6 ms·
Mathematicians have found a hidden 'reset button' for undoing rotation
- tonijn 1y agoDoes it work for brakes?
- peterdsharpe 1y ago[flagged]
- nicklaf 1y agopreprint: https://arxiv.org/abs/2502.14367 https://arxiv.org/abs/2502.14367
- criddell 1y agohttps://archive.is/08ig5 https://archive.is/08ig5
- alwa 1y agoFrom the FAQ: > 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.
- zamadatix 1y agoOne of the very few things from the FAQ I think is wrong. The comments should be for discussion of the content, not how to get to the content. The latter is the what posting something is supposed to be!
- stackedinserter 1y agoBeing in FAQ doesn't make it right.
- gjsman-1000 1y agoEspecially the comments about how “we’re not Reddit, it’s a semi-noob illusion.” If we actually did turn into Reddit, or start acting like Reddit, we can’t say that, because the FAQ is in denial?
- bee_rider 1y agoComplaining about how it used to be better is itself a particularly annoying Reddit-ism, so I can see why they’d want to keep that sort of thing out of here.
- Etheryte 1y agoLikewise something being a law doesn't make it right either, but one should still follow the law of the land for the most part.
- deleted 1y ago[deleted]
- deleted 1y ago[deleted]
- v7n 1y agoI 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 https://en.wikipedia.org/wiki/Anti-twister_mechanism
- dandanua 1y agoIt's not related. The recent result states that you can pick any integer m > 1 and find a scaling factor λ for a given path such that after m repeats of that path you will return to the starting point (except for some infinitesimal number of paths that have a specific structure).
- Syntonicles 1y agoWhat?! 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 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.
- actionfromafar 1y agoI see it, yet I can barely believe it.
- v7n 1y agoAlways happy to share! I came across this while planning a 3D scanning (photogrammetry) rig. Perhaps you'll be the one to figure out gravity can be modelled as a rotation around an axis in a fourth dimension, wrapping clingy spacetime around itself? ;) I'm not clever enough for that.
- meindnoch 1y agoThere's a bit of a caveat with the anti-twister mechanism, namely, that the wiring must be loose enough to pass around the supplied rotating part.
- koolala 1y agoWish they showed a picture of both. A path over time that changes color and two paths combined to recreate it.
- stronglikedan 1y agoup next, unscrambling an egg!
- vlmutolo 1y ago"Scientists unscramble egg proteins" https://www.science.org/content/article/scientists-unscramble-egg-proteins https://www.science.org/content/article/scientists-unscrambl...
- ineedasername 1y agoDoesn’t this sound like a sneaky way for a mathematician to work on time travel?
- swader999 1y agoBaby steps, first is the roulette table.
- echelon 1y agoKardashev Type III civilization: Reverse the light cone, resimulate all moments of the past down to the neurotransmitter level. The thoughts, feelings, and memories locked inside your head. From Neanderthal to Shakespeare to you, we could bring back everyone who has ever lived and put them in a theme park without any of them ever even knowing. Some simulation instances might be completely accurate. For historians or as a kind of theme park or zoo. Maybe that's us right now. Some simulation instances might be for entertainment. They might resemble plain and ordinary, mundane day to day life (like this very moment), and then all of a sudden dramatically morph into a zombie monster outbreak tornado asteroid alien invasion simulator. Or maybe it's obvious when a group of future gamer nerds log into an instance to role play Musk and Zuckerberg and Altman and speed run "winning". Or try to get a "high score". Maybe it'll be eternal heaven - just gifted to us without reason or cause. That'd be nice. Or perhaps and seemingly more likely, a bunch of sadomasochistic hell sims for psychopaths. Where some future quadrillionaire beams up into the matrix to torture poor people that used to live just for fun. It's not like we would have any rights or protections or defense against it. Who knows.
- sebastiennight 1y ago1 - A copy of me is not me. 2 - There might be a form of hubris in thinking that replicating a conscious person by copying all their neurotransmitters is enough to have a continuity between the original and the copy. It can be easily evidenced if you consider that the people who tend to believe this, will have a level of granularity in their beliefs that depend on their era and their own knowledge, so maybe a century ago you'd think copying the nerve/neuron arrangement would be enough, and a few decades later someone would've said that you need the exact arrangement of molecules or atoms, while maybe in 2025 we'd be thinking in terms of electron clouds or quarks. But to think that today we have finally arrived at a complete and final understanding of the basic blocks and surely, there is no possible finer understanding that would make our current view quaint in the eyes of a person from 2085 is the hubris I'm talking about.
- kmarc 1y agoFor 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.
- typpilol 1y agoOr just download the extension that bypasses pay walls lol
- stevenwoo 1y agoI've been doing this for New Scientist and a few other magazines and there's always a few articles that I have found interesting that don't make it to hacker news (the whole magazine with ads comes digitally), though many of the pieces are very short half page articles that mention something new that one has to follow up on one's own for detailed information and there's regular columns like book reviews. This magazine via Libby feature is the only thing that makes me miss having an ipad or larger mobile device for reading convenience. I assume the magazine is paid for by our local library system for access so in some small way there is compensation making its way to the creators which if someone is worried about supporting them, is one way besides a subscription. (I have stopped print subscriptions because I always end up with repository of stuff I need to recycle or throw away).
