Mathematicians have found a hidden 'reset button' for undoing rotation

I've been trying to understand as much of "maths" as I can (now enough to write that in quotes, as there isn't a "single" maths) and still a layman, I love reading about discoveries like these, and the fact that you still can have discoveries in things thought to be so fundamental..

Neat factoid: there is something special about rotations in 3D. They are not "simply-connected", which means that there are 2 distinct classes of rotations. And this property is deeply important in quantum physics.

It's a bit more complicated than "2 classes of rotations", though there is magic indeed. I've tried to explain it in this post https://dandanua.github.io/2021/08/23/the-spin-of-a-human-bo...

There is also this one, which goes into a lot of detail: https://www.youtube.com/watch?v=b7OIbMCIfs4

Unfortunately this subject is above my pay grade, so I gave up :)

I'm also trying to understand the implications of this work.

Does it imply that some for some functions F(x) = y, you can compute x given the value of y without computing the inverse of F ?

If so, what constraints does F need to meet for this ?

Thanks for sharing. I'm very familiar with the basic mechanics of quaternion rotation, and I've been interested in a deeper understanding of this double-cover concept, but I just don't get it. I've seen the belt trick and it feels more like an illusion than an illustration of some deep truth.

I like how you've connected it to spin, but I still don't understand how that is a real physical property rather than a mathematical artifact.

I don't quite grasp the significance of your "different look". Can you suggest any other reading?

Do you mean spinors? And how it takes TWO full rotations to get back to the initial state?

> Unfortunately this subject is above my pay grade, so I gave up :)

Don't feel like that. Even though I'm still a complete layman in everything with massive imposter syndrome, I never felt like I would "never" understand something, because some part of my brain intuitively realizes that if other humans were able to figure something out then I should be able to too.

If something doesn't make sense, it's because I haven't take the same "journey" from the point of view of those scientists who did, I'm just seeing the end result without everything that it's built from and on, and that's where the investment of time and effort comes in, which I am OK with not putting in for things that aren't immediately relative to me, but it's certainly not an "intelligence ceiling".

That look is not that different. I bring attention to the fact that a product of quaternions all close to 1 can be close to -1, which correspond to a 2pi rotation too. This fact is a bit simpler to grasp than a topological explanation, where you consider a topology on the space of all rotations and show that some paths that correspond to 2pi rotation are different than the others. There are multiple youtube videos explaining the topological argument, see, e.g., this one https://www.youtube.com/watch?v=ACZC_XEyg9U.

The topological argument gives a larger picture and probably better understanding, but it is definitely harder.

I see, thanks. Sounds like I was overthinking it.