoryansky I just love your videos.

[@Goman1244]

Physics Videos by Eugene Khutoryansky I

[@Proxyincognito]

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

[@theodoros_1234]

+Gazeth Sonica RIP

[@yoruneko34]

Same

[@Jossandoval]

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

[@kunstderfugue]

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

[@Proxyincognito]

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

[@nyanates]

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

[@maishamohiuddin297]

the animations for this video were amazing!

[@cardor9269]

they missed the seventh three dimensional platonic solid: kissing your homie goodnight

[@ukiitm]

What is the sixth?

[@flabbergabber]

@@ukiitm the Utah teapot

[@PeepingUkulele]

😂 cute

[@PeepingUkulele]

😂 cute

[@ghastgamer5299]

r/SuddendlyGay (Ironic)

[@brianb.8028]

I love how he says “squere”

[@samerinaa]

🐿

[@robertarthropthesecond]

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

[@cupiter7864]

I love the icosa

[@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...???

[@TENNOM]

1) woah 2) how does he edit these vids with those graphics!?!? 3) how do they 3d print those props!?!?

[@Yoedric]

... 3D printers ? =3

[@fuuuuuuu4152]

Prout this guy either didnt notice they are made out of 2d polygons or living in 4D world

[@nya6659]

4D printers are existing in the 4D world.. they look the same as those wireframes

[@NickLM2008]

Answer to 3: 3D printers.

[@Krytax]

1) yes 2) with software 3) with a 3d printer

[@theRealPlaidRabbit]

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

[@burpie3258]

+theRealPlaidRabbit that's offensive, yo.

[@theRealPlaidRabbit]

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

[@burpie3258]

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

[@theRealPlaidRabbit]

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

[@perirana1078]

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

[@alexz635]

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

[@usamazaheer3507]

Alexis Zikas Dude 😂😂

[@davecrupel2817]

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

[@_charademon_]

This video: exists Me, an anime watcher: RAMIEL

[@mamalogon]

I was just looking for this comment.

[@GDSCLag]

@@mamalogon lol same

[@felipe5512]

my brain got a blue screen error and had to shut down to prevent damage

[@jfern6673]

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

[@bilawalnarai]

same :D

[@MK-rc5ow]

@@jfern6673 why are you so triggered just don't read the comment why bother ? xd

[@blue9139]

Mine: What

[@hazel-vf7on]

J Fern Well someone is salty.

[@mekafinchi]

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

[@mekafinchi]

Bryson Sirus Mate do you not understand the use of the phrases “hope(s) for” and “future technology”, particularly when used at the same time? It completely disregards what is possible now, or what we believe to be possible now. I don’t ask you to explain, because it is irrelevant. My statement takes into account nothing about reality but for the fact that it isn’t possible at this moment or in the past. In short, regardless of your theories and ideas, the infinity of the future allows unlimited hope.

[@barsozuguler4744]

@@mekafinchiwait what... *brain.exe not responding

[@That_One_Guy...]

As long as the 4th spatial dimension spaces isn't found, i don't think that's possible

[@AMan-xz7tx]

Two words: Virtual Reality, there’s a 4D toybox simulator that’s looks pretty dope

[@liveintruth4284]

Impossible for the human brain to comprehend no matter what

[@SpicyKdestiny]

This guy is so easy to listen to and explains things in such an engaging, easy to understand way. I have to admit, I literally don't know much past the basic 3D shapes, but the fact that he seems so happy to explain makes me want to enter the 4th and 5th dimensions.

[@RooiGevaar19]

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

[@megamelloco]

Imagine a 4D kid drawing in a 3d paper a house that is a Cross polytope on top of a Hypercube

[@UshiromiyaXyrius]

Yes that's it. I lost you at the 3d paper !

[@Retardah]

Brilliant lol

[@jjjx32]

welll uhh i ummm you seee uh

[@mordechairosenhan456]

The picture will actually be a regular 3D house like yours now. Maybe We are all just pictures of some 4D’s..

[@quinnmoore5985]

We call that Minecraft

[@axlien1893]

i really like this guy, the way he explained everything made it so clear

[@zohaibasif6274]

I just realized if we could see 4d, geometry in school would be so damn crazy

[@justinmolanick7989]

A 2d person is saying The Same about us... itd still be boring cause itd be normal to them.

[@SCWood]

Yeah but 4 dimensional beings would have 4 dimensional brains making them able to comprehend more.

[@_Killkor]

and more tests

[@wrcz]

yeah or imagine how crazy it would be if we could see 2D

[@jjjx32]

@@wrcz give him a minute to figure it out

[@goranmarinic2923]

The best video on YT.

[@KyrusR]

*_SCREAMS IN 546D_*

[@kaedo-2740]

*screams in evangelion reference*

[@wallonice]

*SCREAMS IN 85939285D*

[@jjjx32]

*SCREAMS IN AGONY*

[@IronianKnight]

Simplex or hypercube?

[@Drewwy]

Very Original.

[@Ov3rTheTop]

the teapot killed me. that damn teapot.

[@zanza456]

yea, wtf was that? how is it a Platonic solid? Just because some people like it or use it a lot?

[@Chris-jo1zr]

As a man who works in 3D I love the teapot, it’s a preset in 3Ds Max, like the unifying symbol of my kind.

[@essentialdang]

My brain blue screened half way through

[@Xayuap]

+invalidusername do not use win for rendering higher dimensions

[@jamzsmp]

invalidusername Try using 4D Ram and a floppy disk

[@VansangluraVanchhawng]

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

[@zoranhacker]

OMG 26 minute numberphile video, yeeeeeeeeeeeeeeees!!

[@david4jsus]

Those animations are so cool, and useful

[@Nitya0607]

Wow awesome job on the editing!! Love this channel!!

[@alejandronq645]

Totally agree

[@Nyitemare]

+Nitya Sharma I agree it was really great =D!

[@drustanastrophel9538]

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

[@koyooko5160]

I will use this knowledge of shapes for evil.

[@vapenation7061]

OH NO!

[@brysonsirus7747]

ya, roll someone over with an icosahedron. ):))

[@Amarganeitor]

And what exactly are you going to do, destroy Tokyo and melt some mountain in particular?

[@DogMcMeow]

actually nice shapes

[@CC-hx8gj]

EVILLLLLLLLLL

[@martijnvanweele6204]

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...

[@Ghorda9]

or be HP Lovecraft

[@sambarillas1062]

martijn van weele WTF does that even mean?

[@9Joel9]

Beautiful vid, but the accent was even more beautiful. A mix of German, Dutch, American and hints of Scottish. I hear he's Swiss.

[@logicunknowntoyounooo9400]

He is Swiss-American ^^ but so far a very long time in America.

[@ShellyChambers-jk9en]

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

[@blackheart2728]

the "bewmmm" sound when the animation combines shapes is so satisfying to me.

[@Binyamin.Tsadik]

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

[@Adraria8]

D600

[@reallygoodbook7258]

+Adraria8 all hail the D666

[@laxxius]

Exactly

[@Adraria8]

+A light switch I bet you came from YIAY lol

[@hellNo116]

+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??