Seems like I'll have to make time for the second one too. This `Another Roof` channel has some pretty good content...

Wow, these look like nice links. I'll start with the first one due to the more professional editing before deciding if I wanna dive into the professor's lecture... tnx

[The Hidden Geometry of Error-Free Communication](https://www.youtube.com/watch?v=Tmx-v4FiP6I)

[Einstein Lectures: Maryna Viazovska - Sphere packings in high dimensions and error correcting codes](https://www.youtube.com/watch?v=EjcdRcCjbdU)

not really ELI5, but interesting :)

Scroogey

Mathematicians often visualize this problem in terms of spheres. You can think of each code word as a high-dimensional point at the center of a sphere. If an error-filled message (when represented as a high-dimensional point) lives inside a given sphere, you know that the code word at the sphere’s center was the intended message. You don’t want these spheres to overlap — otherwise, a received message might be interpreted in more than one way. But the spheres shouldn’t be too far apart, either. Packing the spheres tightly means you can communicate more efficiently.

 what the link between error-correcting codes and the spheres is? I don't understand this paragraph.

The rest of the article is quite accessible, even though it is really hard to imagine what this should look like in higher dimensions...

EDIT: seems like it's also at the top of HN

science

Mathematicians Discover New Way for Spheres to ‘Kiss’

> Mathematicians often visualize this problem in terms of spheres. You can think of each code word as a high-dimensional point at the center of a sphere. If an error-filled message (when represented as a high-dimensional point) lives inside a given sphere, you know that the code word at the sphere’s center was the intended message. You don’t want these spheres to overlap — otherwise, a received message might be interpreted in more than one way. But the spheres shouldn’t be too far apart, either. Packing the spheres tightly means you can communicate more efficiently.

Anyone able to explain with an ELI5[^1] what the link between error-correcting codes and the spheres is? I don't understand this paragraph. 

The rest of the article is quite accessible, even though it is really hard to imagine what this should look like in higher dimensions...

EDIT: seems like it's also at the top of HN[^2]

[^1]: more accurately, explain it to me _like I am not a mathematician_
[^2]: https://stacker.news/items/852273/r/south_korea_ln Just having fun with footnotes now.