Why can't you multiply vectors?

Why HN readers recommended it

HN treats it as the best entry point to geometric algebra and an intuitive route to understanding quaternions.

This is a summary from the source dataset, not an endorsement by Hacker News or the video creator.

Video & recommendation details

Creator / channel

Freya Holmér

Topic

geometric algebra

Format

talk

Level

intermediate

HN recommenders in dataset

9

HN mentions in dataset

11

Recommendation years in dataset

2023–2025

These counts and years describe the included Hacker News records; they are not YouTube views or the video’s publication date.

From the original HN conversations

Excerpts from the recorded comments. Follow each source for the full comment and surrounding discussion.

• Freya Holmer, of The Continuity of Splines [0] fame, recently gave a great conference talk about how quaternions naturally arise from the desire to define the multiplication of two vectors if you just agree to one new axiom : v^2 = ||v||^2, or "the square …

• I know people have jumped here to try to explain it to you as a comment, but I highly recommend a recent talk by Freya Holmer. It's a fun little exploration of a seemingly simply question about vectors that motivates the answer you asked. It …

• One of my favorite math/graphics YouTube creators Freya Holmér did an excellent intro to Geometric Algebra not that long ago [1]. If you have any interest in 3d graphics (especially but no limited to splines/Bezier curves) then be sure to check out all of their …