[HN Gopher] Mathematicians have found a hidden 'reset button' fo...
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Mathematicians have found a hidden 'reset button' for undoing
rotation
Author : mikhael
Score : 83 points
Date : 2025-10-16 15:47 UTC (5 days ago)
(HTM) web link (www.newscientist.com)
(TXT) w3m dump (www.newscientist.com)
| tonijn wrote:
| Does it work for brakes?
| v7n wrote:
| 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
| dandanua wrote:
| It's not related. The recent result states that you can pick
| any integer m > 1 and find a scaling factor l 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 wrote:
| 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
| 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 wrote:
| I see it, yet I can barely believe it.
| v7n wrote:
| Always 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 wrote:
| There'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.
| SyzygyRhythm wrote:
| This is important. The mechanism doesn't really work the
| way you want most of the time. I occasionally see a claim
| that you can power a carousel with this method, but it
| doesn't work. You would have to have the cable go out and
| around the carousel structure, and then into the top. And
| the cable would still move relative to the ground and the
| carousel.
|
| You could, in principle, have a totally internal system,
| but with arms that grab and release the cable at intervals
| so that the looped portion can pass by them. You could
| arrange the timing so that electrical contact is never
| lost. But you are still making/breaking contact and it
| starts to lose some apparent advantages compared to a slip
| ring.
|
| That's not to say it isn't still useful for some purposes,
| like maybe a radio antenna that isn't too impacted by a
| cable moving in front on occasion. But it doesn't eliminate
| all uses for a slip ring.
| jojobas wrote:
| And no axle to rotate on.
| crooked-v wrote:
| Damn, that's beautiful. I hope that Mr. Adams mentiond in the
| article got a good return from his patent.
| koolala wrote:
| Wish they showed a picture of both. A path over time that changes
| color and two paths combined to recreate it.
| stronglikedan wrote:
| up next, unscrambling an egg!
| vlmutolo wrote:
| "Scientists unscramble egg proteins"
|
| https://www.science.org/content/article/scientists-unscrambl...
| ineedasername wrote:
| Doesn't this sound like a sneaky way for a mathematician to work
| on time travel?
| swader999 wrote:
| Baby steps, first is the roulette table.
| echelon wrote:
| Kardashev 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 wrote:
| 1 - 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.
| echelon wrote:
| > enough to have a continuity
|
| Who said continuity mattered? How would a copy or
| original know which they were? Does it even matter?
|
| How would you even know you were in a simulation? We
| seemingly don't have the tools to know.
|
| Whatever the case, if you're the copy in the hell
| simulator getting thrown into the meat grinder, I don't
| really think the distinction of "original vs copy" is the
| most pressing issue.
|
| > while maybe in 2025 we'd be thinking in terms of
| electron clouds or quarks.
|
| We can't fathom what level of control over the physical
| world an advanced intelligence might have. Maybe they can
| create entire universes. Maybe there are structures and
| dimensions beyond our understanding. I don't know and
| can't reason about them, but I'm willing to prescribe
| them god powers on account of the fact I have no idea.
|
| Maybe our logic and intuition, tools like Occam's Razor,
| are fixed to an artificial distribution of event
| occurrences that is entirely constructed. Perhaps not
| unlike the fundamental constants of the universe. We
| wouldn't know any differently.
|
| None of this is not measurable. Indistinguishable from
| fantasy.
| DonHopkins wrote:
| Check out Surface Detail by Iain M. Banks:
|
| https://en.wikipedia.org/wiki/Surface_Detail
|
| >Each chapter of the book covers one or more of the six
| main protagonists--Lededje Y'breq, a chattel slave; Joiler
| Veppers, an industrialist and playboy; Gyorni Vatueil, a
| soldier; Prin and Chay, Pavulean academics; and Yime
| Nsokyi, a Quietus agent. Some of the plot occurs in
| simulated environments. As the book begins, a war game--the
| "War in Heaven"--has been running for several decades. The
| outcome of the simulated war will determine whether
| societies are allowed to run artificial Hells, virtual
| afterlives in which the mind-states of the dead are
| tortured. The Culture, fiercely anti-Hell, has opted to
| stay out of the war while accepting the outcome as binding.
| alphan0n wrote:
| > Often dabo girls were specifically instructed by their
| employers to distract players into losing. A common saying in
| dabo was "Watch the wheel, not the girl."
| TomasNieteriter wrote:
| 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.
| kmarc wrote:
| 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.
| typpilol wrote:
| Or just download the extension that bypasses pay walls lol
| stevenwoo wrote:
| I'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).
| kazinator wrote:
| In this case we can just wave bye-bye to the magazine and head
| to the freely available Arxiv paper they are writing about.
| viciousvoxel wrote:
| If you use an ad blocker, just disable inline scripts
| groby_b wrote:
| Or, you know, you could use a mechanism that actually
| guarantees them some revenue and doesn't just burn the
| publication to the ground because you feel entitled to free
| access.
| Razengan wrote:
| 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..
| dist-epoch wrote:
| 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.
| dandanua wrote:
| 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...
| dist-epoch wrote:
| 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 :)
| jkrshnmenon wrote:
| 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 ?
| ra88it wrote:
| https://archive.is/08ig5
| aspenmayer wrote:
| https://arxiv.org/abs/2502.14367
| aspenmayer wrote:
| Archive of TFA:
|
| 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.
| voxleone wrote:
| Quaternion 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 l 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
| ginko wrote:
| 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?
| meindnoch wrote:
| >using a simpler method than computing a full inverse sequence
|
| What are you even talking about? Rotations form a group. Any
| orientation "A" can be reached from any other orientation "B"
| with a _single_ rotation. It 's an O(1) operation. Always has
| been. What you wrote makes no sense whatsoever.
| the__alchemist wrote:
| #1: BM.
|
| #2: His point is that this could be applied compute that
| single rotation.
| meindnoch wrote:
| Makes no sense. Computing the rotation between any two
| orientations (represented as quaternions) is simply a
| matter of dividing one quaternion by the other. It's an
| O(1) operation.
| dukeofdoom wrote:
| This made me wonder if there are knots you can't untangle.
| ekunazanu wrote:
| Yup, the trefoil knot is one
| eightys3v3n wrote:
| I'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.
| kronodeus wrote:
| 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.
| clysm wrote:
| Kind of like... a "hidden reset"...
| andy99 wrote:
| 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.
| vntok wrote:
| > 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 wrote:
| > 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.
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