Mathematicians have found a hidden 'reset button' for undoing rotation
42 comments
·October 16, 2025v7n
dandanua
It'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
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.
meindnoch
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.
v7n
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.
actionfromafar
I see it, yet I can barely believe it.
crooked-v
Damn, that's beautiful. I hope that Mr. Adams mentiond in the article got a good return from his patent.
voxleone
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 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.
kmarc
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.
stevenwoo
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
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
If you use an ad blocker, just disable inline scripts
typpilol
Or just download the extension that bypasses pay walls lol
null
koolala
Wish they showed a picture of both. A path over time that changes color and two paths combined to recreate it.
dukeofdoom
This made me wonder if there are knots you can't untangle.
ineedasername
Doesn’t this sound like a sneaky way for a mathematician to work on time travel?
TomasNieteriter
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.
swader999
Baby steps, first is the roulette table.
alphan0n
> 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."
echelon
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
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.
aspenmayer
Archive of TFA:
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.
tonijn
Does it work for brakes?
Razengan
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
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
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
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 :)
null
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