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!

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.

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

dartagnanx1 : GREAT!

3Blue1Brown : Find the relevant links for the podcast at Since it's hot off the presses, it might still be a few days before it's visible by searching in the itunes store. Also, the version on YouTube can be found here: Also, if y'all haven't already seen Ben Eater's YouTube channel, it's full of some really top notch explanations:

Matheus Bergamo : Which software do you use to make those incredible 2D animations? They're great!

Arnav Verma : This is some gorgeous animation

aghaanantyab : how large is the inner sphere of 1 million dimensions?

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!

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.

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. :)

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

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!

thegustavodag : this video doesnt explain anything dude

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

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 :)

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)].

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.

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

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

BEISisICE : I think this guy watches Rick & Morty

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.

Ciaran : It's Free Real Estate.

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.

ChickenStealer : HOW IS THIS EXAMPLE NOT LOGICAL?!!!! Unless you really really don't know what dimensions are, you should expect that it eventually reaches outside the square!! -Look at a 1 dimensional example: The inner line has size 0. -Then when you add a dimention, the inner circle shifts from the point where it can only be 0 to be slightly bigger. -Add another dimension and the inner sphere has more room because it makes use of the 3rd dimension. -You do not have to think in 5 or more dimensions in your head, but just think of 4D. The inner "4D sphere" will be bigger than the one in the 3D box because it can fit halfway into the extra 4th D space you created between the two sets of 8 3D spheres!! Now keep adding dimensions and the inner sphere will keep growing. Or am I just thinking outside the box?!

Amulaya Bhatia : Came here from HFS this is awesome

iOSMinecraft120 : Woah 3blue1brown also uses momentum woo

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...

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

Flexico Crux : If you were to make your videos into a DVD I would buy it. :3

Daniel Sánchez : Great stuff!

Dust to Dust : This is brilliant..

SeanGorgone : thanks for some unique ways of perceiving higher dimensions mathematically

Alex Blandin : Can we get some math applied to music as higher dimension objects? That'd be pretty cool. Also, would an infinite dimensioned sphere wrap the corner spheres?

Vlad-Haralambie Ispas : Just thank you ^^

Akash Dhiman : Hey Love your videos, i was wondering if you would be interested in doing videos regarding the fourier series representation of a function, kind of like the taylor series video you did.

Oscar Becerril : Such a piece of art

srinath kunapareddy : very well explained!!. Loved it!!!

Mr. LDD : Wow

Nir Karl : how do you do the animations?

Js Yall : Yo the box is 1048576cm^10 in the 10th dimension

Graeme Nicholls : Thank you very much! Loved the use of sliders - the real estate analogy not so much but ho hum - excellent video

reload : Hey Vsauce

Kane Allan : This is a beautiful explanation that i can actually wrap my head around and i think i can actually code this now, wow!

Keith Maynard : Fantastic job!!! This is like an elliptical for the mind. I think the videos should be viewed daily to improve facility with the idea of fourth-dimension objects passing through our 3-D hyperplane. It would be interesting to understand how you created the graphics, they were pretty amazing. Thanks!!!

VELOCITY FPV : I don't get it

SuccMyEgg : *It's free real estate*

Knowledge is everything : Wow !

nfcopier1 : Wonderful video!