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.
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.
Completely 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.
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).
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.
As meindnoch points out, the connection needs to loop over the rotating object. That is no problem if the only affect of the rotation that interests you is the centrifugal force.
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.
What a fascinating project. It looks a real labor of love, and I wish I understood it more deeply. I've been making my own visualization sandboxes like this to explore configuration spaces and groups - but for much simpler, more intuitive physical systems.
I went down a few rabbit holes on the site - is this program also written in Basic?
Yes, specifically the PowerBasic console compiler version 4 (later versions don’t do animation nearly as well). The PowerBasic compilers are no longer being sold and the company appears to be defunct. Anyway, you can do a lot with a good BASIC compiler.
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.
I can't go into detail, but that's essentially my use case. I have a geodesic dome with a cable running up externally, and would like to run it through a hollow shaft coming in through the top which rotates like a carousel. I'm fairly certain this is precisely what I need.
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.
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.
well, if you look at the animation, it surely seems to work, there is no place where it fakes the untwist. I can also replicate that with a belt, but not so smoothly. manually with the belt, the twist from 2 full rotations of the cube are undone by one rotation of the belt around the cube.
There's some Youtube videos out there of people who have built practical versions that work, like this one (with flat cables, even): https://www.youtube.com/watch?v=1x_oQv_qj_U
Sure, but the animation of the wiki page is wrong. The cable that ends at the bottom of the picture is fixed there, while the other end twists. That will result in a twisted cable.
I tried it and it works. The animation uses belts that are very flexible. With a real belt I needed to give it a shake to make it untwist itself, but it does work.
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'.
The 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.
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.
The 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.
> 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.
[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.
My mistake, you said "Classical Mechanics", so I took it as such.
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 ;)
Sorry, with all due respect, I'm not "throwing out" thermodynamics. It's just not relevant to the discovery referenced in the article, which is only concerned with classical mechanics. Thermodynamics is not part of the theory of classical mechanics. I think perhaps you are confusing classical mechanics with classical physics.
I've lost track of the point you're trying to make. Are you still trying to convince everyone that quantum mechanics and thermodynamics are part of the field of classical mechanics?
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 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).
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.
I 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).
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.
>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.
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. It's a non-problem.
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?
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.
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.
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):
this 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
> 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.
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.
> 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.
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.
This 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?
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
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.
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.
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..
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.
Thanks for sharing. I'm very familiar with the basic mechanics of quaternion rotation, and I've been interested in a deeper understanding of this double-cover concept, but I just don't get it. I've seen the belt trick and it feels more like an illusion than an illustration of some deep truth.
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?
That look is not that different. I bring attention to the fact that a product of quaternions all close to 1 can be close to -1, which correspond to a 2pi rotation too. This fact is a bit simpler to grasp than a topological explanation, where you consider a topology on the space of all rotations and show that some paths that correspond to 2pi rotation are different than the others. There are multiple youtube videos explaining the topological argument, see, e.g., this one https://www.youtube.com/watch?v=ACZC_XEyg9U.
The topological argument gives a larger picture and probably better understanding, but it is definitely harder.
> 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".
> 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.
One 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!
Complaining 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.
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.
> 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."
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.
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.
> Who said continuity mattered? How would a copy or original know which they were? Does it even matter?
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.
>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.
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.
The article is 5 pages and the Theorem yielding the factor is on page 4.
The article is here.
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.
Completely 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.
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
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).
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.
As meindnoch points out, the connection needs to loop over the rotating object. That is no problem if the only affect of the rotation that interests you is the centrifugal force.
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.
What a fascinating project. It looks a real labor of love, and I wish I understood it more deeply. I've been making my own visualization sandboxes like this to explore configuration spaces and groups - but for much simpler, more intuitive physical systems.
I went down a few rabbit holes on the site - is this program also written in Basic?
Yes, specifically the PowerBasic console compiler version 4 (later versions don’t do animation nearly as well). The PowerBasic compilers are no longer being sold and the company appears to be defunct. Anyway, you can do a lot with a good BASIC compiler.
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.
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.
I can't go into detail, but that's essentially my use case. I have a geodesic dome with a cable running up externally, and would like to run it through a hollow shaft coming in through the top which rotates like a carousel. I'm fairly certain this is precisely what I need.
Wouldn't a slip ring help here?
The whole point of the anti-twister mechanism is that it doesn't use a slip ring.
And no axle to rotate on.
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.
I see it, yet I can barely believe it.
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.
well, if you look at the animation, it surely seems to work, there is no place where it fakes the untwist. I can also replicate that with a belt, but not so smoothly. manually with the belt, the twist from 2 full rotations of the cube are undone by one rotation of the belt around the cube.
There's some Youtube videos out there of people who have built practical versions that work, like this one (with flat cables, even): https://www.youtube.com/watch?v=1x_oQv_qj_U
Sure, but the animation of the wiki page is wrong. The cable that ends at the bottom of the picture is fixed there, while the other end twists. That will result in a twisted cable.
