> It's ok to post stories from sites with paywalls that have workarounds.
In comments, it's ok to ask how to read an article and to help other users do so. But please don't post complaints about paywalls. Those are off topic.
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.
I'm currently studying group theory and SO3 rotations (quaternions & matrix groups) and I'm also curious about the connection. I still have a lot to learn but I wouldn't be surprised if the reset rotation is unique, if we abstract away variation.
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.
In Ernst Mach's Opera Omnia, his Principia had a `gedenken experiment'
visiting a related question about angular inertia, as an affection of
all the matter in the universe and its simultaneity with local
causation. He inferred by simile of unwinding the trajectory of a toy
spinning top on the possibility of reversing the arrow of time.
For those who struggle with the pay wall: check your local library's (online) membership, it might come with the worldwide library card, which might include the New Scientist magazine.
Mine does, and therefore I can "borrow" (read for free) articles that make it to the mag.
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..
h/t to both criddell and nicklaf who posted replies containing the above to a now [flagged][dead] comment which violates the HN guidelines, which is why I have collated this and reposted it as a top-level comment.
In future, I would advise folks who post archives and workarounds to post them as a top-level comment in addition to and/or instead doing so as replies to others, especially instead of as replies to comments that violate guidelines, as if/when those comments become [dead] for whatever (legitimate or otherwise) reason(s), their child comments also get buried except to those with showdead enabled on their profile, which requires not only an HN account and login, but also requires enabling the showdead option in one’s user profile.
Simplified “undo” mechanism: this result suggests that a given traversal (sequence of rotations) might be “reset” (i.e., returned to origin) using a simpler method than computing a full inverse sequence. That could simplify any functionality in libraries, like SpinStep[0], that deal with “returning to base orientation” or “undoing steps.”
The libraries could include a method: given a sequence of quaternion steps that moved from orientation A to orientation B, compute a scale factor λ and then apply that scaled sequence twice to go from B back to A (or A to A). This offers a deterministic “reset” style operation which may be efficient.
Orientation‐graph algorithms: in libraries used in robotics/spatial AI, the ability to reliably reset orientation (even after complex sequences) might enhance reliability of traversal or recovery in systems that might drift or go off‐course.
Please don't use ChatGPT to advertise your GitHub repositories. As other commenters have noted, this comment doesn't really make sense: it's not a good contribution to the discussion, and it's spam.
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.
Any implications for MRI/ NMR here? The basis of arguably most pulse sequences is undoing rotation in some way, it’s not immediately obvious if this finding could provide any new refocusing sequences.
> Finding such a scaling amounts to solving a trigonometric Diophantine equation, and the solution applies to any physical system governed by SO(3) or SU(2), such as magnetic spins or qubits.
Can anyone comment on the difficulty of solving trigonometric Diophantine equations? Most of the resources I am familiar with only deal with linear or exponential versions.
Does anyone have a link to research itself? I don’t want to sign up to “new scientist” to see behind the sign up screen to see if they included a link or not
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.
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 running the operation twice to reach the identity (rotation 0 compared to baseline), e.g.:
I = R ⊕ (α.R ⊕ α.R)
In their example that would be something like (with alpha=0.3):
In mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it), the belt trick, or the Balinese cup trick (it appears in the Balinese candle dance), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while a second rotation of 360 degrees, a total rotation of 720 degrees, does.
The anti-twister or antitwister mechanism is a method of connecting a flexible link between two objects, one of which is rotating with respect to the other, in a way that prevents the link from becoming twisted. The link could be an electrical cable or a flexible conduit.
This mechanism is intended as an alternative to the usual method of supplying electric power to a rotating device, the use of slip rings. The slip rings are attached to one part of the machine, and a set of fine metal brushes are attached to the other part. The brushes are kept in sliding contact with the slip rings, providing an electrical path between the two parts while allowing the parts to rotate about each other.
However, this presents problems with smaller devices. Whereas with large devices minor fluctuations in the power provided through the brush mechanism are inconsequential, in the case of tiny electronic components, the brushing introduces unacceptable levels of noise in the stream of power supplied. Therefore, a smoother means of power delivery is needed.
A device designed and patented in 1971 by Dale A. Adams and reported in The Amateur Scientist in December 1975, solves this problem with a rotating disk above a base from which a cable extends up, over, and onto the top of the disk. As the disk rotates the plane of this cable is rotated at exactly half the rate of the disk so the cable experiences no net twisting.
What makes the device possible is the peculiar connectivity of the space of 3D rotations, as discovered by P. A. M. Dirac and illustrated in his Plate trick (also known as the string trick or belt trick). Its covering Spin(3) group can be represented by unit quaternions, also known as versors.
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R³ under the operation of composition.
By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry), and orientation (i.e., handedness of space). Composing two rotations results in another rotation, every rotation has a unique inverse rotation, and the identity map satisfies the definition of a rotation. Owing to the above properties (along composite rotations' associative property), the set of all rotations is a group under composition.
