[matmann2001]

Not detracting from this post, but has anyone else noticed there's a front page post about Quaternions or Kalman filters on about a monthly cadence? Wonder why that is?

[paulddraper]

Quaternions and spherical trigonometry - https://news.ycombinator.com/item?id=42880242 - Jan 2025 (48 comments)

Visualizing quaternions (2018) - https://news.ycombinator.com/item?id=38043644 - Oct 2023 (42 comments)

Visualizing quaternions: an explorable video series (2018) - https://news.ycombinator.com/item?id=31083042 - April 2022 (15 comments)

Visualizing quaternions: An explorable video series - https://news.ycombinator.com/item?id=18310788 - Oct 2018 (32 comments)

[Jarmsy]

I have noticed too that HN has an enduring fascination with quaternions, and they seem to reach front page surprisingly frequently (considering that there's not a huge amount of discussion of other geometry topics). I'm certainly not complaining though - I love quaternions too!

[mettamage]

Maybe because it intersects deeply with game dev?

[lawlessone]

yes, that's the module i learnt about them in during college.

IMHO I think for me they're interesting because it felt like mathematically they straddle the line of being nearly impossible for me.

I could just barely do them and felt very accomplished when I could. Anything else was either impossible or easy by comparison.

assuming my maths skills are average here then most people have similar experiences with them.

[xanderlewis]

What in particular did you find difficult about dealing with them?

[lawlessone]

There was something called a slerp that allowed you to get an object to rotate from on orientation to another, similar to a linear interpolation.

This was fine for some things. but if you wanted something to rotate but only in a certain way it was annoying as sometimes it would get from A to B, but go through Z during its rotation.

Getting the order or multiplications right too.

[ahazred8ta]

Spherical linear interpolation, slerp https://en.wikipedia.org/wiki/Slerp (which can sometimes wrap around the wrong way)

For levity, see Acts 12:4 And when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him.

[esafak]

Maybe it's aspirational: things that people don't know, and would like to learn, and perhaps use one day.

[ofalkaed]

I never noticed it until I read Pynchon's Against the Day, I assume I just ignored quaternion posts before then. Great book, enjoyed the way he used quaternions and vectors towards literary ends.

Edit: just noticed we also have a thread on bifurcation, another big topic in Against the Day.

[orangea]

At least this is a topic that the average HN reader is likely to be able to understand and which is closely related to software. Several years ago there was a period where there were periodic posts about things like homotopy type theory and research-level algebraic geometry which inevitably spark only inane misunderstandings and uninformed speculation in the comments. I can only attribute it to some kind of fetish for the frontiers of pure math.

[kisonecat]

AG maybe isn't so connected to software, but HoTT connects to the "functional programming" crowd. https://youtu.be/MVtlD22Y8SQ is me doing some examples.

[mhh__]

They're both simple to motivate and complicated enough to have an allure.

[hassleblad23]

Because quaternions are awesome? :) it definitely feels like a discovery when you learn about them first.

[gamedever]

Are they?

[Let's remove Quaternions from every 3D Engine] https://marctenbosch.com/quaternions/

[xeonmc]

I feel like there should be a followup post "Dear Sir, you have reimplemented quaternions" noting how implementing GA and using it only in 3D gets you precisely right back to quaternions-but-with-a-different-name since they're isomorphic when specialized for 3D.

[defrost]

HN's going to need a windscreen cleaner and a bucket if 3blue1brown and Terence Tao ever collaborate on using adaptive Kalman filters for optimal paths in Quaternion spaces.

[gcr]

no worries, quaternions just make the usual rotations. It’s cyclic.

[mbonnet]

Others have mentioned game dev, but they're also essential for guidance, navigation, and control - spacecraft, aircraft, robotics, etc.

[aap_]

Because quaternions are so cool yet under-appreciated. Unfortunately not many octonion posts.

[rsfern]

Octonions are cool! The one application I’m familiar with is in crystallography - you can represent the interface between two crystals with a unit octonion https://doi.org/10.1016/j.actamat.2018.12.034

(Open access pdf: https://par.nsf.gov/servlets/purl/10098941)

Can you give some pointers to other interesting applications?

[mikhailfranco]

Fundamental physics:

https://www.quantamagazine.org/the-octonion-math-that-could-...

Also see the work of John Baez:

html https://math.ucr.edu/home/baez/octonions/octonions.html

pdf https://math.ucr.edu/home/baez/octonions/octonions.pdf

[adalacelove]

It's because the quaternion is part of the state of the Kalman filter.

[ballooney]

Not in any intrinsic way, it’s just a mildly better way of representing attitude if your state vector includes attitude.

[ballooney]

They’re both quite basic building blocks in state estimation and as SV’s focus shifts from web apps to drone warfare it will only increase in frequency.

[TaurenHunter]

They are posted by the Quaterminions.