(update: I was wrong, not the wiki page)
I tried it and it works. The animation uses belts that are very flexible. With a real belt I needed to give it a shake to make it untwist itself, but it does work.
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'.
Yes, indeed, it can work, I can see it now. But I wonder if/how you can make it practical.
Damn, that's beautiful. I hope that Mr. Adams mentiond in the article got a good return from his patent.
The 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/
[2] https://eoat.net/tooling/?device=c&keyword=End Of Arm Tooling Grippers
Read the paper https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf
Thank you! The article was "too clever" for me.
Yeah exactly. Me too.
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.
Kind of like… a “hidden reset”…
The 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.
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
[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[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.
Comment refers to classical mechanics, not all of classical physics and explicitly not quantum mechanics.
It is not. That’s exactly what it isn’t.
I think you're confusing thermal dynamics with quantum mechanics.
No, thermodynamics just isn't classical mechanics. For example in thermo you have entropy. Entropy doesn't appear in classical mechanics.
Not talking about thermodynamics here. The discovery referenced in this article also does not solve for thermodynamics or entropy.
And yes, you're right, the article does mention this later. I'm still bothered by the sensationalized introduction and title.
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 ;)
Sorry, with all due respect, I'm not "throwing out" thermodynamics. It's just not relevant to the discovery referenced in the article, which is only concerned with classical mechanics. Thermodynamics is not part of the theory of classical mechanics. I think perhaps you are confusing classical mechanics with classical physics.
https://en.wikipedia.org/wiki/Classical_mechanics
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
https://en.wikipedia.org/wiki/Quantum_thermodynamics
I've lost track of the point you're trying to make. Are you still trying to convince everyone that quantum mechanics and thermodynamics are part of the field of classical mechanics?
I never tried to claim quantum was part of classical
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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 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).
I got an iPad many years ago from my employer. I literally only use it for libby :-)
In this case we can just wave bye-bye to the magazine and head to the freely available Arxiv paper they are writing about.
If you use an ad blocker, just disable inline scripts
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.
Or just download the extension that bypasses pay walls lol
https://archive.is/08ig5
From one author's home page (Jean-Pierre Eckmann - 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://arxiv.org/abs/2502.14367
https://arxiv.org/abs/2502.14367 for the technical folks.
I 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).
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.
[0] https://github.com/VoxleOne/SpinStep
> compute a scale factor λ
The paper shows that such a factor must exist but not how to compute it. That is currently unknown and non-trivial.
>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.
#1: BM.
#2: His point is that this could be applied compute that single rotation.
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. It's a non-problem.
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?
You 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
It says:
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
And the answer is that you can do that, but you might have to perform the pulse twice.So it’s similar thinking to spin echoes.
https://en.wikipedia.org/wiki/spin_echoes
I think even conjugating it. The formula for rotation via quats is v->qvq^{-1} = qvq^*/|q|^2.
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.
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):
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`.
this 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
> 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.
Wish they showed a picture of both. A path over time that changes color and two paths combined to recreate it.
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.
> 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.
https://archive.is/08ig5
Thank you!
> Mathematicians thought that they understood how rotation works, but now a new proof has revealed a surprising twist
Clever intro.
How does this help solve a rubix cube?
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.
This 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?
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
https://news.ycombinator.com/item?id=45661035
https://news.ycombinator.com/item?id=45661221
This made me wonder if there are knots you can't untangle.
Every (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
Yup, the trefoil knot is one
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.
Reminds 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://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.
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..
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 ?
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.
Do you mean spinors? And how it takes TWO full rotations to get back to the initial state?
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...
Thanks for sharing. I'm very familiar with the basic mechanics of quaternion rotation, and I've been interested in a deeper understanding of this double-cover concept, but I just don't get it. I've seen the belt trick and it feels more like an illusion than an illustration of some deep truth.
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?
That look is not that different. I bring attention to the fact that a product of quaternions all close to 1 can be close to -1, which correspond to a 2pi rotation too. This fact is a bit simpler to grasp than a topological explanation, where you consider a topology on the space of all rotations and show that some paths that correspond to 2pi rotation are different than the others. There are multiple youtube videos explaining the topological argument, see, e.g., this one https://www.youtube.com/watch?v=ACZC_XEyg9U.
The topological argument gives a larger picture and probably better understanding, but it is definitely harder.
I see, thanks. Sounds like I was overthinking it.
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 :)
> 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".
Does it work for brakes?
up next, unscrambling an egg!
"Scientists unscramble egg proteins"
https://www.science.org/content/article/scientists-unscrambl...
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[flagged]
https://archive.is/08ig5
preprint: https://arxiv.org/abs/2502.14367
From 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.
One 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!
Being in FAQ doesn't make it right.
Likewise something being a law doesn't make it right either, but one should still follow the law of the land for the most part.
Especially 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?
Complaining 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.
Doesn’t this sound like a sneaky way for a mathematician to work on time travel?
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.
Baby steps, first is the roulette table.
> 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."
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.
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.
> 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.
> Who said continuity mattered? How would a copy or original know which they were? Does it even matter?
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.
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.