Mathematicians have found a hidden 'reset button' for undoing rotation • Hacker News Board

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

#71

Post by oh_my_goodness » Wed, Oct 22, 2025, 12:03 AM UTC

cormacrelf wrote: post #62

ginko wrote: post #48

Earlier quoted context omitted.

I must be missing something major here, but given a sequence of rotations combined into a quaternion orientation, can’t you just get the inverse rotation back to the original orientation by inverting the quaternion?

You can absolutely do that and there is nothing for general linear algebra libraries to do. The actual paper is very clear about what it's for: https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf It says: Consider now a general time-dependent field B(t) of duration T. The pulse B(t) may be extremely convoluted ... Can one make the field B(t) return the system to its original state at the end of the pulse...? This…

So it’s similar thinking to spin echoes.

https://en.wikipedia.org/wiki/spin_echoes

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

#72

Post by kronodeus » Wed, Oct 22, 2025, 12:08 AM UTC

godelski wrote: post #64

kronodeus wrote: post #47

This article is written in a very annoying and misleading way. The discovery is not that rotation can be "reset". That is obvious and not surprising at all. Physical systems governed by classical mechanics are reversible just by perfectly inverting all forces, velocities, and rotations. The actual discovery is the shortcut to the original position without the need to perfectly inverse the full sequence of rotations.

> Physical systems governed by classical mechanics are reversible just by perfectly inverting all forces, velocities, and rotations This doesn't really make sense. To do that you'd have to end up bringing in quantum dynamics, and well... we know how that goes. Heat is probably the best example, as even if you were able to track the movement of particles individually you'd have a very difficult time putting them back…

Not talking about thermodynamics here. The discovery referenced in this article also does not solve for thermodynamics or entropy.

And yes, you're right, the article does mention this later. I'm still bothered by the sensationalized introduction and title.

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

#73

Post by kronodeus » Wed, Oct 22, 2025, 12:10 AM UTC

clysm wrote: post #52

kronodeus wrote: post #47

This article is written in a very annoying and misleading way. The discovery is not that rotation can be "reset". That is obvious and not surprising at all. Physical systems governed by classical mechanics are reversible just by perfectly inverting all forces, velocities, and rotations. The actual discovery is the shortcut to the original position without the need to perfectly inverse the full sequence of rotations.

Kind of like… a “hidden reset”…

The title itself is not the problem, although even that is sensationalized. I was referring to the contents of the article, which have statements like this:

"Is there a way for you to spin the top again so it ends up in the exact position it started, as if you had never spun it at all? Surprisingly, yes..."

Which, as an introduction, just misses the mark completely by highlighting the least surprising possible interpretation of the research.

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

#74

Post by godelski » Wed, Oct 22, 2025, 12:34 AM UTC

oh_my_goodness wrote: post #67

godelski wrote: post #64

Earlier quoted context omitted.

> Physical systems governed by classical mechanics are reversible just by perfectly inverting all forces, velocities, and rotations This doesn't really make sense. To do that you'd have to end up bringing in quantum dynamics, and well... we know how that goes. Heat is probably the best example, as even if you were able to track the movement of particles individually you'd have a very difficult time putting them back…

Comment refers to classical mechanics, not all of classical physics and explicitly not quantum mechanics.

  > refers to classical mechanics

Thermodynamics is, in fact, part of classical mechanics

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

#75

Post by oh_my_goodness » Wed, Oct 22, 2025, 12:38 AM UTC

godelski wrote: post #74

oh_my_goodness wrote: post #67

Earlier quoted context omitted.

Comment refers to classical mechanics, not all of classical physics and explicitly not quantum mechanics.

> refers to classical mechanics Thermodynamics is, in fact, part of classical mechanics

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

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

#76

Post by godelski » Wed, Oct 22, 2025, 1:00 AM UTC

kronodeus wrote: post #72

godelski wrote: post #64

Earlier quoted context omitted.

> Physical systems governed by classical mechanics are reversible just by perfectly inverting all forces, velocities, and rotations This doesn't really make sense. To do that you'd have to end up bringing in quantum dynamics, and well... we know how that goes. Heat is probably the best example, as even if you were able to track the movement of particles individually you'd have a very difficult time putting them back…

Not talking about thermodynamics here. The discovery referenced in this article also does not solve for thermodynamics or entropy. And yes, you're right, the article does mention this later. I'm still bothered by the sensationalized introduction and title.

  > Not talking about thermodynamics here.

My mistake, you said "Classical Mechanics", so I took it as such.

But thermodynamics is not required either. Chaos theory would be of important note here. Take the double pendulum for example. It is a chaotic function because unless you have the initial state you cannot make accurate predictions as to its forward time evolution. This is a deterministic system because there is no randomness in the forward time evolution. But it is chaotic because it is sensitive to initial conditions. I think you can see that there's a careful choice of words here and that once we start trying to reverse the evolution we will not be able to do so. We have to deal with injective functions and I'm not sure many people really think P=NP. Just because f(t) has a unique map doesn't mean f^-1(t) does. Do not confuse "deterministic" with "predictable" nor "invertible" (nor "reversible" and "invertible"). Nor should you confuse "Newtonian Mechanics" with "Classical Mechanics".

Besides, I don't think you can throw out thermodynamics just so easily. With it you throw out many things like friction too. Not to mention that you're suggesting you're also throwing out fluid mechanics. For the fun of it, let me introduce you to Norton's dome since we might want to look at determinism in Newtonian Mechanics and a frictionless system ;)

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

#77

Post by godelski » Wed, Oct 22, 2025, 1:25 AM UTC

oh_my_goodness wrote: post #75

godelski wrote: post #74

Earlier quoted context omitted.

> refers to classical mechanics Thermodynamics is, in fact, part of classical mechanics

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

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

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

#78

Post by Starman_Jones » Wed, Oct 22, 2025, 2:27 AM UTC

godelski wrote: post #76

kronodeus wrote: post #72

Earlier quoted context omitted.

Not talking about thermodynamics here. The discovery referenced in this article also does not solve for thermodynamics or entropy. And yes, you're right, the article does mention this later. I'm still bothered by the sensationalized introduction and title.

> Not talking about thermodynamics here. My mistake, you said "Classical Mechanics", so I took it as such. But thermodynamics is not required either. Chaos theory would be of important note here. Take the double pendulum for example. It is a chaotic function because unless you have the initial state you cannot make accurate predictions as to its forward time evolution. This is a deterministic system because there is…

[dead]

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

#79

Post by AugusteDupin » Wed, Oct 22, 2025, 2:34 AM UTC

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 factor.

Apparently – I haven’t read the article – the factor depends on the walk. (One would think the abstract would say if there were.) The theorem says there exists such a factor but not how to find it. As the factor varies from 0 on up, the end point of the twice traveled path, scaled by some factor, is dense in the rotation manifold. It isn’t surprising though the fact that the end of the once traveled path (scaled) is not dense, is.

If the authors cannot give a comparatively simple way to find the factor, or at least bounds on it, the theorem isn’t of much use. It looks like there is too much hype accompanying its announcement.

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

#80

Post by AugusteDupin » Wed, Oct 22, 2025, 2:54 AM UTC

Syntonicles wrote: post #30

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

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 Dale. A. Adams keeps the tubes from twisting. Search “antitwister mechanism patent” for a drawing of the mechanism. As for the principle behind the mechanism, see http://Antitwister.ariwatch.com for a PC program where you can adjust every variable imaginable.