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

newscientist.com

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

#101

Post by Razengan »

dist-epoch wrote: post #29
Razengan wrote: post #22

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.

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

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

#102

Post by Syntonicles »

AugusteDupin wrote: post #80
Syntonicles wrote: post #30

Earlier quoted context omitted.

What?! Thank you! I'm working on a robot with a very expensive slip ring, and need to send high fidelity data through it with shielding. I had no idea this was possible this will make things so much easier! I found a related video you might find interesting. https://www.youtube.com/watch?v=gZvimEf6DFw I'm currently studying group theory and SO3 rotations (quaternions & matrix groups) and I'm also curious about the co…

As meindnoch points out, the connection needs to loop over the rotating object. That is no problem if the only affect of the rotation that interests you is the centrifugal force. When you give plasma (not whole blood) the nurses use a centrifuge machine that seems impossible: one tube goes from you to it (carrying whole blood), another tube goes from it back to you (carrying plasma depleted blood). The mechanism of D…

What a fascinating project. It looks a real labor of love, and I wish I understood it more deeply. I've been making my own visualization sandboxes like this to explore configuration spaces and groups - but for much simpler, more intuitive physical systems.

I went down a few rabbit holes on the site - is this program also written in Basic?

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

#103

Post by Razengan »

dist-epoch wrote: post #34
dandanua wrote: post #32

Earlier quoted context omitted.

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 :)

> 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".

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

#104

Post by amelius »

Luc wrote: post #100
amelius wrote: post #98

Earlier quoted context omitted.

Sure, but the animation of the wiki page is wrong. The cable that ends at the bottom of the picture is fixed there, while the other end twists. That will result in a twisted cable. (update: I was wrong, not the wiki page)

I tried it and it works. The animation uses belts that are very flexible. With a real belt I needed to give it a shake to make it untwist itself, but it does work. It is indeed easy to twist the belt until you have the hang of it. I think the animation is a bit deceptive because even with elastic bands you'd have to provide some way for the correct untwisting to occur. In the animation it happens 'automagically'.

Yes, indeed, it can work, I can see it now. But I wonder if/how you can make it practical.

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

#105

Post by oh_my_goodness »

godelski wrote: post #77
oh_my_goodness wrote: post #75

Earlier quoted context omitted.

It is not. That’s exactly what it isn’t.

I think you're confusing thermal dynamics with quantum mechanics.

No, thermodynamics just isn't classical mechanics. For example in thermo you have entropy. Entropy doesn't appear in classical mechanics.

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

#106

Post by empiricus »

amelius wrote: post #94
v7n wrote: post #7

I was immediately reminded of the anti-twist mechanism, perhaps unrelated but "reset rotation, twice/half" comes up there as well. https://en.wikipedia.org/wiki/Anti-twister_mechanism

Huh, looking just at the link at the top of the box, and forgetting the remainder of the links, this cannot work. I tried it with a flat cable. If you rotate it like that, it becomes twisted.

well, if you look at the animation, it surely seems to work, there is no place where it fakes the untwist. I can also replicate that with a belt, but not so smoothly. manually with the belt, the twist from 2 full rotations of the cube are undone by one rotation of the belt around the cube.

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

#108

Post by [deleted] »

diffeomorphism wrote: post #88
AugusteDupin wrote: post #79

A series of rotations – a discrete walk (or continuous path) in the manifold of the rotation group SO(3) or SU(2) – can of course be inverted (starting from the end, find a walk that returns to the beginning) by performing the steps in reverse. Eckmann et alshow that, for almost all walks, there is another way: starting at the end, perform the steps in the original order (1) twice, and (2) uniformly scaled by a facto…

The article is 5 pages and the Theorem yielding the factor is on page 4.

[deleted]

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

#109

Post by [deleted] »

somenameforme wrote: post #93

I don't entirely understand why they're framing rotations as so complex, outside of a play on words that I don't think they're making. Most rotations just use quaternions which are relatively simple. Their example of robotics uses quaternions and getting the inverse of any rotation is trivial - you literally just flip the signs of the 3 imaginary components of quaternions. For non-unit quaternions, you just then just…

[deleted]

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

#110

Post by [deleted] »

badosu wrote: post #81

I had a hard time trying to parse something understandable from the article. This is what I got from it (I'd be happy to hear someone informed correcting me/confirming). (excerpt from a discussion yesterday I had with some friends not too math inclined) What it seems to be the articles claim is that, you could define a scaling operation in the angles you performed, finding some constant scaling factor (say alpha) and…

[deleted]
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