A Breakthrough in Higher Dimensional Spheres | Infinite Series | PBS Digital Studios

How do you stack hundred-dimensional oranges? Learn about recent breakthroughs in our understanding of hyperspheres in the first episode of Infinite Series, a show that tackles the mysteries and the joy of mathematics. From Logic to Calculus, from Probability to Projective Geometry, Infinite Series both entertains and challenges its viewers to take their math game to the next level.

Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed truths about 8 and 24 dimensions that we don't even understand in 4 dimensions.

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Sphere Packing in Higher Dimensions - Quanta Magazine

Why You Should Care about High-Dimensional Sphere Packing - Scientific American

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux

[chasecarter]

PBS is doing amazing work with their digital content. I'm blown away with the quality of channels like PBS SpaceTime. This is definitely the future of educational content and an invaluable public service.

[TuckerLeeC]

"If you have a cool way to visualize hypersphere..." you deserve a Nobel

[deusexaethera]

Thank god someone finally figured out how to stack 100-dimensional oranges! I was really worried there for a while.

[LeiosLabs]

Holy cow! An entire channel related to mathematical research? this is beautiful!

[tigerburn]

I can show you what hyper dimensions looks like but we'll need a ton of shrooms.

[johnchessant]

Maryna Viazovska has won the 2022 Fields medal for this work!

[supercommie]

The expanding and contracting sphere was the single most intuitive visualization of a hypersphere I have ever been presented. Kudos.

[DaviddeKloet]

7:08 this sounds super exotic but after thinking about it, I realized that the math is actually trivial with Pythagoras' theorem.
The 2^n balls all have radius 1/4, but the distance from their center to the center of the cube is sqrt(n)/4. So the center ball has radius sqrt(n)/4-1/4. When this becomes > 1/2, the center ball grows out of the cube. And with n=9, this is exactly equal.
It might have been nice to show this in the episode, or at least hint at the fact that anyone can do this for themselves with high school math.

[Alex-uixp]

This sounds incredibly useful for the next time I'm packing 8d oranges.

[renauddefrance.at.eurostep]

A pity this series was discontinued :'-(

[caristewart]

I have always sucked at math. Even though I really love trying to learn about all of this stuff, its usually confusing. But I feel like I actually understand this now. Great video!

[TiagoSeiler]

I have a way of visualizing n-dimensional spheres where n > 3, it's just that it's illegal in most states...

[Mathologer]

It's great to now also have a nice PBS channel dedicated to math :)

[natbacli]

Now, this is a math teacher I'll listen to all day.

[KalabawCNC]

This is one of my most favorite math paradox! I remember working this problem in Calculus!! :-D It got me to thinking about a hyper-dimensional version of the Gabriela's horn paradox. Where you take the curve y = 1/x from 1 to infinity and revolve that curve about the x axis. If you tried to fill the resulting shape with paint you can do it. But if you tried to paint the outside you would never have enough paint because the surface area diverges. So what happens when you take the 3d horn shape and revolve it about the Y axis? To make a 4-dimensional hyper-horn? Or take the 4-dimensional hyper-horn and revolve it about the Z axis? What happens to the divergent-convergant ratio of surface area to volume at these higher dimensions? Does it remain a paradox or are we left with varying levels of infinities?

[besmart]

FIRST (in the 47th dimension)

Welcome to the PBSDS fam! Can't wait to see more

[Brisarious]

now im just frustrated that i can't visualize a hypersphere

[nolanwestrich]

I've often tried to wrap my head around 4D, but watching this video about up to 24D is just mind-blowing.

[Jackal_Blitz]

PBS Digital Studios just keeps getting better and better. Love you guys!

[xqta]

She could have mentioned why the diagonal distance increases as the dimension of the hyper cube increases..
Pythagorean theorum ! Then how do we calculate the vacant hyper volume of a hyper cube after it is packed with hyper spheres? I hyper wish to see that !