40 comments
[ 1.7 ms ] story [ 58.3 ms ] thread> It's ok to post stories from sites with paywalls that have workarounds.
In comments, it's ok to ask how to read an article and to help other users do so. But please don't post complaints about paywalls. Those are off topic.
https://en.wikipedia.org/wiki/Anti-twister_mechanism
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 connection. I still have a lot to learn but I wouldn't be surprised if the reset rotation is unique, if we abstract away variation.
Mine does, and therefore I can "borrow" (read for free) articles that make it to the mag.
https://archive.is/08ig5
which is reporting on the linked original publication:
https://journals.aps.org/prl/abstract/10.1103/xk8y-hycn
which has a preprint available:
https://arxiv.org/abs/2502.14367
h/t to both criddell and nicklaf who posted replies containing the above to a now [flagged][dead] comment which violates the HN guidelines, which is why I have collated this and reposted it as a top-level comment.
In future, I would advise folks who post archives and workarounds to post them as a top-level comment in addition to and/or instead doing so as replies to others, especially instead of as replies to comments that violate guidelines, as if/when those comments become [dead] for whatever (legitimate or otherwise) reason(s), their child comments also get buried except to those with showdead enabled on their profile, which requires not only an HN account and login, but also requires enabling the showdead option in one’s user profile.
Positive potential:
Simplified “undo” mechanism: this result suggests that a given traversal (sequence of rotations) might be “reset” (i.e., returned to origin) using a simpler method than computing a full inverse sequence. That could simplify any functionality in libraries, like SpinStep[0], that deal with “returning to base orientation” or “undoing steps.”
The libraries could include a method: given a sequence of quaternion steps that moved from orientation A to orientation B, compute a scale factor λ and then apply that scaled sequence twice to go from B back to A (or A to A). This offers a deterministic “reset” style operation which may be efficient.
Orientation‐graph algorithms: in libraries used in robotics/spatial AI, the ability to reliably reset orientation (even after complex sequences) might enhance reliability of traversal or recovery in systems that might drift or go off‐course.
[0] https://github.com/VoxleOne/SpinStep
Can anyone comment on the difficulty of solving trigonometric Diophantine equations? Most of the resources I am familiar with only deal with linear or exponential versions.
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.
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 running the operation twice to reach the identity (rotation 0 compared to baseline), e.g.:
I = R ⊕ (α.R ⊕ α.R)
In their example that would be something like (with alpha=0.3):
I = (rad(75).X ⊕ rad(20).Y ⊕ ...) ⊕ (rad(0.3x75).X ⊕ rad(0.3x20).Y ⊕ ...) ⊕ (rad(0.3x75).X ⊕ rad(0.3x20).Y ⊕ ...)
Remembering that our rotation action is non-commutative, e.g. `aX ⊕ bY != bY ⊕ aX`.
Clever intro.
The belt trick / plate trick / Dirac's string trick is nicely demonstrated in below video: https://m.youtube.com/watch?v=EgsUDby0X1M
https://en.wikipedia.org/wiki/Plate_trick
In mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it), the belt trick, or the Balinese cup trick (it appears in the Balinese candle dance), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while a second rotation of 360 degrees, a total rotation of 720 degrees, does.
https://en.wikipedia.org/wiki/Anti-twister_mechanism
The anti-twister or antitwister mechanism is a method of connecting a flexible link between two objects, one of which is rotating with respect to the other, in a way that prevents the link from becoming twisted. The link could be an electrical cable or a flexible conduit.
This mechanism is intended as an alternative to the usual method of supplying electric power to a rotating device, the use of slip rings. The slip rings are attached to one part of the machine, and a set of fine metal brushes are attached to the other part. The brushes are kept in sliding contact with the slip rings, providing an electrical path between the two parts while allowing the parts to rotate about each other.
However, this presents problems with smaller devices. Whereas with large devices minor fluctuations in the power provided through the brush mechanism are inconsequential, in the case of tiny electronic components, the brushing introduces unacceptable levels of noise in the stream of power supplied. Therefore, a smoother means of power delivery is needed.
A device designed and patented in 1971 by Dale A. Adams and reported in The Amateur Scientist in December 1975, solves this problem with a rotating disk above a base from which a cable extends up, over, and onto the top of the disk. As the disk rotates the plane of this cable is rotated at exactly half the rate of the disk so the cable experiences no net twisting.
What makes the device possible is the peculiar connectivity of the space of 3D rotations, as discovered by P. A. M. Dirac and illustrated in his Plate trick (also known as the string trick or belt trick). Its covering Spin(3) group can be represented by unit quaternions, also known as versors.
https://en.wikipedia.org/wiki/3D_rotation_group
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R³ under the operation of composition.
By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry), and orientation (i.e., handedness of space). Composing two rotations results in another rotation, every rotation has a unique inverse rotation, and the identity map satisfies the definition of a rotation. Owing to the above properties (along composite rotations' associative property), the set of all rotations is a group under composition.