- kmarc 1y agoI got an iPad many years ago from my employer. I literally only use it for libby :-)
- kazinator 1y agoIn this case we can just wave bye-bye to the magazine and head to the freely available Arxiv paper they are writing about.
- viciousvoxel 1y agoIf you use an ad blocker, just disable inline scripts
- Razengan 1y agoI'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..
- dist-epoch 1y agoNeat 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.
- dandanua 1y agoIt'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-body.html https://dandanua.github.io/2021/08/23/the-spin-of-a-human-bo...
- dist-epoch 1y agoThere is also this one, which goes into a lot of detail: https://www.youtube.com/watch?v=b7OIbMCIfs4 https://www.youtube.com/watch?v=b7OIbMCIfs4 Unfortunately this subject is above my pay grade, so I gave up :)
- Razengan 1y ago> 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".
- ra88it 1y agohttps://archive.is/08ig5 https://archive.is/08ig5
- aspenmayer 1y agohttps://arxiv.org/abs/2502.14367 https://arxiv.org/abs/2502.14367
- defrost 1y agoFrom one author's home page (Jean-Pierre Eckmann - https://fiteoweb.unige.ch/~eckmannj/publications.html https://fiteoweb.unige.ch/~eckmannj/publications.html), the latest version of full paper: Walks in Rotation Spaces Return Home when Doubled and Scaled (with Tsvi Tlusty) Physical Review Letters 135, 147201 (2025) https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf
- aspenmayer 1y agoArchive of TFA: https://archive.is/08ig5 https://archive.is/08ig5 which is reporting on the linked original publication: https://journals.aps.org/prl/abstract/10.1103/xk8y-hycn https://journals.aps.org/prl/abstract/10.1103/xk8y-hycn which has a preprint available: https://arxiv.org/abs/2502.14367 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.
- voxleone 1y agoQuaternion libraries have work to do now. 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 https://github.com/VoxleOne/SpinStep
- ginko 1y agoI 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?
- ogogmad 1y agoI think even conjugating it. The formula for rotation via quats is v->qvq^{-1} = qvq^*/|q|^2.
- cormacrelf 1y agoYou 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 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 pulse is modelled as a long sequence of rotations. For maths purposes if you had such a sequence, you can obviously just multiply all the rotations together and find the inverse very easily. For physics purposes, you don't really have access to each individual rotation, all you can do is tune the pulse. Creating an "inverse pulse" is quite unwieldy, you might literally need to create new hardware. The paper asks "what if we just amplified the pulse? Can we change this alone and make it not impart any rotation?" They are trying to take any pulse B(t) and zero out any rotation it imparts on some particle or whatever by uniformly tuning the field’s magnitude, B(t) → λB(t) or by uniformly stretching or compressing time, B(t) → B(λt) And the answer is that you can do that, but you might have to perform the pulse twice.
- dukeofdoom 1y agoThis made me wonder if there are knots you can't untangle.
- ekunazanu 1y agoYup, the trefoil knot is one
- eightys3v3n 1y agoI'm not sure I follow. Every knot is defined as if you close the ends it cannot be unravelled without cutting the ends again. So the trifoil knot is included in this... but so is almost if not every other knot aren't they? Do we have "knots" that aren't mathematical? I feel like if you tie any "knot" then fix the ends together most or all of them would not be possible to untangle.
- jonathrg 1y agoEvery (mathematical) knot is one that can't be untangled, by definition. Every knot with a cut can be trivially collapsed go a point by moving one of the endpoints to the other one through the path of the knot
- kronodeus 1y agoThis 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.
- clysm 1y agoKind of like… a “hidden reset”…
- kronodeus 1y agoThe 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.
- godelski 1y ago> 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 in order. The development of thermal stat-mech is one of the things that led to the quantum revolution and "new physics". But if you only have a "calculus" based understanding of physics you likely aren't going to be familiar with this. It's not much discussed (it is some) if you didn't start entering upper division physics classes or equivalent coursework. It really shows up when you get into the weeds, but understandably it isn't something stressed before then. Physics is hard enough... Not all classical physics is time symmetric[0]. FWIW, I don't think the article is unclear. I mean they address your point in the first sentence of the second paragraph > Intuitively, it feels like the only way to undo a complicated sequence of rotations is by painstakingly doing the exact opposite motions one by one. [0] There are examples on this page that do not require relativity or quantum mechanics, even though some do. https://en.wikipedia.org/wiki/T-symmetry https://en.wikipedia.org/wiki/T-symmetry [note]: The real paradigm shift in quantum mechanics was that there was information that we could not access. That's what Schrodinger's Cat is about. The cat doesn't sit inside a parallel universe, a quantum superposition. It is just that there is no way to know which of the states the cat is in without opening the box. It says that we cannot have infinite precision, therefore must use statistics. So Einstein's "god doesn't play dice" comment is about that there must be some way to pull back that curtain.
