Thinking outside the 10-dimensional box

"The goal here is genuine understanding, not shock" You're the best.

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

7:59 Why imagine yourself as a bug on that small sphere? A human on a really, really big sphere works too, and you don't even have to imagine that.

It's nice how the video is over 20 minutes long but he doesn't put any midroll ads. Respect man, respect.

22:04 he said the correct number of "one"s. now I'm impressed.

-Quality Content -Clear Information -Awesome Animation -No Ads -No BS I need more channels like this

That point about how far away the corners of the boxes are in higher dimensions is what really made this click intuitively for me. In higher dimensions, there's effectively more space for the outer spheres to fit into the corners of that outer bounding box, and they're located farther from the origin as a result. This leaves more space for that center sphere to take up while still being adjacent to the outer spheres. At no point, however, does the center sphere overtake the corners of either of the boxes.

from now on i will only buy higher dimensional real estate seems more profitable currently

Those numerical sliders are like Braille for higher dimensions.

Hey, im leaving this message to say this video really helped me with my research in economics It has nothing to do with high dimensional spheres, but something about the investigative way you approached the problem made me remember about the way i used to approach mathematical problems when i was younger, and it gave me insight that might help me with a problem ive been stuck for more than 1 month There is something about this way of seeing math that is very powerful, and that frequently gets lost when we are too deep in more analytical and formal approaches. It is hard to define what exactly it is, but this channel's videos are very good at inspiring it

x: moves a little y: it's free real estate

Higher dimensions: exists 3Blue1Brown: IT'S FREE REAL ESTATE

A mathematician and an engineer attend a talk given by a physicist about string theory. The mathematician is obviously enjoying himself, while the engineer is frustrated and lost, especially when the physicist starts talking about higher dimensions. Finally, the engineer asks the mathematician: "How can you possibly visualize something in 11-dimensional space!?" The mathematician replies: "Easy, first visualize it in n-dimensional space, then let n equal 11."

It blows my mind how brilliant some peoples' minds are

Hi, game designer here, I have been struggling to find a visual way to think about balancing the power of mechanics in games that have multiple contributing factors. After giving up on this problem, this video has got me going back to my white board. Higher dimensional game balancing coming soon to a steam library near you!

Thank you so much for explaining WHY it happens, not just that it does. I never imagined the answer would be so simple. The sides of the cube stay the same but the corners get farther and farther away because more dimensions are contributing to them.

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

VISUALIZE HIGHER DIMENSIONS WITH THIS 1 WEIRD TRICK! STEM PROFESSIONALS HATE HIM!

Coordinate: Is close to zero 3B1B: It's free real estate

Now I understand why I suck at mixing/mastering. Its 10 dimensional circle math lol