Mathematicians have found a hidden 'reset button' for undoing rotation
newscientist.com
newscientist.com
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.
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.
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.
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.
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.
I went down a few rabbit holes on the site - is this program also written in Basic?
(update: I was wrong, not the wiki page)
It is indeed easy to twist the belt until you have the hang of it.
I think the animation is a bit deceptive because even with elastic bands you'd have to provide some way for the correct untwisting to occur. In the animation it happens 'automagically'.
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/
[2] https://eoat.net/tooling/?device=c&keyword=End Of Arm Tooling Grippers
"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.
> Physical systems governed by classical mechanics are reversible just by perfectly inverting all forces, velocities, and rotations
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.
[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.
> refers to classical mechanics
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.
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 ;)
See the beginning and the Limits of Validity section. It's "classical mechanics", "quantum", and "relativity".
Thermaldynamics can overlap with quantum but there is a classical regime. Which, let's be clear
Mine does, and therefore I can "borrow" (read for free) articles that make it to the mag.
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.
Walks in Rotation Spaces Return Home when Doubled and Scaled (with Tsvi Tlusty) Physical Review Letters 135, 147201 (2025)
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.
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...?
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)
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.
#2: His point is that this could be applied compute that single rotation.
The paper shows that such a factor must exist but not how to compute it. That is currently unknown and non-trivial.
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`.
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.
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".
I like how you've connected it to spin, but I still don't understand how that is a real physical property rather than a mathematical artifact.
I don't quite grasp the significance of your "different look". Can you suggest any other reading?
The topological argument gives a larger picture and probably better understanding, but it is definitely harder.
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 ?
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
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.
https://www.science.org/content/article/scientists-unscrambl...
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.
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.
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.
Continuity matters because I do not care if this imaginary (digital or physically reconstructed) artifact you came up with sometime in the future lives in a simulation of (your understanding of) my real life or in Sim city.
This thing is not "me", and I was replying to your assertion that
> Maybe it'll be eternal heaven - just gifted to us without reason or cause
This is not "us". This hypothetical is just a bunch of Sims characters running around in some virtual universe.
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.