- andy99 1y agoAny 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.
- vntok 1y ago> For Eckmann, the new work is a showcase of how rich mathematics can be even in a field as well-trod as the study of rotations. Tlusty says that it could also have practical consequences, for instance, in nuclear magnetic resonance (NMR), which is the basis of magnetic resonance imaging (MRI). Here, researchers learn properties of materials and tissues by studying the response of quantum spins inside them to rotations imposed on them by external magnetic fields. The new proof could help develop procedures for undoing unwanted spin rotations that would interfere with the imaging process.
- nyrikki 1y ago> 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.
- ohdeardear 1y ago[dead]
- akst 1y agoDoes 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
- defrost 1y agohttps://news.ycombinator.com/item?id=45661035 https://news.ycombinator.com/item?id=45661035 https://news.ycombinator.com/item?id=45661221 https://news.ycombinator.com/item?id=45661221
- oh_my_goodness 1y agoRead the paper https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf
- badosu 1y agoThank you! The article was "too clever" for me.
- oh_my_goodness 1y agoYeah exactly. Me too.
- AugusteDupin 1y agoA 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.
- diffeomorphism 1y agoThe article is 5 pages and the Theorem yielding the factor is on page 4.
- deleted 1y ago[deleted]
- noobermin 1y agoThe article is here. https://arxiv.org/abs/2502.14367 https://arxiv.org/abs/2502.14367 Sorry, but the existence of such an inversion still is interesting from a mathematical perspective. It isn't "of much use" practically without the inversion formula/calculation, but that's ok. "There exists" is still a fascinating fact.
- pjacotg 1y agoCompletely agree. Beyond being of interest in its own right, "There exists" is a prerequisite for further work in finding a practical approach to find the path.
- badosu 1y agoI 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): 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`.
- deleted 1y ago[deleted]
- SoftTalker 1y ago> Mathematicians thought that they understood how rotation works, but now a new proof has revealed a surprising twist Clever intro.
- ziofill 1y agohttps://arxiv.org/abs/2502.14367 https://arxiv.org/abs/2502.14367 for the technical folks.
- vee-kay 1y agoReminds me of belt/plate trick and anti-twister mechanism. The belt trick / plate trick / Dirac's string trick is nicely demonstrated in below video: https://m.youtube.com/watch?v=EgsUDby0X1M https://m.youtube.com/watch?v=EgsUDby0X1M https://en.wikipedia.org/wiki/Plate_trick 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 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 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.
- Pinegulf 1y agohttps://archive.is/08ig5 https://archive.is/08ig5
- vee-kay 1y agoThank you!
- somenameforme 1y agoI 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 renormalize the result (divide by the sum of the squares of the components).
- deleted 1y ago[deleted]
- Animats 1y agoThe final paragraph: The work could also lead to advances in robotics, says Josie Hughes at the Federal Polytechnic School of Lausanne in Switzerland. For example, a rolling robot could be made to follow a path of repeating segments, comprising a reliable roll-reset-roll motion that could, in theory, go on forever. “Imagine if we had a robot that could morph between any solid body shape, it could then follow any desired path simply through morphing of shape,” she says. Interestingly, that didn't come from the PR department. Hughes is a tenure-track professor whose lab builds unusual flexible robots. They're trying to use LLMs to design special-purpose grippers.[1] That's an interesting idea. Most of the cost in industrial robots is special-purpose end effector tooling. Something that could bang out a design, given "we want to put this thing in there", would be very useful. Here are some examples of end of arm tooling.[2] Auto plants are full of this stuff, and it's all custom. An automated design system for designing all those one-off items would really speed up retooling assembly lines for a new product. Much of the research in robots involves trying to make more human-like grippers. That may be approaching the problem from the wrong end. Cheap custom tooling designed by AIs and maybe 3D printed may be the way to go. That an LLM can do something like that is a surprise, but apparently there's been progress. There's a YC-sized startup opportunity in this. [1] https://www.epfl.ch/labs/create/ https://www.epfl.ch/labs/create/ [2] https://eoat.net/tooling/?device=c&keyword=End https://eoat.net/tooling/?device=c&keyword=End Of Arm Tooling Grippers
- raffraffraff 1y agoHow does this help solve a rubix cube?
- lambdaone 1y agoThis article leads to a paywall where I am, making it of no use. Perhaps someone else has done a better job of summarizing the paper elsewhere, and that should be posted instead?
- DroneBetter 1y agothis doesn't seem very difficult of a result to me; an arbitrary rotation is a move from one endpoint to each other on SO(3) wnich is double-covered by SU(2) ≅ ³; wiog consider the path between endpoints a geodesic then o course two (or even one) appropriately-scaied copies of the originaL rotation will suffice to revert it