Thinking visually about higher dimensions

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U Wot M8 : I just found out this channel and it is fantastic! Please keep making great videos!

dartagnanx1 : GREAT!

VELOCITY FPV : I don't get it

Pwn Tech : i would of thought this video would of been so boring, but it turned out keeping my attention and very educational, as i am a visual learner.

Arnav Verma : This is some gorgeous animation

IgorD : 27 minutes! I'm not watching it! ..Maybe just a couple of minutes out of curiosity ...*watched it all*

Death Grips : *It's free real estate*

Higgins2001 : I'm just clever enough to understand the basics and get excited about implications, and just dumb enough to give up thinking past this video after 2 minutes... (might explain why I only minored in math) However, can someone please help me: I'd love to know at which dimension the VOLUME of the inner sphere exceeds that of the bounding spheres... or if this even happens at all?

maisto : If my math teacher was like this man!

Dane Goodwin : It blows my mind how brilliant some peoples' minds are

Proportionally Accurate : Thank you! This will come in handy next time I'm stacking my 8-dimensional oranges..

Ivan Žuti : Thank you for this video. Now I can't stop thinking if this is somehow related to the expansion of the universe. What if the universe is expanding into a higher dimensional space and we observe it as the expansion? Also what if the big bang was the expansion from a plane into a 3d universe? Mind is melting right now.

BEISisICE : I think this guy watches Rick & Morty

Nilay Patel : Seariously awesome

Jonathan groberg : For some reason, my brain is trying to connect neural networks to higher dimensions problems. Your use of sliders seems very similar to the function of weights determining the value of a neuron, so much so that it seems they must be connected in some way. Also, your video and GoldPlatedGoof's video about higher dimension problems make me wonder, can backpropagation be viewed as a higher dimension problem? Is my brain onto something or do I simply love machine learning so much it is clouding my vision.

Michael Jensen : I'm not super great at math, and this was very intuitive for me, and easy to understand. Thank you for creating and sharing this. :)

Yaman Sanghavi : I beg you; please make a series on tensors (contravariant & covariant) , curvature, manifolds etc. Thank you so much for what you are doing for us.

The_Blazer : 1-dimensional array: a line 2-dimensional array: a square 3-dimensional array: a cube 4-dimensional array: death incarnate

MathCubes : I just found this channel a week or two ago. I almost watch all of the videos on it.

The Flagged Dragon : This has always pissed me off that I can't visualize in higher dimensions when it's sooooo bloody tempting. But if you think about it, it's not that our brains haven't evolved to see in 4 dimensions or anything like that, it would be physically impossible to do it. You'd have to visualize infinitely many 3-D "slices" simultaneously to perceive anything 4-dimensional. I would give literally anything to be able to "see" in higher dimensions.

Naviron Ghost : So in infinite dimensions, the corner spheres have zero area, and the inner sphere has infinite? Wow. AMAZING video by the way, now I get why this works!


Shai Hulud : IMHO by far the best YTvideo on this topic! It has mathematical proof, makes plausible assumptions, and comes up with an understandable way of explaining it's concepts. Congratulations to 3Blue1Brown - got yourself a new subscriber :)

Nilay Patel : Awesome man

Doco bonbon : I always get your videos until the halfway mark, after that it all goes over my head.

Jalfire : It's pretty interesting that even though it is so hard to imagine the possibilities of universes in higher spacial dimensions, that the mathematics in those universes will always be the same with our's. It is nearly impossible to predict the properties of these universes, but the language of math will always be universal. Or you know, multiversal I guess...

David Winsemius : Great stuff. The slider illustration is exactly what statisticians are using when they display higher dimensional data with a "parallel coordinates plot". They connect the coordinate dots with lines and one can then find clusters.

крркркркрк ш : *_i t ' s f r e e r e a l e s t a t e_*

Connor Stegner : Wow. Are you an educator? This was awesome.

Josef Wöss : ohhh nice! Which software do you use for this awesome animations?

Christina Andwena : Ts;dw Too smart; didn't watch

Steve-o : ⛅Hi Sunshine, when you talke about a sphere you're talking about a circumference and an area on the outside of the sphere you're talking about a circumference and an area on the inside of a sphere for each positive there is a negative given that there's an area of the outside an area of the inside how many dimensions have I just hit and I haven't even started yet. For every density on the inside there's an atmosphere on the outside that all leads to existence. May peace an prosperity be with you always. C-ya😎Bye! "✌💖🤗~🌞🌎⚬" ...

TheXalkk : Pretty freakin hard for my little brain) But its interesting)

Scott Goodson : Have you read Matt Parker's book "Things to Make and Do on the 4th Dimension"? It mentions this and he also is a mathematics youtuber [StandUpMaths (you probably know his channel already)].

Amulaya Bhatia : Came here from HFS this is awesome

MD HAMID USMAN : Way Beyond my level !

julijakeit : the _π_ in the video reminds me of Clippit from Windows XP

millertime1202 : Omg I'm learning math. Why couldn't I have been interested in highschool??

focus : How much time does it take to make such awesome looking yet helpful visualizations?

Sam Lee : In celebration of the total eclipse, can you PLEASE do a video talking about how the arrangement of our solar system is so amazingly mathematically intricate?

Carlucio Leite : I'm blown away. Again.

OGF : wow what a simple trick!

Dercio Silveira : Sorry.

Chaos : Amazing videos mate. The way you illustrate these mathematical theories with geometry made it all click for the first time in my life.

jakeinator21 : This video felt like the quickest 27 minutes of my life.

iOSMinecraft120 : Woah 3blue1brown also uses momentum woo

Ryan Santa : To me, this makes me think that in higher dimensions you can fit more and more stuff in the same space- as in there are possibly invisible data/stuff within everything we see in 3D (as in the bigger center sphere). Does this make sense to anyone else?

ayush sharma : Roses are red

Eugene Morgan : this video is exceptional! great idea to visualize 4D

Jimmy Hoff : Someone pay this man!!!